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 &sigma;<sub>0</sub> is the initial yield stress, &beta; 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 is given by:
where &sigma;<sub>0</sub> is the initial yield stress, &beta; 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 12:49, 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.