A three-dimensional crack tip element for energy release rate determination in layered elastic structures

A three-dimensional crack tip element is presented and used to determine energy release rate and mode mix for different types of laminated plates containing delaminations. These results are then compared to predictions by three-dimensional finite element analyses. For all cases, total energy release rates as predicted by the two methods are in good agreement. For delaminations between plies at the same orientation, energy release rate components are determined by the crack tip element using both classical and non-classical definitions. The non-classical definition is one that has been derived in a previous work and, compared to the classical result, is shown to provide superior capability for predicting delamination growth in some graphite/epoxy composites. The classical energy release rate components predicted by the crack tip element are compared to results by three-dimensional finite element analyses and the virtual crack closure technique and good agreement is obtained. For delaminations between plies at different orientations, the crack tip element is used to predict non-classical energy release rate components as well as components based on a finite amount of crack closure. These latter quantities are compared to results by three dimensional finite element analyses and the virtual crack closure technique, and good correlation is obtained. These results indicate that the crack tip element may be used to accurately determine energy release rate components in practical problems of delamination where these components are defined classically, defined by commonly used approaches such as finite crack closure, or defined using a non-classical approach. As such, the element provides a powerful yet adaptable technique for predicting delamination growth in a wide variety of materials.