A Phase-Field Model for the Formation of Martensite and Bainite

Abstract

The phase field method is rapidly becoming the method of choice for simulating the evolution of solid state phase transformations in materials science. Within this area there are transformations primarily concerned with diffusion and those that have a displacive nature. There has been extensive work focussed upon applying the phase field method to diffusive transformations leaving much desired for models that can incorporate displacive transformations. Using the current model, the formation of martensite, which is formed via a displacive transformation, is simulated. The existence of a transformation matrix in the free energy expression along with cubic symmetry operations enables the reproduction of the 24 grain variants of martensite. Furthermore, upon consideration of the chemical free energy term, the model is able to utilise both the displacive and diffusive aspects of bainite formation, reproducing the autocatalytic nucleation process for multiple sheaves using a single phase field variable. Transformation matrices are available for many steels, one of which is used within the model.

Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation, and Experimentation

“…On the other hand, global temperature distributions provided by macroscopic continuum models represent essential input variables for studying the solidification process by means of microstructure models. So-called phase field models based on various spatial and temporal discretization strategies can be considered as one of the most established modeling approaches to study solidification processes [155,41,96,25,142,3,54,89,123,152] but also diffusionless solid-solid phase transformations occurring for example during the formation of martensitic non-equilibrium phases [118,5].…”

Atomic Mechanism of the Bainite Transformation

“…High resolution transmission electron microscopy has shown that the bainite-austenite interface is in reality sharp, less than 1 nm in thickness [24][25][26]. The treatment of the strain energy due to the shape deformation is either absent [20,21] or has been implemented incorrectly with shear occurring in all directions within the habit plane [22,23]. When the shape deformation is neglected, the plate shape is generated by an arbitrary anisotropy of interfacial energy; this procedure amounts to image generation rather than a physical representation.…”

“…A coherency dislocation that can climb conservatively while accomplishing lattice transformation, adapted from [15]. The inset at the right is the representation of the coherency dislocation in a manner analogous to ordinary dislocations that have extra half-planes The first issue is particularly prevalent in phase field models of bainite where the parent, product and interface are all represented in terms of an order parameter; the interface is therefore diffuse [20][21][22][23]. Both, the definition of how the free energy density varies across the boundary and the assumption of particular systematic gradients within the diffuse interface are arbitrary.…”