Onset of Propagation of Planar Cracks in Heterogeneous Media

TL;DR

This paper investigates the critical dynamics of planar crack fronts in heterogeneous media, revealing a second-order transition at critical load and the effects of elastic wave delays and overshoots on crack propagation behavior.

Contribution

It provides a comprehensive analysis of crack front dynamics near criticality, including the effects of elastic waves and overshoots, and introduces simplified models to explain observed phenomena.

Findings

Crack front exhibits a second-order phase transition at critical load.

At criticality, the crack front is self-affine with a roughness exponent of approximately 0.34.

Elastic wave delays do not alter static exponents but affect the dynamic exponent, leading to a transition from continuous to apparent first-order behavior.

Abstract

The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along the crack front which is non-monotonic in time due to the elastic waves in the medium. In the quasistatic limit with instantaneous stress transfer, the crack front exhibits dynamic critical phenomenon, with a second order like transition from a pinned to a moving phase as the applied load is increased through a critical value. At criticality, the crack-front is self-affine, with a roughness exponent $\zeta =0.34\pm 0.02$. The dynamic exponent $z$ is found to be equal to $ 0.74\pm 0.03$ and the correlation length exponent $\nu =1.52\pm 0.02$. These results are in good agreement with those obtained from an epsilon expansion. Sound-travel time delays in the stress transfer do not change the static exponents but the dynamic exponent $z$ becomes exactly one. Real elastic waves, however, lead to overshoots in the stresses above their eventual static value when one part of the crack front moves forward. Simplified models of these stress overshoots are used to show that overshoots are relevant at the depinning transition leading to a decrease in the critical load and an apparent jump in the velocity of the crack front directly to a non-zero value. In finite systems, the velocity also shows hysteretic behaviour as a function of the loading. These results suggest a first order like transition. Possible implications for real tensile cracks are discussed.