Fig. 1: A schematic of the feasible phase transformation domains in stress-space.

a Three dimensional principal stress-space represented by the σ₁, σ₂, and σ₃ principal stress axes (σ₁ = σ₂ = σ₃ is the p-axis, deviatoric planes are perpendicular to this axis). Panels b, c show envelopes outside of which α and β flow (yield) on a particular deviatoric plane. The axes \({\sigma }_{1}^{\prime},{\sigma }_{2}^{\prime}\) and \({\sigma }_{3}^{\prime}\) are projections of stress-space axes σ₁, σ₂, and σ₃ onto the deviatoric plane. As the material is strengthened, the yield envelopes, \({\sigma }_{{{{{{{{\rm{y}}}}}}}}}^{\alpha }\) and \({\sigma }_{{{{{{{{\rm{y}}}}}}}}}^{\beta }\), expand towards the theoretical strength limits \({\sigma }_{{{{{{{{\rm{y}}}}}}}},{{{{{{{\rm{th}}}}}}}}}^{\alpha }\) and \({\sigma }_{{{{{{{{\rm{y}}}}}}}},{{{{{{{\rm{th}}}}}}}}}^{\beta }\). d Stress-space regions for which α → β PTs are feasible (shaded light green). The PT onset boundary is shown in dark green.