More Complete Theory for the Calculation of the Martensite-Start Temperature in Steels

The vital breakthrough in accounting for the influence of chemical composition on the martensite–start temperature (MS) came some 50 years ago1–4) when it was identified that the free energy change for the transformation of austenite to martensite must reach a critical value at the martensite–start temperature (MS). Subsequent refinements included, for example, accounting for the Zener ordering of carbon atoms5) and solid solution strengthening in rich alloys of iron6,7) but the basic principle remains the same as in the pioneering work, based on . The ability to calculate MS has acquired renewed importance in the context of a large variety of steels, both commercial and experimental, which rely on transformation–induced plasticity, or which deal with ultra–fine austenite.8–11) In the latter case, the localised islands or films of austenite are stabilised to martensitic transformation due to their small scale, or when parent austenite is created in a highly refined state by processes such as severe plastic deformation. Although the influence of applied stress in the elastic regime has been established since the days of Patel and Cohen in terms of a mechanical driving force which supplements the chemical term,12) many modern experiments are concerned with the transformation of austenite during straining well beyond its yield strength.13,14) This has caused considerable confusion in the literature since both stress and plastic strain are applied simultaneously, but most refer to this simply as “strain–induced transformation”. Tamura and co–workers15) pointed out that many of the observations could be explained on the basis of stress alone, even when the deformation is plastic. Several recent studies support this contention, that so–called strain–induced martensite in studies where stress and strain have been applied simultaneously, can be explained on the basis of stress alone.16–21) Indeed, transformation textures for displacive products can often be explained on the basis of variant selection due to stress alone.22) There have been limited experiments in which the effect of strain alone was studied. In an elegant study23) of pre–deformed single crystals of austenite, transformed on cooling to martensite, where variant selection occurred due to the anisotropic nature of the dislocation debris. However, such anisotropy should be reduced in polycrystalline samples where multiple slip should operate,24) and experiments on bainite growing in pre–strained austenite failed to reveal variant selection. However, there are two special effects of large plastic strains that cannot be neglected. The scale of the austenite grain structure defined in terms of a mean lineal intercept is changed by the deformation. Secondly, the introduction of dislocation debris can mechanically stabilise the austenite.8,25–30) Mechanical stabilisation occurs because the movement of glissile martensite-austenite interfaces is hindered by the dislocation debris, and can lead to a complete cessation of transformation. The phenomenon has recently been quantitatively expressed.31) The aim of the present work was to create a model for the martensite–start temperature which takes all of the effects described above into account. It is emphasised that the individual and validated components of such a model already exist in the literature; the present work represents a hopefully useful consolidation of theory.