Difference between revisions of "Linear Hardening"
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In the linear [[Hardening Laws|hardening law]], the yield stress is given by | In the linear [[Hardening Laws|hardening law]], the yield stress is given by | ||
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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> | ||
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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 | ||
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<math>\alpha = \sum \sqrt{2\over3}\ ||d\varepsilon_p||</math> | <math>\alpha = \sum \sqrt{2\over3}\ ||d\varepsilon_p||</math> | ||
where dε<sub>p</sub> is the incremental plastic strain tensor in one time step. | where dε<sub>p</sub> is the incremental plastic strain tensor in one time step. | ||
Revision as of 11:50, 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 = \sum \sqrt{2\over3}\ ||d\varepsilon_p|| }[/math]
where dεp is the incremental plastic strain tensor in one time step.