Interior Nucleation of Martensite in a Cubic-to-Tetragonal Phase Transformation

Abstract

Using a variational model based on non-linear elasticity we investigate whether in a cubic-to-tetragonal phase transformation it is energetically preferable to nucleate martensite within austenite. Under minimal growth assumptions on the free energy density W away from the wells, we derive explicit upper bounds on W qc (I), i.e. on the macroscopic free energy density of a region that has been macroscopically deformed by the identity map. The bounds only depend on material parameters, the temperature difference and the growth of W away from the wells. By comparing W qc (I) and W (I) we conclude that nucleation is always energetically preferable and are able to provide quantitative upper bounds for the gain in negative energy due to nucleation. MSC (2010): 74A50, 74N05, 74N15

Measurement of martensitic packet size by EBSD in the high strength steel X38CrMoV5-1 and estimation of its influence on cleavage fracture

“…Once martensite nucleates it is well known that its length grows at rates near to the speed of sound. Thus the relationship between the thickness and length of martensite laths remains almost constant [17], and their growth is halted by the plastic deformation produced during the transformation. The calculated values of between 0.59 and 0.68 µm for the martensitic crystallographic unit are a little higher than the average width of martensite laths, about 0.30 µm measured by optical microscopy.…”

Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

“…Another approach is based on the average gradients which can be obtained mixing the martensitic variants [17]. Interior nucleation with incompatibilities was addressed in [18,19]. Nucleation with branched microstructures was considered in [20].…”