Difference between revisions of "Steinberg-Cochran-Guinan Hardening"
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<math>\sigma_y = \sigma_0\bigl(1 + \beta \varepsilon_p^n){G(T,P)\over G_0}</math> | <math>\sigma_y = \sigma_0\bigl(1 + \beta \varepsilon_p^n){G(T,P)\over G_0}</math> | ||
where σ<sub>0</sub> is the initial yield stress, β and n are hardening law properties, <math>\varepsilon_p</math> is the cumulative plastic strain, G(T,P) is the shear modulus (which may depend on temperature and pressure), and G<sub>0</sub> is the initial shear modulus. The shear modulus temperature and pressure dependence | where σ<sub>0</sub> is the initial yield stress, β and n are hardening law properties, <math>\varepsilon_p</math> is the cumulative plastic strain, G(T,P) is the shear modulus (which may depend on temperature and pressure), and G<sub>0</sub> is the initial shear modulus. The shear modulus temperature and pressure dependence are given by: | ||
<math>{G(T,P)\over G_0} = 1 + {G_P'\over G_0} P J^{1/3} + {G_T'\over G_0}(T-T_0)</math> | <math>{G(T,P)\over G_0} = 1 + {G_P'\over G_0} P J^{1/3} + {G_T'\over G_0}(T-T_0)</math> | ||
Revision as of 11:49, 27 March 2013
In the Steinberg-Cochran-Guinan hardening law, the yield stress is given by
[math]\displaystyle{ \sigma_y = \sigma_0\bigl(1 + \beta \varepsilon_p^n){G(T,P)\over G_0} }[/math]
where σ0 is the initial yield stress, β and n are hardening law properties, [math]\displaystyle{ \varepsilon_p }[/math] is the cumulative plastic strain, G(T,P) is the shear modulus (which may depend on temperature and pressure), and G0 is the initial shear modulus. The shear modulus temperature and pressure dependence are given by:
[math]\displaystyle{ {G(T,P)\over G_0} = 1 + {G_P'\over G_0} P J^{1/3} + {G_T'\over G_0}(T-T_0) }[/math]
where J is the relative volume change (V/V0), GP' and GT' are coefficients for pressure and temperature affects, T is current temperature, and T0 is a reference temperature.
Hardening Law Properties
This hardening law can set the following properties:
| Property | Description |
|---|---|
| yield | Initial yield stress (&sigma_0) at zero pressure and the reference temperature. Enter in units of MPa. |
| betahard | Yield stress hardening term &beta. It is dimensionless. |
| nhard | Exponent on cumulative plastic strain in hardening term. It is dimensionless. |
| GPpG0 | The (Gp'/G0) ratio term for pressure dependence of shear modulus. Enter in units MPa-1. Enter 0 to omit pressure dependence in shear modulus. |
| GTpG0 | The (GT'/G0) ratio term for temperature dependence of shear modulus. Enter in units MPa-1. Enter 0 to omit temperature dependence in shear modulus. |
| yieldMax | Maximum yield stress. Enter in units of MPa. |