Difference between revisions of "Nonlinear Hardening 2"
Jump to navigation
Jump to search
| (5 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
In this nonlinear [[Hardening Laws|hardening law]], the yield stress is given by | In this nonlinear [[Hardening Laws|hardening law]], the yield stress is given by | ||
| |||
<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 equivalent 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. If K < 0, the law is softening instead of hardening. The amount of softening can be limited by the <tt>yieldMin</tt> property. | ||
An alternate [[Nonlinear Hardening 1|nonlinear hardening law]] is also available. | An alternate [[Nonlinear Hardening 1|nonlinear hardening law]] is also available. | ||
| Line 13: | Line 14: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Property !! Description | ! Property !! Description !! Units !! Default | ||
|- | |- | ||
| yield || The initial yield stress | | yield || The initial yield stress. This stress corresponds to the axial stress at yield during uniaxial, 3D loading. || [[ConsistentUnits Command#Legacy and Consistent Units|pressure units]] || Large | ||
|- | |- | ||
| Khard || The | | Khard || The hardening parameter K for nonlinear hardening. || dimensionless || 0 | ||
|- | |- | ||
| nhard || The | | nhard || The hardening exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening|linear hardening]] instead. || dimensionless || 1 | ||
|- | |||
| yieldMin || The minimum yield stress. This minimum only matters when using negative <tt>Khard</tt> or when modeling softening plasticity || [[ConsistentUnits Command#Legacy and Consistent Units|pressure units]] || 0 | |||
|} | |} | ||
| Line 26: | Line 29: | ||
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 = \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. | ||
Latest revision as of 13:46, 25 April 2017
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. If K < 0, the law is softening instead of hardening. The amount of softening can be limited by the yieldMin property.
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 | Units | Default |
|---|---|---|---|
| yield | The initial yield stress. This stress corresponds to the axial stress at yield during uniaxial, 3D loading. | pressure units | Large |
| Khard | The hardening parameter K for nonlinear hardening. | dimensionless | 0 |
| nhard | The hardening exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use linear hardening instead. | dimensionless | 1 |
| yieldMin | The minimum yield stress. This minimum only matters when using negative Khard or when modeling softening plasticity | pressure units | 0 |
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.