Stress intensity factors

The stress intensity factor distribution along each crack front is always calculated when the results of a finite element analysis are processed by Zencrack. If there are multiple loads steps in the f.e. analysis, for example due to the application of a thermal transient, then results for each step are processed giving the variation of stress intensity factors through the load history.

The calculations are based on the relative opening, sliding and tearing displacements derived from an orthogonal set of axes at each crack front node, as shown in the example below for a symmetry model. These relative displacements are used to calculate the stress intensity factors using equations derived from the Westergaard solution for the stress field around a crack tip. The equations that are used are valid for linear elastic isotropic materials.

The relative opening displacement is also an important quantity in determining a local "open" or "closed" status for a crack front node. This status has implications for crack growth integration.

If the analysis also includes a j-integral evaluation, a conversion of the j-integral to mode I stress intensity factor is also reported. This is strictly only valid if there are no mode II or mode III effects present.

The following are calculated:

• Ki, Kii and Kiii from nodal displacements using crack tip opening displacemets (CTOD) - only valid for linear elastic isotropic materials
• equivalent energy release rate from displacement-based Ki, Kii and Kiii
• Ki from energy release rate (mode I conversion for Abaqus, Finas and Marc interfaces only)
• relative opening displacements to define a proper "open" or "closed" status at crack front and crack face nodes
• the local crack growth direction from the local maximum energy release rate
• the local crack growth direction from the stress intensity factors.