Modeling growth paths of interacting crack pairs in elastic media

Abstract

The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the 'En-Passant' family of crack growth problems, in which a pair of initially parallel, offset cracks propagate nontrivially toward each other under far-field opening stress. We utilize boundary integral and perturbation methods of linear elasticity, Linear Elastic Fracture Mechanics, and common crack opening criteria to calculate the first analytical model for curved En-Passant crack paths. The integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the corresponding limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results and existing experimental data to verify certain approximation steps.

An adaptive quasicontinuum approach for modeling fracture in networked materials: Application to modeling of polymer networks

“…Furthermore, these results show how the two cracks emerging from the double notches interact with each other at different µ values. The crack path shape for the case of µ = 0.05 matches previously reported experimental and numerical observations [38,39] .It also matches the numerical results for elastomeric materials fractured by cross-link failure using the phase field method [9]. However, our results suggests that local topology may have a profound effect on this crack path that may be challenging to capture using fully homogenized approaches.…”

On the formation of ridges and burnished debris along internal fatigue crack propagation in 42CrMo4 steel

“…The type of interaction of parallel cracks when their tips grow towards each other and curve around some mutual centre instead of direct connection is called ‘en passant’ cracks (EPCs). EPCs are known to form in polymers, 45 glasses, 46 earth crust and rock, 47 concrete, 48 paper, 49 etc. Such universality means that EPC phenomenon is scale invariant and stress driven for both brittle and ductile materials.…”

Path (un)predictability of two interacting cracks in polycarbonate sheets using Digital Image Correlation

“…This is a simple version of a complicated process that is described in detail in ref. 17 where multiple criteria for crack propagation and strain field values are compared in en passant geometry.…”

“…In ( a ) at t  = 20 s the strain is still small and looks symmetric. In ( b ) t  = 55 s K II component has positive values based on the geometry1718 which means that the crack turns counterclockwise. This is seen as repulsion: the strain maximum is above the horizontal line.…”