Roughness effects on the critical fracture toughness of materials under uniaxial stress

The Griffith criterion is applied for the calculation of the critical fracture toughness upon which the formation of a rough self-affine crack (which is characterized by the rms roughness amplitude a, the correlation length xi, and the roughness exponent H) commences. For large crack sizes R much greater than xi, the stress field singularity close to the crack tip involves the value -1/2 in both the strong and weak roughness Limit. In the latter Limit, the fracture toughness K remains close to the classical value K approximate to 2(gamma E)(1/2) with gamma the surface tension and E the Young modulus, while in the strong roughness limit it becomes significantly large [>2(gamma E)1/2] following the asymptotic behavior K approximate to 2(gamma E)(1/2) (sigma/E-H)(1/2). (C) 1998 American Institute of Physics.