Quasi-Static Cracks and Minimal Energy Surfaces

We compare the roughness of minimal energy(ME) surfaces and scalar "quasi-static" fracture surfaces(SQF). Two dimensional ME and SQF surfaces have the same roughness scaling, w ¸ L i (L is system size) with i = 2=3. The 3-d ME and SQF results at strong disorder are consistent with the randombond Ising exponent i(d 3) ß 0:21(5 \Gamma d) (d is bulk dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger prefactor. ME surfaces undergo a "weakly rough" to "algebraically rough" transition in 3-d, suggesting a similar behavior in fracture. 62.20.Mk, 03.40.Dz, 46.30.Nz, 81.40.Np Typeset using REVT E X Current address Fracture [1] continues to attract the attention of the materials theory community, with the full spectrum of theoretical tools currently being applied to its analysis [1--6]. Cracks are usually self-affine and their roughness can be characterised by a roughness exponent (i), which may take on a few distinct values [7--9](here we calculate the "out-of-..