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Chapter 1. INRODUCTION
1 .1 Historical Perspective
Materials are so important in the development of civilization that we associate Ages with them. In the origin of human life on Earth, the Stone Age, people used only natural materials, like stone, clay, skins, and wood. When people found copper and how to make it harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The next big step was the discovery of a cheap process to make steel around 1850, which enabled the railroads and the building of the modern infrastructure of the industrial world.
1.2 Materials Science and Engineering
Understanding of how materials behave like they do, and why they differ in properties was only possible with the atomistic understanding allowed by quantum mechanics, that first explained atoms and then solids starting in the 1930s. The combination of physics, chemistry, and the focus on the relationship between the properties of a material and its microstructure is the domain of Materials Science. The development of this science allowed designing materials and provided a knowledge base for the engineering applications (Materials Engineering).
Structure :
• At the atomic level: arrangement of atoms in different ways. (Gives different properties for graphite
than diamond both forms of carbon.)
• At the microscopic level: arrangement of small grains of material that can be identified by
microscopy. (Gives different optical properties to transparent vs. frosted glass.)
Properties are the way the material responds to the environment. For instance, the mechanical, electrical and magnetic properties are the responses to mechanical, electrical and magnetic forces, respectively. Other important properties are thermal (transmission of heat, heat capacity), optical (absorption, transmission and scattering of light), and the chemical stability in contact with the environment (like corrosion resistance).
Processing of materials is the application of heat (heat treatment), mechanical forces, etc. to affect their microstructure and, therefore, their properties.
1.3 Why Study Materials Science and Engineering?
• To be able to select a material for a given use based on considerations of cost and performance.
• To understand the limits of materials and the change of their properties with use.
• To be able to create a new material that will have some desirable properties.
All engineering disciplines need to know about materials. Even the most "immaterial", like software or system engineering depend on the development of new materials, which in turn alter the economics, like software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing (industrial engineering) and complex environmental systems.
1.4 Classification of Materials
Like many other things, materials are classified in groups, so that our brain can handle the complexity. One could classify them according to structure, or properties, or use. The one that we will use is according to the way the atoms are bound together:
Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together. Metals are usually strong, conduct electricity and heat well and are opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.
Semiconductors: the bonding is covalent (electrons are shared between atoms). Their electrical properties depend extremely strongly on minute proportions of contaminants. They are opaque to visible light but transparent to the infrared. Examples: Si, Ge, GaAs.
Ceramics: atoms behave mostly like either positive or negative ions, and are bound by Coulomb forces between them. They are usually combinations of metals or semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides). Examples: glass, porcelain, many minerals.
Polymers: are bound by covalent forces and also by weak van der Waals forces, and usually based on H, C and other non-metallic elements. They decompose at moderate temperatures (100 – 400 C), and are lightweight. Other properties vary greatly. Examples: plastics (nylon, Teflon, polyester) and rubber.
Other categories are not based on bonding. A particular microstructure identifies composites, made of different materials in intimate contact (example: fiberglass, concrete, wood) to achieve specific properties. Biomaterials can be any type of material that is biocompatible and used, for instance, to replace human body parts.
1.5 Advanced Materials
Materials used in "High-Tec" applications, usually designed for maximum performance, and normally expensive. Examples are titanium alloys for supersonic airplanes, magnetic alloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.
1.6 Modern Material's Needs
• Engine efficiency increases at high temperatures: requires high temperature structural materials
• Use of nuclear energy requires solving problem with residues, or advances in nuclear waste
processing.
• Hypersonic flight requires materials that are light, strong and resist high temperatures.
• Optical communications require optical fibers that absorb light negligibly.
• Civil construction – materials for unbreakable windows.
• Structures: materials that are strong like metals and resist corrosion like plastics.
Chapter 2. ATOMIC STRUCTURE AND BONDING 2.2 Fundamental Concepts
Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19^ Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10 -27^ kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, N (^) av = 6.023 × 10 23. Note that N (^) av = 1 gram/1 amu.
Calculating n, the number of atoms per cm 3 in a piece of material of density d (g/cm^3 ).
n = Nav × d / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density d = 1.8 g/ cm^3 , M =12, we get 6 × 10 23 atoms/mol × 1.8 g/cm^3 / 12 g/mol) = 9 × 10 22 C/cm^3.
For a molecular solid like ice, one uses the molecular mass, M(H 2 O) = 18. With a density of 1 g/cm^3 , one obtains n = 3.3 × 10^22 H 2 O/cm 3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 10^22 atoms/cm 3.
Most solids have atomic densities around 6 × 10 22 atoms/cm^3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.
2.3 Electrons in Atoms
The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Thus, Z is what characterizes the atom.
The electrons form a cloud around the neutron, of radius of 0.05 – 2 nanometers. Electrons do not move in circular orbits, as in popular drawings, but in 'fuzzy' orbits. We cannot tell how it moves, but only say what is the probability of finding it at some distance from the nucleus. According to quantum mechanics, only certain orbits are allowed (thus, the idea of a mini planetary system is not correct). The orbits are identified by a principal quantum number n , which can be related to the size, n = 0 is the smallest; n = 1, 2 .. are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and so is the projection in a specific direction m. The structure of the atom is determined by the Pauli exclusion principle , only two electrons can be placed in an orbit with a given n, l, m – one for each spin. Table 2.1 in the textbook gives the number of electrons in each shell (given by n ) and subshells (given by l ).
2.4 The Periodic Table
Elements are categorized by placing them in the periodic table. Elements in a column share similar properties. The noble gases have closed shells , and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H 2 , N 2 , and NaCl.
The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds.
2.5 Bonding Forces and Energies
To discuss crystalline structures it is useful to consider atoms as being hard spheres, with well-defined radii. In this scheme, the shortest distance between two like atoms is one diameter.
3.3 Unit Cells
The unit cell is the smallest structure that repeats itself by translation through the crystal. We construct these symmetrical units with the hard spheres. The most common types of unit cells are the faced-centered cubic (FCC), the body-centered cubic (FCC) and the hexagonal close-packed (HCP). Other types exist, particularly among minerals. The simple cube (SC) is often used for didactical purpose, no material has this structure. 3.4 Metallic Crystal Structures
Important properties of the unit cells are
• The type of atoms and their radii R.
• cell dimensions (side a in cubic cells, side of base a and height c in HCP) in terms of R.
• n , number of atoms per unit cell. For an atom that is shared with m adjacent unit cells, we only count
a fraction of the atom, 1/ m.
• CN , the coordination number, which is the number of closest neighbors to which an atom is bonded.
• APF , the atomic packing factor, which is the fraction of the volume of the cell actually occupied by
the hard spheres. APF = Sum of atomic volumes/Volume of cell.
Unit Cell n CN a / R APF
SC 1 6 2 0.
BCC 2 8 4Ö 3 0.
FCC 4 12 2Ö 2 0.
HCP 6 12 0.
The closest packed direction in a BCC cell is along the diagonal of the cube; in a FCC cell is along the diagonal of a face of the cube.
3.5 Density Computations
The density of a solid is that of the unit cell, obtained by dividing the mass of the atoms ( n atoms x M atom) and dividing by V (^) c the volume of the cell ( a^3 in the case of a cube). If the mass of the atom is given in amu ( A ), then we have to divide it by the Avogadro number to get Matom. Thus, the formula for the density is:
3.6 Polymorphism and Allotropy Some materials may exist in more than one crystal structure, this is called polymorphism. If the material is an elemental solid, it is called allotropy. An example of allotropy is carbon, which can exist as diamond, graphite, and amorphous carbon.
3.11 Close-Packed Crystal Structures The FCC and HCP are related, and have the same APF. They are built by packing spheres on top of each other, in the hollow sites (Fig. 3.12 of book). The packing is alternate between two types of sites, ABABAB.. in the HCP structure, and alternates between three types of positions, ABCABC… in the FCC crystals.
Crystalline and Non-Crystalline Materials
3.12 Single Crystals
Crystals can be single crystals where the whole solid is one crystal. Then it has a regular geometric structure with flat faces. 3.13 Polycrystalline Materials
A solid can be composed of many crystalline grains, not aligned with each other. It is called polycrystalline. The grains can be more or less aligned with respect to each other. Where they meet is called a grain boundary.
3.14 Anisotropy Different directions in the crystal have a different packing. For instance, atoms along the edge FCC crystals are more separated than along the face diagonal. This causes anisotropy in the properties of crystals; for instance, the deformation depends on the direction in which a stress is applied.
3.15 X-Ray Diffraction Determination of Crystalline Structure – not covered 3.16 Non-Crystalline Solids
In amorphous solids, there is no long-range order. But amorphous does not mean random, since the distance between atoms cannot be smaller than the size of the hard spheres. Also, in many cases there is some form of short-range order. For instance, the tetragonal order of crystalline SiO 2 (quartz)^ is^ still^ apparent^ in amorphous SiO 2 (silica glass.)
Chapter-4: IMPERFECTIONS
Imperfections in Solids
4.1 Introduction
Materials are often stronger when they have defects. The study of defects is divided according to their dimension:
0D (zero dimension) – point defects: vacancies and interstitials. Impurities.
1D – linear defects: dislocations (edge, screw, mixed)
2D – grain boundaries, surfaces. 3D – extended defects: pores, cracks.
Point Defects
4.2 Vacancies and Self-Interstitials A vacancy is a lattice position that is vacant because the atom is missing. It is created when the solid is formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal vibrations.
An interstitial is an atom that occupies a place outside the normal lattice position. It may be the same type of atom as the others (self interstitial) or an impurity atom.
In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect. This means that the forces are not balanced in the same way as for other atoms in the solid, which results in lattice distortion around the defect. The number of vacancies formed by thermal agitation follows the law:
NV = N^ A × exp(-QV /kT)
where N (^) A is the total number of atoms in the solid, Q^ V is the energy required to form a vacancy, k is Boltzmann constant, and T the temperature in Kelvin (note, not in oC or oF).
When QV is given in joules, k = 1.38 × 10-23^ J/atom-K. When using eV as the unit of energy, k = 8.62 × 10^ - eV/atom-K.
Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical vacancy formation energies. For instance, Q (^) V(Cu) = 0.9 eV/atom. This means that NV /NA at room temperature is exp(-36) = 2. × 10-16, an insignificant number. Thus, a high temperature is needed to have a high thermal concentration of vacancies. Even so, NV/N (^) A is typically only about 0.0001 at the melting point.
4.3 Impurities in Solids
All real solids are impure. A very high purity material, say 99.9999% pure (called 6N – six nines) contains ~ 6 × 10^16 impurities per cm^3.
Impurities are often added to materials to improve the properties. For instance, carbon added in small amounts to iron makes steel, which is stronger than iron. Boron impurities added to silicon drastically change its electrical properties.
Solid solutions are made of a host, the solvent or matrix) which dissolves the solute (minor component). The ability to dissolve is called solubility. Solid solutions are:
• homogeneous
• maintain crystal structure
• contain randomly dispersed impurities (substitutional or interstitial)
Factors for high solubility
• Similar atomic size (to within 15%)
• Similar crystal structure
• Similar electronegativity (otherwise a compound is formed)
• Similar valence
Composition can be expressed in weight percent, useful when making the solution, and in atomic percent, useful when trying to understand the material at the atomic level.
Miscellaneous Imperfections
4.4 Dislocations—Linear Defects
This is the case when the diffusion flux depends on time, which means that a type of atoms accumulates in a region or that it is depleted from a region (which may cause them to accumulate in another region).
5.5 Factors That Influence Diffusion
As stated above, there is a barrier to diffusion created by neighboring atoms that need to move to let the diffusing atom pass. Thus, atomic vibrations created by temperature assist diffusion. Also, smaller atoms diffuse more readily than big ones, and diffusion is faster in open lattices or in open directions. Similar to the case of vacancy formation, the effect of temperature in diffusion is given by a Boltzmann factor: D = D 0 ×
exp(–Qd /kT).
5.6 Other Diffusion Paths
Diffusion occurs more easily along surfaces, and voids in the material (short circuits like dislocations and grain boundaries) because less atoms need to move to let the diffusing atom pass. Short circuits are often unimportant because they constitute a negligible part of the total area of the material normal to the diffusion flux..
Chapter-6: Mechanical Properties of Metals
1. Introduction
Often materials are subject to forces (loads) when they are used. Mechanical engineers calculate those forces and material scientists how materials deform (elongate, compress, twist) or break as a function of applied load, time, temperature, and other conditions.
Materials scientists learn about these mechanical properties by testing materials. Results from the tests depend on the size and shape of material to be tested (specimen), how it is held, and the way of performing the test. That is why we use common procedures, or standards , which are published by the ASTM.
.2 Concepts of Stress and Strain
To compare specimens of different sizes, the load is calculated per unit area, also called normalization to the area. Force divided by area is called stress. In tension and compression tests, the relevant area is that perpendicular to the force. In shear or torsion tests, the area is perpendicular to the axis of rotation. s = F / A (^) 0 tensile or compressive stress
t = F / A (^) 0 shear stress
The unit is the Megapascal = 10^6 Newtons/m^2.
There is a change in dimensions, or deformation elongation, D L as a result of a tensile or compressive stress. To enable comparison with specimens of different length, the elongation is also normalized, this time to the length L. This is called strain, e.
e = D L / L The change in dimensions is the reason we use A (^) 0 to indicate the initial area since it changes during deformation. One could divide force by the actual area, this is called true stress (see Sec. 6.7).
For torsional or shear stresses, the deformation is the angle of twist, q (Fig. 6.1) and the shear strain is given by:
g = tg q
.3 Stress—Strain Behavior
Elastic deformation. When the stress is removed, the material returns to the dimension it had before the load was applied. Valid for small strains (except the case of rubbers).
Deformation is reversible, non permanent Plastic deformation. When the stress is removed, the material does not return to its previous dimension but there is a permanent , irreversible deformation. In tensile tests, if the deformation is elastic , the stress-strain relationship is called Hooke's law: s = E e
That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. In some cases, the relationship is not linear so that E can be defined alternatively as the local slope:
E = ds/de
Shear stresses produce strains according to:
t = G g where G is the shear modulus.
Elastic moduli measure the stiffness of the material. They are related to the second derivative of the interatomic potential, or the first derivative of the force vs. internuclear distance (Fig. 6.6). By examining these curves we can tell which material has a higher modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic..
.4 Anelasticity
Here the behavior is elastic but not the stress-strain curve is not immediately reversible. It takes a while for the strain to return to zero. The effect is normally small for metals but can be significant for polymers.
.5 Elastic Properties of Materials
Materials subject to tension shrink laterally. Those subject to compression, bulge. The ratio of lateral and axial strains is called the Poisson's ratio n_._
n = elateral/eaxial The elastic modulus, shear modulus and Poisson's ratio are related by E = 2 G (1+n)
.6 Tensile Properties
Yield point. If the stress is too large, the strain deviates from being proportional to the stress. The point at which this happens is the yield point because there the material yields, deforming permanently (plastically).
Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is called yield stress , and is an important measure of the mechanical properties of materials. In practice, the yield stress is chosen as that causing a permanent strain of 0.002 (strain offset, Fig. 6.9.)
The yield stress measures the resistance to plastic deformation.
The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched beyond repair, but the motion of dislocations, which involves breaking and reforming bonds.
Plastic deformation is caused by the motion of dislocations.
Tensile strength. When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength (s (^) TS ) , and then falls as the material starts to develop a neck and it finally breaks at the fracture point (Fig. 6.10).
Note that it is called strength, not stress, but the units are the same, MPa.
For structural applications, the yield stress is usually a more important property than the tensile strength, since once the it is passed, the structure has deformed beyond acceptable limits.
Ductility. The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation emax or maximum area reduction.
%EL = emax x 100 %
%AR = ( A (^) 0 -^ A^ f)/ A^ 0
These are measured after fracture (repositioning the two pieces back together).
Resilience. Capacity to absorb energy elastically. The energy per unit volume is the
area under the strain-stress curve in the elastic region. Toughness. Ability to absorb energy up to fracture. The energy per unit volume is the total area under the strain-stress curve. It is measured by an impact test (Ch. 8).
.7 True Stress and Strain
When one applies a constant tensile force the material will break after reaching the tensile strength. The material starts necking (the transverse area decreases) but the stress cannot increase beyond s (^) TS. The ratio of the force to the initial area, what we normally do, is called
.4 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).
.5 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).
t R =^ s cos f cos l
If the shear stress reaches the critical resolved shear stress t CRSS , slip (plastic deformation) can start. The stress needed is:
s y =^ t CRSS / ( cos f cos l )max
at the angles at which t CRSS is a maximum. The minimum stress needed for yielding is when^ f^ =^ l^ = 45 degrees: s y = 2 t CRSS. Thus, dislocations will occur first at slip planes oriented close to this angle with respect to the applied stress (Figs. 7.8 and 7.9).
.6 Plastic Deformation of Polycrystalline Materials
Slip directions vary from crystal to crystal. When plastic deformation occurs in a grain, it will be constrained by its neighbors which may be less favorably oriented. As a result, polycrystalline metals are stronger than single crystals (the exception is the perfect single crystal, as in whiskers.)
.7 Deformation by Twinning
This topic is not included. Mechanisms of Strengthening in Metals
General principles. Ability to deform plastically depends on ability of dislocations to move. Strengthening consists in hindering dislocation motion. We discuss the methods of grain-size reduction, solid-solution alloying and strain hardening. These are for single-phase metals. We discuss others when treating alloys. Ordinarily, strengthening reduces ductility.
.8 Strengthening by Grain Size Reduction
This is based on the fact that it is difficult for a dislocation to pass into another grain, especially if it is very misaligned. Atomic disorder at the boundary causes discontinuity in slip planes. For high-angle grain boundaries, stress at end of slip plane may trigger new dislocations in adjacent grains. Small angle grain boundaries are not effective in blocking dislocations.
The finer the grains, the larger the area of grain boundaries that impedes dislocation motion. Grain-size reduction usually improves toughness as well. Usually, the yield strength varies with grain size d according to:
s y = s 0 + k (^) y / d 1/
Grain size can be controlled by the rate of solidification and by plastic deformation.
.9 Solid-Solution Strengthening
Adding another element that goes into interstitial or substitutional positions in a solution increases strength. The impurity atoms cause lattice strain (Figs. 7.17 and 7.18) which can "anchor" dislocations. This occurs when the strain caused by the alloying element compensates that of the dislocation, thus achieving a state of low potential energy. It costs strain energy for the dislocation to move away from this state (which is like a potential well). The scarcity of energy at low temperatures is why slip is hindered. Pure metals are almost always softer than their alloys.
.10 Strain Hardening
Ductile metals become stronger when they are deformed plastically at temperatures well below the melting point ( cold working). (This is different from hot working is the shaping of materials at high temperatures where large deformation is possible.) Strain hardening (work hardening) is the reason for the elastic recovery discussed in Ch. 6.8. The reason for strain hardening is that the dislocation density increases with plastic deformation (cold work) due to multiplication. The average distance between dislocations then decreases and dislocations start blocking the motion of each one.
The measure of strain hardening is the percent cold work (%CW), given by the relative reduction of the original area, A (^) 0 to the final value A d :
%CW = 100 ( A 0 – A^ d)/ A^ 0 Recovery, recrystallization and Grain Growth
Plastic deformation causes 1) change in grain size, 2) strain hardening, 3) increase in the dislocation density. Restoration to the state before cold-work is done by heating through two processes: recovery and recrystallization. These may be followed by grain growth.
.11 Recovery
Heating à increased diffusion à enhanced dislocation motion à relieves internal strain energy and reduces the number of dislocation. The electrical and thermal conductivity are restored to the values existing before cold working.
.12 Recrystallization
Strained grains of cold-worked metal are replaced, upon heating, by more regularly-spaced grains. This occurs through short-range diffusion enabled by the high temperature. Since recrystallization occurs by diffusion, the important parameters are both temperature and time.
The material becomes softer, weaker, but more ductile (Fig. 7.22).
Recrystallization temperature : is that at which the process is complete in one hour. It is typically 1/3 to 1/2 of the melting temperature. It falls as the %CW is increased. Below a "critical deformation", recrystallization does not occur.
.13 Grain Growth
The growth of grain size with temperature can occur in all polycrystalline materials. It occurs by migration of atoms at grain boundaries by diffusion, thus grain growth is faster at higher temperatures. The "driving force" is the reduction of energy, which is proportional to the total area. Big grains grow at the expense of the small ones.
Chapter 8. FAILURE
1. Introduction
Failure of materials may have huge costs. Causes included improper materials selection or processing, the improper design of components, and improper use.
2. 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 is fatigue failure:
I. crack initiation at high stress points (stress raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture
N final =^ N initiation +^ N^ propagation
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 : d e/ 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 Q (^) c are constants for a given material:
d e/ dt = K s n^ exp(- Q c/ 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-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. a single solid solution
b. two separated, essentially pure components.
c. two separated solid solutions.
d. 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
.a locate composition and temperature in diagram
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–Fe 3 C) 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—Fe 3 C 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
• Fe 3 C (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 (Fe 3 C).
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-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.
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 (Fe 3 C or iron carbide). When cooling proceeds below the eutectoid temperature (727 o^ C) 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 T (^) o before the transformation occurs, and keep it at that temperature over time. The horizontal line that indicates constant temperature T o 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 Diagrams - not covered
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.
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 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 Al 2 O 3 )
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. gives the coordination number and geometry as a function of rC /rA. For example, in the NaCl structure (Fig. 13.2), r (^) C = r (^) Na = 0.102 nm, rA =rCl .= 0.181 nm, so r (^) C/r (^) A.= 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 Si 4+^ as the cation and O^ 2-^ as the anion.^ rSi = 0. nm, rO .= 0.14 nm, so r (^) C/r (^) A = 0.286. From table 13.2 this implies coordination number = 4, that is tetrahedral coordination (Fig. 13.9). The tetrahedron is charged: Si4+^ + 4 O 2-^ Þ (Si O 4 ) 4-^. Silicates differ on how the tetrahedra are arranged. In silica, (SiO 2 ), 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 SiO 2 because the addition of Na 2 O (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 C 60 molecule, also known as fullerene or bucky-ball
(after the architect Buckminster Fuller who designed the geodesic structure that C 60 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.
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 (Fig. 13.1).
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 Diagrams (not covered)
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.
