Separation of crack extension modes in orthotropic delamination models

Abstract

In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict delamination in layered materials. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode I and mode II energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, A.In this work, a method is presented for using the VCCT to extract A-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials.The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, A-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-'tip fields is used to determine the explicit A dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on A. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that A-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The A-independent modes extracted using this technique can also serve as guides for testing .the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique

“…Consequently, G I and G II become dependent on the assumed crack-extension size, �, in the finite element simulations. Various pro cedures have been suggested to extract meaning ful �-independent parameters from the oscillatory SERRs in order to characterize the interface crack (Toya 1992;Chow and Atluri 1995;Beuth 1996;Sun and Qian 1997). We will show that the expres sions for G I and G II used by these authors are identical.…”

“…Thus, to design reliable layered structures, it is par amount that the mechanics of the interface crack is understood. Fracture toughness of bimaterial interfaces has received attention through analyt ical (e.g., Rice 1988;Hutchinson and Suo 1992), experimental (e.g., Charalambides et al 1989;Wang and Suo 1990;Yuuki et al 1994;Ikeda et al 1998) and numerical simulations (e.g., Sun and Jih 1987;Matos et al 1989;Toya 1992;Beuth 1996;Bjerken and Persson 2001).…”

“…Obtaining mode mixity for an interface crack using the VCCT has proven to be more challenging (Sun and Jih 1987;Raju et al 1988;Dattaguru et al 1994). However, several approaches have been suggested to extract consistent mode mixity values using the VCCT (Toya 1992;Chow and Atluri 1995;Beuth 1996;Sun and Qian 1997;Bjerken and Persson 2001).…”

“…To this end, we will in Chapters 3-4 re-derive the equations that are needed to extract mode mixity from the VCCT results of SERRs us ing asymptotic stress and displacement field near the crack tip. The derivation is intended to estab lish a clear link between various approaches (Toya 1992;Chow and Atluri 1995;Beuth 1996;Sun and Qian 1997). Furthermore, a simple quadratic equa tion is derived that can be used to obtain the SIFbased mode mixity.…”

“…In addition, an approach by Bjerken and Persson (2001) is examined and found attrac tive for providing acceptable values of mode mixity with significantly less computational efforts. Fur ther, a modified definition of mode mixity, based on SERRs (Beuth 1996), is shown as an alternative measure for characterizing an interface crack.…”