Energy release rate and j-integral

The energy release rate and the more general j-integral are fracture mechanics parameters that can be calculated as a post processing exercise following a finite element analysis. Abaqus/Standard, Finas and Marc all have a capability to allow calculation of these parameters - the user merely supplies the necessary input data. The core of this data is the specification of one or more virtual crack extensions. The f.e. code returns the energy release rate or j-integral value associated with this virtual crack extension.

In a Zencrack analysis all of the required input data for the relevant option in the f.e. code is created by Zencrack. The schematic to the right shows a fan of seven virtual crack extensions within the normal plane at a crack front node. These extensions return energy release rate values denoted here by G1 to G7. When plotted as a function of angle around the crack tip, it is possible to extract the angle at which the maximum energy release rate occurs and the magnitude of this value, denoted by Thetamax and Gmax respectively. In a crack growth analysis the Gmax and Thetamax terms are calculated by Zencrack and used during crack growth integration.

For a 3D crack front the amount of data required to specify the energy release rate calculations can be considerable. The processing of the results also requires a certain amount of effort. Zencrack removes the manual effort involved in these tasks by automatically creating the input and processing the subsequent results after completion of the finite element analysis. The Gmax term and a crack growth direction vector are reported for each node along the crack front.

The energy release rate is calculated for a specified number of "contours" in the Abaqus and Finas interfaces. These contours relate to the number of rings of elements around the crack front in the focused meshes of the crack-blocks. Within the Zencrack input the user can control the calculated number of contours and the way in which the results should be used to drive a crack growth analysis. Results for all calculated contours are extracted and reported in the Zencrack output files to allow checking for path dependency.