Damage Initiation for Fiber-Reinforced Composites Using Multiscale Modeling

Damage initiation refers to the onset of degradation at a material point. Abaqus/Standard supports the failure criterion by Mayes (2001), who followed the work by Hashin (1980). The general form of Hashin's quadratic failure criterion is

Assuming the transverse failure of unidirectional fiber-reinforced composites is matrix dominated, the coefficients $K_2$ and $K_3$ can be set to zero, which reduces the fiber failure criterion to:

Fiber tension ( ${\hat{\sigma }}_{11}^f\ge 0$ ):

$$F_f^t=K_1^{f,t}{I}_1^2+K_4^f{I}_4\mathrm{.}$$

Fiber compression ( ${\hat{\sigma }}_{11}^f<0$ ):

$$F_f^c=K_1^{f,c}{I}_1^2+K_4^f{I}_4\mathrm{.}$$

The coefficients in the failure criterion can be determined from measured unidirectional composite strengths for pure tension, compression, and in-plane shear loading. In the case of pure tension and compression, ${\sigma }_{11}^f\ne 0,{\sigma }_{12}^f=0$ ; therefore, the coefficients $K_1^{f,t},K_1^{f,c}$ can be determined by

The same fiber failure criterion also applies to the fiber material inside the yarn of a woven composite.

DAMAGE INITIATION,CRITERION=HSNFIBER,ALPHA=$\alpha$

$K_1^{f,t}$
,$K_1^{f,c}$
,$K_4^f$

ALLOWABLE STRESS,TYPE=UD

ALLOWABLE STRESS,TYPE=WOVEN

Assuming the longitudinal failure of a unidirectional fiber-reinforced composite is fiber dominated, $K_1^m$ can be set to zero, which simplifies the matrix failure criterion to:

Matrix tension ( ${\hat{\sigma }}_{22}^m+{\hat{\sigma }}_{33}^m\ge 0$ ):

$$F_m^t=K_2^{m,t}{I}_2^2+K_3^m{I}_3+K_4^m{I}_4\mathrm{.}$$

Matrix compression ( ${\hat{\sigma }}_{22}^m+{\hat{\sigma }}_{33}^m<0$ ):

$$F_m^c=K_2^{m,c}{I}_2^2+K_3^m{I}_3+K_4^m{I}_4\mathrm{.}$$

${\hat{\sigma }}_{22}^m,{\hat{\sigma }}_{33}^m$ are the components of the effective stress tensor, $\hat{\mathbf{\sigma }}$ , that is used to evaluate the initiation criteria and is computed from

DAMAGE INITIATION,CRITERION=HSNMATRIX
$K_2^{m,t}$
,$K_2^{m,c}$
,$K_3^m$
,$K_4^m$

DAMAGE INITIATION,CRITERION=TSINVMATRIX
$A_2^{m,t}$
,$A_2^{m,c}$
,$K_4^m$

You can choose not to specify the coefficients directly in the definition of the constituent damage criterion. In that case you need to specify the allowable stress of the composite in the multiscale material definition. Then Abaqus/Standard computes the volume-averaged constituent stresses using the homogenization method specified, and the failure criterion coefficients using the equations above. When you specify the allowable stresses at the composite level, Abaqus/Standard ignores failure coefficients specified at the constituent level.

In a woven composite matrix, failure can occur before the ultimate failure of the composite. In addition to the ultimate composite strengths, you must specify the strengths of the composite at the initial failure of the matrix inside the tows.

ALLOWABLE STRESS,TYPE=UD
$X^T$
,$X^C$
$Y^T$
$Y^C$
$S^L$
$S^T$

ALLOWABLE STRESS,TYPE=WOVEN
$X^T$
,$X^C$
,$S^L$
,$X_0^T$
$X_0^C$
$S_0^L$