1. Bilinear Isotropic Hardening Behavior MAE 5700 Final Project Raghavendar Ranganathan Bradly Verdant Ranny Zhao

2. Overview Problem Statement Illustration of bilinear isotropic hardening plasticity with an example of an interference fit between a shaft and a bushing assembly Plasticity Model Yield criterion Flow rule Hardening rule Governing Equations Numerical Implementation FE Results 2

3. Elastic-Plastic Analysis Elastic Analysis 3 Quarter model-Plane Stress- interference with an outer rigid body Elastic Plastic Behavior

4. Material Curve 4 Bilinear: Approximation of the more realistic multi-linear stress-strain relation True Stress vs. True Strain curve

5. Yield Criterion 5

6. Yield Surface 6

7. Flow Rule (plastic straining) 7

8. Hardening Rule Description of changing of yield surface with progressive yielding Allows the yield surface to expand and change shape as the material is plastically loaded 8 Elastic Plastic Elastic Plastic Yield Surface after Loading Initial Yield Surface

9. Hardening Types 1. Isotropic Hardening2. Kinematic Hardening 22 Initial Yield Surface 11 Subsequent Yield Surface 22 Initial Yield Surface 11 Subsequent Yield Surface 9

10. Consistency Condition 10

11. Governing Equations 11

12. 12 Stress and strain states at load step ‘n’ at disposal Compute restoring forces and Residual Update stresses and strains Proceed to next load step Implementation The material yield from previous step is used as basis

13. ANSYS RESULTS- Von Mises Stress Elastic-Plastic Analysis Elastic Analysis 13

14. ANSYS Results- Radial Stress (X-Plot) 14 Elastic-Plastic AnalysisElastic Analysis

15. ANSYS Results- Hoop Stress (Y-Plot) 15 Elastic-Plastic AnalysisElastic Analysis

16. ANSYS Results- Deformation 16 Elastic-Plastic Analysis Elastic Analysis Elastic-Plastic Analysis Elastic Analysis

17. Thank You Question? 17