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Biomaterials Week 4 10/6/2008 Properties of materials Chap 6 Diffusion Chap 7 Mechanical Properties 1 Chap 6 Diffusion 2 Why study diffusion Heat treatment to improve their properties. During heat treatment: always involve atomic diffusion Heat treating temperature and time, and/or cooling rate are predictable, using mathematics of diffusion and appropriate diffusion 3 Learning Objectives 1. Name and describe the two atomic mechanisms of diffusion. 2. Distinguish between steady-state and nonsteady-state diffusion. 3. (a) Write Fick‘s first and second laws in equation form, and define all parameters. (b) Note the kind of diffusion for which each of these equations is normally applied. 4 Learning Objectives 4. Write the solution to Fick‘s second law for diffusion into a semi-infinite solid when the concentration of diffusing species at the surface is held constant. Define all parameters in this equation. 5. Calculate the diffusion coefficient for some material at a specified temperature, given the appropriate diffusion constants. 6. Note one difference in diffusion mechanisms for metals and ionic solids. 5 Diffusion: introduction Diffusion: the phenomenon of material transport by atomic motion Include: – atomic mechanisms by which diffusion occurs – Mathematics of diffusion – Influence of temperature and diffusing species on the rate of diffusion 6 Diffusion couple- copper-nickel Figure 6.1 (a) A copper—nickel diffusion couple before a high— temperature heat treatment (b) Schematic representations of Cu (colored circles) and Ni (gray circles) atom locations within the diffusion couple. (c) Concentrations of copper and nickel as a function of position across the couple. 7 Diffusion couple- copper-nickel Figure 6.2 (a) A copper—nickel diffusion couple after a high-temperature heat treatment, showing the alloyed diffusion zone. (b) Schematic representations of Cu (colored circles) and Ni (gray circles) atom locations within the couple. (c) Concentrations of copper and nickel as a function of position across the couple. 8 Diffusion couple The heating couple is heated for an extended period at an elevated temperature and cooled to room temperature Results indicated that copper atoms have migrated or diffused into nickel, and nickel has diffused into copper Interdiffusion (impurity diffusion): one metal diffuse into another Self diffusion: pure metal, all atoms exchanging positions are of the same type 9 6.2 Diffusion mechanisms Atomic perspective view: diffusion is just the stepwise migration of atoms from lattice site to lattice site. For atom to make such a move: (1) there must be an empty adjacent site (2) the atom must have sufficient energy to break bonds with its neighbor atoms and then cause some lattice distortion during the displacement. 10 6.2 Diffusion mechanisms At specific temperature some small fraction of the total number of atoms in capable of diffusive motion, by virtue of the magnitude of their vibrational energies. The fraction increase with rising temperature 11 Two dominate for metallic diffusion: Vacancy diffusion Interstitial diffusion: 12 Vacancy diffusion The interchange of an atom from a normal lattice position to an adjacent vacant lattice site or vacancy Necessitate the presence of vacancies, and the extent to which vacancy diffusion can occur is a function of the number of the defects that are present 13 Vacancy diffusion (Fig 6.3 a) 14 Vacancy diffusion Since diffusing atoms and vacancies exchange positions, the diffusion of atoms in one direction corresponding to motion of vacancies in the opposite direction Both self-diffusion and interdiffusion occur by this mechanism 15 Interstitial diffusion Atoms that migrate from an interstitial position to a neighboring one that is empty. Hydrogen, carbon, nitrogen, and oxygen which have atoms that are small enough to fit into the interstitial positions. In most metal alloy, interstitial diffusion occurs much more rapidly than diffusion by vacancy mode. Interstitial atoms are smaller and thus more mobile. 16 Interstitial diffusion (Fig 6.3 b) 17 6.3 Steady-state diffusion: Diffusion flux (J): Mass (or, equivalently, the number of atoms) M diffusing through and perpendicular to a unit cross-sectional area of solid per unit of time J = M/At (6.1a) – A: area across which diffusion occurring – and t: elapsed diffusion time. 18 6.3 Steady-state diffusion J = (1/A) (dM/dt) (6.1b) – J: kg/m2 -s or atoms/m2 –s – Steady state diffusion: Diffusion flux does not change with time – Concentration of diffusion species on both surface of the plate are held constant 19 6.3 Steady state diffusion 20 6.3 Steady-state diffusion When concentration C is plotted vs. position (or distance) within the solid x, the resulting curve is termed the concentration profile: The slope at particular point on this curve is the concentration gradient 21 6.3 Steady-state diffusion Concentration gradient: dC /dx (6.2a) In the present treatment, the concentration profile is assumed to be linear, 22 6.3 Steady state diffusion Concentration gradient = △C/ △x = (CA – CB)/(xA -xB) (6.2b) It is sometimes convenient to express concentration in terms of mass of diffusing species per unit volume of solid (kg/m3) 23 6.3 Steady state diffusion For steady state diffusion in a single direction is relatively simple, the flux is proportional to the concentration gradient through the expression J = -D (dC)/ (dx) (6.3) – D: diffusion coefficient (m^2)/sec – Negative sign: the expression indicate the direction of diffusion is shown the concentration gradient, from high to a low concentration Fick‘s first law 24 6.3 Steady state diffusion Driving force used in the context of what compels a reaction to occur For diffusion reaction: several such forces are possible; but when diffusion is according to Eq. 6.3, the concentration gradient is the driving force J = -D (dC)/ (dx) (6.3) 25 Diffusion flux computation 26 6.4 Nonsteady-state diffusion Most practical diffusion situations are nonsteady-state ones The diffusion flux and the concentration gradient at some particular point in a solid vary with time, with a net accumulation or depletion of the diffusing species resulting. 27 6.4 Nonsteady-state diffusion Concentration profiles at three different diffusion times. Under conditions of nonsteady state: 28 6.4 Nonsteady-state diffusion The partial differential equation: (∂C/∂t) = ∂/ ∂x(D* ∂C/∂x) (6.4a) Fick‘s second law If diffusion coefficient is independent of composition (∂C/∂t) = (D* ∂2C/∂x2) (6.4b) 29 6.4 Nonsteady-state diffusion For semi-infinite solid in which surface concentration is held constant Frequently, the source of the diffusing species is a gas phase, the partial pressure of which is maintained at a constant value. The following assumptions are made: – Before diffusion, any of the diffusing solute atoms in the solid are uniformly distributed with concentration of C0 – the value of x at the surface is zero and increases with distance into solid – the time is taken to be zero the instant before the diffusion process begins 30 6.4 Nonsteady-state diffusion (∂C/∂t) = (D* ∂2C/∂x2) B.Cs: for t=0, C = C0 at 0 ≤ x ≤ ∞ For t > 0, C = Cs (the constant surface concentration) at x =0 C = C0 at x= ∞ Solution (Cx-C0)/(Cs-C0) = 1- erf (x/2√Dt) – Cx represent the concentration at depth x after time t – erf (x/2√Dt) is Gaussian error function – erf(x) = 2/√π∫0xe-y2dy 31 6.4 Nonsteady-state diffusion 32 6.4 Nonsteady-state diffusion The concentration parameters appear in Eq 6.5 are noted in Fig 6.6, a concentration profile taken at a specific time 33 6.4 Nonsteady-state diffusion Equ. 6.5 thus demonstrates the relationship among concentration, position, and time. – That Cx being a function of the dimensionless parameter x/√Dt, – maybe determined at any time and position if parameters C0, Cs and D are known 34 6.4 Nonsteady-state diffusion Suppose that it is desired to achieve some specific concentration of solute, C1 in an alloy; The left hand side of Equ 6.5 (Cx-C0)/(Cs-C0) = 1- erf (x/2√Dt) now becomes (C1 – C0 )/ ( Cs – C0 ) = constant 35 6.4 Nonsteady-state diffusion This being the case, the right hand side of this same expression is also a constant, And x/2√Dt = constant Or x2 / Dt = constant 36 6.4 Nonsteady-state diffusion 37 38 39 40 6.5 Factors influence diffusion: Diffusing species Temperature 41 Diffusing species The magnitude of the diffusion coefficient D is indicative of the rate at which atom diffuse Coefficient, both self and interdiffusion, for several metallic systems are listed in Table 6.2 The diffusion species and host material influence the diffusion coefficient This comparison also provides a contrast between rates of diffusion via vacancy and interstitial modes Self diffusion occurs by a vacancy mechanism, whereas carbon diffusion in iron is interstitial 42 Diffusion data 43 Temperature The diffusion rate increase 6 order of magnitude from 500 to 900C The temperature dependence of diffusion coefficients is related to temperature according to D = D 0 exp ( - Qd / RT) where D0 = a temperature-independent preexponential (m2/s) Qd = the activation energy for diffusion (J/mol, cal/mol. or eV/atom) R = the gas constant. 8.31 J/moI-K, 1.987 cal/mol-K, or 8.62 X 10-5 eV/atom-K T = absolute temperature (K) 44 Temperature The activation energy may be thought of as that energy required to produce the diffusive motion of one mole of atoms. A large activation energy results in a relatively small diffusion coefficient. Table 6.2 also contains a listing of D0 and Qd values for several diffusion systems. Taking natural logarithms of Equation 6.8 yields 45 Temperature Since D0,Qd and R are all constants. Equation 6.9b takes on the form of an equation of a straight line: y = b + mx where y and x are analogous, respectively, to the variables log D and l/T. Thus, if log D is plotted versus the reciprocal of the absolute temperature. a straight line should result, having slope and intercept of -Qd/2.3R and log D0, respectively. This is, in fact, the manner in which the values of Qd, and D0 are determined experimentally. From such a plot (or several alloy systems (Figure 6.7), it may be noted that linear relationships exist for all cases shown. 46 Diffusion coefficient vs. reciprocal temperature 47 Diffusion coefficient determination 48 Design example 49 50 Design example 51 Design example 52 6.6 Other diffusion paths Atomic migration may also occur along dislocations, grain boundaries, and external surfaces. These are sometimes called ‗short-circuit‖ diffusion path inasmuch as rates are much faster than for bulk diffusion. However, in most situations short— circuit contributions to the overall diffusion flux are insignificant because the cross-sectional areas of these paths are extremely small. 53 6.7 DIFFUSION IN IONIC AND POLYMERIC MATERIALS Ionic Materials For ionic compounds, the phenomenon of diffusion is more complicated than for metals inasmuch as it is necessary to consider the diffusive motion of two types of ions that have opposite charges. Diffusion in these materials usually occurs by a vacancy mechanism (Figure 6.3a). 54 6.7 DIFFUSION IN IONIC AND POLYMERIC MATERIALS And, as we noted in Section 5.3. in order to maintain charge neutrality in an ionic material, the following may be said about vacancies: (1) ion vacancies occur in pairs [as with Schottky defects (Figure 5.3)]. (2) they form in nonstoichiometric compounds (Figure 5.4), and (3) they-are created by substitutional impurity ions having different charge states from the host ions (Example Problem 5.2). 55 Ionic Materials In any event, associated with the diffusive motion of electrical charge. And in order to maintain localized charge neutrality in the vicinity of this moving ion, it is necessary that another species having an equal and opposite charge accompany the ion‘s diffusive motion. Possible charged species include another vacancy, an impurity atom, or an electronic carrier [i.e., a free electron or hole (Section 12.6)]. It follows that the rate of diffusion of these electrically charged couples is limited by the diffusion rate of the slowest moving species. 56 Ionic Materials When an external electric held is applied across au ionic solid, the electrically charged ions migrate (i.e.. diffuse) in response to forces that are brought to bear on them. And, as we discuss in Section 12.16. this ionic motion gives rise to an electric current. Furthermore, the electrical conductivity is a function of the diffusion coefficient (Equation 12.23). Consequently, much of the diffusion data for ionic solids come from electrical conductivity measurements. 57 Polymeric Materials For polymeric materials, we are more interested in the diffusive motion of small foreign molecules (e.g., 02, H20, CO2,. CH4) between the molecular chains than in tile diffusive motion of atoms within the chain structures. A polymer‘s permeability and absorption characteristics relate to the degree to which foreign substances diffuse into the material. Penetration of these foreign substances can lead to swelling and/or chemical reactions with the polymer molecules, and often to a depreciation of the material‘s mechanical and physical properties (Section 16.11). 58 Polymeric Materials Rates of diffusion are greater through amorphous regions than through crystalline regions: the structure of amorphous material is more ―open.‖ This diffusion mechanism may be considered to be analogous to interstitial diffusion in metals— that is, in polymers, diffusive movement from one open amorphous region to an adjacent open one. Foreign molecule size also affects the diffusion rate: smaller molecules diffuse faster than larger ones. Furthermore, diffusion is more rapid for foreign molecules that are chemically inert than for those that react with the polymer. 59 Polymeric Materials For some applications low diffusion rates through polymeric materials are desirable, as with food and beverage packaging and with automobile tires and inner tubes. Polymer membranes are often used as filters to selectively separate one chemical species from another (or others) (e.g.. the desalinization of water). In such instances it is normally the case that the diffusion rate of the substance to be filtered is significantly greater than that for the other substance (s). 60 Summary: Diffusion Diffusion mechanism: step-wise atom motion, self diffusion, interdifffusion, vacancy, interstitial Steady state diffusion Non-steady state diffusion Factors influence diffusion 61 Chap 7 Mechanical Properties 62 Why study mechanical properties It is incumbent on engineers to understand how the various mechanical properties are measured and what these properties represent; They may be called upon to design structures/components using predetermined materials such that unacceptable levels of deformation and/or failure will not occur. We demonstrate this procedure with respect to the design of a tensile-testing apparatus in Design Example 7.1. 63 Learning Objectives 1. Define engineering stress and engineering strain. 2. State Hooke‘s law, and note the conditions under which it is valid. 3. Define Poisson‘s ratio. 4. Given an engineering stress - strain diagram, determine (a) the modulus of elasticity, (b) the yield strength (0.002 strain offset), and (c) the tensile strength, and (d) estimate the percent elongation. 64 Learning Objectives 5. For the tensile deformation of a ductile cylindrical specimen, describe changes in specimen profile to the point of fracture. 6. Compute ductility in terms of both percent elongation and percent reduction of area for a material that is loaded in tension to fracture. 7. Compute the flexural strengths of ceramic rod specimens that have been bent to fracture in three-point loading. 8. Make schematic plots of the three characteristic stress—strain behaviors observed for polymeric materials. 65 Learning Objectives 9. Name the two most common hardness- testing techniques; note two differences between them. 10. (a) Name and briefly describe the two different microhardness testing techniques, and (b) cite situations for which these techniques are generally used. 11. Compute the working stress for a ductile material. 66 7.1 Mechanical properties- Introduction Subject to force or load Consideration: applied load, duration, environment Testing of materials: ASTM (American Society for Testing Materials) 67 7.2 Concepts of Stress and Strain Principal ways which load may be applied: 1. Tensile loading 2. Compression 3. Shearing 4. Torsion 68 Standard Tension Test Normally: circular, rectangular also used Narrow uniform center region Standard diameter: 12.8 mm, length: 4 times diameter, 60 mm Gauge length: 50mm 69 Engineering stress and strain Engineering stress: σ= F/A0 Engineering Strain: ε= (li-l0)/l0= ∆l/ l0 70 71 Geometric consideration of the stress state Normal stress: σ‘= σcos2θ = σ(1+cos 2 θ)/2 Shear stress: τ‘= σsin θ cosθ = σ(sin 2 θ/2) 72 73 74 Stress-strain behavior σ=Eε E: modulus of elasticity 75 Stress-strain behavior Nonlinear behavior: Tangent or secant modulus 76 Fig 7.6 Stress strain behavior Atomic scale: small changes in the interatomic spacing and stretching of interatomic bonds. Modulus of elasticity: measure of the resistance to separation of adjacent atoms/ions/molecules Modulus is proportional to the slope of the interatomic force-separation curve at equilibrium spacing: E proportional to (dF/dr)r0 77 Force vs. interatomic separation 78 79 Stress strain behavior As would be expected, the imposition of compressive, shear, or torsional stresses also evokes elastic behavior. The stress—strain characteristics at low stress levels are virtually the same for both tensile and compressive situations, to include the magnitude of the modulus of elasticity. Shear stress and strain are proportional to each other through the expression where G is the shear modulus, the slope of the linear elastic region of the shear stress—strain curve, Table 7.1 also gives the shear moduli for a number of the common metals. 80 7.4 Anelasticity Anelasticity: elastic deformation continue after load applied, and upon load release some finite time is required for complete recovery. Time dependent: loading rate dependent Viscoelastic behavior 81 Anelasticity Up to this point. it has been assumed that elastic deformation is time independent, that is, that an applied stress produces an instantaneous elastic strain that remains constant over the period of time the stress is maintained. It has also been assumed that upon release of the load the strain is totally recovered, that is. that the strain immediately returns to zero. In most engineering materials, however. there will also exist a time-dependent elastic strain component. That is, elastic deformation will continue after the stress application, and upon load release some finite time is required for complete recovery. 82 Anelasticity This time-dependent elastic behavior is known as anelasticity and it is due to time-dependent microscopic and atomistic processes that are attendant to the deformation. For metals the anelastic component is normally small and is often neglected. However, for some polymeric materials its magnitude is significant; in this case it is termed viscoelastic behavior, which is the discussion topic of Section 7.15. 83 Elastic behavior of materials Tensile stress in z direction Constriction in the lateral direction Poisson ratio: ν=-εx/ εz= =-εy/ εz Theoretically: isotropic material ν=0.25, max= 0.5 Many metal and alloy: 0.25 to 0.35 84 Poisson ratio For isotropic materials: E=2G(1+ν) In most metal: G is about 0.4E Elastically anisotropic: E varies with crystallographic direction, 85 Mechanical Behavior: Metals 86 Mechanical Behavior: Metals For most metallic materials, elastic deformation persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain (Hooke‘s law, Equation 7.5. ceases to he valid), and permanent, nonrecoverable. or plastic deformation occurs. Figure 7.10a plots schematically the tensile stress— strain behavior into the plastic region for a typical metal. The transition from elastic to plastic is a gradual one for most metals: some curvature results at the onset of plastic deformation. which increases more rapidly with rising stress. 87 88 Mechanical Behavior: Metals From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors as large numbers of atoms or molecules move relative to one another; upon removal of the stress they do not return to their original positions. This permanent deformation for metals is accomplished by means of a process called slip, which involves the motion of dislocations as discussed in Section 8.3. 89 Mechanical properties of Metal Yielding: proportional limit (Fig 7.10 a & b) Tensile strength: the stress at the maximum on the engineering stress-strain curve. (Fig 7.11) Ductility: percent elongation or percent reduction in area Ductility: Deform plastically before fracture Degree of allowable deformation during fabrication Brittle materials: fracture strain less than 5% 90 92 Temperature on mechanical properties Table 7-2: room temperature values of yield strength, tensile strength, and ductility Sensitive to prior deformation, presence of impurities, and/or heat treatment Modulus is not sensitive to them Yield and tensile strength decline with temp. Ductility increase with temp. 93 Table 7.2 Room-Temperature Mechanical Properties (in Tension) 94 Table 7.2 Room-Temperature Mechanical Properties (in Tension) 95 Table 7.2 Room-Temperature Mechanical Properties (in Tension) 96 Temperature effects on stress strain curves Engineering stress-strain behavior for iron at 3 temperatures: Tensile strength, Yield strength ↘; ductility ↗ with tempearture↗ 97 Resilience and toughness Resilience: capacity of a material to absorb energy when it is deformed elastically. Modulus of resilience: Ur = ∫0εσdε Linear elastic region: Ur = 1/2 σyεy Ur = 1/2 σyεy=1/2 σy(σy/E)= σy2/2E Resilience materials: high yield strengths and low moduli, such as spring 98 Resilience 99 Toughness: materials absorb energy up to fracture 100 True stress and strain Pass point M, material become weaker (Fig 7.11) In fact, increase in strength, however, reduction in cross sectional area Resulting reduction in the load-bearing capacity True stress: σT : load divided by the instantaneous cross-sectional area Ai 101 102 True stress and strain σT = F/Ai εT = ln(li/l0) If no volume change Aili = A0l0 True and engineering stress and strain σT = σ(1+ ε) εT = ln (1+ ε) Only valid before necking 103 True stress and strain Corrected stress within the neck is lower than the stress from applied load and real neck cross-sectional area Corrected stress: take into account the complex stress state without neck region 104 True stress and strain True Stress-strain curve from onset of plastic deformation to beginning of necking can be approximated by σT= K εTn Table 7-4 105 106 Mechanical behavior- Ceramics Flexural strength Stress strain behavior not ascertained by tensile test: Difficult to prepare specimens having requiring geometry Difficult to grip brittle materials without fracture them 0.1% strain, perfect align to avoid bending is difficult 107 Bending test 108 Bending (Flexure) test Transverse bending Rod specimens bent in 3-point or 4-point Top part under compression Bottom part under tension Tension strength is about 1/10 of compression strength The stresses at fracture using this flexure test: Flexural strength, modulus of rupture, fracture strength, or bend strength 109 Flexural strength Stress: Mc/I For rectangular cross section: σfs=3FfL/2bd2 Circular cross section σfs=3FfL/πR3 The tensile stresses of ceramics in Table 7.2 are flexural stress 110 Porosity on the mechanical properties of ceramics Ceramics fabrication: from powder During ensuring heat treatment, much of this porosity will be eliminated. In case of some residual porosity: deleterious influence on elastic properties and modulus The modulus is function of volume fraction porosity E= E0 (1-1.9P + 0.9 P2) 111 Influence of porosity on the modulus 112 Porosity on the mechanical properties of ceramics Porosity decrease the flexural strength: Reduce the cross sectional area Stress concentrators (about 2) Influence of porosity on strength is rather dramatic: 10 vol% porosity decrease 50% strength σfs= σoexp(-nP) 113 Porosity on the flexural strength 114 115 Bending test 116 Mechanical behavior: Polymer Mechanical characteristics are sensitive to: loading rate, temperature, environment Some modification of the testing techniques, specimen configurations are necessary. Especially for highly elastic materials, such as rubber 117 3 typical stress strain curves A: Brittle polymer B: Plastic polymers C: Totally elastic: rubber like elasticity, elastomers 118 Plastic polymer Yield point taken as a maximum on the curve, beyond the termination of the linear-elastic region Tensile strength: at fracture Tensile strength may be greater or less then yield strength 119 Polymer vs. metal E: 7M – 4G (polymer) 100s G (metal Tensile strength: 100Mpa (Polymer) 4100 MPa (Metal) 120 Temperature effect at polymer Polymers are more sensitive to temperature. Increase temperature produce: Decrease elastic modulus Reduce tensile strength Enhance ductility Decreasing rate of deformation has the same influence on the stress-strain behavior as increasing temperature, softer and ductile 121 PMMA (poly methyl methacrylate) 122 Viscoelastic deformation An amorphous polymer: like glass at low temperature; elastic, conformity to Hooke‘s law, σ= E ε Rubbery solid: intermediate temperature; combine elastic and viscous, viscoelaticity Viscous liquid: higher temperature; viscous or liquidlike behavior 123 Viscoelastic deformation 124 Viscoelastic deformation Relaxation Modulus Creep Modulus 125 Viscoelastic deformation B: elastic deformation: instantaneous, total deformation occurs the instant the stress is applied or release; upon release, the deformation is totally recovered D: viscous deformation: deformation or strain is not instantaneous; response to an applied stress, deformation delay or depends on time. Also the deformation is not reversible 126 Viscoelastic deformation C: Viscoelastic: instantaneous elastic strain once load, followed by a viscous time- dependent strain, a form of anelasticity Silicone polymer (silly putty): roll into a ball and drop onto a surface, it bounce elastically; it can also be pulled like a rubber 127 Viscoelastic relaxation modulus Stress relaxation: a specimen is initially strained rapidly in tension to a low stain level, the stress necessary to maintain the strain level is measured as function of time, which temperature is hold constant relaxation modulus Er(t) = σ(t) /ε0 The magnitude of the relaxation modulus is a function of temperature 128 Viscoelastic relaxation modulus The decrease of Et (r) with time Lower Et (r) level with increasing temperature 129 Viscoelastic Amorphous polystyrene: Glassy region: rigid and brittle, independent of temp. Leathery or glass transition: deformation time dependent and not total recoverable Rubbery; elastic and viscous present Rubbery flow and viscous flow 130 Relaxation 131 Relaxation modulus: crystalline, lightly cross-link, and amorphous Polystyrene materials having several molecular configurations (C): amorphous (B): lightly cross linked atactic polystyrene, the rubbery region form a plateau that extends to the temperature at which the polymer decomposes, no melting (A): totally crystalline isotactic PS: glass temp. less obvious (small volume of amorphous), relaxation modulus is relatively high. 132 Relaxation modulus: crystalline, lightly cross-link, and amorphous 133 Viscoelastic creep Viscoelastic creep: susceptible to time- dependent deformation when stress level is maintained constant Stress is applied instantaneously and is maintained at control level while strain is measured as function of time Creep compliance: Ec(t) = σ0/ε(t) 134 Creep 135 Hardness Measure of a material‘s resistance to localized plastic deformation (small dent or scratch) Natural minerals: Mohs scale Reasons for hardness test: Simple and inexpensive Relatively nondestructive Other mechanical properties may be estimated from hardness data, like tensile strength 136 Rockwell hardness test Most common, simple Several different scales from combination of various indenters and loads Indenters include all metal alloy and conical diamond (Brale) Hardness number is determined by difference in depth of penetration resulting from the application of initial minor load followed by a larger major load 137 Hardness test technique 138 Rockwell hardness scale 139 Superficial Rockwell hardness scale 140 Rockwell hardness scale When specifying Rockwell and superficial hardness: both hardness number and scale symbol must be indicated 80 HRB: Rockwell hardness of 80Kg on B scale 60 HR30W: superficial hardness of 60 on the 30W scale 141 Other hardness tests Brinell hardness test Knoop and Vickers micro hardness test 142 Hardness conversion- ASTM E140 143 Correlation between hardness and TS For Steel: TS(MPa) = 3.45 X HB HB: Brinell hardness TS(psi)=500 X HB 144 Design/safety factors σw = σy/N N: factor of safety, 1.2 to 4 145 146

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