Physics of Deformation

Abstract

An adequate knowledge of crystallography and crystal defects (particularly, dislocations) is of paramount importance in explaining the deformation of solids. This chapter, therefore, first presents an overview of crystal structures and defects with particular reference to dislocations. Then the role of crystallographic/slip system (crystallographic/slip planes and directions) and dislocation movements in plastic deformation, are discussed. The main topics include: crystal systems, crystal structures, planes/directions, Miller Indices, dislocation movements, deformation mechanisms – slip and twinning; plastic deformation – rolling, deformation of single crystals, and Schmid’s law. This chapter contains 13 worked examples, 15 diagrams, and 15 formulae.

Questions and Problems

• 2.1. Diagrammatically illustrate the seven crystal systems.

• 2.2. Explain the applications of crystallographic directions and planes in plastic deformation.

• 2.3. Why is the (actual) strength of a real crystalline material much lower than the theoretically predicted strength of otherwise perfect crystal?

• 2.4. (a) Draw sketches for edge dislocation and screw dislocation indicating Burger’s vector for each type of dislocation. (b) Explain the role of dislocation movement in deformation.

• 2.5. Explain deformation by slip with the aid of diagrams.

• 2.6. (a) Define the following terms: (i) slip plane, (ii) slip direction, (iii) slip system.

  (b) Draw a sketch showing slip plane and slip directions in a BCC unit cell.

• 2.7. FCC and BCC metals be easily deformed by slip, but HCP metals not. Explain.

• 2.8. Differentiate between the following terms: (a) slip and twinning, (b) resolved shear stress and the critical resolved shear stress, (c) amorphous and crystalline solids.

• 2.9. The atomic radius of silver (FCC) is 0.1445 nm. Compute the lattice parameter for silver

• 2.10. Sketch the crystallographic planes with the Miller Indices: (100) and (0$\overline{1}$0).

• 2.11. A tensile stress of 1.8 MPa acts on a single crystals causing deformation by slip. The angle between the tensile axis and normal to the slip plane is 56°.The angle between the tensile axis and slip direction is 48°. Calculate the resolved shear stress on the slip plane.

• 2.12. Calculate the critical resolved shear stress for a single crystal of copper at a dislocation density of 1000 mm⁻². Hint: use the data in Example 2.12.

• 2.13. In a stressed single crystal of zinc, the angle between the tensile axis and normal to the slip plane is 65°. Three possible slip directions make angles of 70°, 50°, and 30° with the tensile axis. Calculate the yield strength of zinc, if its critical resolved shear stress is 0.91 MPa.

• 2.14. Sketch the crystallographic direction with Miller Indices [01$\overline{3}$] and [112].

• 2.15. A metal plate with thickness 47 mm was rolled to 30 mm thickness and then again rolled down to 12 mm thickness. Calculate the (a) true strain (b) draft, and (c) % reduction.