Dissipated Energy at a Bimaterial Crack Tip Under Cyclic Loading

by Daily, Jeremy S

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This, and previous energy-based approaches in the literature, suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. The goal of the current research is to extend the dissipated energy approach to steady-state crack growth under mixed-mode I/II loading conditions, with application to cyclic delamination of ductile bimaterial interfaces. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. The total plastic dissipation per cycle is obtained by 2-D elastic-plastic finite element analysis of a stationary crack in a general mixed-mode specimen geometry under constant amplitude loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material. Results extended to general elastic-plastic mismatches provide substantial insight into the effects of crack-tip constraint, material hardening behavior and applied mode-mix ratio on the dissipated energy during fatigue crack growth. A consistent definition of the mode mix ratio is presented based on minimizing the elastic strain energy at a crack tip. Next, application of the current theory is demonstrated for thermomechanical fatigue of bonded bimaterials. Finally, the plastic dissipation computations are erformed in a probabilistic framework in an attempt to assess the variability of the fatigue crack growth rate based on variation in bulk properties.