Steinberg-Cochran-Guinan Hardening

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 is 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), G_P' and G_T' 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.