Finite size and geometrical non-linear effects during crack pinning by heterogeneities: An analytical and experimental study

Abstract

Crack pinning by heterogeneities is a central toughening mechanism in the failure of brittle materials. So far, most analytical explorations of the crack front deformation arising from spatial variations of fracture properties have been restricted to weak toughness contrasts using first order approximation and to defects of small dimensions with respect to the sample size. In this work, we investigate the non-linear effects arising from larger toughness contrasts by extending the approximation to the second order, while taking into account the finite sample thickness. Our calculations predict the evolution of a planar crack lying on the mid-plane of a plate as a function of the material parameters and the loading conditions, especially in the case of a single infinitely elongated obstacle. Peeling experiments are presented which validate the approach and evidence that the second order term broadens its range of validity in terms of toughness contrast values. The work highlights the non-linear response of the crack front to strong defects and the central role played by the thickness of the specimen on the pinning process.

Nonlinear Focusing in Dynamic Crack Fronts and the Microbranching Transition

“…Taking f to be time-independent and v → 0, Eq. (2) recovers, in the limit f /l → 0, the corrections to G calculated for quasistatic crack fronts [37]. On the other hand, assuming that f does not depend on z, the history functional is identically zero, and Eq.…”

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

“…The role of heterogeneities in dynamic fracture processes is studied across various length scales, ranging from kilometres for earthquakes [20,35], to millimetres for composite plates [71] or heterogeneous thin films [64] or even to nanometres in metallic glasses [48]. Heterogeneities can have a complex influence on a crack propagation by nucleating daughter cracks or exhibit a transition from weak to strong pinning regime [50].…”

Topological defects govern crack front motion and facet formation on broken surfaces

“…For a localized 𝛿𝐴, Eq. (1) produces a locally concave profile with long-range logarithmic tails, as seen when interfacial crack fronts encounter a tough strip [27][28][29] . We find that front deformation due to a step at 𝑧 = is well-described by the asymmetric profile…”