Orthotropic Failure Surface
Introduction
This damage initiation law predicts failure in orthotropic materials. Because it deals with a specific material type, this law is only appropriate for OrthoSoftening materials.
Failure Surface
This failure surface has nine failure properties. First, are three tensile strengths [math]\displaystyle{ \sigma_{ii}^{(c)} }[/math] where i is x, y, or z that give tensile strength in the three material direciton
Second, are six shear strengths [math]\displaystyle{ \tau_{ij,i}^{(c)} }[/math] that give the shear in the three material symmetry planes (with ij = xy, xa, or yz). When shear in one of these reaches this stress, the material initiates damage. The second index give the direction of the shear crack in that plane. For example,
[math]\displaystyle{ \tau_{ij} \gt \min\bigl(\tau_{ij}^{(i,c)},\tau_{ij}^{(j,c)}\bigr) \ &{\rm with}\ \hat{\vec n} = \left\{ \begin{array}{ll} \vec{\hat j} & {\rm if}\ \tau_{ij}^{(i,c)}\lt \tau_{ij}^{(j,c)} \\ \vec{\hat i} & {\rm if}\ \tau_{ij}^{(i,c)}\gt \tau_{ij}^{(j,c)} \end{array}\right. }[/math]
The first two shear strength are for failure at maximum shear stress in planes parallel to the axial direction. When failure occurs in such a plane, the resulting crack will either be parallel to the axial direction with normal in transverse direction (if [math]\displaystyle{ \tau_A \lt \tau_T }[/math]) or parallel to the transverse direction with normal in the axial direction (if [math]\displaystyle{ \tau_T\lt \tau_A }[/math]) . The last shear strength is for failure in the isotropic plane, which occurs in the maximum shear stress direction in that plane.
Damage Law Properties
The following table lists the input properties for this initiation law
| Property | Description | Units | Default |
|---|---|---|---|
| sigmacA | Critical stress for failure in the axial direction (output as sigcA) | pressure units | infinite |
| sigmac | Critical transverse tensile strength for tensile failure in the isotropic plane (output as sigcT) | pressure units | infinite |
| taucA | Critical shear stress for failure due to axial shear stress with failure parallel to the axial direction | pressure units | infinite |
| taucT | Critical shear stress for failure due to axial shear stress with failure through the axial direction | pressure units | infinite |
| tauc | Critical transverse shear stress for shear failure n the isotropic plane (output as taucRS) | pressure units | infinite |
Notice this law has two axial shear strengths (taucA and taucT). If failure occurs by shear in a plane parallel to the axial direction, the failure and crack orientation will be determined by the minimum of taucA and taucT. Even though the maximum value is never used to initiate failure, it is still needed for damage evolution. For example, in wood, taucA is called "shear parallel strength", tauT is called "shear perpendicular strength", and tauc is called "rolling shear strength". For wood, tauT is much larger than taucA, which means shear failure is by shear cracks parallel to the wood fibers in the axial direction. But, if the wood initiates failure by tension parallel tot he fibers and then is loaded in shear, the shear damage evolution will be determined by softening law based on tauT.