  The mechanical properties of a material are intimately related to its
microstructure. This is particularly important for predicting mechanical
behavior of polycrystalline metals, where microstructural variations dictate
the expected material strength. Until now, the lack of microstructural
variability in available datasets precluded the development of robust
physics-based theoretical models that account for randomness of
microstructures. To address this, we have developed a probabilistic machine
learning framework to predict the flow stress as a function of variations in
the microstructural features. In this framework, we first generated an
extensive database of flow stress for a set of over a million randomly sampled
microstructural features, and then applied a combination of mixture models and
neural networks on the generated database to quantify the flow stress
distribution and the relative importance of microstructural features. The
results show excellent agreement with experiments and demonstrate that across a
wide range of grain size, the conventional Hall-Petch relationship is
statistically valid for correlating the strength to the average grain size and
its comparative importance versus other microstructural features. This work
demonstrates the power of the machine-learning based probabilistic approach for
predicting polycrystalline strength, directly accounting for microstructural
variations, resulting in a tool to guide the design of polycrystalline metallic
materials with superior strength, and a method for overcoming sparse data
limitations.
