# Bilinear Isotropic Hardening Behavior - PowerPoint PPT Presentation

Bilinear Isotropic Hardening Behavior

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Bilinear Isotropic Hardening Behavior

## Bilinear Isotropic Hardening Behavior

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##### Presentation Transcript

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

2. 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 Overview

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

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

5. Determines the stress levels at which yield will be initiated • Given by f({ • Written in general as F() = 0 where F = - • for isotropic hardening (von Mises stress) • + • is function of accumulated plastic strain • For Bilinear: Yield Criterion

6. (isotropic hardening) Yield Surface

7. Where indicates the direction of plastic straining, and is the magnitude of plastic deformation • Occurs when • Plastic potential (Q) – a scalar value function of stress tensor components and is similar to yield surface F • Associative rule: F = Q Flow Rule (plastic straining)

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

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

10. Consistency Condition

11. Strong form • Weak form • = [B]d • Matrix form • Where Governing Equations

12. Stress and strain states at load step ‘n’ at disposal The material yield from previous step is used as basis Load step ‘n+1’ with load increment Compute from and from Trail Displacement Updated Displacement If < Compute If Compute using NRI such that dF = 0 Compute restoring forces and Residual Perform Newton Rapshon iterations for equilibrium by updating Update stresses and strains Proceed to next load step Implementation

13. Elastic-Plastic Analysis Elastic Analysis ANSYS RESULTS- Von Mises Stress Geometry: Quarter model- OD = 10in; ID = 6in; Boundary-Rigid- OD=9.9in Material: E=30e6psi; =0.3; = 36300psi; = 75000psi (tangent modulus)

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

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

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

17. Question? Thank You