Chaotic Crack Size and Fracture Stiffness

摘要

The effect of chaotic crack size on the fracture stiffness of a distribution of coplanarrnflat elliptic cracks is examined. The crack lengths are computed as discrete elementsrnof a chaotic sequence resulting from the solutions of different first order iterativernmaps. The iterative maps considered are generalized logistic maps of the form xi+1=rnr x_i~α(1-x_i)~β with the parameters r, α and β being positive and the variable xi, whichrnrepresents the non-dimensional crack length of the ith crack with respect to therndistance of neighbouring cracks, ranging from 0 to 1. For several r, α and β values,rnthe chaotic sequence of crack lengths is computed from the respective iterative map.rnSubsequently, the chaotic crack opening areas for non-interacting cracks arernobtained for mode I crack loading. The fracture stiffness of a plane containing arnlarge number of such cracks is then computed from the inverse of the sum of thernsquared crack lengths. The fracture compliance is, thus, proportional to the energyrnproduced by the iterative map.