Predicting the available work from deformation-induced α′′ martensite formation in metastable β Ti alloys

Deformation-induced α′′ martensite formation is essential to the mechanical properties of a variety of metastable β Ti alloys by extending elasticity or contributing to work-hardening during plastic deformation. Nevertheless, to date, a comprehensive analysis of the effect of β texture and applied stress state on the martensitic transformation to α′′ is still lacking. The present study therefore provides a detailed analysis of the work which is made available from the shape strain of the martensitic transformation under a variety of in-plane stress states and as a function of β crystal orientation. The available work was found to strongly depend on the applied stress state and the parent grain orientation. The shape strain of the martensitic transformation was obtained from applying the phenomenological theory of martensite crystallography. In cases where this theory was not applicable, an approximation of the shape strain by the Bain strain was found to provide a good approximation of the available work. Analysis of three different metastable β Ti alloys showed no strong effect of the alloy composition on the available work. Martensite formation from typical cold- and warm-rolling β texture components under different stress states is discussed. Cases are highlighted to show how the cold- and warm-rolling β textures can be tailored to hinder martensite formation upon subsequent industrial forming operations.

Optimality of general lattice transformations with applications to the Bain strain in steel

This article provides a rigorous proof of a conjecture by E. C. Bain in 1924 on the optimality of the so-called Bain strain based on a criterion of least atomic movement. A general framework that explores several such optimality criteria is introduced and employed to show the existence of optimal transformations between any two Bravais lattices. A precise algorithm and a graphical user interface to determine this optimal transformation is provided. Apart from the Bain conjecture concerning the transformation from face-centred cubic to body-centred cubic, applications include the face-centred cubic to body-centred tetragonal transition as well as the transformation between two triclinic phases of terephthalic acid.