Material-independent crack arrest statistics. (English) Zbl 1065.74059
Summary: The propagation of (planar) cracks in a heterogeneous brittle material characterized by a random field of toughness is considered, taking into account explicitly the effect of the crack front roughness on the local stress intensity factor. In the so-called strong-pinning regime, the onset of crack propagation appears to map onto a second-order phase transition characterized by universal critical exponents which are independent of the local characteristics of the medium. Propagation over large distances can be described by using a simple one-dimensional model, with a correlation length and an effective macroscopic toughness distribution that scale in a non-trivial fashion with the crack front length. As an application of the above concepts, the arrest of indentation cracks is addressed, and an analytical expression for the statistical distribution of crack radii at arrest is derived. The analysis of indentation crack radii on alumina is shown to obey the predicted algebraic expression for the radius distribution and its dependence on the indentation load.
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