Cracking solids

The fracturing of brittle solids using lattice models yields complex crack shapes due to the disorder in the material.

The figure shows a hydraulic crack produced with Frank Tzschichholz. The stress distribution is visualized by birefingence patterns numerically obtained from the eigenvalues of the tensor. For more detail see our paper in Phys. Rev. B, Vol.49, p.7056-7059 (1994). In a further work published in Physica Review E, Vol.51, p. 1961-1970 (1995) we obtained the pressure fluctuations and acoustic emission signals in a two-dimensional hydraulic crack.

With Stephane Roux we edited in 1990 a book about fracture of heterogenoeus materials entitled: "Statistical Models for the Fracture of Disordered Media" which appeared in North Holland. In this book you find the following article which reviews the scaling laws we discovered for the brittle failure of heterogeneous solids. The original article on the scaling of beam networks (with Alex Hansen) was published in Phys. Rev. B, Vol.39, p.637-648 (1989) and on scalar networks including Lucilla de Arcangelis was published in Phys. Rev. B, Vol.40, p.877-880 (1989).

With Janos Kertesz and Lucilla de Arcangelis I was able to find fractal cracks obtained under shear even without heterogeneities as published in Europhys. Lett., Vol.10, p.147-152 (1989) by considering at the crack surface the accumulation of damage. More details about this are given in a proceedings of a meeting in Erice 1988 published by Plenum Press were in particular the application to corrosion stress cracking. In fact with Victor Horwath we did measure the fractal dimension of experimental corrosion cracks as published in Chaos, Solitons and Fractals, Vol.1, p.395-400 (1992).

With Janos Kertesz I also studied the stability of a circular hole in a stretched membrane using linear stability analysis as published in Physica A, Vol.178, p.409-412 (1991).

In various occasions I reviewed the above works on fractures as for example in the colourful book on Fractals edited by Armin Bunde and Shlomo Havlin (Springer, 1991) or in an article published in Physica A, Vol.221, p.125-133 (1995).