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Spiral crack leading edge instability in mixed mode fracture

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Document pages: 11 pages

Abstract: Plane crack growth under pure tensile load (mode I) is usually stable. However, when shear stresses parallel to the crack front are superimposed, it becomes generally unstable (mode III). In this mixed mode (I   +   III), in the loading configuration, the initially flat parent crack will be divided into a series of sub cracks, which rotate in the direction of maximum tensile stress 1. This segment produces stepped fracture surfaces with characteristic "spear " marks observed in a wide range of Engineering 2, 3, 4, 5, 6, 7 and geological materials 1 and 8. The origin of this instability is still poorly understood, and there is a lack of theory to predict the scale of surface roughness. Here, we conduct large-scale simulation of mixed mode I   +   III using continuous medium for brittle fracturese-field method9,10,11 that describes the complete three-dimensional crack-front evolution. The simulations reveal that planar crack propagation is linearly unstable against helical deformations of the crack front, which evolve nonlinearly into a segmented array of finger-shaped daughter cracks. Furthermore, during their evolution, facets gradually coarsen owing to the growth competition of daughter cracks in striking analogy with the coarsening of finger patterns observed in nonequilibrium growth phenomena12,13,14. We show that the dynamically preferred unstable wavelength is governed by the balance of the destabilizing effect of far-field stresses and the stabilizing effect of cohesive forces on the process zone scale, and we derive a theoretical estimate for this scale using a new propagation law for curved cracks in three dimensions. The rotation angles of coarsened facets are also compared to theoretical predictions and available experimental data.

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