1.4 Definition of Design: (S ‘94)
Designing is such a vast field that it is defined in several ways. Various definitions of designing as pronounced by well-known designers are
“Design is that which defines solutions to problem which have previously been solved in a different way”
“Design is the conscious human process of planning physical things that display a new form in response to some pre-determined need”.
“Design is an act of collecting all pertinent information for the production of goods and services to meet some human need”.
The design of any component includes two things,
(i) Product design
(ii) Process design
The product design involves the development of specification for a product that will be functionally sound, good in appearance, and will give satisfactory performance for an adequate life.
The process design involves developing methods of manufacture of the products so that the component can be produced at a reasonably low cost.
1.5 History of Design Process
(i) Design by Single Person
(ii) Over-the-wall design
(iii) Simultaneous Engineering
(iv) Concurrent Engineering
(v) Integrated design and Manufacture.
In olden times one person could design and manufacture an entire product. Even for a large project such as the design of a ship or a bridge, one person had sufficient knowledge of the Physics, Materials and manufacturing processes to manage all aspects of the design and construction of the project. This period is referred to as the period of design by single person in the history of design.
By the middle of the 20th century products and manufacturing processes became so complex that, one person could not handle all aspects of design and manufacturing. This situation led to over-the-wall design process.
In this method each functional departments were separated from others, as shown by wall. There was only one-way communications between Customer, Marketing, Engg. Design and production department. The customers ‘throw’ their needs to marketing department. The marketing department may throw the customer needs to the design department, in many instances, orally. The Engg. Design department may conceive a design and hands it over to the manufacturing sections. The manufacturing department interprets that design and makes the product according to what they think suitable. Unfortunately, often what is manufactured by a company using over-the-wall process is not what the customers had in mind. This is due to lack of interaction between the different departments. Thus, this single direction over-the-wall approach is inefficient and costly and may result in poor quality products.
By the early 1980’s the concept of simultaneous engineering emerged. This philosophy emphasized simultaneous development of the manufacturing process- the goal was the simultaneous development of the product and the manufacturing process. This was accomplished by assigning manufacturing representatives to be members of design team, so that they could interact with the design engineers throughout the designs process.
In the 1980’s the simultaneous design philosophy was broadened and called concurrent engineering. A short definition of concurrent engineering is the simultaneous progression of all aspects, at all stages of product development, product specification, design, process and equipment etc. In concurrent engineering the primary focus is on the integration of teams of people having a stake in the product, design tools, and techniques and information about the product and the processes used to develop and manufacture it. Tools and techniques connect the teams with the information. Although many of the tools are computer-based, much design work is still done with pencil and paper. In fact, concurrent engineering is 80% company culture and 20% computer support.
With the advent of computer technology, drastic changes have taken place in the field of design and manufacturing. The result was a completely integrated design and manufacturing system. This system makes a good use of technologies such as CAD/CAM, FMS etc. The computer integrated manufacturing systems (CIMS) moves towards the ‘Factory of the future’. CIMS is necessary for better quality, efficiency and productivity.
Tuesday, February 26, 2008
CHAPTER 1 DEFINITION OF ENGINEERING DESIGN
Introduction:
The economic future of India depends on our ability to design, make and sell competitive products. Excellent design and effective manufacture are the pre-requisites of a successive industry. There is a general impression that the quality of Indian products can still be improved. The fact that consumers have lost their confidence on Indian-made products cannot be denied. This problem can be solved only by designing and manufacturing better products through improved methodology. Keeping this in view, the subject “Design and manufacturing” purpose to present the methods and procedures of design and manufacture.
Although engineers are not the only people who design things, the professional practice of engineering is largely concerned with design. It is usually said that design is the essence of engineering.
The ability to design is both a science and an art. The science can be learned through procedures developed by eminent scholars. But the art can be learned only by doing desi
2. Shopping goods
These are expensive and people buy it less frequently.
E.g. Jewellary garments etc.
3. Specialty goods
These are purchased, taking extra pain.
E.g. Rare objects like stamps.
4. Industrial goods.
These are items used in the production of other items.
Eg. Raw materials.
Another way of classifying products is into,
(a) Continuous Products, and
(b) Discrete products
The continuous products are those which are produced in a continuous fashion. For example, plates, sheets, tubes and bars etc are produced in very long lengths, and then these are cut into desired lengths.
On the other hand, discrete products are produced one after another, each in separate units.
On the basis of the output product, the Industry is usually named as continuous industry and discrete industry.
1.3 Requirements in a good product
1. Customer Satisfaction
2. Profit
How to achieve customer satisfaction?
-The product should function properly.
-It must have desired accuracy
-It must have desired reliability
-It must be easy to operate
-It must be serviceable
-It must make minimum space utilization
-It must withstand rough handling
-Pleasant appearances.
-Reasonable price.
How can it be profitable?
-It must be easy to manufacture
-The raw material must be cheap and easily available
-The manufacturing process has to the decided on the basis of quantity to be produced
-It must use standard parts
-It must be easy to pack and distribute.
The economic future of India depends on our ability to design, make and sell competitive products. Excellent design and effective manufacture are the pre-requisites of a successive industry. There is a general impression that the quality of Indian products can still be improved. The fact that consumers have lost their confidence on Indian-made products cannot be denied. This problem can be solved only by designing and manufacturing better products through improved methodology. Keeping this in view, the subject “Design and manufacturing” purpose to present the methods and procedures of design and manufacture.
Although engineers are not the only people who design things, the professional practice of engineering is largely concerned with design. It is usually said that design is the essence of engineering.
The ability to design is both a science and an art. The science can be learned through procedures developed by eminent scholars. But the art can be learned only by doing desi
Types of Products
A product is the tangible end result of a manufacturing process and is meant for satisfying human needs. The product can be classified as follows: -
1. Convenience goods
These are less expensive and are clustered around shops and restaurants.
A product is the tangible end result of a manufacturing process and is meant for satisfying human needs. The product can be classified as follows: -
1. Convenience goods
These are less expensive and are clustered around shops and restaurants.
These can be purchased at consumer’s convenience.
E.g. Cigarette, Candy, Magazines etc.
E.g. Cigarette, Candy, Magazines etc.
2. Shopping goods
These are expensive and people buy it less frequently.
E.g. Jewellary garments etc.
3. Specialty goods
These are purchased, taking extra pain.
E.g. Rare objects like stamps.
4. Industrial goods.
These are items used in the production of other items.
Eg. Raw materials.
Another way of classifying products is into,
(a) Continuous Products, and
(b) Discrete products
The continuous products are those which are produced in a continuous fashion. For example, plates, sheets, tubes and bars etc are produced in very long lengths, and then these are cut into desired lengths.
On the other hand, discrete products are produced one after another, each in separate units.
On the basis of the output product, the Industry is usually named as continuous industry and discrete industry.
1.3 Requirements in a good product
1. Customer Satisfaction
2. Profit
How to achieve customer satisfaction?
-The product should function properly.
-It must have desired accuracy
-It must have desired reliability
-It must be easy to operate
-It must be serviceable
-It must make minimum space utilization
-It must withstand rough handling
-Pleasant appearances.
-Reasonable price.
How can it be profitable?
-It must be easy to manufacture
-The raw material must be cheap and easily available
-The manufacturing process has to the decided on the basis of quantity to be produced
-It must use standard parts
-It must be easy to pack and distribute.
SYLLABUS OF FUNDAMENTALS OF DESIGN AND MANUFACTURING
Group A
Engineering design process and its structure. Identification and analysis of need, product design specifications, standards of performance and constraints.
Searching for design concepts; morphological analysis, brainstorming. Evaluation of design concepts for physical reliability, economic feasibility and utility.
Detailed design; design for manufacture, assembly, shipping, maintenance, use, and recyclability.
Design checks for clarity, simplicity, modularity and safety. Standardization and size ranges.
Reliability and robust design. Design organisation and communication, . technical reports, drawings, presentations and models.
Concept of manufacturing; classification of manufacturing processes. Fundamentals of casting. Basic understanding of commonly used casting processes (sand casting, investment casting and permanent mould casting processes).
Fundamentals of metal forming; hot and cold working; basic understanding of primary metal forming processes (rolling, forging, extrusion and drawing processes, punching and blanking).
Fundamentals of metal cutting; tool-work interaction for production of machined surfaces. Classification of machining processes. Basic machining operations (turning, shaping, planning, drilling and milling processes).
Group B
Fundamentals of grinding and finishing; overview of unconventional machining processes; fundamentals of welding processes; introduction to primary welding and allied processes; selection of manufacturing processes. Design for manufacturability.
Need for integration-commercial, economic and technological perspective; basic tools of integration; concept of a system. introduction to information technology and its elements.
Introduction to group technology; introduction to simulation and database management systems.
Elements of integration:-eontrol1ers, sensors, robots, automated machines; AGVs, AS, RS, etc.
Product and process design- for integration; design for economic manufacturing; design for manufacturing integration.
Introduction to computer aided process planning; selection of machine tools.
Engineering design process and its structure. Identification and analysis of need, product design specifications, standards of performance and constraints.
Searching for design concepts; morphological analysis, brainstorming. Evaluation of design concepts for physical reliability, economic feasibility and utility.
Detailed design; design for manufacture, assembly, shipping, maintenance, use, and recyclability.
Design checks for clarity, simplicity, modularity and safety. Standardization and size ranges.
Reliability and robust design. Design organisation and communication, . technical reports, drawings, presentations and models.
Concept of manufacturing; classification of manufacturing processes. Fundamentals of casting. Basic understanding of commonly used casting processes (sand casting, investment casting and permanent mould casting processes).
Fundamentals of metal forming; hot and cold working; basic understanding of primary metal forming processes (rolling, forging, extrusion and drawing processes, punching and blanking).
Fundamentals of metal cutting; tool-work interaction for production of machined surfaces. Classification of machining processes. Basic machining operations (turning, shaping, planning, drilling and milling processes).
Group B
Fundamentals of grinding and finishing; overview of unconventional machining processes; fundamentals of welding processes; introduction to primary welding and allied processes; selection of manufacturing processes. Design for manufacturability.
Need for integration-commercial, economic and technological perspective; basic tools of integration; concept of a system. introduction to information technology and its elements.
Introduction to group technology; introduction to simulation and database management systems.
Elements of integration:-eontrol1ers, sensors, robots, automated machines; AGVs, AS, RS, etc.
Product and process design- for integration; design for economic manufacturing; design for manufacturing integration.
Introduction to computer aided process planning; selection of machine tools.
Group B
Heat treatment . Iron-carbon system. Annealing, normalising, hardening,. critical cooling rate, hardenability, age hardening, surface hardening, tempering.
Thermal properties . High temperature materials; materials for cryogenic application, thermally insulating materials. (Specific heat, thermal conductivity, thermal expansion).
Ceramic materials and polymers . Silicon structures, polymerism . in glass, electrical properties of ceramic phases, rocks, building stones, refractories.
Polymerisation mechanism , structural properties of polymer, thermoplastics, thermosets, elastomer, resins, composites, particles and fibre reinforced composite. Composite material including nano material.
Electronic properties . Magnetism, diamagnetism, paramagnetism, ferromagnetism, magnetic energy, zone theory of solids, zones in conductors and insulators.
Heat treatment . Iron-carbon system. Annealing, normalising, hardening,. critical cooling rate, hardenability, age hardening, surface hardening, tempering.
Thermal properties . High temperature materials; materials for cryogenic application, thermally insulating materials. (Specific heat, thermal conductivity, thermal expansion).
Ceramic materials and polymers . Silicon structures, polymerism . in glass, electrical properties of ceramic phases, rocks, building stones, refractories.
Polymerisation mechanism , structural properties of polymer, thermoplastics, thermosets, elastomer, resins, composites, particles and fibre reinforced composite. Composite material including nano material.
Electronic properties . Magnetism, diamagnetism, paramagnetism, ferromagnetism, magnetic energy, zone theory of solids, zones in conductors and insulators.
Syllabus of Material Science And Engineering
Group A
Introduction to materials . Metal and alloys, ceramics, polymers and semi conducting materials-introduction and application as engineering materials.
Defects in solids . Point, line and surface defects. Diffusion in solids.
Phase diagrams . Mono-component and binary systems, non-equilibrium system, phase diagram and. application in crystalline and non-crystalline solids.
Mechanical properties . Tensile strength, yield strength, elastic and viscoelastic properties, creep, stress relaxation and impact. Fracture behaviour. Ductile fracture, Griffith theory, effect of heat treatment and temperature on properties of metals.
Deformation of metals. Elastic and plastic deformation, slip, twin, dislocation theory, critical resolved shear stress, deformation in polycrystalline materials; season cracking, Bachinger's effect, strengthening mechanics; work hardening recovery, crystallization and grain growth, cold and hot working. .
Introduction to materials . Metal and alloys, ceramics, polymers and semi conducting materials-introduction and application as engineering materials.
Defects in solids . Point, line and surface defects. Diffusion in solids.
Phase diagrams . Mono-component and binary systems, non-equilibrium system, phase diagram and. application in crystalline and non-crystalline solids.
Mechanical properties . Tensile strength, yield strength, elastic and viscoelastic properties, creep, stress relaxation and impact. Fracture behaviour. Ductile fracture, Griffith theory, effect of heat treatment and temperature on properties of metals.
Deformation of metals. Elastic and plastic deformation, slip, twin, dislocation theory, critical resolved shear stress, deformation in polycrystalline materials; season cracking, Bachinger's effect, strengthening mechanics; work hardening recovery, crystallization and grain growth, cold and hot working. .
remainig part of chapter-17
Dielectric Materials
Capacitors require dielectrics of high e that can function at high frequencies (small relaxation times). Many of the ceramics have these properties, like mica, glass, and porcelain). Polymers usually have lower .
Ferroelectricity
Ferroelectric materials are ceramics that exhibit permanent polarization in the absence of an electric field. This is due to the asymmetric location of positive and negative charges within the unit cell. Two possible arrangements of this asymmetry results in two distinct polarizations, which can be used to code "0" and "1" in ferroelectric memories. A typical ferroelectric is barium titanate, BaTiO3, where the Ti4+ is in the center of the unit cell and four O2- in the central plane can be displaced to one side or the other of this central ion
Piezoelectricity
In a piezolectric material, like quartz, an applied mechanical stress causes electric polarization by the relative displacement of anions and cations.
Capacitors require dielectrics of high e that can function at high frequencies (small relaxation times). Many of the ceramics have these properties, like mica, glass, and porcelain). Polymers usually have lower .
Ferroelectricity
Ferroelectric materials are ceramics that exhibit permanent polarization in the absence of an electric field. This is due to the asymmetric location of positive and negative charges within the unit cell. Two possible arrangements of this asymmetry results in two distinct polarizations, which can be used to code "0" and "1" in ferroelectric memories. A typical ferroelectric is barium titanate, BaTiO3, where the Ti4+ is in the center of the unit cell and four O2- in the central plane can be displaced to one side or the other of this central ion
Piezoelectricity
In a piezolectric material, like quartz, an applied mechanical stress causes electric polarization by the relative displacement of anions and cations.
remainig part of chapter 17
Conduction in Ionic Materials
In ionic materials, the band gap is too large for thermal electron promotion. Cation vacancies allow ionic motion in the direction of an applied electric field, this is referred to as ionic conduction. High temperatures produce more vacancies and higher ionic conductivity.
At low temperatures, electrical conduction in insulators is usually along the surface, due to the deposition of moisture that contains impurity ions.
Electrical Properties of Polymers
Polymers are usually good insulators but can be made to conduct by doping. Teflon is an exceptionally good insulator.
Dielectric Behavior
A dielectric is an electrical insulator that can be made to exhibit an electric dipole structure (displace the negative and positive charge so that their center of gravity is different).
Capacitance
When two parallel plates of area A, separated by a small distance l, are charged by +Q, –Q, an electric field develops between the plates
E = D/ee0
where D = Q/A. e0 is called the vacuum permittivity and e the relative permittivity, or dielectric constant (e = 1 for vacuum). In terms of the voltage between the plates, V = E l,
V = Dl/ee0 = Q l/Aee0 = Q / C
The constant C= Aee0/l is called the capacitance of the plates.
Field Vectors and Polarization
The dipole moment of a pair of positive and negative charges (+q and –q) separated at a distance d is p = qd. If an electric field is applied, the dipole tends to align so that the positive charge points in the field direction. Dipoles between the plates of a capacitor will produce an electric field that opposes the applied field. For a given applied voltage V, there will be an increase in the charge in the plates by an amount Q' so that the total charge becomes Q = Q' + Q0, where Q0 is the charge of a vacuum capacitor with the same V. With Q' = PA, the charge density becomes D = D0 E + P, where the polarization P = e0 (e–1) E .
Types of Polarization
Three types of polarization can be caused by an electric field:
Electronic polarization: the electrons in atoms are displaced relative to the nucleus.
Ionic polarization: cations and anions in an ionic crystal are displaced with respect to each other.
Orientation polarization: permanent dipoles (like H2O) are aligned.
Frequency Dependence of the Dielectric Constant
Electrons have much smaller mass than ions, so they respond more rapidly to a changing electric field. For electric field that oscillates at very high frequencies (such as light) only electronic polarization can occur. At smaller frequencies, the relative displacement of positive and negative ions can occur. Orientation of permanent dipoles, which require the rotation of a molecule can occur only if the oscillation is relatively slow (MHz range or slower). The time needed by the specific polarization to occur is called the relaxation time.
Dielectric Strength
Very high electric fields (>108 V/m) can free electrons from atoms, and accelerate them to such high energies that they can, in turn, free other electrons, in an avalanche process (or electrical discharge). This is called dielectric breakdown, and the field necessary to start the is called the dielectric strength or breakdown strength.
In ionic materials, the band gap is too large for thermal electron promotion. Cation vacancies allow ionic motion in the direction of an applied electric field, this is referred to as ionic conduction. High temperatures produce more vacancies and higher ionic conductivity.
At low temperatures, electrical conduction in insulators is usually along the surface, due to the deposition of moisture that contains impurity ions.
Electrical Properties of Polymers
Polymers are usually good insulators but can be made to conduct by doping. Teflon is an exceptionally good insulator.
Dielectric Behavior
A dielectric is an electrical insulator that can be made to exhibit an electric dipole structure (displace the negative and positive charge so that their center of gravity is different).
Capacitance
When two parallel plates of area A, separated by a small distance l, are charged by +Q, –Q, an electric field develops between the plates
E = D/ee0
where D = Q/A. e0 is called the vacuum permittivity and e the relative permittivity, or dielectric constant (e = 1 for vacuum). In terms of the voltage between the plates, V = E l,
V = Dl/ee0 = Q l/Aee0 = Q / C
The constant C= Aee0/l is called the capacitance of the plates.
Field Vectors and Polarization
The dipole moment of a pair of positive and negative charges (+q and –q) separated at a distance d is p = qd. If an electric field is applied, the dipole tends to align so that the positive charge points in the field direction. Dipoles between the plates of a capacitor will produce an electric field that opposes the applied field. For a given applied voltage V, there will be an increase in the charge in the plates by an amount Q' so that the total charge becomes Q = Q' + Q0, where Q0 is the charge of a vacuum capacitor with the same V. With Q' = PA, the charge density becomes D = D0 E + P, where the polarization P = e0 (e–1) E .
Types of Polarization
Three types of polarization can be caused by an electric field:
Electronic polarization: the electrons in atoms are displaced relative to the nucleus.
Ionic polarization: cations and anions in an ionic crystal are displaced with respect to each other.
Orientation polarization: permanent dipoles (like H2O) are aligned.
Frequency Dependence of the Dielectric Constant
Electrons have much smaller mass than ions, so they respond more rapidly to a changing electric field. For electric field that oscillates at very high frequencies (such as light) only electronic polarization can occur. At smaller frequencies, the relative displacement of positive and negative ions can occur. Orientation of permanent dipoles, which require the rotation of a molecule can occur only if the oscillation is relatively slow (MHz range or slower). The time needed by the specific polarization to occur is called the relaxation time.
Dielectric Strength
Very high electric fields (>108 V/m) can free electrons from atoms, and accelerate them to such high energies that they can, in turn, free other electrons, in an avalanche process (or electrical discharge). This is called dielectric breakdown, and the field necessary to start the is called the dielectric strength or breakdown strength.
remainig part of chapter 17
Electrical Characteristics of Commercial Alloys
The best material for electrical conduction (lower resistivity) is silver. Since it is very expensive, copper is preferred, at an only modest increase in r. To achieve low r it is necessary to remove gases occluded in the metal during fabrication. Copper is soft so, for applications where mechanical strength is important, the alloy CuBe is used, which has a nearly as good r. When weight is important one uses Al, which is half as good as Cu. Al is also more resistant to corrosion.
When high resistivity materials are needed, like in electrical heaters, especially those that operate at high temperature, nichrome (NiCr) or graphite are used.
Intrinsic Semiconduction
Semiconductors can be intrinsic or extrinsic. Intrinsic means that electrical conductivity does not depend on impurities, thus intrinsic means pure. In extrinsic semiconductors the conductivity depends on the concentration of impurities.
Conduction is by electrons and holes. In an electric field, electrons and holes move in opposite direction because they have opposite charges. The conductivity of an intrinsic semiconductor is:
s = n e me + p e mh
where p is the hole concentration and mh the hole mobility. One finds that electrons move much faster than holes:
me > mh
In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the conduction band. Thus:
n = p
Thus, s = 2 n e (me + mh) (only for intrinsic semiconductors).
Extrinsic Semiconduction
Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called p-type if p>n and n-type if n>p. They are made by doping, the addition of a very small concentration of impurity atoms. Two common methods of doping are diffusion and ion implantation.
Excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix. For instance phosphorous, with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Thus, elements in columns V and VI of the periodic table are donors for semiconductors in the IV column, Si and Ge. The energy level of the donor state is close to the conduction band, so that the electron is promoted (ionized) easily at room temperature, leaving a hole (the ionized donor) behind. Since this hole is unlike a hole in the matrix, it does not move easily by capturing electrons from adjacent atoms. This means that the conduction occurs mainly by the donated electrons (thus n-type).
Excess holes are produced by substitutional impurities that have fewer valence electrons per atom than the matrix. This is the case of elements of group II and III in column IV semiconductors, like B in Si. The bond with the neighbors is incomplete and so they can capture or accept electrons from adjacent silicon atoms. They are called acceptors. The energy level of the acceptor is close to the valence band, so that an electron may easily hop from the valence band to complete the bond leaving a hole behind. This means that conduction occurs mainly by the holes (thus p-type).
The Temperature Variation of Conductivity and Carrier Concentration
Temperature causes electrons to be promoted to the conduction band and from donor levels, or holes to acceptor levels. The dependence of conductivity on temperature is like other thermally activated processes:
s = A exp(–Eg/2kT)
where A is a constant (the mobility varies much more slowly with temperature). Plotting ln s vs. 1/T produces a straight line of slope Eg/2k from which the band gap energy can be determined. Extrinsic semiconductors have, in addition to this dependence, one due to the thermal promotion of electrons from donor levels or holes from acceptor levels. The dependence on temperature is also exponential but it eventually saturates at high temperatures where all the donors are emptied or all the acceptors are filled.
This means that at low temperatures, extrinsic semiconductors have larger conductivity than intrinsic semiconductors. At high temperatures, both the impurity levels and valence electrons are ionized, but since the impurities are very low in number and they are exhausted, eventually the behavior is dominated by the intrinsic type of conductivity.
Semiconductor Devices
A semiconductor diode is made by the intimate junction of a p-type and an n-type semiconductor (an n-p junction). Unlike a metal, the intensity of the electrical current that passes through the material depends on the polarity of the applied voltage. If the positive side of a battery is connected to the p-side, a situation called forward bias, a large amount of current can flow since holes and electrons are pushed into the junction region, where they recombine (annihilate). If the polarity of the voltage is flipped, the diode operates under reverse bias. Holes and electrons are removed from the region of the junction, which therefore becomes depleted of carriers and behaves like an insulator. For this reason, the current is very small under reverse bias. The asymmetric current-voltage characteristics of diodes is used to convert alternating current into direct current. This is called rectification.
A p-n-p junction transistor contains two diodes back-to-back. The central region is very thin and is called the base. A small voltage applied to the base has a large effect on the current passing through the transistor, and this can be used to amplify electrical signals (Fig. 19.22). Another common device is the MOSFET transistor where a gate serves the function of the base in a junction transistor. Control of the current through the transistor is by means of the electric field induced by the gate, which is isolated electrically by an oxide layer.
The best material for electrical conduction (lower resistivity) is silver. Since it is very expensive, copper is preferred, at an only modest increase in r. To achieve low r it is necessary to remove gases occluded in the metal during fabrication. Copper is soft so, for applications where mechanical strength is important, the alloy CuBe is used, which has a nearly as good r. When weight is important one uses Al, which is half as good as Cu. Al is also more resistant to corrosion.
When high resistivity materials are needed, like in electrical heaters, especially those that operate at high temperature, nichrome (NiCr) or graphite are used.
Intrinsic Semiconduction
Semiconductors can be intrinsic or extrinsic. Intrinsic means that electrical conductivity does not depend on impurities, thus intrinsic means pure. In extrinsic semiconductors the conductivity depends on the concentration of impurities.
Conduction is by electrons and holes. In an electric field, electrons and holes move in opposite direction because they have opposite charges. The conductivity of an intrinsic semiconductor is:
s = n e me + p e mh
where p is the hole concentration and mh the hole mobility. One finds that electrons move much faster than holes:
me > mh
In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the conduction band. Thus:
n = p
Thus, s = 2 n e (me + mh) (only for intrinsic semiconductors).
Extrinsic Semiconduction
Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called p-type if p>n and n-type if n>p. They are made by doping, the addition of a very small concentration of impurity atoms. Two common methods of doping are diffusion and ion implantation.
Excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix. For instance phosphorous, with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Thus, elements in columns V and VI of the periodic table are donors for semiconductors in the IV column, Si and Ge. The energy level of the donor state is close to the conduction band, so that the electron is promoted (ionized) easily at room temperature, leaving a hole (the ionized donor) behind. Since this hole is unlike a hole in the matrix, it does not move easily by capturing electrons from adjacent atoms. This means that the conduction occurs mainly by the donated electrons (thus n-type).
Excess holes are produced by substitutional impurities that have fewer valence electrons per atom than the matrix. This is the case of elements of group II and III in column IV semiconductors, like B in Si. The bond with the neighbors is incomplete and so they can capture or accept electrons from adjacent silicon atoms. They are called acceptors. The energy level of the acceptor is close to the valence band, so that an electron may easily hop from the valence band to complete the bond leaving a hole behind. This means that conduction occurs mainly by the holes (thus p-type).
The Temperature Variation of Conductivity and Carrier Concentration
Temperature causes electrons to be promoted to the conduction band and from donor levels, or holes to acceptor levels. The dependence of conductivity on temperature is like other thermally activated processes:
s = A exp(–Eg/2kT)
where A is a constant (the mobility varies much more slowly with temperature). Plotting ln s vs. 1/T produces a straight line of slope Eg/2k from which the band gap energy can be determined. Extrinsic semiconductors have, in addition to this dependence, one due to the thermal promotion of electrons from donor levels or holes from acceptor levels. The dependence on temperature is also exponential but it eventually saturates at high temperatures where all the donors are emptied or all the acceptors are filled.
This means that at low temperatures, extrinsic semiconductors have larger conductivity than intrinsic semiconductors. At high temperatures, both the impurity levels and valence electrons are ionized, but since the impurities are very low in number and they are exhausted, eventually the behavior is dominated by the intrinsic type of conductivity.
Semiconductor Devices
A semiconductor diode is made by the intimate junction of a p-type and an n-type semiconductor (an n-p junction). Unlike a metal, the intensity of the electrical current that passes through the material depends on the polarity of the applied voltage. If the positive side of a battery is connected to the p-side, a situation called forward bias, a large amount of current can flow since holes and electrons are pushed into the junction region, where they recombine (annihilate). If the polarity of the voltage is flipped, the diode operates under reverse bias. Holes and electrons are removed from the region of the junction, which therefore becomes depleted of carriers and behaves like an insulator. For this reason, the current is very small under reverse bias. The asymmetric current-voltage characteristics of diodes is used to convert alternating current into direct current. This is called rectification.
A p-n-p junction transistor contains two diodes back-to-back. The central region is very thin and is called the base. A small voltage applied to the base has a large effect on the current passing through the transistor, and this can be used to amplify electrical signals (Fig. 19.22). Another common device is the MOSFET transistor where a gate serves the function of the base in a junction transistor. Control of the current through the transistor is by means of the electric field induced by the gate, which is isolated electrically by an oxide layer.
remainig part of chapter 17
Energy Band Structures in Solids
When atoms come together to form a solid, their valence electrons interact due to Coulomb forces, and they also feel the electric field produced by their own nucleus and that of the other atoms. In addition, two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion. The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same property (which include the energy). As a result of all these effects, the valence electrons of atoms form wide valence bands when they form a solid. The bands are separated by gaps, where electrons cannot exist. The precise location of the bands and band gaps depends on the type of atom (e.g., Si vs. Al), the distance between atoms in the solid, and the atomic arrangement (e.g., carbon vs. diamond).
In semiconductors and insulators, the valence band is filled, and no more electrons can be added, following Pauli's principle. Electrical conduction requires that electrons be able to gain energy in an electric field; this is not possible in these materials because that would imply that the electrons are promoted into the forbidden band gap.
In metals, the electrons occupy states up to the Fermi level. Conduction occurs by promoting electrons into the conduction band, that starts at the Fermi level, separated by the valence band by an infinitesimal amount.
Conduction in Terms of Band and Atomic Bonding Models
Conduction in metals is by electrons in the conduction band. Conduction in insulators is by electrons in the conduction band and by holes in the valence band. Holes are vacant states in the valence band that are created when an electron is removed.
In metals there are empty states just above the Fermi levels, where electrons can be promoted. The promotion energy is negligibly small so that at any temperature electrons can be found in the conduction band. The number of electrons participating in electrical conduction is extremely small.
In insulators, there is an energy gap between the valence and conduction bands, so energy is needed to promote an electron to the conduction band. This energy may come from heat, or from energetic radiation, like light of sufficiently small wavelength.
A working definition for the difference between semiconductors and insulators is that in semiconductors, electrons can reach the conduction band at ordinary temperatures, where in insulators they cannot. The probability that an electron reaches the conduction band is about exp(-Eg/2kT) where Eg is the band gap and kT has the usual meaning. If this probability is, say, <> 55. At room temperature, 2kT = 0.05 eV; thus Eg > 2.8 eV can be used as the condition for an insulator.
Besides having relatively small Eg, semiconductors have covalent bond, whereas insulators usually are partially ionic bonded.
Electron Mobility
Electrons are accelerated in an electric field E, in the opposite direction to the field because of their negative charge. The force acting on the electron is -eE, where e is the electric charge. This force produces a constant acceleration so that, in the absence of obstacles (in vacuum, like inside a TV tube) the electron speeds up continuously in an electric field. In a solid, the situation is different. The electrons scatter by collisions with atoms and vacancies that change drastically their direction of motion. Thus electrons move randomly but with a net drift in the direction opposite to the electric field. The drift velocity is constant, equal to the electric field times a constant called the mobility m,
vd= – me E
which means that there is a friction force proportional to velocity. This friction translates into energy that goes into the lattice as heat. This is the way that electric heaters work.
The electrical conductivity is:
s = n e me
where n is the concentration of electrons (n is used to indicate that the carriers of electricity are negative particles).
Electrical Resistivity of Metals
The resistivity then depends on collisions. Quantum mechanics tells us that electrons behave like waves. One of the effects of this is that electrons do not scatter from a perfect lattice. They scatter by defects, which can be:
atoms displaced by lattice vibrations
vacancies and interstitials
dislocations, grain boundaries
impurities One can express the total resistivity rtot by the Matthiessen rule, as a sum of resistivities due to thermal vibrations, impurities and dislocations. illustrates how the resistivity increases with temperature, with deformation, and with alloying
When atoms come together to form a solid, their valence electrons interact due to Coulomb forces, and they also feel the electric field produced by their own nucleus and that of the other atoms. In addition, two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion. The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same property (which include the energy). As a result of all these effects, the valence electrons of atoms form wide valence bands when they form a solid. The bands are separated by gaps, where electrons cannot exist. The precise location of the bands and band gaps depends on the type of atom (e.g., Si vs. Al), the distance between atoms in the solid, and the atomic arrangement (e.g., carbon vs. diamond).
In semiconductors and insulators, the valence band is filled, and no more electrons can be added, following Pauli's principle. Electrical conduction requires that electrons be able to gain energy in an electric field; this is not possible in these materials because that would imply that the electrons are promoted into the forbidden band gap.
In metals, the electrons occupy states up to the Fermi level. Conduction occurs by promoting electrons into the conduction band, that starts at the Fermi level, separated by the valence band by an infinitesimal amount.
Conduction in Terms of Band and Atomic Bonding Models
Conduction in metals is by electrons in the conduction band. Conduction in insulators is by electrons in the conduction band and by holes in the valence band. Holes are vacant states in the valence band that are created when an electron is removed.
In metals there are empty states just above the Fermi levels, where electrons can be promoted. The promotion energy is negligibly small so that at any temperature electrons can be found in the conduction band. The number of electrons participating in electrical conduction is extremely small.
In insulators, there is an energy gap between the valence and conduction bands, so energy is needed to promote an electron to the conduction band. This energy may come from heat, or from energetic radiation, like light of sufficiently small wavelength.
A working definition for the difference between semiconductors and insulators is that in semiconductors, electrons can reach the conduction band at ordinary temperatures, where in insulators they cannot. The probability that an electron reaches the conduction band is about exp(-Eg/2kT) where Eg is the band gap and kT has the usual meaning. If this probability is, say, <> 55. At room temperature, 2kT = 0.05 eV; thus Eg > 2.8 eV can be used as the condition for an insulator.
Besides having relatively small Eg, semiconductors have covalent bond, whereas insulators usually are partially ionic bonded.
Electron Mobility
Electrons are accelerated in an electric field E, in the opposite direction to the field because of their negative charge. The force acting on the electron is -eE, where e is the electric charge. This force produces a constant acceleration so that, in the absence of obstacles (in vacuum, like inside a TV tube) the electron speeds up continuously in an electric field. In a solid, the situation is different. The electrons scatter by collisions with atoms and vacancies that change drastically their direction of motion. Thus electrons move randomly but with a net drift in the direction opposite to the electric field. The drift velocity is constant, equal to the electric field times a constant called the mobility m,
vd= – me E
which means that there is a friction force proportional to velocity. This friction translates into energy that goes into the lattice as heat. This is the way that electric heaters work.
The electrical conductivity is:
s = n e me
where n is the concentration of electrons (n is used to indicate that the carriers of electricity are negative particles).
Electrical Resistivity of Metals
The resistivity then depends on collisions. Quantum mechanics tells us that electrons behave like waves. One of the effects of this is that electrons do not scatter from a perfect lattice. They scatter by defects, which can be:
atoms displaced by lattice vibrations
vacancies and interstitials
dislocations, grain boundaries
impurities One can express the total resistivity rtot by the Matthiessen rule, as a sum of resistivities due to thermal vibrations, impurities and dislocations. illustrates how the resistivity increases with temperature, with deformation, and with alloying
Chapter 17. Electrical Properties
Electrical Conduction
Ohm’s Law
When an electric potential V is applied across a material, a current of magnitude I flows. In most metals, at low values of V, the current is proportional to V, according to Ohm's law:
I = V/R
where R is the electrical resistance. R depends on the intrinsic resistivity r of the material and on the geometry (length l and area A through which the current passes).
R = rl/A
Electrical Conductivity
The electrical conductivity is the inverse of the resistivity: s = 1/r.
The electric field in the material is E=V/l, Ohm's law can then be expressed in terms of the current density j = I/A as:
j = s E
The conductivity is one of the properties of materials that varies most widely, from 107 (W-m) typical of metals to 10-20 (W-m) for good electrical insulators. Semiconductors have conductivities in the range 10-6 to 104 (W-m).
Electronic and Ionic Conduction
In metals, the current is carried by electrons, and hence the name electronic conduction. In ionic crystals, the charge carriers are ions, thus the name ionic conduction
Ohm’s Law
When an electric potential V is applied across a material, a current of magnitude I flows. In most metals, at low values of V, the current is proportional to V, according to Ohm's law:
I = V/R
where R is the electrical resistance. R depends on the intrinsic resistivity r of the material and on the geometry (length l and area A through which the current passes).
R = rl/A
Electrical Conductivity
The electrical conductivity is the inverse of the resistivity: s = 1/r.
The electric field in the material is E=V/l, Ohm's law can then be expressed in terms of the current density j = I/A as:
j = s E
The conductivity is one of the properties of materials that varies most widely, from 107 (W-m) typical of metals to 10-20 (W-m) for good electrical insulators. Semiconductors have conductivities in the range 10-6 to 104 (W-m).
Electronic and Ionic Conduction
In metals, the current is carried by electrons, and hence the name electronic conduction. In ionic crystals, the charge carriers are ions, thus the name ionic conduction
Chapter 16. Composites
16.1 Introduction
The idea is that by combining two or more distinct materials one can engineer a new material with the desired combination of properties (e.g., light, strong, corrosion resistant). The idea that a better combination of properties can be achieved is called the principle of combined action.
New - High-tech materials, engineered to specific applications
Old - brick-straw composites, paper, known for > 5000 years.
A type of composite that has been discussed is perlitic steel, which combines hard, brittle cementite with soft, ductile ferrite to get a superior material.
Natural composites: wood (polymer-polymer), bones (polymer-ceramics).
Usual composites have just two phases:
matrix (continuous)
dispersed phase (particulates, fibers)
Properties of composites depend on
properties of phases
geometry of dispersed phase (particle size, distribution, orientation)
amount of phase
Classification of composites: three main categories:
particle-reinforced (large-particle and dispersion-strengthened)
fiber-reinforced (continuous (aligned) and short fibers (aligned or random)
structural (laminates and sandwich panels)
Particle-reinforced composites
These are the cheapest and most widely used. They fall in two categories depending on the size of the particles:
large-particle composites, which act by restraining the movement of the matrix, if well bonded.
dispersion-strengthened composites, containing 10-100 nm particles, similar to what was discussed under precipitation hardening. The matrix bears the major portion of the applied load and the small particles hinder dislocation motion, limiting plastic deformation.
16.2 Large-Particle Composites
Properties are a combination of those of the components. The rule of mixtures predicts that an upper limit of the elastic modulus of the composite is given in terms of the elastic moduli of the matrix (Em) and the particulate (Ep) phases by:
Ec = EmVm + EpVp
where Vm and Vp are the volume fraction of the two phases. A lower bound is given by:
Ec = EmEp / (EpVm + EmVp)
modulus of composite of WC particles in Cu matrix vs. WC concentration.
Concrete
The most common large-particle composite is concrete, made of a cement matrix that bonds particles of different size (gravel and sand.) Cement was already known to the Egyptians and the Greek. Romans made cement by mixing lime (CaO) with volcanic ice.
In its general from, cement is a fine mixture of lime, alumina, silica, and water. Portland cement is a fine powder of chalk, clay and lime-bearing minerals fired to 1500o C (calcinated). It forms a paste when dissolved in water. It sets into a solid in minutes and hardens slowly (takes 4 months for full strength). Properties depend on how well it is mixed, and the amount of water: too little - incomplete bonding, too much - excessive porosity.
The advantage of cement is that it can be poured in place, it hardens at room temperature and even under water, and it is very cheap. The disadvantages are that it is weak and brittle, and that water in the pores can produce crack when it freezes in cold weather.
Concrete is cement strengthened by adding particulates. The use of different size (stone and sand) allows better packing factor than when using particles of similar size.
Concrete is improved by making the pores smaller (using finer powder, adding polymeric lubricants, and applying pressure during hardening.
Reinforced concrete is obtained by adding steel rods, wires, mesh. Steel has the advantage of a similar thermal expansion coefficient, so there is reduced danger of cracking due to thermal stresses. Pre-stressed concrete is obtained by applying tensile stress to the steel rods while the cement is setting and hardening. When the tensile stress is removed, the concrete is left under compressive stress, enabling it to sustain tensile loads without fracturing. Pre-stressed concrete shapes are usually prefabricated. A common use is in railroad or highway bridges.
Cermets
are composites of ceramic particles (strong, brittle) in a metal matrix (soft, ductile) that enhances toughness. For instance, tungsten carbide or titanium carbide ceramics in Co or Ni. They are used for cutting tools for hardened steels.
Reinforced rubber
is obtained by strengthening with 20-50 nm carbon-black particles. Used in auto tires.
16.3 Dispersion-Strengthened Composites
Use of very hard, small particles to strengthen metals and metal alloys. The effect is like precipitation hardening but not so strong. Particles like oxides do not react so the strengthening action is retained at high temperatures.
Fiber-reinforced composites
In many applications, like in aircraft parts, there is a need for high strength per unit weight (specific strength). This can be achieved by composites consisting of a low-density (and soft) matrix reinforced with stiff fibers.
The strength depends on the fiber length and its orientation with respect to the stress direction.
The efficiency of load transfer between matrix and fiber depends on the interfacial bond.
16.4 Influence of Fiber Length
Normally the matrix has a much lower modulus than the fiber so it strains more. This occurs at a distance from the fiber. Right next to the fiber, the strain is limited by the fiber. Thus, for a composite under tension, a shear stress appears in the matrix that pulls from the fiber. The pull is uniform over the area of the fiber. This makes the force on the fiber be minimum at the ends and maximum in the middle, like in the tug-of-war game.
To achieve effective strengthening and stiffening, the fibers must be larger than a critical length lc, defined as the minimum length at which the center of the fiber reaches the ultimate (tensile) strength sf, when the matrix achieves the maximum shear strength tm:
lc = sf d /2 tm
Since it is proportional to the diameter of the fiber d, a more unified condition for effective strengthening is that the aspect ratio of the fiber is l/d > sf /2 tm.
16.5 Influence of Fiber Orientation
The composite is stronger along the direction of orientation of the fibers and weakest in a direction perpendicular to the fiber. For discontinuous, random fibers, the properties are isotropic.
16.6 Polymer Matrix Composites
Largest and most diverse use of composites due to ease of fabrication, low cost and good properties.
Glass-fiber reinforced composites (GFRC) are strong, corrosion resistant and lightweight, but not very stiff and cannot be used at high temperatures. Applications include auto and boat bodies, aircraft components.
Carbon-fiber reinforced composites (CFRC) use carbon fibers, which have the highest specific module (module divided by weight). CFRC are strong, inert, allow high temperature use. Applications include fishing rods, golf clubs, aircraft components.
Kevlar, and aremid-fiber composite can be used as textile fibers. Applications include bullet-proof vests, tires, brake and clutch linings.
Wood:
This is one of the oldest and the most widely used structural material. It is a composite of strong and flexible cellulose fibers (linear polymer) surrounded and held together by a matrix of lignin and other polymers. The properties are anisotropic and vary widely among types of wood. Wood is ten times stronger in the axial direction than in the radial or tangential directions.
The idea is that by combining two or more distinct materials one can engineer a new material with the desired combination of properties (e.g., light, strong, corrosion resistant). The idea that a better combination of properties can be achieved is called the principle of combined action.
New - High-tech materials, engineered to specific applications
Old - brick-straw composites, paper, known for > 5000 years.
A type of composite that has been discussed is perlitic steel, which combines hard, brittle cementite with soft, ductile ferrite to get a superior material.
Natural composites: wood (polymer-polymer), bones (polymer-ceramics).
Usual composites have just two phases:
matrix (continuous)
dispersed phase (particulates, fibers)
Properties of composites depend on
properties of phases
geometry of dispersed phase (particle size, distribution, orientation)
amount of phase
Classification of composites: three main categories:
particle-reinforced (large-particle and dispersion-strengthened)
fiber-reinforced (continuous (aligned) and short fibers (aligned or random)
structural (laminates and sandwich panels)
Particle-reinforced composites
These are the cheapest and most widely used. They fall in two categories depending on the size of the particles:
large-particle composites, which act by restraining the movement of the matrix, if well bonded.
dispersion-strengthened composites, containing 10-100 nm particles, similar to what was discussed under precipitation hardening. The matrix bears the major portion of the applied load and the small particles hinder dislocation motion, limiting plastic deformation.
16.2 Large-Particle Composites
Properties are a combination of those of the components. The rule of mixtures predicts that an upper limit of the elastic modulus of the composite is given in terms of the elastic moduli of the matrix (Em) and the particulate (Ep) phases by:
Ec = EmVm + EpVp
where Vm and Vp are the volume fraction of the two phases. A lower bound is given by:
Ec = EmEp / (EpVm + EmVp)
modulus of composite of WC particles in Cu matrix vs. WC concentration.
Concrete
The most common large-particle composite is concrete, made of a cement matrix that bonds particles of different size (gravel and sand.) Cement was already known to the Egyptians and the Greek. Romans made cement by mixing lime (CaO) with volcanic ice.
In its general from, cement is a fine mixture of lime, alumina, silica, and water. Portland cement is a fine powder of chalk, clay and lime-bearing minerals fired to 1500o C (calcinated). It forms a paste when dissolved in water. It sets into a solid in minutes and hardens slowly (takes 4 months for full strength). Properties depend on how well it is mixed, and the amount of water: too little - incomplete bonding, too much - excessive porosity.
The advantage of cement is that it can be poured in place, it hardens at room temperature and even under water, and it is very cheap. The disadvantages are that it is weak and brittle, and that water in the pores can produce crack when it freezes in cold weather.
Concrete is cement strengthened by adding particulates. The use of different size (stone and sand) allows better packing factor than when using particles of similar size.
Concrete is improved by making the pores smaller (using finer powder, adding polymeric lubricants, and applying pressure during hardening.
Reinforced concrete is obtained by adding steel rods, wires, mesh. Steel has the advantage of a similar thermal expansion coefficient, so there is reduced danger of cracking due to thermal stresses. Pre-stressed concrete is obtained by applying tensile stress to the steel rods while the cement is setting and hardening. When the tensile stress is removed, the concrete is left under compressive stress, enabling it to sustain tensile loads without fracturing. Pre-stressed concrete shapes are usually prefabricated. A common use is in railroad or highway bridges.
Cermets
are composites of ceramic particles (strong, brittle) in a metal matrix (soft, ductile) that enhances toughness. For instance, tungsten carbide or titanium carbide ceramics in Co or Ni. They are used for cutting tools for hardened steels.
Reinforced rubber
is obtained by strengthening with 20-50 nm carbon-black particles. Used in auto tires.
16.3 Dispersion-Strengthened Composites
Use of very hard, small particles to strengthen metals and metal alloys. The effect is like precipitation hardening but not so strong. Particles like oxides do not react so the strengthening action is retained at high temperatures.
Fiber-reinforced composites
In many applications, like in aircraft parts, there is a need for high strength per unit weight (specific strength). This can be achieved by composites consisting of a low-density (and soft) matrix reinforced with stiff fibers.
The strength depends on the fiber length and its orientation with respect to the stress direction.
The efficiency of load transfer between matrix and fiber depends on the interfacial bond.
16.4 Influence of Fiber Length
Normally the matrix has a much lower modulus than the fiber so it strains more. This occurs at a distance from the fiber. Right next to the fiber, the strain is limited by the fiber. Thus, for a composite under tension, a shear stress appears in the matrix that pulls from the fiber. The pull is uniform over the area of the fiber. This makes the force on the fiber be minimum at the ends and maximum in the middle, like in the tug-of-war game.
To achieve effective strengthening and stiffening, the fibers must be larger than a critical length lc, defined as the minimum length at which the center of the fiber reaches the ultimate (tensile) strength sf, when the matrix achieves the maximum shear strength tm:
lc = sf d /2 tm
Since it is proportional to the diameter of the fiber d, a more unified condition for effective strengthening is that the aspect ratio of the fiber is l/d > sf /2 tm.
16.5 Influence of Fiber Orientation
The composite is stronger along the direction of orientation of the fibers and weakest in a direction perpendicular to the fiber. For discontinuous, random fibers, the properties are isotropic.
16.6 Polymer Matrix Composites
Largest and most diverse use of composites due to ease of fabrication, low cost and good properties.
Glass-fiber reinforced composites (GFRC) are strong, corrosion resistant and lightweight, but not very stiff and cannot be used at high temperatures. Applications include auto and boat bodies, aircraft components.
Carbon-fiber reinforced composites (CFRC) use carbon fibers, which have the highest specific module (module divided by weight). CFRC are strong, inert, allow high temperature use. Applications include fishing rods, golf clubs, aircraft components.
Kevlar, and aremid-fiber composite can be used as textile fibers. Applications include bullet-proof vests, tires, brake and clutch linings.
Wood:
This is one of the oldest and the most widely used structural material. It is a composite of strong and flexible cellulose fibers (linear polymer) surrounded and held together by a matrix of lignin and other polymers. The properties are anisotropic and vary widely among types of wood. Wood is ten times stronger in the axial direction than in the radial or tangential directions.
Friday, February 22, 2008
Chapter 15. Polymers. Characteristics, Applications and Processing
Stress-Strain Behavior
The description of stress-strain behavior is similar to that of metals, but a very important consideration for polymers is that the mechanical properties depend on the strain rate, temperature, and environmental conditions.
The stress-strain behavior can be brittle, plastic and highly elastic (elastomeric or rubber-like), . 1. Tensile modulus (modulus) and tensile strengths are orders of magnitude smaller than those of metals, but elongation can be up to 1000 % in some cases. The tensile strength is defined at the fracture point and can be lower than the yield strength.
Mechanical properties change dramatically with temperature, going from glass-like brittle behavior at low temperatures (like in the liquid-nitrogen demonstration) to a rubber-like behavior at high temperatures.
In general, decreasing the strain rate has the same influence on the strain-strength characteristics as increasing the temperature: the material becomes softer and more ductile.
Deformation of Semicrystalline Polymers
Many semicrystalline polymers have the spherulitic structure and deform in the following steps :
· elongation of amorphous tie chains
· tilting of lamellar chain folds towards the tensile direction
· separation of crystalline block segments
· orientation of segments and tie chains in the tensile direction
The macroscopic deformation involves an upper and lower yield point and necking. Unlike the case of metals, the neck gets stronger since the deformation aligns the chains so increasing the tensile stress leads to the growth of the neck..
Factors that Influence the Mechanical Properties of Polymers
The tensile modulus decreases with increasing temperature or diminishing strain rate.
Obstacles to the steps mentioned in 16.4 strengthen the polymer. Examples are cross-linking (aligned chains have more van der Waals inter-chain bonds) and a large mass (longer molecules have more inter-chain bonds). Crystallinity increases strength as the secondary bonding is enhanced when the molecular chains are closely packed and parallel. Pre-deformation by drawing, analogous to strain hardening in metals, increases strength by orienting the molecular chains. For undrawn polymers, heating increases the tensile modulus and yield strength, and reduces the ductility - opposite of what happens in metals.
Crystallization, Melting, and Glass Transition Phenomena
Crystallization rates are governed by the same type of S-curves we saw in the case of metals. Nucleation becomes slower at higher temperatures.
The melting behavior of semicrystalline polymers is intermediate between that of crystalline materials (sharp density change at a melting temperature) and that of a pure amorphous material (slight change in slope of density at the glass-transition temperature). The glass transition temperature is between 0.5 and 0.8 of the melting temperature.
The melting temperature increases with the rate of heating, thickness of the lamellae, and depends on the temperature at which the polymer was crystallized.
Melting involves breaking of the inter-chain bonds, so the glass and melting temperatures depend on:
· chain stiffness (e.g., single vs. double bonds)
· size, shape of side groups
· size of molecule
· side branches, defects
· cross-linking
Rigid chains have higher melting temperatures.
Thermoplastic and Thermosetting Polymers
Thermoplastic polymers (thermoplasts) soften reversibly when heated (harden when cooled back)
Thermosetting polymers (thermosets) harden permanently when heated, as cross-linking hinder bending and rotations. Thermosets are harder, more dimensionally stable, and more brittle than thermoplasts.
Viscoelasticity
At low temperatures, amorphous polymers deform elastically, like glass, at small elongation. At high temperatures the behavior is viscous, like liquids. At intermediate temperatures, the behavior, like a rubbery solid, is termed viscoelastic.
Viscoelasticity is characterized by the viscoelastic relaxation modulus
Er = s(t)/e0.
If the material is strained to a value e0.it is found that the stress needs to be reduced with time to maintain this constant value of strain (see figs. 16.11 and 16.12).
In viscoelastic creep, the stress is kept constant at s0 and the change of deformation with time e(t) is measured. The time-dependent creep modulus is given by
Ec = s0/e(t).
Deformation and Elastomers
Elastomers can be deformed to very large strains and the spring back elastically to the original length, a behavior first observed in natural rubber. Elastic elongation is due to uncoiling, untwisting and straightening of chains in the stress direction.
To be elastomeric, the polymer needs to meet several criteria:
· must not crystallize easily
· have relatively free chain rotations
· delayed plastic deformation by cross-linking (achieved by vulcanization).
· be above the glass transition temperature
Fracture of Polymers
As other mechanical properties, the fracture strength of polymers is much lower than that of metals. Fracture also starts with cracks at flaws, scratches, etc. Fracture involves breaking of covalent bonds in the chains. Thermoplasts can have both brittle and ductile fracture behaviors. Glassy thermosets have brittle fracture at low temperatures and ductile fracture at high temperatures.
Glassy thremoplasts often suffer grazing before brittle fracture. Crazes are associated with regions of highly localized yielding which leads to the formation of interconnected microvoids . Crazing absorbs energy thus increasing the fracture strength of the polymer.
Miscellaneous Characteristics
Polymers are brittle at low temperatures and have low impact strengths (Izod or Charpy tests), and a brittle to ductile transition over a narrow temperature range.
Fatigue is similar to the case of metals but at reduced loads and is more sensitive to frequency due to heating which leads to softening.
Polymerization
Polymerization is the synthesis of high polymers from raw materials like oil or coal. It may occur by:
· addition (chain-reaction) polymerization, where monomer units are attached one at a time
· condensation polymerization, by stepwise intermolecular chemical reactions that produce the mer units.
Elastomers
In vulcanization, crosslinking of the elastomeric polymer is achieved by an irreversible chemical reaction usually at high temperatures (hence ‘vulcan’), and usually involving the addition of sulfur compounds. The S atoms are the ones that form the bridge cross-links. Elastomers are thermosetting due to the cross-linking.
Rubbers become harder and extend less with increasing sulfur content. For automobile applications, synthetic rubbers are strengthened by adding carbon black.
In silicone rubbers, the backbone C atoms are replaced by a chain of alternating silicon and oxygen atoms. These elastomers are also cross-linked and are stable to higher temperatures than C-based elastomers.
Wednesday, February 20, 2008
Chapter 14.Polymers
14.1 Introduction
Polymers are common in nature, in the form of wood, rubber, cotton, leather, wood, silk, proteins, enzymes, starches, cellulose. Artificial polymers are made mostly from oil. Their use has grown exponentially, especially after WW2. The key factor is the very low production cost and useful properties (e.g., combination of transparency and flexibility, long elongation).
14.2 Hydrocarbon Molecules
Most polymers are organic, and formed from hydrocarbon molecules. These molecules can have single, double, or triple carbon bonds. A saturated hydrocarbon is one where all bonds are single, that is, the number of atoms is maximum (or saturated). Among this type are the paraffin compounds, CnH2n+2 . In contrast, non-saturated hydrocarbons contain some double and triple bonds.
Isomers are molecules that contain the same molecules but in a different arrangement. An example is butane and isobutane.
14.3 Polymer Molecules
Polymer molecules are huge, macromolecules that have internal covalent bonds. For most polymers, these molecules form very long chains. The backbone is a string of carbon atoms, often single bonded.
Polymers are composed of basic structures called mer units. A molecule with just one mer is a monomer.
14.4 The Chemistry of Polymer Molecules
Examples of polymers are polyvinyl chloride (PVC), poly-tetra-chloro-ethylene (PTFE or Teflon), polypropylene, nylon and polystyrene. Chains are represented straight but in practice they have a three-dimensional, zig-zag structure .
When all the mers are the same, the molecule is called a homopolymer. When there is more than one type of mer present, the molecule is a copolymer.
14.5 Molecular Weight
The mass of a polymer is not fixed, but is distributed around a mean value, since polymer molecules have different lengths. The average molecular weight can be obtained by averaging the masses with the fraction of times they appear (number-average) or with the mass fraction of the molecules (called, improperly, a weight fraction).
The degree of polymerization is the average number of mer units, and is obtained by dividing the average mass of the polymer by the mass of a mer unit.
Polymers of low mass are liquid or gases, those of very high mass (called high-polymers, are solid). Waxes, paraffins and resins have intermediate masses.
14.6 Molecular Shape
Polymers are usually not linear; bending and rotations can occur around single C-C bonds (double and triple bonds are very rigid) (Fig. 15.5). Random kings and coils lead to entanglement, like in the spaghetti structure.
14.7 Molecular Structure
Typical structures are :
linear (end-to-end, flexible, like PVC, nylon)
branched
cross-linked (due to radiation, vulcanization, etc.)
network (similar to highly cross-linked structures).
14.8 Molecular Configurations
The regularity and symmetry of the side-groups can affect strongly the properties of polymers. Side groups are atoms or molecules with free bonds, called free-radicals, like H, O, methyl, etc.
If the radicals are linked in the same order, the configuration is called isostatic
In a stereoisomer in a syndiotactic configuration, the radical groups alternative sides in the chain.
In the atactic configuration, the radical groups are positioned at random.
14.9 Copolymers
Copolymers, polymers with at least two different types of mers can differ in the way the mers are arranged. Shows different arrangements: random, alternating, block, and graft.
14.10 Polymer Crystallinity
Crystallinity in polymers is more complex than in metals . Polymer molecules are often partially crystalline (semicrystalline), with crystalline regions dispersed within amorphous material. .
Chain disorder or misalignment, which is common, leads to amorphous material since twisting, kinking and coiling prevent strict ordering required in the crystalline state. Thus, linear polymers with small side groups, which are not too long form crystalline regions easier than branched, network, atactic polymers, random copolymers, or polymers with bulky side groups.
Crystalline polymers are denser than amorphous polymers, so the degree of crystallinity can be obtained from the measurement of density.
14.11 Polymer Crystals
Different models have been proposed to describe the arrangement of molecules in semicrytalline polymers. In the fringed-micelle model, the crystallites (micelles) are embedded in an amorphous matrix . Polymer single crystals grown are shaped in regular platelets (lamellae) . Spherulites are chain-folded crystallites in an amorphous matrix that grow radially in spherical shape “grains”.
Polymers are common in nature, in the form of wood, rubber, cotton, leather, wood, silk, proteins, enzymes, starches, cellulose. Artificial polymers are made mostly from oil. Their use has grown exponentially, especially after WW2. The key factor is the very low production cost and useful properties (e.g., combination of transparency and flexibility, long elongation).
14.2 Hydrocarbon Molecules
Most polymers are organic, and formed from hydrocarbon molecules. These molecules can have single, double, or triple carbon bonds. A saturated hydrocarbon is one where all bonds are single, that is, the number of atoms is maximum (or saturated). Among this type are the paraffin compounds, CnH2n+2 . In contrast, non-saturated hydrocarbons contain some double and triple bonds.
Isomers are molecules that contain the same molecules but in a different arrangement. An example is butane and isobutane.
14.3 Polymer Molecules
Polymer molecules are huge, macromolecules that have internal covalent bonds. For most polymers, these molecules form very long chains. The backbone is a string of carbon atoms, often single bonded.
Polymers are composed of basic structures called mer units. A molecule with just one mer is a monomer.
14.4 The Chemistry of Polymer Molecules
Examples of polymers are polyvinyl chloride (PVC), poly-tetra-chloro-ethylene (PTFE or Teflon), polypropylene, nylon and polystyrene. Chains are represented straight but in practice they have a three-dimensional, zig-zag structure .
When all the mers are the same, the molecule is called a homopolymer. When there is more than one type of mer present, the molecule is a copolymer.
14.5 Molecular Weight
The mass of a polymer is not fixed, but is distributed around a mean value, since polymer molecules have different lengths. The average molecular weight can be obtained by averaging the masses with the fraction of times they appear (number-average) or with the mass fraction of the molecules (called, improperly, a weight fraction).
The degree of polymerization is the average number of mer units, and is obtained by dividing the average mass of the polymer by the mass of a mer unit.
Polymers of low mass are liquid or gases, those of very high mass (called high-polymers, are solid). Waxes, paraffins and resins have intermediate masses.
14.6 Molecular Shape
Polymers are usually not linear; bending and rotations can occur around single C-C bonds (double and triple bonds are very rigid) (Fig. 15.5). Random kings and coils lead to entanglement, like in the spaghetti structure.
14.7 Molecular Structure
Typical structures are :
linear (end-to-end, flexible, like PVC, nylon)
branched
cross-linked (due to radiation, vulcanization, etc.)
network (similar to highly cross-linked structures).
14.8 Molecular Configurations
The regularity and symmetry of the side-groups can affect strongly the properties of polymers. Side groups are atoms or molecules with free bonds, called free-radicals, like H, O, methyl, etc.
If the radicals are linked in the same order, the configuration is called isostatic
In a stereoisomer in a syndiotactic configuration, the radical groups alternative sides in the chain.
In the atactic configuration, the radical groups are positioned at random.
14.9 Copolymers
Copolymers, polymers with at least two different types of mers can differ in the way the mers are arranged. Shows different arrangements: random, alternating, block, and graft.
14.10 Polymer Crystallinity
Crystallinity in polymers is more complex than in metals . Polymer molecules are often partially crystalline (semicrystalline), with crystalline regions dispersed within amorphous material. .
Chain disorder or misalignment, which is common, leads to amorphous material since twisting, kinking and coiling prevent strict ordering required in the crystalline state. Thus, linear polymers with small side groups, which are not too long form crystalline regions easier than branched, network, atactic polymers, random copolymers, or polymers with bulky side groups.
Crystalline polymers are denser than amorphous polymers, so the degree of crystallinity can be obtained from the measurement of density.
14.11 Polymer Crystals
Different models have been proposed to describe the arrangement of molecules in semicrytalline polymers. In the fringed-micelle model, the crystallites (micelles) are embedded in an amorphous matrix . Polymer single crystals grown are shaped in regular platelets (lamellae) . Spherulites are chain-folded crystallites in an amorphous matrix that grow radially in spherical shape “grains”.
Chapter 13. Ceramics - Applications and Processing
13.1 Introduction
Ceramics properties that are different from those of metals lead to different uses. In structures, designs must be done for compressive loads. The transparency to light of many ceramics leads to optical uses, like in windows, photographic cameras, telescopes and microscopes. Good thermal insulation leads to use in ovens, the exterior tiles of the Shuttle orbiter, etc. Good electrical isolation are used to support conductors in electrical and electronic applications. The good chemical inertness shows in the stability of the structures thousands of years old.
13.2 Glass Properties
A special characteristic of glasses is that solidification is gradual, through a viscous stage, without a clear melting temperature. The specific volume does not have an abrupt transition at a temperature but rather shows a change in slope at the glass-transition temperature (Fig. 14.3).
The melting point, working point, softening point and annealing point are defined in terms of viscosity, rather than temperature (Fig. 14.4), and depend on glass composition..
13.4 Heat Treating Glasses
Similar to the case of metals, annealing is used at elevated temperatures is used to remove stresses, like those caused by inhomogeneous temperatures during cooling. Strengthening by glass tempering is done by heating the glass above the glass transition temperature but below the softening point and then quenched in an air jet or oil bath. The interior, which cools later than the outside, tries to contract while in a plastic state after the exterior has become rigid. This causes residual compressive stresses on the surface and tensile stresses inside. To fracture, a crack has first to overcome the residual compressive stress, making tempered glass less susceptible to fracture. This improvement leads to use in automobile windshields, glass doors, eyeglass lenses, etc
Ceramics properties that are different from those of metals lead to different uses. In structures, designs must be done for compressive loads. The transparency to light of many ceramics leads to optical uses, like in windows, photographic cameras, telescopes and microscopes. Good thermal insulation leads to use in ovens, the exterior tiles of the Shuttle orbiter, etc. Good electrical isolation are used to support conductors in electrical and electronic applications. The good chemical inertness shows in the stability of the structures thousands of years old.
13.2 Glass Properties
A special characteristic of glasses is that solidification is gradual, through a viscous stage, without a clear melting temperature. The specific volume does not have an abrupt transition at a temperature but rather shows a change in slope at the glass-transition temperature (Fig. 14.3).
The melting point, working point, softening point and annealing point are defined in terms of viscosity, rather than temperature (Fig. 14.4), and depend on glass composition..
13.4 Heat Treating Glasses
Similar to the case of metals, annealing is used at elevated temperatures is used to remove stresses, like those caused by inhomogeneous temperatures during cooling. Strengthening by glass tempering is done by heating the glass above the glass transition temperature but below the softening point and then quenched in an air jet or oil bath. The interior, which cools later than the outside, tries to contract while in a plastic state after the exterior has become rigid. This causes residual compressive stresses on the surface and tensile stresses inside. To fracture, a crack has first to overcome the residual compressive stress, making tempered glass less susceptible to fracture. This improvement leads to use in automobile windshields, glass doors, eyeglass lenses, etc
Tuesday, February 19, 2008
remaining part of chapter-12
12.5 Imperfections in Ceramics
Imperfections include point defects and impurities. Their formation is strongly affected by the condition of charge neutrality (creation of unbalanced charges requires the expenditure of a large amount of energy.
Non-stoichiometry refers to a change in composition so that the elements in the ceramic are not in the proportion appropriate for the compound (condition known as stoichiometry). To minimize energy, the effect of non-stoichiometry is a redistribution of the atomic charges Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is a vacancy- interstitial pair of cations (placing large anions in an interstitial position requires a lot of energy in lattice distortion). A Schottky-defect is the a pair of nearby cation and anion vacancies.
Introduction of impurity atoms in the lattice is likely in conditions where the charge is maintained. This is the case of electronegative impurities that substitute a lattice anions or electropositive substitutional impurities. This is more likely for similar ionic radii since this minimizes the energy required for lattice distortion. Defects will appear if the charge of the impurities is not balanced.
12.6 Ceramic Phase
to be prepare
12.7 Brittle Fracture of Ceramics
The brittle fracture of ceramics limits applications. It occurs due to the unavoidable presence of microscopic flaws (micro-cracks, internal pores, and atmospheric contaminants) that result during cooling from the melt. The flaws need to crack formation, and crack propagation (perpendicular to the applied stress) is usually transgranular, along cleavage planes. The flaws cannot be closely controlled in manufacturing; this leads to a large variability (scatter) in the fracture strength of ceramic materials.
The compressive strength is typically ten times the tensile strength. This makes ceramics good structural materials under compression (e.g., bricks in houses, stone blocks in the pyramids), but not in conditions of tensile stress, such as under flexure.
Plastic deformation in crystalline ceramics is by slip, which is difficult due to the structure and the strong local (electrostatic) potentials. There is very little plastic deformation before fracture.
Non-crystalline ceramics, like common glass deform by viscous flow (like very high-density liquids). Viscosity decreases strongly with increases temperature.
Imperfections include point defects and impurities. Their formation is strongly affected by the condition of charge neutrality (creation of unbalanced charges requires the expenditure of a large amount of energy.
Non-stoichiometry refers to a change in composition so that the elements in the ceramic are not in the proportion appropriate for the compound (condition known as stoichiometry). To minimize energy, the effect of non-stoichiometry is a redistribution of the atomic charges Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is a vacancy- interstitial pair of cations (placing large anions in an interstitial position requires a lot of energy in lattice distortion). A Schottky-defect is the a pair of nearby cation and anion vacancies.
Introduction of impurity atoms in the lattice is likely in conditions where the charge is maintained. This is the case of electronegative impurities that substitute a lattice anions or electropositive substitutional impurities. This is more likely for similar ionic radii since this minimizes the energy required for lattice distortion. Defects will appear if the charge of the impurities is not balanced.
12.6 Ceramic Phase
to be prepare
12.7 Brittle Fracture of Ceramics
The brittle fracture of ceramics limits applications. It occurs due to the unavoidable presence of microscopic flaws (micro-cracks, internal pores, and atmospheric contaminants) that result during cooling from the melt. The flaws need to crack formation, and crack propagation (perpendicular to the applied stress) is usually transgranular, along cleavage planes. The flaws cannot be closely controlled in manufacturing; this leads to a large variability (scatter) in the fracture strength of ceramic materials.
The compressive strength is typically ten times the tensile strength. This makes ceramics good structural materials under compression (e.g., bricks in houses, stone blocks in the pyramids), but not in conditions of tensile stress, such as under flexure.
Plastic deformation in crystalline ceramics is by slip, which is difficult due to the structure and the strong local (electrostatic) potentials. There is very little plastic deformation before fracture.
Non-crystalline ceramics, like common glass deform by viscous flow (like very high-density liquids). Viscosity decreases strongly with increases temperature.
Chapter 12. Ceramics - Structures and Properties
12.1 Introduction
Ceramics are inorganic and non-metallic materials that are commonly electrical and thermal insulators, brittle and composed of more than one element (e.g., two in Al2O3)
Ceramic Structures
12.2 Crystal Structures
Ceramic bonds are mixed, ionic and covalent, with a proportion that depends on the particular ceramics. The ionic character is given by the difference of electronegativity between the cations (+) and anions (-). Covalent bonds involve sharing of valence electrons. Very ionic crystals usually involve cations which are alkalis or alkaline-earths (first two columns of the periodic table) and oxygen or halogens as anions.
The building criteria for the crystal structure are two:
maintain neutrality
charge balance dictates chemical formula
achieve closest packing
the condition for minimum energy implies maximum attraction and minimum repulsion. This leads to contact, configurations where anions have the highest number of cation neighbors and viceversa.
The parameter that is important in determining contact is the ratio of cation to anion radii, rC/rA. Table 13.2 gives the coordination number and geometry as a function of rC/rA. For example, in the NaCl structure (Fig. 13.2), rC = rNa = 0.102 nm, rA =rCl.= 0.181 nm, so rC/rA.= 0.56. From table 13.2 this implies coordination number = 6, as observed for this rock-salt structure.
Other structures were shown in class, but will not be included in the test.
12.3 Silicate Ceramics
Oxygen and Silicon are the most abundant elements in Earth’s crust. Their combination (silicates) occur in rocks, soils, clays and sand. The bond is weekly ionic, with Si4+ as the cation and O2- as the anion. rSi = 0.04 nm, rO.= 0.14 nm, so rC/rA = 0.286. From table 13.2 this implies coordination number = 4, that is tetrahedral coordination (Fig. 13.9).
The tetrahedron is charged: Si4+ + 4 O2- Þ (Si O4)4-. Silicates differ on how the tetrahedra are arranged. In silica, (SiO2), every oxygen atom is shared by adjacent tetrahedra. Silica can be crystalline (e.g., quartz) or amorphous, as in glass.
Soda glasses melt at lower temperature than amorphous SiO2 because the addition of Na2O (soda) breaks the tetrahedral network. A lower melting point makes it easy to form glass to make, for instance, bottles.
12.4 Carbon
Carbon is not really a ceramic, but an allotropic form, diamond, may be thought as a type of ceramic. Diamond has very interesting and even unusual properties:
diamond-cubic structure (like Si, Ge)
covalent C-C bonds
highest hardness of any material known
very high thermal conductivity (unlike ceramics)
transparent in the visible and infrared, with high index of refraction
semiconductor (can be doped to make electronic devices)
metastable (transforms to carbon when heated)
Synthetic diamonds are made by application of high temperatures and pressures or by chemical vapor deposition. Future applications of this latter, cheaper production method include hard coatings for metal tools, ultra-low friction coatings for space applications, and microelectronics.
Graphite has a layered structure with very strong hexagonal bonding within the planar layers (using 3 of the 3 bonding electrons) and weak, van der Waals bonding between layers using the fourth electron. This leads to easy interplanar cleavage and applications as a lubricant and for writing (pencils). Graphite is a good electrical conductor and chemically stable even at high temperatures. Applications include furnaces, rocket nozzles, electrodes in batteries.
A recently (1985) discovered formed of carbon is the C60 molecule, also known as fullerene or bucky-ball (after the architect Buckminster Fuller who designed the geodesic structure that C60 resembles.) Fullerenes and related structures like bucky-onions amd nanotubes are exceptionally strong. Future applications are as a structural material and possibly in microelectronics, due to the unusual properties that result when fullerenes are doped with other atoms.
Ceramics are inorganic and non-metallic materials that are commonly electrical and thermal insulators, brittle and composed of more than one element (e.g., two in Al2O3)
Ceramic Structures
12.2 Crystal Structures
Ceramic bonds are mixed, ionic and covalent, with a proportion that depends on the particular ceramics. The ionic character is given by the difference of electronegativity between the cations (+) and anions (-). Covalent bonds involve sharing of valence electrons. Very ionic crystals usually involve cations which are alkalis or alkaline-earths (first two columns of the periodic table) and oxygen or halogens as anions.
The building criteria for the crystal structure are two:
maintain neutrality
charge balance dictates chemical formula
achieve closest packing
the condition for minimum energy implies maximum attraction and minimum repulsion. This leads to contact, configurations where anions have the highest number of cation neighbors and viceversa.
The parameter that is important in determining contact is the ratio of cation to anion radii, rC/rA. Table 13.2 gives the coordination number and geometry as a function of rC/rA. For example, in the NaCl structure (Fig. 13.2), rC = rNa = 0.102 nm, rA =rCl.= 0.181 nm, so rC/rA.= 0.56. From table 13.2 this implies coordination number = 6, as observed for this rock-salt structure.
Other structures were shown in class, but will not be included in the test.
12.3 Silicate Ceramics
Oxygen and Silicon are the most abundant elements in Earth’s crust. Their combination (silicates) occur in rocks, soils, clays and sand. The bond is weekly ionic, with Si4+ as the cation and O2- as the anion. rSi = 0.04 nm, rO.= 0.14 nm, so rC/rA = 0.286. From table 13.2 this implies coordination number = 4, that is tetrahedral coordination (Fig. 13.9).
The tetrahedron is charged: Si4+ + 4 O2- Þ (Si O4)4-. Silicates differ on how the tetrahedra are arranged. In silica, (SiO2), every oxygen atom is shared by adjacent tetrahedra. Silica can be crystalline (e.g., quartz) or amorphous, as in glass.
Soda glasses melt at lower temperature than amorphous SiO2 because the addition of Na2O (soda) breaks the tetrahedral network. A lower melting point makes it easy to form glass to make, for instance, bottles.
12.4 Carbon
Carbon is not really a ceramic, but an allotropic form, diamond, may be thought as a type of ceramic. Diamond has very interesting and even unusual properties:
diamond-cubic structure (like Si, Ge)
covalent C-C bonds
highest hardness of any material known
very high thermal conductivity (unlike ceramics)
transparent in the visible and infrared, with high index of refraction
semiconductor (can be doped to make electronic devices)
metastable (transforms to carbon when heated)
Synthetic diamonds are made by application of high temperatures and pressures or by chemical vapor deposition. Future applications of this latter, cheaper production method include hard coatings for metal tools, ultra-low friction coatings for space applications, and microelectronics.
Graphite has a layered structure with very strong hexagonal bonding within the planar layers (using 3 of the 3 bonding electrons) and weak, van der Waals bonding between layers using the fourth electron. This leads to easy interplanar cleavage and applications as a lubricant and for writing (pencils). Graphite is a good electrical conductor and chemically stable even at high temperatures. Applications include furnaces, rocket nozzles, electrodes in batteries.
A recently (1985) discovered formed of carbon is the C60 molecule, also known as fullerene or bucky-ball (after the architect Buckminster Fuller who designed the geodesic structure that C60 resembles.) Fullerenes and related structures like bucky-onions amd nanotubes are exceptionally strong. Future applications are as a structural material and possibly in microelectronics, due to the unusual properties that result when fullerenes are doped with other atoms.
Saturday, February 16, 2008
remaining part of chap-11
11.6 Influence of Quenching Medium, Specimen Size, and Geometry
The cooling rate depends on the cooling medium. Cooling is fastest using water, then oil, and then air. Fast cooling brings the danger of warping and formation of cracks, since it is usually accompanied by large thermal gradients.
The shape and size of the piece, together with the heat capacity and heat conductivity are important in determining the cooling rate for different parts of the metal piece. Heat capacity is the energy content of a heated mass, which needs to be removed for cooling. Heat conductivity measures how fast this energy is transported to the colder regions of the piece.
Precipitation Hardening
Hardening can be enhanced by extremely small precipitates that hinder dislocation motion. The precipitates form when the solubility limit is exceeded. Precipitation hardening is also called age hardening because it involves the hardening of the material over a prolonged time.
11.7 Heat Treatments
Precipitation hardening is achieved by:
a) solution heat treatment where all the solute atoms are dissolved to form a single-phase solution.
b) rapid cooling across the solvus line to exceed the solubility limit. This leads to a supersaturated solid solution that remains stable (metastable) due to the low temperatures, which prevent diffusion.
c) precipitation heat treatment where the supersaturated solution is heated to an intermediate temperature to induce precipitation and kept there for some time (aging).
If the process is continued for a very long time, eventually the hardness decreases. This is called overaging.
The requirements for precipitation hardening are:
appreciable maximum solubility
solubility curve that falls fast with temperature composition of the alloy that is less than the maximum solubility
11.8 Mechanism of Hardening
Strengthening involves the formation of a large number of microscopic nuclei, called zones. It is accelerated at high temperatures. Hardening occurs because the deformation of the lattice around the precipitates hinder slip. Aging that occurs at room temperature is called natural aging, to distinguish from the artificial aging caused by premeditated heating.
11.9 Miscellaneous Considerations
Since forming, machining, etc. uses more energy when the material is hard, the steps in the processing of alloys are usually:
solution heat treat and quench
do needed cold working before hardening
do precipitation hardening
Exposure of precipitation-hardened alloys to high temperatures may lead to loss of strength by overaging.
The cooling rate depends on the cooling medium. Cooling is fastest using water, then oil, and then air. Fast cooling brings the danger of warping and formation of cracks, since it is usually accompanied by large thermal gradients.
The shape and size of the piece, together with the heat capacity and heat conductivity are important in determining the cooling rate for different parts of the metal piece. Heat capacity is the energy content of a heated mass, which needs to be removed for cooling. Heat conductivity measures how fast this energy is transported to the colder regions of the piece.
Precipitation Hardening
Hardening can be enhanced by extremely small precipitates that hinder dislocation motion. The precipitates form when the solubility limit is exceeded. Precipitation hardening is also called age hardening because it involves the hardening of the material over a prolonged time.
11.7 Heat Treatments
Precipitation hardening is achieved by:
a) solution heat treatment where all the solute atoms are dissolved to form a single-phase solution.
b) rapid cooling across the solvus line to exceed the solubility limit. This leads to a supersaturated solid solution that remains stable (metastable) due to the low temperatures, which prevent diffusion.
c) precipitation heat treatment where the supersaturated solution is heated to an intermediate temperature to induce precipitation and kept there for some time (aging).
If the process is continued for a very long time, eventually the hardness decreases. This is called overaging.
The requirements for precipitation hardening are:
appreciable maximum solubility
solubility curve that falls fast with temperature composition of the alloy that is less than the maximum solubility
11.8 Mechanism of Hardening
Strengthening involves the formation of a large number of microscopic nuclei, called zones. It is accelerated at high temperatures. Hardening occurs because the deformation of the lattice around the precipitates hinder slip. Aging that occurs at room temperature is called natural aging, to distinguish from the artificial aging caused by premeditated heating.
11.9 Miscellaneous Considerations
Since forming, machining, etc. uses more energy when the material is hard, the steps in the processing of alloys are usually:
solution heat treat and quench
do needed cold working before hardening
do precipitation hardening
Exposure of precipitation-hardened alloys to high temperatures may lead to loss of strength by overaging.
Chapter 11. Thermal Processing of Metal Alloys
Annealing Processes
11.1 Introduction
Annealing is a heat treatment where the material is taken to a high temperature, kept there for some time and then cooled. High temperatures allow diffusion processes to occur fast. The time at the high temperature (soaking time) is long enough to allow the desired transformation to occur. Cooling is done slowly to avoid the distortion (warping) of the metal piece, or even cracking, caused by stresses induced by differential contraction due to thermal inhomogeneities. Benefits of annealing are:
relieve stresses
increase softness, ductility and toughness
produce a specific microstructure
11.2 Process Annealing
Deforming a piece that has been strengthened by cold working requires a lot of energy. Reverting the effect of cold work by process annealing eases further deformation. Heating allows recovery and recrystallization but is usually limited to avoid excessive grain growth and oxidation.
11.3 Stress Relief
Stresses resulting from machining operations of non-uniform cooling can be eliminated by stress relief annealing at moderately low temperatures, such that the effect of cold working and other heat treatments is maintained.
11.4 Annealing of Ferrous Alloys
Normalizing (or austenitizing) consists in taking the Fe-C alloy to the austenitic phase which makes the grain size more uniform, followed by cooling in air.
Full anneal involves taking hypoeutectoid alloys to the austenite phase and hypereutectoid alloys over the eutectoid temperature (Fig. 11.1) to soften pieces which have been hardened by plastic deformation, and which need to be machined.
Spheroidizing consists in prolongued heating just below the eutectoid temperature, which results in the soft spheroidite structure discussed in Sect. 10.5. This achieves maximum softness that minimizes the energy needed in subsequent forming operations.
Heat Treatment of Steels
1.5 Hardenability
To achieve a full conversion of austenite into hard martensite, cooling needs to be fast enough to avoid partial conversion into perlite or bainite. If the piece is thick, the interior may cool too slowly so that full martensitic conversion is not achieved. Thus, the martensitic content, and the hardness, will drop from a high value at the surface to a lower value in the interior of the piece. Hardenability is the ability of the material to be hardened by forming martensite.
Hardenability is measured by the Jominy end-quench test (Fig. 11.2). Hardenability is then given as the dependence of hardness on distance from the quenched end. High hardenability means that the hardness curve is relatively flat.
11.1 Introduction
Annealing is a heat treatment where the material is taken to a high temperature, kept there for some time and then cooled. High temperatures allow diffusion processes to occur fast. The time at the high temperature (soaking time) is long enough to allow the desired transformation to occur. Cooling is done slowly to avoid the distortion (warping) of the metal piece, or even cracking, caused by stresses induced by differential contraction due to thermal inhomogeneities. Benefits of annealing are:
relieve stresses
increase softness, ductility and toughness
produce a specific microstructure
11.2 Process Annealing
Deforming a piece that has been strengthened by cold working requires a lot of energy. Reverting the effect of cold work by process annealing eases further deformation. Heating allows recovery and recrystallization but is usually limited to avoid excessive grain growth and oxidation.
11.3 Stress Relief
Stresses resulting from machining operations of non-uniform cooling can be eliminated by stress relief annealing at moderately low temperatures, such that the effect of cold working and other heat treatments is maintained.
11.4 Annealing of Ferrous Alloys
Normalizing (or austenitizing) consists in taking the Fe-C alloy to the austenitic phase which makes the grain size more uniform, followed by cooling in air.
Full anneal involves taking hypoeutectoid alloys to the austenite phase and hypereutectoid alloys over the eutectoid temperature (Fig. 11.1) to soften pieces which have been hardened by plastic deformation, and which need to be machined.
Spheroidizing consists in prolongued heating just below the eutectoid temperature, which results in the soft spheroidite structure discussed in Sect. 10.5. This achieves maximum softness that minimizes the energy needed in subsequent forming operations.
Heat Treatment of Steels
1.5 Hardenability
To achieve a full conversion of austenite into hard martensite, cooling needs to be fast enough to avoid partial conversion into perlite or bainite. If the piece is thick, the interior may cool too slowly so that full martensitic conversion is not achieved. Thus, the martensitic content, and the hardness, will drop from a high value at the surface to a lower value in the interior of the piece. Hardenability is the ability of the material to be hardened by forming martensite.
Hardenability is measured by the Jominy end-quench test (Fig. 11.2). Hardenability is then given as the dependence of hardness on distance from the quenched end. High hardenability means that the hardness curve is relatively flat.
Remaining part of chapter 10
Microstructural and Property Changes in Fe-C Alloys
10.5 Isothermal Transformation Diagrams
We use as an example the cooling of an eutectoid alloy (0.76 wt% C) from the austenite (g- phase) to pearlite, that contains ferrite (a) plus cementite (Fe3C or iron carbide). When cooling proceeds below the eutectoid temperature (727 oC) nucleation of pearlite starts. The S-shaped curves (fraction of pearlite vs. log. time, fig. 10.3) are displaced to longer times at higher temperatures showing that the transformation is dominated by nucleation (the nucleation period is longer at higher temperatures) and not by diffusion (which occurs faster at higher temperatures).
The family of S-shaped curves at different temperatures can be used to construct the TTT (Time-Temperature-Transformation) diagrams (e.g., fig. 10.4.) For these diagrams to apply, one needs to cool the material quickly to a given temperature To before the transformation occurs, and keep it at that temperature over time. The horizontal line that indicates constant temperature To intercepts the TTT curves on the left (beginning of the transformation) and the right (end of the transformation); thus one can read from the diagrams when the transformation occurs. The formation of pearlite shown in fig. 10.4 also indicates that the transformation occurs sooner at low temperatures, which is an indication that it is controlled by the rate of nucleation. At low temperatures, nucleation occurs fast and grain growth is reduced (since it occurs by diffusion, which is hindered at low temperatures). This reduced grain growth leads to fine-grained microstructure (fine pearlite). At higher temperatures, diffusion allows for larger grain growth, thus leading to coarse pearlite.
At lower temperatures nucleation starts to become slower, and a new phase is formed, bainite. Since diffusion is low at low temperatures, this phase has a very fine (microscopic) microstructure.
Spheroidite is a coarse phase that forms at temperatures close to the eutectoid temperature. The relatively high temperatures caused a slow nucleation but enhances the growth of the nuclei leading to large grains.
A very important structure is martensite, which forms when cooling austenite very fast (quenching) to below a maximum temperature that is required for the transformation. It forms nearly instantaneously when the required low temperature is reached; since no thermal activation is needed, this is called an athermal transformation. Martensite is a different phase, a body-centered tetragonal (BCT) structure with interstitial C atoms. Martensite is metastable and decomposes into ferrite and pearlite but this is extremely slow (and not noticeable) at room temperature.
In the examples, we used an eutectoid composition. For hypo- and hypereutectoid alloys, the analysis is the same, but the proeutectoid phase that forms before cooling through the eutectoid temperature is also part of the final microstructure.
10.6 Continuous Cooling Transformation
10.7 Mechanical Behavior of Fe-C Alloys
The strength and hardness of the different microstructures is inversely related to the size of the microstructures. Thus, spheroidite is softest, fine pearlite is stronger than coarse pearlite, bainite is stronger than pearlite and martensite is the strongest of all. The stronger and harder the phase the more brittle it becomes.
10.8 Tempered Martensite
Martensite is so brittle that it needs to be modified in many practical cases. This is done by heating it to 250-650 oC for some time (tempering) which produces tempered martensite, an extremely fine-grained and well dispersed cementite grains in a ferrite matrix.
10.5 Isothermal Transformation Diagrams
We use as an example the cooling of an eutectoid alloy (0.76 wt% C) from the austenite (g- phase) to pearlite, that contains ferrite (a) plus cementite (Fe3C or iron carbide). When cooling proceeds below the eutectoid temperature (727 oC) nucleation of pearlite starts. The S-shaped curves (fraction of pearlite vs. log. time, fig. 10.3) are displaced to longer times at higher temperatures showing that the transformation is dominated by nucleation (the nucleation period is longer at higher temperatures) and not by diffusion (which occurs faster at higher temperatures).
The family of S-shaped curves at different temperatures can be used to construct the TTT (Time-Temperature-Transformation) diagrams (e.g., fig. 10.4.) For these diagrams to apply, one needs to cool the material quickly to a given temperature To before the transformation occurs, and keep it at that temperature over time. The horizontal line that indicates constant temperature To intercepts the TTT curves on the left (beginning of the transformation) and the right (end of the transformation); thus one can read from the diagrams when the transformation occurs. The formation of pearlite shown in fig. 10.4 also indicates that the transformation occurs sooner at low temperatures, which is an indication that it is controlled by the rate of nucleation. At low temperatures, nucleation occurs fast and grain growth is reduced (since it occurs by diffusion, which is hindered at low temperatures). This reduced grain growth leads to fine-grained microstructure (fine pearlite). At higher temperatures, diffusion allows for larger grain growth, thus leading to coarse pearlite.
At lower temperatures nucleation starts to become slower, and a new phase is formed, bainite. Since diffusion is low at low temperatures, this phase has a very fine (microscopic) microstructure.
Spheroidite is a coarse phase that forms at temperatures close to the eutectoid temperature. The relatively high temperatures caused a slow nucleation but enhances the growth of the nuclei leading to large grains.
A very important structure is martensite, which forms when cooling austenite very fast (quenching) to below a maximum temperature that is required for the transformation. It forms nearly instantaneously when the required low temperature is reached; since no thermal activation is needed, this is called an athermal transformation. Martensite is a different phase, a body-centered tetragonal (BCT) structure with interstitial C atoms. Martensite is metastable and decomposes into ferrite and pearlite but this is extremely slow (and not noticeable) at room temperature.
In the examples, we used an eutectoid composition. For hypo- and hypereutectoid alloys, the analysis is the same, but the proeutectoid phase that forms before cooling through the eutectoid temperature is also part of the final microstructure.
10.6 Continuous Cooling Transformation
10.7 Mechanical Behavior of Fe-C Alloys
The strength and hardness of the different microstructures is inversely related to the size of the microstructures. Thus, spheroidite is softest, fine pearlite is stronger than coarse pearlite, bainite is stronger than pearlite and martensite is the strongest of all. The stronger and harder the phase the more brittle it becomes.
10.8 Tempered Martensite
Martensite is so brittle that it needs to be modified in many practical cases. This is done by heating it to 250-650 oC for some time (tempering) which produces tempered martensite, an extremely fine-grained and well dispersed cementite grains in a ferrite matrix.
Chapter-10: Phase Transformations in Metals
10.1 Introduction
The goal is to obtain specific microstructures that will improve the mechanical properties of a metal, in addition to grain-size refinement, solid-solution strengthening, and strain-hardening.
10.2 Basic Concepts
Phase transformations that involve a change in the microstructure can occur through:
Diffusion
Maintaining the type and number of phases (e.g., solidification of a pure metal, allotropic transformation, recrystallization, grain growth.
Alteration of phase composition (e.g., eutectoid reactions, see 10.5)
Diffusionless
Production of metastable phases (e.g., martensitic transformation, see 10.5)
10.3 The Kinetics of Solid-State Reactions
Change in composition implies atomic rearrangement, which requires diffusion. Atoms are displaced by random walk. The displacement of a given atom, d, is not linear in time t (as would be for a straight trajectory) but is proportional to the square root of time, due to the tortuous path: d = c(Dt) 1/2 where c is a constant and D the diffusion constant. This time-dependence of the rate at which the reaction (phase transformation) occurs is what is meant by the term reaction kinetics.
D is called a constant because it does not depend on time, but it depends on temperature as we have seen in Ch. 5. Diffusion occurs faster at high temperatures.
Phase transformation requires two processes: nucleation and growth. Nucleation involves the formation of very small particles, or nuclei (e.g., grain boundaries, defects). This is similar to rain happening when water molecules condensed around dust particles. During growth, the nuclei grow in size at the expense of the surrounding material.
The kinetic behavior often has the S-shape form of Fig. 10.1, when plotting percent of material transformed vs. the logarithm of time. The nucleation phase is seen as an incubation period, where nothing seems to happen. Usually the transformation rate has the form r = A e-Q/RT (similar to the temperature dependence of the diffusion constant), in which case it is said to be thermally activated.
10.4 Multiphase Transformations
To describe phase transformations that occur during cooling, equilibrium phase diagrams are inadequate if the transformation rate is slow compared to the cooling rate. This is usually the case in practice, so that equilibrium microstructures are seldom obtained. This means that the transformations are delayed (e.g., case of supercooling), and metastable states are formed. We then need to know the effect of time on phase transformations
The goal is to obtain specific microstructures that will improve the mechanical properties of a metal, in addition to grain-size refinement, solid-solution strengthening, and strain-hardening.
10.2 Basic Concepts
Phase transformations that involve a change in the microstructure can occur through:
Diffusion
Maintaining the type and number of phases (e.g., solidification of a pure metal, allotropic transformation, recrystallization, grain growth.
Alteration of phase composition (e.g., eutectoid reactions, see 10.5)
Diffusionless
Production of metastable phases (e.g., martensitic transformation, see 10.5)
10.3 The Kinetics of Solid-State Reactions
Change in composition implies atomic rearrangement, which requires diffusion. Atoms are displaced by random walk. The displacement of a given atom, d, is not linear in time t (as would be for a straight trajectory) but is proportional to the square root of time, due to the tortuous path: d = c(Dt) 1/2 where c is a constant and D the diffusion constant. This time-dependence of the rate at which the reaction (phase transformation) occurs is what is meant by the term reaction kinetics.
D is called a constant because it does not depend on time, but it depends on temperature as we have seen in Ch. 5. Diffusion occurs faster at high temperatures.
Phase transformation requires two processes: nucleation and growth. Nucleation involves the formation of very small particles, or nuclei (e.g., grain boundaries, defects). This is similar to rain happening when water molecules condensed around dust particles. During growth, the nuclei grow in size at the expense of the surrounding material.
The kinetic behavior often has the S-shape form of Fig. 10.1, when plotting percent of material transformed vs. the logarithm of time. The nucleation phase is seen as an incubation period, where nothing seems to happen. Usually the transformation rate has the form r = A e-Q/RT (similar to the temperature dependence of the diffusion constant), in which case it is said to be thermally activated.
10.4 Multiphase Transformations
To describe phase transformations that occur during cooling, equilibrium phase diagrams are inadequate if the transformation rate is slow compared to the cooling rate. This is usually the case in practice, so that equilibrium microstructures are seldom obtained. This means that the transformations are delayed (e.g., case of supercooling), and metastable states are formed. We then need to know the effect of time on phase transformations
Remainig part of chapter 9
9.13 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
a-ferrite (BCC) Fe-C solution
g-austenite (FCC) Fe-C solution
d-ferrite (BCC) Fe-C solution
liquid Fe-C solution
Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
9.14 Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar or layered structure of two phases: a-ferrite and cementite (Fe3C).
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch. 10.
9.15 The Influence of Other Alloying Elements
As mentioned in section 7.9, alloying strengthens metals by hindering the motion of dislocations. Thus, the strength of Fe–C alloys increase with C content and also with the addition of other elements.
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
a-ferrite (BCC) Fe-C solution
g-austenite (FCC) Fe-C solution
d-ferrite (BCC) Fe-C solution
liquid Fe-C solution
Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
9.14 Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar or layered structure of two phases: a-ferrite and cementite (Fe3C).
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch. 10.
9.15 The Influence of Other Alloying Elements
As mentioned in section 7.9, alloying strengthens metals by hindering the motion of dislocations. Thus, the strength of Fe–C alloys increase with C content and also with the addition of other elements.
Chapter-9: PHASE DIAGRAMS
9.1 Introduction
Definitions
Component: pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water, in a syrup.)
Solvent: host or major component in solution.
Solute: dissolved, minor component in solution.
System: set of possible alloys from same component (e.g., iron-carbon system.)
Solubility Limit: Maximum solute concentration that can be dissolved at a given temperature.
Phase: part with homogeneous physical and chemical characteristics
9.2 Solubility Limit
Effect of temperature on solubility limit. Maximum content: saturation. Exceeding maximum content (like when cooling) leads to precipitation.
9.3 Phases
One-phase systems are homogeneous. Systems with two or more phases are heterogeneous, or mixtures. This is the case of most metallic alloys, but also happens in ceramics and polymers.
A two-component alloy is called binary. One with three components, ternary.
9.4 Microstructure
The properties of an alloy do not depend only on concentration of the phases but how they are arranged structurally at the microscopy level. Thus, the microstructure is specified by the number of phases, their proportions, and their arrangement in space.
A binary alloy may be
a single solid solution
two separated, essentially pure components.
two separated solid solutions.
a chemical compound, together with a solid solution.
The way to tell is to cut the material, polish it to a mirror finish, etch it a weak acid (components etch at a different rate) and observe the surface under a microscope.
9.5 Phase Equilibria
Equilibrium is the state of minimum energy. It is achieved given sufficient time. But the time to achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy minimum may have a long life and appear to be stable. This is called a metastable state.
A less strict, operational, definition of equilibrium is that of a system that does not change with time during observation.
Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the quantities of phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into another. Sometimes diagrams are given with pressure as one of the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at one atmosphere.
9.6 Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal structure (FCC), near the same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid above the liquidus line.
The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
locate composition and temperature in diagram
In two phase region draw tie line or isotherm
note intersection with phase boundaries. Read compositions.
Fractions: lever rule
construct tie line (isotherm)
obtain ratios of line segments lengths.
Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the point in the diagram is close to the phase line, the fraction of that phase is large.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.
b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves by diffusion, following the equilibrium values that can be derived from the tie-line method. However, diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)
9.7 Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction (%).
Solvus line: limit of solubility
Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and the eutectic temperature.
Note:
the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).
At most two phases can be in equilibrium within a phase field.
Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid + liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further. The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase (Fig. 9.16).
9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical compositions. When using the lever rules, intermetallic compounds are treated like any other phase, except they appear not as a wide region but as a vertical line.
9.9 Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and proeutectoid microstructures.
Solid Phase 1 à Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs when heating.
Solid Phase 1 + liquid à Solid Phase 2
9.10 Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change in composition, like allotropic transformations (e.g., a-Fe to g-Fe) or melting transitions in pure solids. 9.13 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
a-ferrite (BCC) Fe-C solution
g-austenite (FCC) Fe-C solution
d-ferrite (BCC) Fe-C solution
liquid Fe-C solution
Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
Definitions
Component: pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water, in a syrup.)
Solvent: host or major component in solution.
Solute: dissolved, minor component in solution.
System: set of possible alloys from same component (e.g., iron-carbon system.)
Solubility Limit: Maximum solute concentration that can be dissolved at a given temperature.
Phase: part with homogeneous physical and chemical characteristics
9.2 Solubility Limit
Effect of temperature on solubility limit. Maximum content: saturation. Exceeding maximum content (like when cooling) leads to precipitation.
9.3 Phases
One-phase systems are homogeneous. Systems with two or more phases are heterogeneous, or mixtures. This is the case of most metallic alloys, but also happens in ceramics and polymers.
A two-component alloy is called binary. One with three components, ternary.
9.4 Microstructure
The properties of an alloy do not depend only on concentration of the phases but how they are arranged structurally at the microscopy level. Thus, the microstructure is specified by the number of phases, their proportions, and their arrangement in space.
A binary alloy may be
a single solid solution
two separated, essentially pure components.
two separated solid solutions.
a chemical compound, together with a solid solution.
The way to tell is to cut the material, polish it to a mirror finish, etch it a weak acid (components etch at a different rate) and observe the surface under a microscope.
9.5 Phase Equilibria
Equilibrium is the state of minimum energy. It is achieved given sufficient time. But the time to achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy minimum may have a long life and appear to be stable. This is called a metastable state.
A less strict, operational, definition of equilibrium is that of a system that does not change with time during observation.
Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the quantities of phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into another. Sometimes diagrams are given with pressure as one of the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at one atmosphere.
9.6 Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal structure (FCC), near the same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid above the liquidus line.
The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
locate composition and temperature in diagram
In two phase region draw tie line or isotherm
note intersection with phase boundaries. Read compositions.
Fractions: lever rule
construct tie line (isotherm)
obtain ratios of line segments lengths.
Note: the fractions are inversely proportional to the length to the boundary for the particular phase. If the point in the diagram is close to the phase line, the fraction of that phase is large.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.
b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves by diffusion, following the equilibrium values that can be derived from the tie-line method. However, diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)
9.7 Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction (%).
Solvus line: limit of solubility
Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and the eutectic temperature.
Note:
the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).
At most two phases can be in equilibrium within a phase field.
Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid + liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further. The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase (Fig. 9.16).
9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical compositions. When using the lever rules, intermetallic compounds are treated like any other phase, except they appear not as a wide region but as a vertical line.
9.9 Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and proeutectoid microstructures.
Solid Phase 1 à Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs when heating.
Solid Phase 1 + liquid à Solid Phase 2
9.10 Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change in composition, like allotropic transformations (e.g., a-Fe to g-Fe) or melting transitions in pure solids. 9.13 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:
a-ferrite (BCC) Fe-C solution
g-austenite (FCC) Fe-C solution
d-ferrite (BCC) Fe-C solution
liquid Fe-C solution
Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in a- ferrite is 0.022 wt%. d-ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into a-Fe and C when heated for several years between 650 and 770 C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)
Tuesday, February 5, 2008
Chapter 8. FAILURE
Introduction
Failure of materials may have huge costs. Causes included improper materials selection or processing, the improper design of components, and improper use.
Fundamentals of Fracture
Fracture is a form of failure where the material separates in pieces due to stress, at temperatures below the melting point. The fracture is termed ductile or brittle depending on whether the elongation is large or small.
Steps in fracture (response to stress):
track formation
track propagation
Ductile vs. brittle fracture
Ductile/ Brittle
deformation extensive/ little
track propagation slow, /needs stress fast
type of materials most metals (not too cold) /ceramics, ice, cold metals
warning permanent elongation /none
strain energy higher /lower
fractured surface rough/ smoother
necking yes/ no
Ductile Fracture
Stages of ductile fracture
Initial necking
small cavity formation (microvoids)
void growth (elipsoid) by coalescence into a crack
fast crack propagation around neck. Shear strain at 45o
final shear fracture (cup and cone)
The interior surface is fibrous, irregular, which signify plastic deformation.
Brittle Fracture
There is no appreciable deformation, and crack propagation is very fast. In most brittle materials, crack propagation (by bond breaking) is along specific crystallographic planes (cleavage planes). This type of fracture is transgranular (through grains) producing grainy texture (or faceted texture) when cleavage direction changes from grain to grain. In some materials, fracture is intergranular. Principles of Fracture Mechanics
Fracture occurs due to stress concentration at flaws, like surface scratches, voids, etc. If a is the length of the void and r the radius of curvature, the enhanced stress near the flaw is:
sm » 2 s0 (a/r)1/2
where s0 is the applied macroscopic stress. Note that a is 1/2 the length of the flaw, not the full length for an internal flaw, but the full length for a surface flaw. The stress concentration factor is:
Kt = sm/s0 » 2 (a/r)1/2
Because of this enhancement, flaws with small radius of curvature are called stress raisers.
Impact Fracture Testing
Normalized tests, like the Charpy and Izod tests measure the impact energy required to fracture a notched specimen with a hammer mounted on a pendulum. The energy is measured by the change in potential energy (height) of the pendulum. This energy is called notch toughness.
Ductile to brittle transition occurs in materials when the temperature is dropped below a transition temperature. Alloying usually increases the ductile-brittle transition temperature (Fig. 8.19.) For ceramics, this type of transition occurs at much higher temperatures than for metals.
Fatigue
Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It can happen in bridges, airplanes, machine components, etc. The characteristics are:
long period of cyclic strain
the most usual (90%) of metallic failures (happens also in ceramics and polymers)
is brittle-like even in ductile metals, with little plastic deformation
it occurs in stages involving the initiation and propagation of cracks.
Cyclic Stresses
These are characterized by maximum, minimum and mean stress, the stress amplitude, and the stress ratio
The S—N Curve
S—N curves (stress-number of cycles to failure) are obtained using apparatus like the one shown in Fig. 8.21. Different types of S—N curves are shown in Fig. 8.22.
Fatigue limit (endurance limit) occurs for some materials (like some ferrous and Ti allows). In this case, the S—N curve becomes horizontal at large N . This means that there is a maximum stress amplitude (the fatigue limit) below which the material never fails, no matter how large the number of cycles is.
For other materials (e.g., non-ferrous) the S—N curve continues to fall with N.
Failure by fatigue shows substantial variability (Fig. 8.23).
Failure at low loads is in the elastic strain regime, requires a large number of cycles (typ. 104 to 105). At high loads (plastic regime), one has low-cycle fatigue (N <>Crack Initiation and Propagation
Stages is fatigue failure:
I. crack initiation at high stress points (stress raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture
Nfinal = Ninitiation + Npropagation
Stage I - propagation
slow
along crystallographic planes of high shear stress
flat and featureless fatigue surface
Stage II - propagation
crack propagates by repetive plastic blunting and sharpening of the crack tip. (Fig. 8.25.)
. Crack Propagation Rate (not covered)
. Factors That Affect Fatigue Life
Mean stress (lower fatigue life with increasing smean).
Surface defects (scratches, sharp transitions and edges). Solution:
polish to remove machining flaws
add residual compressive stress (e.g., by shot peening.)
case harden, by carburizing, nitriding (exposing to appropriate gas at high temperature)
. Environmental Effects
Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained. Solution:
eliminate restraint by design
use materials with low thermal expansion coefficients.
Corrosion fatigue. Chemical reactions induced pits which act as stress raisers. Corrosion also enhances crack propagation. Solutions:
decrease corrosiveness of medium, if possible.
add protective surface coating.
add residual compressive stresses.
Creep
Creep is the time-varying plastic deformation of a material stressed at high temperatures. Examples: turbine blades, steam generators. Keys are the time dependence of the strain and the high temperature.
. Generalized Creep Behavior
At a constant stress, the strain increases initially fast with time (primary or transient deformation), then increases more slowly in the secondary region at a steady rate (creep rate). Finally the strain increases fast and leads to failure in the tertiary region. Characteristics:
Creep rate: de/dt
Time to failure.
. Stress and Temperature Effects
Creep becomes more pronounced at higher temperatures (Fig. 8.37). There is essentially no creep at temperatures below 40% of the melting point.
Creep increases at higher applied stresses.
The behavior can be characterized by the following expression, where K, n and Qc are constants for a given material:
de/dt = K sn exp(-Qc/RT)
. Data Extrapolation Methods (not covered.)
. Alloys for High-Temperature Use
These are needed for turbines in jet engines, hypersonic airplanes, nuclear reactors, etc. The important factors are a high melting temperature, a high elastic modulus and large grain size (the latter is opposite to what is desirable in low-temperature materials).
Some creep resistant materials are stainless steels, refractory metal alloys (containing elements of high melting point, like Nb, Mo, W, Ta), and superalloys (based on Co, Ni, Fe.)
Failure of materials may have huge costs. Causes included improper materials selection or processing, the improper design of components, and improper use.
Fundamentals of Fracture
Fracture is a form of failure where the material separates in pieces due to stress, at temperatures below the melting point. The fracture is termed ductile or brittle depending on whether the elongation is large or small.
Steps in fracture (response to stress):
track formation
track propagation
Ductile vs. brittle fracture
Ductile/ Brittle
deformation extensive/ little
track propagation slow, /needs stress fast
type of materials most metals (not too cold) /ceramics, ice, cold metals
warning permanent elongation /none
strain energy higher /lower
fractured surface rough/ smoother
necking yes/ no
Ductile Fracture
Stages of ductile fracture
Initial necking
small cavity formation (microvoids)
void growth (elipsoid) by coalescence into a crack
fast crack propagation around neck. Shear strain at 45o
final shear fracture (cup and cone)
The interior surface is fibrous, irregular, which signify plastic deformation.
Brittle Fracture
There is no appreciable deformation, and crack propagation is very fast. In most brittle materials, crack propagation (by bond breaking) is along specific crystallographic planes (cleavage planes). This type of fracture is transgranular (through grains) producing grainy texture (or faceted texture) when cleavage direction changes from grain to grain. In some materials, fracture is intergranular. Principles of Fracture Mechanics
Fracture occurs due to stress concentration at flaws, like surface scratches, voids, etc. If a is the length of the void and r the radius of curvature, the enhanced stress near the flaw is:
sm » 2 s0 (a/r)1/2
where s0 is the applied macroscopic stress. Note that a is 1/2 the length of the flaw, not the full length for an internal flaw, but the full length for a surface flaw. The stress concentration factor is:
Kt = sm/s0 » 2 (a/r)1/2
Because of this enhancement, flaws with small radius of curvature are called stress raisers.
Impact Fracture Testing
Normalized tests, like the Charpy and Izod tests measure the impact energy required to fracture a notched specimen with a hammer mounted on a pendulum. The energy is measured by the change in potential energy (height) of the pendulum. This energy is called notch toughness.
Ductile to brittle transition occurs in materials when the temperature is dropped below a transition temperature. Alloying usually increases the ductile-brittle transition temperature (Fig. 8.19.) For ceramics, this type of transition occurs at much higher temperatures than for metals.
Fatigue
Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It can happen in bridges, airplanes, machine components, etc. The characteristics are:
long period of cyclic strain
the most usual (90%) of metallic failures (happens also in ceramics and polymers)
is brittle-like even in ductile metals, with little plastic deformation
it occurs in stages involving the initiation and propagation of cracks.
Cyclic Stresses
These are characterized by maximum, minimum and mean stress, the stress amplitude, and the stress ratio
The S—N Curve
S—N curves (stress-number of cycles to failure) are obtained using apparatus like the one shown in Fig. 8.21. Different types of S—N curves are shown in Fig. 8.22.
Fatigue limit (endurance limit) occurs for some materials (like some ferrous and Ti allows). In this case, the S—N curve becomes horizontal at large N . This means that there is a maximum stress amplitude (the fatigue limit) below which the material never fails, no matter how large the number of cycles is.
For other materials (e.g., non-ferrous) the S—N curve continues to fall with N.
Failure by fatigue shows substantial variability (Fig. 8.23).
Failure at low loads is in the elastic strain regime, requires a large number of cycles (typ. 104 to 105). At high loads (plastic regime), one has low-cycle fatigue (N <>Crack Initiation and Propagation
Stages is fatigue failure:
I. crack initiation at high stress points (stress raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture
Nfinal = Ninitiation + Npropagation
Stage I - propagation
slow
along crystallographic planes of high shear stress
flat and featureless fatigue surface
Stage II - propagation
crack propagates by repetive plastic blunting and sharpening of the crack tip. (Fig. 8.25.)
. Crack Propagation Rate (not covered)
. Factors That Affect Fatigue Life
Mean stress (lower fatigue life with increasing smean).
Surface defects (scratches, sharp transitions and edges). Solution:
polish to remove machining flaws
add residual compressive stress (e.g., by shot peening.)
case harden, by carburizing, nitriding (exposing to appropriate gas at high temperature)
. Environmental Effects
Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained. Solution:
eliminate restraint by design
use materials with low thermal expansion coefficients.
Corrosion fatigue. Chemical reactions induced pits which act as stress raisers. Corrosion also enhances crack propagation. Solutions:
decrease corrosiveness of medium, if possible.
add protective surface coating.
add residual compressive stresses.
Creep
Creep is the time-varying plastic deformation of a material stressed at high temperatures. Examples: turbine blades, steam generators. Keys are the time dependence of the strain and the high temperature.
. Generalized Creep Behavior
At a constant stress, the strain increases initially fast with time (primary or transient deformation), then increases more slowly in the secondary region at a steady rate (creep rate). Finally the strain increases fast and leads to failure in the tertiary region. Characteristics:
Creep rate: de/dt
Time to failure.
. Stress and Temperature Effects
Creep becomes more pronounced at higher temperatures (Fig. 8.37). There is essentially no creep at temperatures below 40% of the melting point.
Creep increases at higher applied stresses.
The behavior can be characterized by the following expression, where K, n and Qc are constants for a given material:
de/dt = K sn exp(-Qc/RT)
. Data Extrapolation Methods (not covered.)
. Alloys for High-Temperature Use
These are needed for turbines in jet engines, hypersonic airplanes, nuclear reactors, etc. The important factors are a high melting temperature, a high elastic modulus and large grain size (the latter is opposite to what is desirable in low-temperature materials).
Some creep resistant materials are stainless steels, refractory metal alloys (containing elements of high melting point, like Nb, Mo, W, Ta), and superalloys (based on Co, Ni, Fe.)
Chapter 7. DISLOCATIONS AND STRENGTHENING MECHANISM
Introduction
The key idea of the chapter is that plastic deformation is due to the motion of a large number of dislocations. The motion is called slip. Thus, the strength (resistance to deformation) can be improved by putting obstacles to slip.
Basic Concepts
Dislocations can be edge dislocations, screw dislocations and exist in combination of the two (Ch. 4.4). Their motion (slip) occurs by sequential bond breaking and bond reforming (Fig. 7.1). The number of dislocations per unit volume is the dislocation density, in a plane they are measured per unit area.
Characteristics of Dislocations
There is strain around a dislocation which influences how they interact with other dislocations, impurities, etc. There is compression near the extra plane (higher atomic density) and tension following the dislocation line (Fig. 7.4)
Dislocations interact among themselves (Fig. 7.5). When they are in the same plane, they repel if they have the same sign and annihilate if they have opposite signs (leaving behind a perfect crystal). In general, when dislocations are close and their strain fields add to a larger value, they repel, because being close increases the potential energy (it takes energy to strain a region of the material).
The number of dislocations increases dramatically during plastic deformation. Dislocations spawn from existing dislocations, and from defects, grain boundaries and surface irregularities.
Slip Systems
In single crystals there are preferred planes where dislocations move (slip planes). There they do not move in any direction, but in preferred crystallographic directions (slip direction). The set of slip planes and directions constitute slip systems.
The slip planes are those of highest packing density. How do we explain this? Since the distance between atoms is shorter than the average, the distance perpendicular to the plane has to be longer than average. Being relatively far apart, the atoms can move more easily with respect to the atoms of the adjacent plane. (We did not discuss direction and plane nomenclature for slip systems.)
BCC and FCC crystals have more slip systems, that is more ways for dislocation to propagate. Thus, those crystals are more ductile than HCP crystals (HCP crystals are more brittle).
Slip in Single Crystals
A tensile stress s will have components in any plane that is not perpendicular to the stress. These components are resolved shear stresses. Their magnitude depends on orientation (see Fig. 7.7).
tR = s cos f cos l
If the shear stress reaches the critical resolved shear stress tCRSS, slip (plastic deformation) can start. The stress needed is:
sy = tCRSS / (cos f cos l)max
at the angles at which tCRSS is a maximum. The minimum stress needed for yielding is when f = l = 45 degrees: sy = 2tCRSS. Thus, dislocations will occur first at slip planes oriented close to this angle with respect to the applied stress
The key idea of the chapter is that plastic deformation is due to the motion of a large number of dislocations. The motion is called slip. Thus, the strength (resistance to deformation) can be improved by putting obstacles to slip.
Basic Concepts
Dislocations can be edge dislocations, screw dislocations and exist in combination of the two (Ch. 4.4). Their motion (slip) occurs by sequential bond breaking and bond reforming (Fig. 7.1). The number of dislocations per unit volume is the dislocation density, in a plane they are measured per unit area.
Characteristics of Dislocations
There is strain around a dislocation which influences how they interact with other dislocations, impurities, etc. There is compression near the extra plane (higher atomic density) and tension following the dislocation line (Fig. 7.4)
Dislocations interact among themselves (Fig. 7.5). When they are in the same plane, they repel if they have the same sign and annihilate if they have opposite signs (leaving behind a perfect crystal). In general, when dislocations are close and their strain fields add to a larger value, they repel, because being close increases the potential energy (it takes energy to strain a region of the material).
The number of dislocations increases dramatically during plastic deformation. Dislocations spawn from existing dislocations, and from defects, grain boundaries and surface irregularities.
Slip Systems
In single crystals there are preferred planes where dislocations move (slip planes). There they do not move in any direction, but in preferred crystallographic directions (slip direction). The set of slip planes and directions constitute slip systems.
The slip planes are those of highest packing density. How do we explain this? Since the distance between atoms is shorter than the average, the distance perpendicular to the plane has to be longer than average. Being relatively far apart, the atoms can move more easily with respect to the atoms of the adjacent plane. (We did not discuss direction and plane nomenclature for slip systems.)
BCC and FCC crystals have more slip systems, that is more ways for dislocation to propagate. Thus, those crystals are more ductile than HCP crystals (HCP crystals are more brittle).
Slip in Single Crystals
A tensile stress s will have components in any plane that is not perpendicular to the stress. These components are resolved shear stresses. Their magnitude depends on orientation (see Fig. 7.7).
tR = s cos f cos l
If the shear stress reaches the critical resolved shear stress tCRSS, slip (plastic deformation) can start. The stress needed is:
sy = tCRSS / (cos f cos l)max
at the angles at which tCRSS is a maximum. The minimum stress needed for yielding is when f = l = 45 degrees: sy = 2tCRSS. Thus, dislocations will occur first at slip planes oriented close to this angle with respect to the applied stress
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