Heart-shaped crack-tip zones - Effect of the zone length

In this report the general influence of different elastic modules ahead of a crack tip and in the bulk on the stress intensity factors will be discussed again. From the FE results obtained in Report [1], and the theoretical solution by Merkle [3] K = K$_{appl}$$\sqrt{\frac{E}{E_{0}}}$ it becomes clear that the FE-results for relative zone sizes $\omega$/a >0 must deviate from the exact solution but are also in rather good agreement with the theoretic results for finite $\omega$/a. In this report also results are compiled for cracks fully embedded in zones with reduced module. Such cracks show stress intensity factors completely different from a $\sqrt{ E/E_{0}}$ -dependency. Nevertheless, it can be concluded that the stress intensity factors on the basis of the J-integral agree with those obtained by COD evaluation. As an approximate description of the observed E/E$_{0}$-dependency we suggest $\frac{K}{K_{appl}}$ $\cong$$\frac{2E}{E+E_{0}}$