MAT_ZA
Material properties
*MAT_ZA
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid, eosid
$\sigma_g$, $k_h$, $l$, $K$, $n$, $B$, $B_0$
$\alpha_0$, $\alpha_1$, $\beta_0$, $\beta_1$, $\dot{\varepsilon}_0$
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid, eosid
$\sigma_g$, $k_h$, $l$, $K$, $n$, $B$, $B_0$
$\alpha_0$, $\alpha_1$, $\beta_0$, $\beta_1$, $\dot{\varepsilon}_0$
Parameter definition
Variable
Description
mid
Unique material identification number
$\rho$
Density
$E$
Young's modulus
$\nu$
Poisson's ratio
did
Damage property command ID
tid
Thermal property command ID
eosid
Equation-of-state ID
$\sigma_g$
Athermal flow stress
$k_h$
Microstructural stress intensity
$l$
Average grain diameter
$K$
Crystal structure dependent parameter (=0 for FCC)
$n$
Strain hardening parameter
$B$
Strain rate hardening/thermal softening parameter (used for BCC)
$B_0$
Strain rate hardening/thermal softening parameter (used for FCC)
$\alpha_0$
Thermal softening parameter (used for FCC)
$\alpha_1$
Strain rate hardening/thermal softening parameter (used for FCC)
$\beta_0$
Thermal softening parameter (used for BCC)
$\beta_1$
Strain rate hardening/thermal softening parameter (used for BCC)
$\dot{\varepsilon}_0$
Reference strain rate
Description
This is the Zerilli-Armstrong constitutive model in its general form. The von Mises flow stress is defined as:
$\displaystyle{\sigma_y = \sigma_a + B \mathrm{e}^{-\beta T} + B_0 \sqrt{\varepsilon_p} \mathrm{e}^{-\alpha T}}$
where $T$ is the current temperature. The athermal part of the flow stress is defined as:
$\displaystyle{ \sigma_a = \sigma_g + \frac{k_h}{\sqrt{l}}+ K \varepsilon_p^n}$
where $k_h / \sqrt{l}$ is the Hall-Petch strengthening limit. The exponents $\alpha$ and $\beta$ are defined as:
$\displaystyle{ \alpha = \alpha_0 - \alpha_1 \mathrm{ln}\frac{\dot{\varepsilon}_p}{\dot{\varepsilon}_0}}$
$\displaystyle{ \beta = \beta_0 - \beta_1 \mathrm{ln}\frac{\dot{\varepsilon}_p}{\dot{\varepsilon}_0}}$
where $\dot{\varepsilon}_p$ is the current effective plastic strain rate. The used parameters depend on the crystal structure of the material. Generally, materials with FCC structure are described as:
$\displaystyle{\sigma_y = \sigma_a + B_0 \sqrt{\varepsilon_p} \mathrm{e}^{-\alpha T}}$
and BCC materials as:
$\displaystyle{\sigma_y = \sigma_a + B \mathrm{e}^{-\beta T}}$
