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
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.