1- d Deterministic Crack Pattern Formation as a Growth Process with Restrictions

Abstract

Multiple crack propagation caused by thermal shock can be described as a motion in a time-dependent potential with the restriction that no subsequent crack closure (healing) is possible. For equidistant parallel cracks, bifurcation analysis and determination of the post-critical behaviour yield hierarchically ordered crack patterns, as experimentally observed. The theory is applied to a quenched strip, using BEM-calculations for the exact fracture mechanical problem. In order to demonstrate the selection of crack arrest and the influence of broken symmetry, a simple potential ansatz is studied numerically. The mutual inhibition of growing structural elements can be regarded as a structure-forming principle which works for Laplacian structures, too.