Virtual crack extension method for calculating rates of energy release rate and numerical simulation of crack growth in two and three dimensions.

摘要

This thesis develops an analytical virtual crack extension method for calculating rates of energy release rate and provides a numerical procedure for simulating a growth of multiple crack systems in two and three dimensions.; First, the thesis generalizes the analytical virtual crack extension method presented by Lin and Abel by providing the higher order derivatives of energy release rate due to crack extension for multiply cracked bodies in two and three dimensions. It provides derivations and verifications of the following: extension to the general case of multiple crack systems in two and three dimensions, extension to axisymmetric case, inclusion of crack-face and thermal loading, and evaluation of the second derivative of energy release rate. The salient feature of this method is that the energy release rate and its higher order derivatives for multiple crack systems are computed in a single analysis. Maximum errors for the mesh density used in the examples are about 0.2% for energy release rate, 2–4% for its first derivatives, and 5–10% for its second derivative.; Second, this thesis proposes crack-growth model and numerical procedure for simulation of a growth of planar cracks in two and three dimensions, using the first derivative of the energy release rate provided by the present virtual crack extension method. The model is based on the concept of maximizing the total energy released as a crack propagates, which results in the problem of constrained optimization. The main advantages of this approach are threefold: (a) the present approach provides crucial information about the stability of a propagating crack; (b) the interaction between crack extensions at different points along the crack front is considered in the shape prediction; (c) the energy release rates and their derivatives at all points along the crack front can be accurately calculated by the present virtual crack extension method in a single analysis.; Third, this thesis provides an approximate numerical procedure for simulating a growth of non-straight cracks in two dimensions. In the approach, the potential energy variation during the next kink extension is approximated as a quadratic polynomial function of the kink extension in the preferred direction of propagation. The energy release rate and its derivative variations, G( l) and $6$G(l)/$6$l, during the kink extension are approximated as linear and constant functions of the kink extension, by using the energy release rate and its derivative at the half-way point of the next kink extension range, respectively. The present approach provides an excellent quadratic polynomial approximation for potential energy variation during various kink extension ranges, with differences of less than 1% from the actual variation of potential energy obtained by finite element analysis. This research demonstrates that, through numerical simulation of inclined central cracks subjected to wedge force on the crack surface, the present approach can predict a reasonable crack-growth pattern and stability consistent with predictions made under this study.