"Optional title"
did, erode, noic
$W_c$, $G_I$, $\sigma_s$, $t_s$, $\alpha_s$, $\beta_s$
Parameter definition
Variable | Description |
---|---|
did | Unique damage identification number |
erode | Element erosion flag |
noic | Flag to turn off cracking along interface between different materials |
$W_c$ | Damage parameter |
$G_I$ | Fracture energy parameter (only used with node splitting) |
$\sigma_s$ | Spall strength (threshold stress) |
$t_s$ | Time to develop spall fracture at threshold stress |
$\alpha_s$ | Exponent controlling time to develop spall fracture |
$\beta_s$ | Parameter controlling the pressure dependency |
Description
This is the Cockcroft-Latham failure criterion. It has been complemented with a tensile fracture/spalling criterion. Ductile damage is defined as:
$\displaystyle{D_d = \frac{1}{W_c} \int_0^{\varepsilon_{eff}^p} \mathrm{max}(0,\sigma_1) \mathrm{d}\varepsilon_{eff}^p}$
where $\sigma_1$ is the maximum principal stress. The complementing tensile damage is defined as:
$\displaystyle{ D_t = \frac{1}{t_s} \int_0^{t} (\bar{\sigma}_1 / \sigma_s )^{\alpha_s} \mathrm{d}t}$
$\bar{\sigma}_1$ is defined as:
$\bar{\sigma}_1 = \sigma_1^{dev} - (1-\beta_s) \cdot p$
where $\sigma_1^{dev}$ is the maximum deviatoric principal stress and $p$ is the pressure. With $\beta_s = 0$, $\bar{\sigma}_1$ equals the maximum principal stress. Note that the tensile fracture/spalling term only contributes to the damage growth if $\bar{\sigma}_1 \geq \sigma_s$. The material is assumed to fail when one of the damage parameters reaches 1.
Example
Defining damage parameter
The following input defines a damage parameter that depends on the distance from the material surface.
Wc0 = 200.0e6 # on the surface
Wc1 = 400.0e6 # in the interior
dist_ref = 0.001
*PROP_DAMAGE_CL
1
[fcn(23)]
*FUNCTION
23
%Wc0 + (%Wc1 - %Wc0)*(1 - exp(-dist_surf/%dist_ref))