Tag Archives: FEM

Phase transformations

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.

Distribution of martensite (blue is austenite, red is martensite) in an austenitic metal sheet at three stages during a deep-drawing process at 213K.
Distribution of martensite (blue is austenite, red is martensite) in an austenitic metal sheet at three stages during a deep-drawing process at 213K.

Specifically, the latter kind of materials, undergoing microstructural changes in terms of austenite-martensite transformation, have in recent years gained increasing attention in relation to shape memory alloys (SMAs) and alloys exhibiting transformation-induced plasticity (TRIP steels).

Description of phase transformations is further involved due to the strong temperature-dependence of the process. Combined with significant differences in mechanical properties between the phases and the volumetric deformations accompanying e.g. martensitic phase transformations, strongly thermo-mechanically coupled phenomena arise.

The presence of martensite also changes the fracture behavior of a material since the martensite is considerably harder than the more ductile austenite parent phase. This influences e.g. initiation and propagation of crack and may become detrimental to metal forming and forging processes.

Continuum scale modeling of recrystallization

Adopting a continuum mechanical approach, recrystallization can be modeled using an internal variable representation of the pertaining quantities, such as the average grain size and the dislocation density. The macro-scale material behavior will in this way be based on parameters related to the evolving microstructure.

An example of continuum-scale modeling and simulation of ECAP-processing of Aluminum is given in Hallberg et al. (2010). Some results on the distributions of grain size and dislocation density in the work piece are shown in the figures below.

Results from simulations of ECAP-processing. The top figure shows the distribution of average grain size after and two ECAP-passes, respectively. The bottom figure shows the distribution of normalized dislocation density, also after one and two ECAP-passes, respectively. Note that after two passes, both grain size and dislocation density remain at relatively constant levels all through the specimen along the indicated lines.

Results from simulations of ECAP-processing. The top figure shows the distribution of average grain size after and two ECAP-passes, respectively. The bottom figure shows the distribution of normalized dislocation density, also after one and two ECAP-passes, respectively. Note that after two passes, both grain size and dislocation density remain at relatively constant levels all through the specimen along the indicated lines.
Results from simulations of ECAP-processing. The top figure shows the distribution of average grain size after and two ECAP-passes, respectively. The bottom figure shows the distribution of normalized dislocation density, also after one and two ECAP-passes, respectively. Note that after two passes, both grain size and dislocation density remain at relatively constant levels all through the specimen along the indicated lines.

 

Animation showing a 2D level set simulation of Dynamic Discontinuous Recrystallization (DDRX)

A simple 2D simulation of dynamic discontinuous recrystallization (DDRX) in pure Cu at an elevated temperature. The simulation is based on level sets in a finite element setting. Adaptive remeshing is performed in each step. The animation speed is increased compared to actual time.