The GrainSize class manages the laws estimating the stress based on the size of grains and the laws governing the evolution of their size. When this size is taken into account, both laws must be defined (the stress due to grain size is taken into account in the plastic criterion).
Perzyna model
Stress:
$$ \sigma_d =K\,d^p\,\left (\dot{\bar{\varepsilon}}^{pl} \right )^m\,\left (\bar{\varepsilon}^{pl} \right )^n $$
Evolution of grain size :
$$ \dot{d}=\dfrac{\alpha_1}{d^Q}+\dfrac{\alpha_2 \dot{\bar{\varepsilon}}^{pl}}{d^R} $$
| Name | Metafor Code | Dependency |
|---|---|---|
| Viscosity $K $ | PERZYNAGS_K | TO|TM |
| Sensitivity to strain rate $m $ | PERZYNAGS_M | TO|TM |
| Hardening of viscous terms $n $ | PERZYNAGS_N | TO|TM |
| Sensitivity to grain size $p $ | PERZYNAGS_P | TO|TM |
| Coefficient of static growth $\alpha_1$ | PERZYNAGS_ALPHA1 | TO|TM |
| Coefficient of dynamic growth $\alpha_2$ | PERZYNAGS_ALPHA2 | TO|TM |
| Exponent of static growth $Q $ | PERZYNAGS_Q | TO|TM |
| Exponent of dynamic growth $R $ | PERZYNAGS_R | TO|TM |
Prandtl model
Stress:
$$ \sigma_{d}= \dfrac{1}{\beta}\, \mbox{arcsinh} \left(\dfrac{\dot{\bar{\varepsilon}}^{pl}d^p}{A}\right) $$
Evolution of grain size :
$$ \dot{d}= \dfrac{\alpha_1}{d^Q} + \dfrac{\alpha_2\dot{\bar{\varepsilon}}^{pl}}{d^R} $$
| Name | Metafor Code | Dependency |
|---|---|---|
| Viscosity $A $ | SINH_A | TO|TM |
| Viscosity $\beta$ | SINH_BETA | TO|TM |
| Sensitivity to grain size $p $ | SINH_P | TO|TM |
| Coefficient of static growth $\alpha_1$ | SINH_ALPHA1 | TO|TM |
| Coefficient of dynamic growth $\alpha_2$ | SINH_ALPHA2 | TO|TM |
| Exponent of static growth $q $ | SINH_Q | TO|TM |
| Exponent of dynamic growth $r $ | SINH_R | TO|TM |