## Slide #1.

Plasticity Jake Blanchard Spring 2008
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## Slide #2.

Analysis of Plastic Behavior Plastic deformation in metals is an inherently nonlinear process Studying it in ANSYS is much like a transient problem ◦ Instead of time steps, we have load steps ◦ Elements must support plasticity ◦ We must define stress-strain curve
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## Slide #3.

Typical Stress Strain Curve 1. 2. 3. UTS YS Rupture
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## Slide #4.

Defining Materials in ANSYS Start with elastic modulus, poisson’s ratio, and yield stress Then we must define plastic behavior
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## Slide #5.

Models in ANSYS Bilinear Kinematic Hardening – constant slope after yielding Multilinear Kinematic Hardening – series of straight lines after yielding Nonlinear Kinematic Hardening Similar models exist for isotropic hardening Isotropic vs. kinematic determines how yield surface changes after yielding (kinematic means compressive yield increases as tensile yield increases) Others are more exotic; these will suffice for our needs
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## Slide #6.

Defining Parameters in GUI Materials Model is: ◦ Structural ◦ Nonlinear ◦ Inelastic ◦ Rate Independent ◦ Isotropic ◦ Mises ◦ Bilinear Graph with Plot/Data Tables or List/Properties/Data Tables
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## Slide #7.

Approach for inelastic analysis Apply loads gradually – one load step with many substeps (ramped) Second load step will remove the pressure Even though analysis is quasi-static, we use time to differentiate load steps. So set time at end of first step to 1 second and time at end of second step to 2 seconds. (These are arbitrary.) The first load step should still be in the elastic region. I usually let ANSYS control time steps (automatic stepping).
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## Slide #8.

Sample Problem Thick cylinder E=200 Gpa =0.3 YS=150 MPa Bilinear-kinematic hardening – slope after yielding=2 Gpa Inner radius=20 cm Outer radius=30 cm Loaded by internal pressure
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## Slide #9.

Steps At what pressure will yielding first occur? Where does yielding first occur? What fraction of the cylinder area yields when the pressure increases to 1.2 times the yield pressure? At what pressure does the entire area yield? What happens if we remove the
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