3, MSE 791 Mechanical Properties of Nanostructured Materials

Module 3: Fundamental Physics and Materials Design Lecture 1 1. What is strain (work) hardening? What is the mechanism for strain hardening? 2. What are the factors that determine the strength of a metal? List some factors that can

enhance the strength. 3. What are the factors that determine the ductility of a metal? List two mechanical factors

that can enhance the ductility. 4. Nanostructured metals usually have low ductility. Explain why in terms of mechanical

behavior and deformation mechanisms. 5. The figure below shows that the nanostructured Ti becomes unstable (necking) at very low

strain under tensile test. Can you conclude that the nanostructured Ti is brittle? Justify your answer.

Fig. 3-1. Tensile stress-strain curves of nanostructured Ti. 6. How are atoms stacked in bcc, fcc and hcp structures? Explain with the help of sketches. 7. Draw bcc, fcc and hcp crystal structures. Draw all close-packed direction, and close-

packed planes in fcc and hcp structures. Sketch the {110} and {112} slip planes in bcc structure.

8. The figure below shows a screw dislocation. Assuming the sense (vector) of the dislocation line is pointing downward, draw a circuit to determine its Burgers vector. What if the sense of the dislocation line is reversed?

Fig. 3-2. Schematics of a screw dislocation.

9. The figure below shows an edge dislocation. Assuming the sense (vector) of the dislocation line is pointing into the paper, draw a circuit to determine its Burgers vector. What if the sense of the dislocation line is reversed?

Fig. 3-3. Schematics of an edge dislocation.

10. The figure below shows a dislocation (dotted line) and its Burgers vectors at three locations. Are these three Burgers vector the same? Mark the senses of the dislocation line at the three locations.

Fig. 3-4. Schematics of a dislocation in a cubic crystal.

11. The figure below shows three dislocations meeting at one point. What is the relationship among b1, b2, and b3.

Fig. 3-5. Schematics of a net work of three dislocations meeting at one dislocation node. 12. The figure below shows three dislocations meeting at one point. What is the relationship among b1, b2, and b3?

Fig. 3-6. Schematics of a net work of three dislocations meeting at one dislocation node.

13. The figure below shows atom packing on the (111) plane. A, B, and C marks the possible stacking positions for all close-packed layers. a) Draw a lattice dislocation and show how it can dissociate into two partial dislocations, b) b1, b2, and b3 represent the three Burgers vectors of partial dislocations on the (111) plane. The slip of a partial dislocation generates a stacking fault in its wake. Do b1, b2, and b3 produce the same type of stacking faults in terms of stacking sequence? c) Do b1, and -b3 produce the same type of stacking faults in terms of stacking sequence? Show your steps in reaching your conclusion.

Fig. 3-7. Schematics of close packed (111) plane in an fcc crystal, the possible stacking positions and three partial dislocations, b1, b2, and b3.

14. The figures below illustrate the relationship between an fcc unite cell and a Thompson tetrahedron. List the Burgers vectors of all lattice dislocations, partial dislocations and stair-rod dislocations in the Thompson tetrahedron.

Fig. 3-8. Thompson tetrahedron 15. Using the above Thompson tetrahedron, a lattice dislocation Burgers vector can be dissociated into pairs of partials. Write the dissociation equations.

Lecture 2:

1. See Figure 3-7, verify that the slip of b1, b2, and b3 on successive (111) planes will produce a deformation twin. Can the mixture of b1, b2, and b3 and -b1, -b2, and -b3

produce a twin? Demonstrate it using sequence of b2, -b1, b3, b3, -b2, b2 and -b3.

2. b3 on successive (111) planes will produce a deformation twin. Can the mixture of b1, b2, and b3 and -b1, -b2, and -b3 produce a twin? Demonstrate it using sequence of b2, -b1, b3, b3, -b2, b2 and -b3.

3. The two white lines in the figure represent two close packed planes. Calculate the angle between these two white lines using fcc crystal structure.

Fig. 2-3. The high-resolution image of a twin in a fcc crystal. 4. Prove that the glides of three partials, b1, b2, and b3, on three successive slip planes produce a twin without producing macroscopic strain. Lecture 3 1. Describe the dislocation emission process of a Frank-Read source. 2. Describe the pole twinning mechanism. Does this mechanism produce a macroscopic strain? 3. Why does nano-meter sized grains often contains no dislocations? 4. Why grain boundary sliding/grain rotation become more important at very small grain sizes, e.g. < 20 nm?

5. Why dislocation emission from grain boundaries may become dominate deformation mechanism in nanocrystalline metals? 6. List possible twinning mechanisms in nanocrystalline fcc metals. 7. Define non-equilibrium grain boundary. 8. Describe two dislocation reaction processes on dislocation multiplication on the grain boundaries. Lecture 4 1. Calculate the shear strain produced by a deformation twin that is produced by the glide of partial dislocations with the same Burgers vector in an fcc metal. 2. Calculate the shear strain produced by a deformation twin that is produced by alternative gliding of partial dislocations with two different Burgers vectors in an fcc metal. 3. Explain how random activation of partials can produce a twin without producing macroscopic strain. 4. Explain how cooperative slip of three partial mechanism produce a twin without macroscopic strain. 5. What role does twins without macroscopic strain play in the deformation of nanomaterials 6. Why is it easier for nanocrystalline grains to produce twins with no macrostrain? Lecture 5 1. Describe the grain size effect on deformation twinning for fcc metals (draw a graph). 2. Explain how and why the detwinning during deformation is affected by grain size. What is the implication of this to the stability of microstructures.

3. Define the stable and unstable stacking fault energies on a generalized stacking fault energy curve. 4. Explain why the coarse-grained metals are harder to deform by twinning with decreasing grain size? Lecture 6 1. What is difference in the strain sensitivity behaviors of nanocrystalline bcc and fcc metals as a function of grain size? 2. Compare the cores of screw dislocations in fcc and bcc metals. 3. Compare the cores of screw and edge dislocations in bcc metals. 4. In a bcc metal, why is the deformation behavior controlled by screw dislocations? 5. How does a screw dislocation move in a bcc metal? How about an edge dislocation? 6. Why does a screw dislocation in a bcc metal needs high thermal activation to move? 7. Compare a coarse-grained bcc metal with a coarse-grained fcc metal, which one has higher strain rate sensitivity? Why? 8. How grain size affect the strain rate sensitivity of a nanocrystalline fcc metal? Why? 9. How grain size affect the strain rate sensitivity of a bcc metal? Why? Lecture 7 1. Why do nanocrystalline materials usually have low ductility?

2. Why do nanocrystalline materials usually have low strain hardening rate? 3. Derive the Considère's Criterion. 4. List 3 possible approaches to simultaneously increase the strength and ductility of nano fcc metals. 5. How grain size affect twinning in hcp metals?