45475-AC10
Statistical Theories of Failure in Polycrystalline Materials
The corrosion resistance and mechanical properties of many polycrystalline metals can be significantly enhanced by grain boundary engineering. Of particular relevance to this work is the experimental observation, originally by Wells et al., that the onset of a percolating path of weak grain boundaries may be implicated in a marked degradation of corrosion resistance. Our work focused upon developing more realistic models of grain boundary networks and on calculating the degree of grain boundary engineering required to terminate percolation of weak grain boundaries. A second focus of the analysis was the fracture surfaces of grain boundary engineered materials, which have been measured by Professor Reed using confocal microscopy. These surfaces were approximated by the minimum cut in our fully constrained polygrain models and the transition from intergranular to mixed mode fracture was monitored as a function of the extent of grain boundary engineering.
We used the group theory method developed in the Dr Reed’s group to impose full grain boundary constraints on polygrain models generated using the Potts model. Our previous work showed that uncorrelated film grain structures require a length fraction of 0.38(2) of special boundaries (which we take to be sigma 3,9,27) to terminate weak boundary percolation. In this work we found that grain boundary constraint raises this fraction to 0.55(5). This means that a significantly higher number of special boundaries is required to terminate percolation than would be suggested by random percolation processes. This is due to the strong triple junction correlations which occur due to grain boundary constraints, as has been demonstrated in earlier experimental and theoretical studies. The behaviors of the energy, roughness and weak grain boundary fraction of the minimum energy surface were analysed as a function of the degree of grain boundary engineering. These behaviors appear to be quite different than that of the uncorrelated grain boundary network and seem to indicate a change in the universality class due to grain boundary constraint. Larger scale calculations are under way to test this possibility and a paper presenting our results has appeared and two more are in preparation. The graduate student supported by the grant, Kim McGarrity, will complete her thesis during Fall 2009. Her work has concentrated on two dimensional models and extensions to fully constrained three dimensional models are planned.
