Modeling of Martensitic Phase Transformation

Phase transformations in metallic materials have a major impact on vital engineering aspects of the material behavior such as ductility, strength and formability. Some phase transformations, such as the formation of pearlite and bainite, occur through diffusion-based processes where the constituents in the microstructure are redistributed. Being based on diffusion, these kinds of phase transformations tend to be relatively slow. On the other hand, phase transformations can also proceed by pure displacements in the crystal lattice structure. This is typical for the very rapid and diffusionless formation of martensite in austenitic steels by martensitic phase transformation.

A phenomenological model of martensitic phase transformation

Taking a continuum-mechanical perspective, a phenomenological finite strain plasticity model is established, treating the volume fraction of martensite as an internal variable. Along with a transformation condition, dependent on the state of deformation and on temperature, this allows the evolution of the martensitic phase to be traced. The presence of a transformation condition allows establishment of a transformation potential surface, much like the yield condition and yield surface found in plasticity theory.

Transformation surface in the deviatoric and meridian planes, an central part of the model of martensitic phase transformation
Transformation surface in deviatoric stress space and in the meridian plane.

Depending on which one is active, the yield and transformation conditions determine the response of the material. The relative influence of austenite and martensite on mechanical material properties is considered through a homogenization procedure, based on the phase fractions.

Extensions and applications of the phase transformation model

The original model has been extended in several steps, for example taking full thermo-mechanical coupling and high strain rate deformation into consideration. The model is suitable for large-scale simulations of metal forming processes involving materials exposed to martensitic phase transformation. It has been employed in studies of, for example, metal forming, surface treatment by laser peening and fracture.

Zones at the crack tip exposed to martensitic phase transformation
Transformation zones in the near vicinity of a crack tip.

Simulation of Martensitic Phase Transformation under Laser Shock Peening

In laser shock peening (LSP), the surface of the work piece is covered with an ablative layer which may consist of a layer of black paint or a metallic foil. A laser beam – typically with an intensity in the range between 1 GW/cm2 and 20 GW/cm2 – is focused on the peening region, causing the ablative layer to vaporize. The temperature of the vaporized material increase very rapidly to temperatures in the order of 10 000K which results in ionization and plasma formation. The laser pulse is usually very short (3-30 ns) and the plasma continues to absorb the laser energy during the duration of the pulse. The temperature increase in the plasma gives rise to a hydrodynamic pressure shock wave which propagates into the work piece. The LSP process can provide a pressure of up to 10 GPa in a spot measuring a few millimeters in radius. The pressure wave propagates into the work piece and cause plastic deformations and in some cases also martensitic phase transformation. Following peening, relaxation takes place during which residual compressive stresses develop. These compressive stresses provide the desired improvement of wear, fatigue and corrosion resistance of the work piece surface.

Project and collaborators

The project employs numerical simulations to study the residual stresses which develop due to plastic deformation and martensitic phase transformation during LSP and is a collaboration with researchers at the University of Ljubljana.