Difference between revisions of "Linear Hardening"
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<math>\sigma_y = \sigma_{Y0} + E_p\alpha = \sigma_{Y0}(1+K\alpha)</math> | <math>\sigma_y = \sigma_{Y0} + E_p\alpha = \sigma_{Y0}(1+K\alpha)</math> | ||
where <math>\sigma_{Y0}</math> is initial yield stress, E<sub>p</sub> is the plastic modulus, α is equivalent plastic strain, and K is a hardening coefficient. | where <math>\sigma_{Y0}</math> is initial yield stress, E<sub>p</sub> is the plastic modulus, α is cumulative equivalent plastic strain, and K is a hardening coefficient. | ||
== Hardening Law Properties == | == Hardening Law Properties == | ||
Revision as of 10:12, 22 May 2013
In the linear hardening law, the yield stress is given by
[math]\displaystyle{ \sigma_y = \sigma_{Y0} + E_p\alpha = \sigma_{Y0}(1+K\alpha) }[/math]
where [math]\displaystyle{ \sigma_{Y0} }[/math] is initial yield stress, Ep is the plastic modulus, α is cumulative equivalent plastic strain, and K is a hardening coefficient.
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. |
| Ep | The plastic modulus (enter in units of MPa). This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default is 0.0 which results in an elastic-perfectly plastic material or a material with no work hardening. |
| Khard | Alternatively, you can enter this dimensionless parameter for hardening. It is only used if Ep is not entered and when entered, it is convert to Ep using Ep = [math]\displaystyle{ \sigma_{Y0}K }[/math]. |
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 = \sqrt{2\over3}\ ||d\varepsilon_p|| }[/math]