Plastic Deformation in Single or Polycrystalline Materials

1. Plastic Deformation in Single or Polycrystalline Materials Dr. Richard Chung Department of Chemical and Materials Engineering San Jose State University

2. Learning Objectives • Explain the deformation mechanisms of plastic flow in single and polycrystalline materials • List factors affecting the plastic deformation process in single and polycrystalline materials • Calculate and interpret the effects of critical resolved shear stress in single and poly crystals • Identify geometrically necessary dislocations developed along grain boundaries (in polycrystalline) • Examine slip systems of a material and determine most favorable slip system • Compare the stress-strain relationships between single and polycrystalline material

3. Plastic deformation in Single Crystals • Critical resolved shear stress is the driving force. • This stress depends on temperature, strain rate, and impurity in material. • Plastic straining (such as work hardening) enables multiple slip  increases strain rate • Slip Dislocation interactions may immobilize dislocations in a single crystal  reduces strain rate

4. Critical Resolved Shear Stress m is determined by the slip plane w.r.t. the tensile axis

5. Schmid’s Law This formula is used to determine the relationship between tensile yield strength and critical resolved shear stress. (y > CRSS ) Except for BCC transition metals, for most of the material, CRSS is independent of y and m

6. CRITICAL RESOLVED SHEAR STRESS • Condition for dislocation motion: • Crystal orientation can make it easy or hard to move disl. CRSS is the minimum shear stress required to initiate slip. 5

7. CALCULATE RESOLVED SHEAR STRESS Example: Compute the resolved shear stress along a (110) plane and in a [ī11] direction when a tensile stress of 52 MPa is applied in the [010] direction of a BCC single crystal iron. Answer: First, we need to calculate the angle  (between [110] and [010] ) and the angle  ([ī11] and [010]) Normal to the (110) plane

8. The resolved shear stress is 21.3 MPa. Also, if a critical resolved shear stress is given, then the yield stress could be calculated accordingly.

9. DISLATION MOTION IN POLYCRYSTALS • Slip planes & directions (l, f) change from one crystal to another. • tRwill vary from one crystal to another. • The crystal with the largest tR yields first. • Other (less favorably oriented) crystals yield later. Adapted from Fig. 7.10, Callister 7e. (Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) 300 mm 6

10. If the Slip plane is perpendicular to the Tensile Stress • =0o , and =90o cos = 1 and cos =0 CRSS =0 This means even if the applied tensile stress is enormous, the critical resolved shear stress is simply zero. The dislocations can’t move (slip can’t occur).

11. CRSS vs. Strain Rate and Temperature

12. Factors Affecting CRSS • Increasing temperature: decrease CRSS • Increasing strain Rate: increase CRSS In region II, the CRSS is not a function of temperature and strain rate. • Increasingimpurity: increaseCRSS • Increasing dislocation density: increaseCRSS

13. For temperature < 0.77 Tm (Region I and II), the critical resolved shear stress can be expressed using two terms. a is the athermal component of stress (long range internal stress field); * is the thermal stress (short range inter-atomic spacing)

17. Three Stages of Work Hardening in A Shear Stress-Shear Strain Curve Stage I Stage IIStage III (no work (linear (exhaustion hardening) hardening) hardening) CRSS 

18. Wavy Slip Steps in BCC Iron

20. Why 45o?

21. Plastic Flow in Polycrystalline Materials Plastic Deformation Mechanisms • The stress required for plastic flow increases with the increase of dislocation density • Geometrically necessary dislocations help transfer stress to the flow stress of plastic flow

22. Slip Mechanisms • Slip mechanisms are similar in single and polycrystals. The stress-strain behavior differ somewhat. • The slip processes occur within individual crystals of polycrystal aggregate • The strain displacements across grain boundaries must match the spacing between individual grains

23. Plastic Deformation Mechanisms • The stress required for plastic flow increases with the increase of dislocation density • Geometrically necessary dislocations help transfer stress to the flow stress of plastic flow

27. Conclusion • When τRSS (resolved shear stress) reaches a critical value the slip system will occur. • τCRSS is a function of temperature, material purity and strain rate • At region I, the τCRSS increases with decreases in temperature and increase in strain rate • At region II, the τCRSS is independent of temperature and strain rate • At high temperature region (region III) the τCRSS decreases when temperature increases and strain rate decreases • Work hardening in single crystals can be divided into 3 stages: glide and plastic strain, dislocation density increases resulting in immobilization, strain rate decreases.

28. Conclusion (continued) • Comparing to single crystals, polycrystalline requires higher stresses in order to be plastically deformed. • Yielding in BCC metals is temperature dependent, whereas FCC metals are not temperature sensitive • Number of grains and grain size play important roles in metal strengthening