Influence of heterogeneities on crack propagation

Abstract

The influence of material heterogeneities is studied in the context of dynamic failure. We consider a pre-strained plate problem, the homogeneous case of which has been widely studied both experimentally and numerically. This setup is used to isolate the effects of the elastic field resulting from pre-straining and stress wave interactions throughout the crack propagation by adding stiffer and denser regions in the plate. While the crack tip is pushed away by stiffer inclusions, it is attracted to the denser ones. With the presence of denser media, only a portion of the total elastic energy in the system is effectively used to drive crack propagation, leading to a drop in the velocity of its tip in comparison to the homogeneous case. The crack velocity is shown to be an invalid criterion for crack branching. Instead, we introduce an effective stored energy to analyze the crack velocity and the emergence of crack branching instabilities.

Offsetting Losses: Bargaining Power and Rebel Attacks on Peacekeepers

“…The phase field method can be straightforwardly extended to dynamics, which has been shown by, primarily, Bourdin, Larsen and Richardson [36,37] who proved the existence and convergence of solutions to dynamic phase field problems for fracture, as well as [2,38,39]. Especially interesting in relation to the current work are the works of Bleyer et al [3], Ylmaz et al [4] and Kuhn and Müller [40]. While our approach to evaluate energy release rate directly from dissipated energy is similar to that of the former two, the latter uses an equivalent concept of the near-field -integral, , tip which is evaluated in a contour around the crack tip [40].…”

“…One of the most debated is the choice of the strain energy split (Eqs. (4) and (5)). In the split we have used, damage evolution is driven by tensile strain-related energy.…”

“…A striking example is that crack propagation velocities close to or even above the Rayleigh velocity (c R ) have been observed, both experimentally and numerically, in materials with a weak zone embedded in an otherwise homogeneous material [1][2][3]. Previous studies suggest that crack dynamics is primarily governed by the amount and distribution of energy, and the rate at which this energy can be released [3,4]. Elastic heterogeneities, primarily variations in local Young's moduli, affect the strain energy distribution and influence the crack path by either attracting or repelling a crack.…”

“…Elastic heterogeneities, primarily variations in local Young's moduli, affect the strain energy distribution and influence the crack path by either attracting or repelling a crack. Dynamic heterogeneities, which include variations in both local density and local stiffness, affect the dynamic response and wave propagation velocities of the material, and can influence the kinetic energy distribution in a specimen, which in turn influences the crack dynamics [4].…”

Experimental and numerical study of the interaction between dynamically loaded cracks and pre-existing flaws in edge loaded PMMA specimens

“…Dynamic crack growth in brittle materials is largely dominated by the interaction of the growing crack with pre-existing flaws, such as voids and micro-cracks, as well as their evolution under the applied load and the interactions among them [1,2]. The interaction of the waves radiating from the propagating crack tip with existing heterogeneities makes the dynamic fracture process highly sensitive to variations in the local microstructure [2][3][4][5][6][7]. Having an understanding of the interaction of the growing crack with its surroundings may assist in developing a better design scheme considering energy dissipation, directional strength, and control of the fracture path.…”