The effect of loading rate on ductile fracture toughness and fracture surface roughness

The variation of ductile crack growth resistance and fracture surface roughness with loading rate is modeled under mode I plane strain, small scale yielding conditions. Three-dimensional calculations are carried out using an elastic–viscoplastic constitutive relation for a progressively cavitating solid with two populations of void nucleating second phase particles. Larger inclusions that result in void nucleation at an early stage are modeled as discrete void nucleation sites while smaller particles that require large strains to nucleate voids are homogeneously distributed. The calculations are carried out for two values of density of the larger inclusions, 3.6% and 7.1%, and for prescribed loading rates K̇̇I ranging from 1×105MPams−1 to 5×107MPams−1. The ductile fracture mode is found to undergo a transition from one that can be regarded as growth of a dominant main crack at the lower loading rates to one dominated by damage nucleation and micro-cracking ahead of the main crack at the higher loading rates. The values of JIC, the tearing modulus, TR, the total plastic dissipation and the plastic dissipation in the fracture process region are all found to increase with increasing loading rate. However, the ratio of plastic dissipation in the fracture process region to total plastic dissipation decreases with increasing prescribed loading rate. The fracture surfaces are found to display two self-affine regimes, with a Hurst exponent β≈0.60 at small length scales and with β≈0.45 at larger length scales. The multi-fractal spectra indicate multi-affine behavior in most cases but a range of loading rates and length scales exhibiting mono-affine behavior is also found. Parameters characterizing the fracture surface statistics, including the length scale at which a transition from a power law tail to an exponential tail occurs, are related to the mode of crack growth/damage accumulation. A linear relation is found between the values of JIC and TR and the saturation value of the correlation function of the surface roughness for K̇̇I<3×107MPams−1.