Damage initiation models

These are models which predict the onset of damage based on the accumulated equivalent plastic strain. They can only be used for models for which the equivalent plastic strain is calculated, i.e. *DEFORMATION PLASTICITY, *PLASTIC (with isotropic or orthotropic elasticity, including Johnson-Cook hardening), *CREEP and *MOHR COULOMB. Damage is initiated if the damage initiation criterion $\omega_D$ reaches a limit provided by the user,usually 1. $\omega_D$ is calculated as the sum of the change in equivalent plastic strain in each increment divided by the equivalent plastic strain at the onset of damage ${\epsilon }_D^{\text{peq}}$:

$$\omega_D = \sum \frac{\Delta \epsilon^{\text{peq}} }{\epsilon_D^{\text{peq}}}.$$ (518)

According to the Rice-Tracey model ${\epsilon }_D^{\text{peq}}$ satisfies:

$${\epsilon }_D^{\text{peq}}=1.65 \epsilon _0^{RT} \exp \left( - \frac{3 \sigma_{hy}}{2 \sigma_{vm}} \right),$$ (519)

where $\sigma_{hy}$ is the hydrostatic stress and $\sigma_{vm}$ the von Mises stress. The ratio of both is called the triaxiality $\eta=\sigma_{hy}/\sigma_{vm}$. For a one-dimensional tensile test it takes the value 1/3.

According to the Johnson-Cook model ${\epsilon }_D^{\text{peq}}$ is determined by:

$${\epsilon }_D^{\text{peq}}= (d_1 + d_2 \exp ( -d_3 \eta )) ( 1 + ... ...\epsilon }^{\text{peq}}}{\dot{\epsilon }_0 } \right) \left [1-(T^*)^m \right ],$$ (520)

where

$$T^* = 0 \;\;\; \; T<T_0$$

$$T^* = \left(\frac{T-T_0}{T_m-T_0}\right) \;\;\; \; T_0 \le T \le T_m$$

$$T^* = 1 \;\;\; \; T>T_m$$ (521)

Here, $d_1, d_2, d_3, d_4, d_5,\dot{\epsilon_0},T_0$ and $T_m$ are material constants. The constant $T_0$ has the physical meaning of transition temperature, i.e. the temperature above which the equivalent strain at the onset of damage starts to increase and $T_m$ has the physical meaning of melt temperature, i.e. the temperature above which ${\epsilon }_D^{\text{peq}}$ remains constant. The model is meant to describe highly dynamic phenomena.

As soon as the damage initiation criterion reaches the user-defined limit in any integration point within this element, the element is deleted.