Roughness of tensile crack fronts in heterogenous materi - als

– The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent ζ = 1/2, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for ζ. Introduction. – The dynamics of cracks in heterogeneous media is a rich field encompassing a large range of physical phenomena. In such situations a commonly studied quantity is the so called roughness exponent ζ. However, it is important to distinguish at least three different roughness exponents [1]: one describing the roughness in the direction perpendicular to the crack propagation, a second the roughness in the direction of the propagation, and a third one (which will interest us in the following) describing the in-plane roughness of the crack front during its propagation through the material. The exponent characterizing this in-plane roughness, has been measured in different materials, where it was found to be in the range 0.5–0.6, over at least two decades [2, 3]. Despite numerous efforts [4–6], there is unfortunately no satisfactory theory that predicts the value of this exponent. In this paper we intend to contribute to the theoretical understanding of this problem. For that purpose we use an equation of motion of the crack front h(x) derived previously [7]. This equation contains two important ingredients-irreversibility of the propagation of the crack front and nonlinear effects. It is given by