# Metafor

ULiege - Aerospace & Mechanical Engineering

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doc:user:elements:volumes:grainsize

# Grain Size

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).

## PerzynaGrainSize

#### Description

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 :

$$\dot{d}=\dfrac{\alpha_1}{d^Q}+\dfrac{\alpha_2 \dot{\bar{\varepsilon}}^{pl}}{d^R}$$

#### Parameters

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

## SinhGrainSize

#### Description

Prandtl model

Stress:

$$\sigma_{d}= \dfrac{1}{\beta}\, \mbox{arcsinh} \left(\dfrac{\dot{\bar{\varepsilon}}^{pl}d^p}{A}\right)$$

Evolution of grain size :

$$\dot{d}= \dfrac{\alpha_1}{d^Q} + \dfrac{\alpha_2\dot{\bar{\varepsilon}}^{pl}}{d^R}$$

#### Parameters

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 