On a mathematical theory for the crystallography of shear transformations in metals: Unification of mechanisms

Abstract

A theory for shear transformations in crystalline materials linking their Crystallography, atomic-scale mechanisms and Thermodynamics is introduced. The lattice and transformation function are treated as vector space and functions respectively to overcome shortcomings of classical matrix-based theories for martensite crystallography. The extremum principle is used to obtain the atomic paths minimising and maximising the energy from all possible solutions, therefore explaining which sequences are more Thermodynamically feasible. The face-centred cubic (FCC)→body-centred cubic (BCC) transformation in Fe is used as case study. The theory predicts that the average values of the extrema correspond to the crystallography, shear magnitude, interface defects and habit planes of main transformations in Fe, i.e. Widmanstätten Ferrite, Bainite, lath martensite, plate and lenticular martensite. Bainite represents the macroscopic average minimum energy configuration, whereas Widmanstätten Ferrite corresponds to a local and discrete minimum energy configuration. Lath martensite corresponds to the average shear configurations minimising atomic displacements when there is no other driving force, e.g. diffusion, whereas the maximum energy configurations correspond to plate and lenticular martensite forming twin pairs. Targeted results for the FCC→hexagonal close-packed lattice transformation are presented to demonstrate the robustness of the theory. The predictions are combined with elasticity theory to compute the Driving Force and predict the start temperatures – therefore connecting for the first time – local and macroscopic crystallographic features with the Thermodynamics of shear-controlled structures in Fe. This work presents new results towards addressing longstanding challenges in Materials Science such as theoretically demonstrating that Bainite is a shear transformation.