Command manual

Command list

MAT_ZA

Material properties
Attention: This command is in the beta stage and the format may change over time.
*MAT_ZA
"Optional title"
mid, $\rho$, $E$, $\nu$, did, tid, eosid
$\sigma_g$, $k_h$, $l$, $K$, $n$, $B$, $B_0$
$\alpha_0$, $\alpha_1$, $\beta_0$, $\beta_1$, $\dot{\epsilon}_0$

Parameter definition

VariableDescription
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)
$\dot{\epsilon}_0$ Reference strain rate
default: 1

Description

This is the Zerilli-Armstrong constitutive model in its general form. The von Mises flow stress is defined as:

$\displaystyle{\sigma_y = \sigma_a + B \mathrm{e}^{-\beta T} + B_0 \sqrt{\epsilon_p} \mathrm{e}^{-\alpha T}}$

where $T$ is the current temperature. The athermal part of the flow stress is defined as:

$\displaystyle{ \sigma_a = \sigma_g + \frac{k_h}{\sqrt{l}}+ K \epsilon_p^n}$

where $k_h / \sqrt{l}$ is the Hall-Petch strengthening limit. The exponents $\alpha$ and $\beta$ are defined as:

$\displaystyle{ \alpha = \alpha_0 - \alpha_1 \mathrm{ln}\frac{\dot{\epsilon}_p}{\dot{\epsilon}_0}}$
$\displaystyle{ \beta = \beta_0 - \beta_1 \mathrm{ln}\frac{\dot{\epsilon}_p}{\dot{\epsilon}_0}}$

where $\dot{\epsilon}_p$ 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:

$\displaystyle{\sigma_y = \sigma_a + B_0 \sqrt{\epsilon_p} \mathrm{e}^{-\alpha T}}$

and BCC materials as:

$\displaystyle{\sigma_y = \sigma_a + B \mathrm{e}^{-\beta T}}$