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 of5) 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