Statistics of ductile fracture surfaces: the effect of material parameters

Abstract

The effect of material parameters on the statistics of fracture surfaces is analyzed under small scale yielding conditions. Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid with two populations of void nucleating second phase particles represented. Large particles that result in void nucleation at an early stage are modeled discretely while small particles that require large strains to nucleate are homogeneously distributed. The three dimensional analysis permits modeling of a three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. Material parameters characterizing void nucleation are varied and the statistics of the resulting fracture surfaces is investigated. All the fracture surfaces are found to be self-affine over a size range of about two orders of magnitude with a very similar roughness exponent of $0.56\,\pm \,0.03$. In contrast, the full statistics of the fracture surfaces is found to be more sensitive to the material microscopic fracture properties: height fluctuations are shown to crossover from a Student’s distribution with power law tails at small scales to a Gaussian behavior at large scales, but this transition occurs at a material dependent length scale. Using the family of Student’s distributions, this transition can be described introducing an additional exponent $\mu = 0.15\,\pm \,0.02$, the value of which compares well with recent experimental findings. The description of the roughness distribution used here gives a more complete quantitative characterization of the fracture surface morphology which allows a better comparison with experimental data and an easier interpretation of the roughness properties in terms of microscopic failure mechanisms.