Difference between revisions of "Nonlinear Hardening 1"
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<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math> | <math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math> | ||
where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative plastic strain, and K and n are dimensionless hardening law coefficients. | where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients. | ||
An alternate [[Nonlinear Hardening 2|nonlinear hardening law]] is also available. | An alternate [[Nonlinear Hardening 2|nonlinear hardening law]] is also available. | ||
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This [[Hardening Laws|hardening law]] defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as | This [[Hardening Laws|hardening law]] defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as | ||
<math>\alpha = \sqrt{2\over3}\ ||d\varepsilon_p||</math> | <math>\alpha = \Sum \sqrt{2\over3}\ ||d\varepsilon_p||</math> | ||
where "epsilon;<sub>p</sub> is the incremental plastic strain tensor in one time step. | |||
Revision as of 10:20, 22 May 2013
In this nonlinear hardening law, the yield stress is given by
[math]\displaystyle{ \sigma_y = \sigma_{Y0}(1+K\alpha)^n }[/math]
where [math]\displaystyle{ \sigma_{Y0} }[/math] is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients.
An alternate nonlinear hardening law is also available.
Hardening Law Properties
The material parameters in this hardening law are defined with the following properties:
| Property | Description |
|---|---|
| yield | The initial yield stress (enter in units of MPa). This stress corresponds to the axial stress at yield during uniaxial, 3D loading. |
| Khard | The dimensionless parameter K for nonlinear hardening. |
| nhard | The dimensionless exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use linear hardening instead. |
History Data
This hardening law defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as
[math]\displaystyle{ \alpha = \Sum \sqrt{2\over3}\ ||d\varepsilon_p|| }[/math]
where "epsilon;p is the incremental plastic strain tensor in one time step.