1.(a)Draw a typical stress strain curve for a precipitation-hardening system containing small,coherent,G-P zone.What is the model of dislocation motion in such a crystal and what is the rate controlling mechanism in the model? (b)What is the Orowan Friedel relation for flow stress in a dispersion-hardening system and how does it relate to microstructural parameters?Assume intermediate strength obstacles. 2.a)Discuss the complications in determining the true stress-true strain diagram in tension. b)Give a basic definition of toughness.What is involved in the engineering concept of toughness? c)Using the von Mises yielding condition,at what value of o will you expect yielding for the state of stresso2=20.(o =0)? d)In an elastic triaxial stress state (o1,02,03)give the expression for o2 in plane strain(δ，=O) 3.a)Discuss the implications of macroscopic compatibility constraints on the deformation of a grain in a poly-crystal.Discuss both elastic and plastic effects. b)What is the Friedel-Orowan equation To what classes of engineering alloys or microstructures is it applicable? 4.Explain how high-temperature creep is controlled by self diffusion, i)in the Nabarro-Herring Creep region ii)in the Andrade"power"creep region where ko4s, iii)how do the following factors affect Andrade "power"creep? iv)grain size v)stacking fault energy vi)temperature 5.(a)Explain how recrystallization textures can be formed in a severely cold worked alloy. (b)Explain how each of the following can influence the development of a crystallization texture. (i)A fine ppt.(e.g.,AIN in steel)which goes into solution slowly on heating. (ii)The inadvertent formation of y grains in a Fe-3Si which has been annealed at 1150 C.(It is inadvertent because the steel would have remained all a if it had been adequately decarburied before
1. (a) Draw a typical stress strain curve for a precipitation-hardening system containing small, coherent, G-P zone. What is the model of dislocation motion in such a crystal and what is the rate controlling mechanism in the model? (b) What is the Orowan Friedel relation for flow stress in a dispersion-hardening system and how does it relate to microstructural parameters? Assume intermediate strength obstacles. 2. a) Discuss the complications in determining the true stress-true strain diagram in tension. b) Give a basic definition of toughness. What is involved in the engineering concept of toughness? c) Using the von Mises yielding condition, at what value of σ 1 will you expect yielding for the state of stress 2 2 .( 0) σ = σ σ y = ? d) In an elastic triaxial stress state 123 (, , ) σ σ σ give the expression for σ 2 in plane strain ( 2 δ = 0 ) 3. a) Discuss the implications of macroscopic compatibility constraints on the deformation of a grain in a poly-crystal. Discuss both elastic and plastic effects. b) What is the Friedel-Orowan equation ? To what classes of engineering alloys or microstructures is it applicable? 4. Explain how high-temperature creep is controlled by self diffusion, ⅰ) in the Nabarro-Herring Creep region ⅱ) in the Andrade “power” creep region where , 4.5 kσ ⅲ) how do the following factors affect Andrade “power” creep? ⅳ） grain size ⅴ) stacking fault energy ⅵ) temperature 5. (a) Explain how recrystallization textures can be formed in a severely cold worked alloy. (b) Explain how each of the following can influence the development of a crystallization texture. (ⅰ) A fine ppt.(e.g., AlN in steel) which goes into solution slowly on heating. ( ) The inadvertent formation of ⅱ γ grains in α Fe-3Si which has been annealed at 1150 C. (It is inadvertent because the steel would have remained all α if it had been adequately decarburied before
annealing.) 6.Discuss the role of stacking fault energy in the microstructural and mechanical-property changes which result from the cold working of an annealed alloy and from the recovery of a cold-working alloy. 7.The catalyst in an automotive exhaust system consists of many very fine particles (10nm diam.)of metal (Pt)on a ceramic (alumina)substrate.The fineness is necessary to provide the maximum surface area per unit volume of precious metal. A dominant mechanism of deterioration for such a catalyst is the coarsening of these particles.This process parallels Ostwald ripening in solids. Discuss,with approximate equations,how the rate of coarsening would depend on:surface tension,surface diffusion coefficient,concentration of absorbed metal atoms,and temperature. 8.A metal-forming operation involves the compression of a cylinder of a fec metal to give a 50%reduction in height.(At room temperature the flow stress of the fcc metals shows little strain rate sensitivity.)This operation is done at room temperature where dynamic recovery occurs.At both temperatures the compression is done at several different strain rates with the max.and min.rates differing by an order of magnitude. (a)On a plot of load vs.strain rate show how the max.load required for the compression varies with strain rate.Show the plot for room temperature and elevated temperature on the same graph. (b)How would you expect the microstructure to differ for samples done at the two temperatures?The examination is made with a TEM using samples deformed at the slowest strain rate. (c)What would you see in the microstructure that would indicate the sample had undergone dynamic recrystallization instead of dynamic recovery? 9 (a)Define,using words and any figures you find appropriate,the following qualifying words as applied to continuum material behavior.For example,a material model may be called"rigid plastic."For each word of this type,show the meaning clearly. rigid visco-elastic visco-plastic anelastic elastic plastic ideal plastic (b)Discuss which kinds of laws listed in part (a)would be most appropriate for each of the following continuum analysis problems and why.Include in your material description only the most important effect:that is,the ones that are essential to a reasonably accurate solution. 1)Forming of an automobile fender from plain-carbon steel at room temperature. 2)Hot rolling of aluminum slabs. 3)Analysis of buckling initiation in vertical support columns. 4)Interaction energies between separated dislocations in a single crystal
annealing.) 6. Discuss the role of stacking fault energy in the microstructural and mechanical-property changes which result from the cold working of an annealed alloy and from the recovery of a cold-working alloy. 7. The catalyst in an automotive exhaust system consists of many very fine particles (10nm diam.) of metal (Pt) on a ceramic (alumina) substrate. The fineness is necessary to provide the maximum surface area per unit volume of precious metal. A dominant mechanism of deterioration for such a catalyst is the coarsening of these particles. This process parallels Ostwald ripening in solids. Discuss, with approximate equations, how the rate of coarsening would depend on: surface tension, surface diffusion coefficient , concentration of absorbed metal atoms, and temperature. 8. A metal-forming operation involves the compression of a cylinder of a fcc metal to give a 50% reduction in height. (At room temperature the flow stress of the fcc metals shows little strain rate sensitivity.) This operation is done at room temperature where dynamic recovery occurs. At both temperatures the compression is done at several different strain rates with the max. and min. rates differing by an order of magnitude. (a) On a plot of load vs. strain rate show how the max. load required for the compression varies with strain rate. Show the plot for room temperature and elevated temperature on the same graph. (b) How would you expect the microstructure to differ for samples done at the two temperatures? The examination is made with a TEM using samples deformed at the slowest strain rate. (c) What would you see in the microstructure that would indicate the sample had undergone dynamic recrystallization instead of dynamic recovery? 9 (a) Define, using words and any figures you find appropriate, the following qualifying words as applied to continuum material behavior. For example, a material model may be called “rigid plastic.” For each word of this type, show the meaning clearly. rigid visco-elastic visco-plastic anelastic elastic plastic ideal plastic (b) Discuss which kinds of laws listed in part (a) would be most appropriate for each of the following continuum analysis problems and why. Include in your material description only the most important effect: that is, the ones that are essential to a reasonably accurate solution. 1) Forming of an automobile fender from plain-carbon steel at room temperature. 2) Hot rolling of aluminum slabs. 3) Analysis of buckling initiation in vertical support columns. 4) Interaction energies between separated dislocations in a single crystal
5)Evaluation of the work done in the dynamic advance of a real crack in a pure metal polycrystal. (c)Discuss the following yield function in terms of isotropy,pressure-dependence, and Baushinger effect. f=AlG,-G2+Bla:-03+Clo:-0; 10.Many creep theories are based on the concept of pure vacancy diffusion.Yet the models can fit power law dependences of laws dependences of creep rate on stress with exponent n varying from 1 to 5.Describe how this can come about and provide a detailed derivation for n=5.Does this type of model apply for polycrystals Solid-solutions?Complex engineering alloys?Why or why not? 11.(a)Starting from first principles and definitions,prove that the stress tensor has only six independent components.Illustrate your arguments carefully. (b)Starting from first principles,derive the mechanical equilibrium equations for an infinitesimal element of material.Assume no body forces. 12.Describe how each of the following kinds of experiments can be used to understand creep mechanisms.Specifically,also state how these tests may be used to differentiate between Class I (solid solution)and Class II (pure metal)creep.Be specific in regard to the kinds of information you expect to get from each kind or series of test(s). (a)A series of creep tests done at fixed temperature,but various stresses. (b)A series of creep tests done at fixed stress but various temperatures.(Some people believe these kinds of tests should be done at fixed a/E.What difference does it make?) (c)Creep tests with discontinuous stress changes. (d)High temperature tests with discontinuous changes in strain rate imposed. (e)Creep tests followed up with characterization with transmission electron microscopy. 13.Porosity or voids are a common,if not the most prevalent,casting defect in cast alloys.Describe the various forms of porosity which occur in alloy castings and identify the mechanism(s)and phenomena which are responsible for each type of porosity.Where possible,give criteria which indicate the solidification conditions for which each type porosity should not occur.Discuss how the various forms of porosity are controlled as part of the foundry practices. 14.(a)Discuss the models which have been proposed for the nucleation of new grains during static recrystallization.Use diagrams to supplement your discussion. (b)Discuss the microstructures which develop hot working to large strains. 15.The lattice parameters of platinum(fcc)and Pt3Al(cubic,ordered)have been reported as 0.39239nm.and 0.3876nm.,respectively.Terminal solid solutions of
5) Evaluation of the work done in the dynamic advance of a real crack in a pure metal polycrystal.. (c) Discuss the following yield function in terms of isotropy, pressure-dependence, and Baushinger effect. 12 13 23 M N P fA B C = − + −+ − σ σ σσ σσ 10. Many creep theories are based on the concept of pure vacancy diffusion. Yet the models can fit power law dependences of laws dependences of creep rate on stress with exponent n varying from 1 to 5. Describe how this can come about and provide a detailed derivation for n=5. Does this type of model apply for polycrystals ? Solid-solutions? Complex engineering alloys? Why or why not? 11. (a) Starting from first principles and definitions, prove that the stress tensor has only six independent components. Illustrate your arguments carefully. (b) Starting from first principles, derive the mechanical equilibrium equations for an infinitesimal element of material. Assume no body forces. 12. Describe how each of the following kinds of experiments can be used to understand creep mechanisms. Specifically, also state how these tests may be used to differentiate between Class I (solid solution) and Class II (pure metal) creep. Be specific in regard to the kinds of information you expect to get from each kind or series of test(s). (a) A series of creep tests done at fixed temperature, but various stresses. (b) A series of creep tests done at fixed stress but various temperatures. (Some people believe these kinds of tests should be done at fixed a/E. What difference does it make?) (c) Creep tests with discontinuous stress changes. (d) High temperature tests with discontinuous changes in strain rate imposed. (e) Creep tests followed up with characterization with transmission electron microscopy. 13. Porosity or voids are a common, if not the most prevalent, casting defect in cast alloys. Describe the various forms of porosity which occur in alloy castings and identify the mechanism(s) and phenomena which are responsible for each type of porosity. Where possible, give criteria which indicate the solidification conditions for which each type porosity should not occur. Discuss how the various forms of porosity are controlled as part of the foundry practices. 14. (a) Discuss the models which have been proposed for the nucleation of new grains during static recrystallization. Use diagrams to supplement your discussion. (b) Discuss the microstructures which develop hot working to large strains. 15. The lattice parameters of platinum (fcc) and Pt3Al (cubic, ordered) have been reported as 0.39239nm. and 0.3876nm., respectively. Terminal solid solutions of
Pt(Al)can be rendered supersaturated and aged to cause continuous precipitation of the stable phase Pt3Al.In binary Al(Cu)alloys continuous precipitation of the stable phase CuAl2 can occur.In this case typical lattice parameters are 0.404nm. for die aluminum solid solution and 0.607nm,0.607nm,0.487nm for me complex tetragonal unit cell (12 atoms)of CuAl2. Using the concepts of classical nucleation theory discuss,in detail,the transformations you would predict to occur when terminal solutions of these alloys are slowly cooled to room temperature. 16.Misruns,cold shuts,and incomplete fills are casting defects frequently attributed to inadequate fluidity. (a)Define fluidity relevant to cold mold casting processes such as the sand or permanent mold casting methods.Identify the casting variables which control fluidity and indicate the expected interrelation between the casting variables and fluidity (b)Define fluidity relevant to hot mold casting processes such as the investment casting processes.Identify the casting variables which control fluidity and indicate the expected interrelations between the casting variables and fluidity. Where possible,provide quantitative relations between fluidity and the casting variables in responding to both parts(a)and(b). 17.Consider two ferrous alloys which are deformed at 800C(0.60 Tm).One is an annealed,coarse grained,fully ferritic (bcc)iron with a fairly uniform grain size which has an average grain diameter of 70 4m.The other is a microduplex alloy which has an average grain diameter of2m and consists of 30 volume percent austenite and 70 volume percent ferrite. (a)Both of these materials are crept at constant stress such that the steady-state strain rate is approximately 10-5 s-1.Sketch the resulting time-elongation plots.Use the same set of axes for both curves. (b)Sketch the stress versus steady-state strain rate relationship for each material.Use the same set of axes for both curves.Be precise and describe the physical origins of the behavior you show. (c)Imagine now that you will make a 5-layer laminated composite (alternating sheets)of these two steels,with greater than 80 volume-percent of the duplex alloy.Draw the tensile stress versus steady-state strain rate relationship that you would expect for this composite material loaded in a tensile direction which is parallel to the interfaces.What assumptions must you make in making this graph? (d)Using the plot above,sketch the relationship that you expect to see between tensile elongation and creep stress for the laminated composite:(i)if 80% duplex alloy,(ii)if 60%duplex alloy.State what assumptions you must make (assume constant stress creep)
Pt(Al) can be rendered supersaturated and aged to cause continuous precipitation of the stable phase Pt3Al. In binary Al(Cu) alloys continuous precipitation of the stable phase CuAl2 can occur. In this case typical lattice parameters are 0.404nm. for die aluminum solid solution and 0.607nm, 0.607nm, 0.487nm for me complex tetragonal unit cell (12 atoms) of CuAl2. Using the concepts of classical nucleation theory discuss, in detail, the transformations you would predict to occur when terminal solutions of these alloys are slowly cooled to room temperature. 16. Misruns, cold shuts, and incomplete fills are casting defects frequently attributed to inadequate fluidity. (a) Define fluidity relevant to cold mold casting processes such as the sand or permanent mold casting methods. Identify the casting variables which control fluidity and indicate the expected interrelation between the casting variables and fluidity. (b) Define fluidity relevant to hot mold casting processes such as the investment casting processes. Identify the casting variables which control fluidity and indicate the expected interrelations between the casting variables and fluidity. Where possible, provide quantitative relations between fluidity and the casting variables in responding to both parts (a) and (b). 17. Consider two ferrous alloys which are deformed at 800°C (0.60 Tm). One is an annealed, coarse grained, fully ferritic (bcc) iron with a fairly uniform grain size μ which has an average grain diameter of 70 m. The other is a microduplex alloy μ which has an average grain diameter of 2 m and consists of 30 volume percent austenite and 70 volume percent ferrite. (a) Both of these materials are crept at constant stress such that the steady-state strain rate is approximately 10-5 s-1. Sketch the resulting time-elongation plots. Use the same set of axes for both curves. (b) Sketch the stress versus steady-state strain rate relationship for each material. Use the same set of axes for both curves. Be precise and describe the physical origins of the behavior you show. (c) Imagine now that you will make a 5-layer laminated composite (alternating sheets) of these two steels, with greater than 80 volume-percent of the duplex alloy. Draw the tensile stress versus steady-state strain rate relationship that you would expect for this composite material loaded in a tensile direction which is parallel to the interfaces. What assumptions must you make in making this graph? (d) Using the plot above, sketch the relationship that you expect to see between tensile elongation and creep stress for the laminated composite: (i) if 80% duplex alloy, (ii) if 60% duplex alloy. State what assumptions you must make (assume constant stress creep)
18.What are the physical mechanisms for "nucleation"in recrystallization?How does the nucleation rate enter the expression for the rate of recrystallization?Give a detailed expression for the rate of grain growth during recrystallization. 19.Aluminum alloys are noted for their tendencies to show precipitation sequences involving zones and other metastable transition precipitates.Select such an alloy (e.g.Al-Cu,Al-Ag,Al-Mg-Si,Al-Cu-Mg,etc.),describe the characteristics of the precipitation processes and discuss them in terms of the concepts of nucleation theory. 20.The microstructures resulting from solidification of alloys depend primarily on the alloy composition and the three solidification variables: (a)thermal gradient in the liquid at the liquid-solid interface,GL (b)isothermal advance rate or solidification velocity,R,and (c)local quench rate,T. The occurrence of many casting defects,such as shrinkage porosity and macrosegregation patterns,including freckles,also depend on the same variables given above. Draw two GL versus R plots,one for a binary alloy which solidifies as a single phase solid solution,the other for a binary alloy which solidifies as a eutectic.On each GL-R graph,indicate the various regions of expected morphologies and state any quantitative relations for the boundaries or transitions between the various regions.Also indicate those GL-R-T conditions for which various casting defects are anticipated. 21.Dynamic recovery and dynamic recrystallization are associated with the hot working,e.g.rolling,of metals and alloys. (a)What is the most common method used to investigate these processes? (b)What kind of problem or difficulty might be associated with this experimental method? (c)Discuss the results of experiments of this kind with an emphasis on the microstructures which are produced during hot working. 22.Suppose you were asked to design an experiment to quantitatively examine the predictions of classical nucleation theory for homogeneous nucleation during the initial stages of the decomposition of a solid solution.First describe what you would like your experiment to achieve and then discuss what problems you would expect to encounter. 23.(a)Discuss the relationship between the apparent density of a powder and the particle size of the powder. (b)Describe the morphological characteristics of powder particles prepared by the electrolyte,carbonyl,oxide reduction and atomization processes. (c)Discuss the relative rates of sintering of a coarse powder and a fine powder and
18. What are the physical mechanisms for "nucleation" in recrystallization? How does the nucleation rate enter the expression for the rate of recrystallization? Give a detailed expression for the rate of grain growth during recrystallization. 19. Aluminum alloys are noted for their tendencies to show precipitation sequences involving zones and other metastable transition precipitates. Select such an alloy (e.g. Al-Cu, Al-Ag, Al-Mg-Si, Al-Cu-Mg, etc.), describe the characteristics of the precipitation processes and discuss them in terms of the concepts of nucleation theory. 20. The microstructures resulting from solidification of alloys depend primarily on the alloy composition and the three solidification variables: (a) thermal gradient in the liquid at the liquid-solid interface, GL (b) isothermal advance rate or solidification velocity, R , and (c) local quench rate, T . The occurrence of many casting defects, such as shrinkage porosity and macrosegregation patterns, including freckles, also depend on the same variables given above. Draw two GL versus R plots, one for a binary alloy which solidifies as a single phase solid solution, the other for a binary alloy which solidifies as a eutectic. On each GL -R graph, indicate the various regions of expected morphologies and state any quantitative relations for the boundaries or transitions between the various regions. Also indicate those GL-R-T conditions for which various casting defects are anticipated. 21. Dynamic recovery and dynamic recrystallization are associated with the hot working, e.g. rolling, of metals and alloys. (a) What is the most common method used to investigate these processes? (b) What kind of problem or difficulty might be associated with this experimental method? (c) Discuss the results of experiments of this kind with an emphasis on the microstructures which are produced during hot working. 22. Suppose you were asked to design an experiment to quantitatively examine the predictions of classical nucleation theory for homogeneous nucleation during the initial stages of the decomposition of a solid solution. First describe what you would like your experiment to achieve and then discuss what problems you would expect to encounter. 23. (a) Discuss the relationship between the apparent density of a powder and the particle size of the powder. (b) Describe the morphological characteristics of powder particles prepared by the electrolyte, carbonyl, oxide reduction and atomization processes. (c) Discuss the relative rates of sintering of a coarse powder and a fine powder and