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). The second index gives the direction of the shear crack in that plane and the crack has normal in the j direction. Each shear plane has two shear strengths. Failure initiates by shear when:

     [math]\displaystyle{ \tau_{ij} \gt \min\bigl(\tau_{ij,i}^{(c)},\tau_{ij,j}^{(c)}\bigr) }[/math]

The crack that forms is in the i direction with normal in the [math]\displaystyle{ \vec{\hat j} }[/math] direction if [math]\displaystyle{ \tau_{ij,i}^{(c)} \lt \tau_{ij,j}^{(c)} }[/math], otherwise the crack normal is in the [math]\displaystyle{ \vec{\hat i} }[/math] direction.

Damage Law Properties

The following table lists the input properties for this initiation law

Property	Description	Units	Default
sigmaXXc	Critical stress for failure by tension in the material x direction	pressure units	infinite
sigmaYYc	Critical stress for failure by tension in the material y direction	pressure units	infinite
sigmaZZc	Critical stress for failure by tension in the material z direction	pressure units	infinite
tauXY-Xc	Critical stress for failure by shear in the material x-y plane. The crack that forms is in the x direction with normal in the y direction.	pressure units	infinite
tauXY-Yc	Critical stress for failure by shear in the material x-y plane. The crack that forms is in the y direction with normal in the x direction.	pressure units	infinite
tauXZ-Xc	Critical stress for failure by shear in the material x-z plane. The crack that forms is in the x direction with normal in the z direction.	pressure units	infinite
tauXZ-Zc	Critical stress for failure by shear in the material x-z plane. The crack that forms is in the z direction with normal in the x direction.	pressure units	infinite
tauYZ-Yc	Critical stress for failure by shear in the material y-z plane. The crack that forms is in the y direction with normal in the z direction.	pressure units	infinite
tauYZ-Zc	Critical stress for failure by shear in the material y-z plane. The crack that forms is in the z direction with normal in the y direction.	pressure units	infinite

Even though the maximum shear value for each ij plane is never used to initiate failure, they are still needed for damage evolution. For example, if the material initiates failure by tension in the x direction, the shear damage evolution will be determined by softening laws based on shear strengths with the same normal (i.e., tauXY-Yc and tauXZ-Zc) even if they are larger that the other shear strengths for those planes.