Abstract
Allotropic phase transformations may be driven by the application of stresses in many materials; this has been especially well-documented for pressure driven transformations. Recent advances in strengthening materials allow for the application of very large shear stresses as well - opening up vast new regions of stress space. This means that the stress space is six-dimensional (rather than one for pressure) and that phase transformations depend upon crystal/grain orientation. We propose a novel approach for predicting the role of the entire stress tensor on phase transformations in grains of all orientations in any material. This multiscale approach is density functional theory based and guided by nonlinear elasticity. We focus on stress tensor dependent allotropic phase transformations in iron at high pressure and ultra-fine grained nickel and titanium. The results are quantitatively consistent with a range of experimental observations in these disparate systems. This approach enables the balanced design of high strength-high ductility materials.