Dislocation-obstacle interactions are established as an effective strengthening mechanism within metallic materials. Several example material systems include Mg and Al alloys as well as those found in nuclear reactors. In each of these systems, the unit process governing material strength is the bypass of obstacles by dislocation glide; in this process the inverse of the spacing between obstacles sets the material strength. On the mesoscale, spatial distributions of obstacles in alloy systems is known to be stochastic in nature. Since alloy strengthening scales inversely with obstacle spacing, a spatial distribution of obstacles yields a statistical distribution of strengths.
The objective of this talk is to elucidate relations between planar obstacle density (ρ), size (D), and alloy strength (τcrit). To this end, we present high-throughput statistical simulations of dislocation-obstacle bypass for randomly generated spatial distributions of obstacles. We demonstrate a probabilistic interpretation of the results by treating τcrit as a random variable with an associated distribution function. We further develop a weakest link type statistical analysis in which the key quantity is the spatial distribution of link lengths between obstacles. Through our results and analysis, we find that both the expectation and standard deviation of τcrit approximately scale with ∼ sqrt(ρ) ln(D). Our analysis corroborates our simulations and unifies similar studies found in the literature.