Chapter 7: Plastic Deformation

1. Chapter 7: Plastic Deformation • Permanent • Bonds are broken  net movement of large numbers of molecules  change in shape SLIP - plastic deformation by dislocation motion • Depends on incrementally breaking bonds.

2. Goldie the caterpillar - moves using “dislocation” mechanism

3. DEFINITIONS • Dislocation density • Total dislocation length per unit volume [mm disl/mm3], • Number of dislocations that intersect per unit area [disl/mm2] OR • Sources -- solidification, plastic deformation, thermal stresses

4. B. Strain energy -- fraction of deformation energy retained during plastic deformation (about 95% dissipated as heat). • Strain energy is stored in lattice strains. • Strain fields interact (repel, or attract and cancel) with each other.

5. C. Slip Systems • Dislocations do not move with the same degree of ease on all crystallographic directions • Slip System defined by: • Slip plane – preferred plane of dislocation motion (most dense atom packing, i.e., highest planar density) • Slip direction – direction of movement (highest linear density) to minimize distortions • Depends on crystal structure Example: FCC crystal structure • 111 family  slip plane • 4 planes • family  slip direction • 3 directions per slip plane • 12 slip systems: • 4 planes and 3 directions

6. More slip systems  more choices for dislocation motion  more ductile

7. Slip in Singe Crystal • Resolved Shear Stress: angle between F and normal to slip plane Where: angle between F and slip direction

8. Note: There are many slip systems (different values of and ).The most favorable one is where is maximum. Slip occurs when

9. Example: • Consider a single crystal of BCC iron oriented such that a tensile stress is applied along [010] direction. • Compute the resolved shear stress along a (110) plane and in a [111] direction when a tensile stress of 7500 psi is applied. • If slip occurs on a (110) plane and in a [111] direction and the critical resolved shear stress is 4350 psi, calculate the yield strength. a) 3060 psi, b) 10,600 psi

10. Polycrystals • More than one grain. Slip planes & directions (l, f) change from one grain to another. • tRwill vary from one crystal to another. The crystal with the largest tR yields first. • Stronger than single crystal. Grain boundaries serve as constraint. 300 mm

11. Strengthening Mechanisms Strength is related to ease of plastic deformation motion To increase strength, restrict dislocation motion. A. Grain Size Reduction • Grain boundaries are barriers to slip. • Smaller grain size  larger total grain boundary area stronger. • Rate of solidification, plastic deformation, and heat treatment • Hall-Petch Equation:

12. EXAMPLE: Grain size strengthening • 70wt%Cu-30wt%Zn brass alloy • Data:

13. B. Solid Solution Hardening • • Introduce impurity atoms to increase hardness and tensile strength. • Impurity atoms interact with dislocations to restrict motion.

14. Example: Solid Solution Hardening • Tensile strength & yield strength increase w/ wt% Ni. • Empirical relation: • Alloying increases sy and TS.

15. C. Strain hardening (or work hardening or cold working) • Room temperature deformation. • Common forming operations change the cross sectional area: -Forging -Rolling -Drawing -Extrusion

16. Coldwork Effects: • A ductile metal becomes harder and stronger when plastically deformed • Plastic deformation increases dislocation density  more difficult to move dislocations. • Yield strength (sy ) increases. • Tensile strength (TS) increases. • Ductility (%EL or %AR) decreases. Strain-hardening exponent, n - ability to strain harden sT = K eTn

17. Example: Cold work • What is the tensile strength & ductility after cold working?

18. Reversing Effects of Cold Work • 1 hour treatment at Tanneal decreases TS and increases %EL. • Effects of cold work are reversed! • 3 Annealing stages

19. 1. Recovery • At elevated temperatures, some stored strain energy is recovered by enhanced atomic diffusion  reduce the number of dislocations. • Driving force: reduction in strain energy 2. Recrystallization • Formation of a new set of grains that are strain free with low dislocation densities. • Driving force: Differrence in internal energy between strained and unstrained material • Recrystallization Temperature – Temperature at which recrystallization is completed in 1 hr. • Higher %CW, higher driving force, lower recrystallization temperature

20. • New crystals are formed: --have a small dislocation density --small (fine grains) --consume cold-worked crystals by diffusion. 33% cold worked brass New crystals nucleate after 3 sec. at 580C. After 4 seconds After 8 seconds

21. 3.Grain Growth • • At longer times, larger grains consume smaller ones. • • Migration of grain boundaries by short-range diffusion of atoms from one side of boundary to the other • Driving force: reduction in grain boundary area, and hence grain boundary surface energy After 8 s, 580C After 15 min, 580C coefficient dependent on material and T. • Empirical Relation: exponent typ. ~ 2 elapsed time grain diam. at time t.