Solid Mechanics

Faculty of Engineering, LTH

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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.

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.


Internal variable-modeling of martensitic phase transformation

Taking a continuum-mechanical perspective, the isothermal model in [1] introduces the volume fraction of martensite, denoted by z, 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. The transformation surface is illustrated in deviatoric stress space and in the meridian plane below. 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.

The isothermal model in [1] is further elaborated in [2], where full thermo-mechanical coupling is considered. The models in [1,2] are suitable for large-scale simulations of metal forming processes involving materials exposed to martensitic phase transformation. The application to sheet metal forming is illustrated below by images from simulations of a deep-drawing process.

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The transformation surface in deviatoric stress space (left) and in the meridian plane (right), respectively.
Volume fraction of martensite in a stainless steel sheet during deep-drawing at different temperatures. Note that three different drawing stages are shown at each temperature. a) 213K, b) 233K, c) 293K and d) 313K.

Martensitic phase transformation and fracture

As the relatively ductile austenite phase is transformed in to harder and more brittle martensite in the vicinity stress-concentrations, the material conditions change and also the conditions for crack formation and propagation. Fatigue fracture can be considerably influenced by this kind of diffusionless phase transformation due to the higher fracture strength of martensite, compared to that of austenite. In [3,4] the influence of martensite formation on fracture behavior and crack tip conditions is investigated, as illustrated below.

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Distribution of martensite in the vicinity of the notch in a 3-point bending specimen.
Transformed zone at a crack tip, located at the coordinates (0,0), at two temperatures. Results obtained from FE-simulations. The individual contour curves correspond to different load levels.


  1. A constitutive model for the formation of martensite in austenitic steels under large strain plasticity, Håkan Hallberg, Paul Håkansson and Matti Ristinmaa, International Journal of Plasticity (2007), 23, 1213-1239.
  2. Thermo-mechanically coupled model of diffusionless phase transformation in austenitic steel, Håkan Hallberg, Paul Håkansson and Matti Ristinmaa, International Journal of Solids and Structures (2010), 47, 1580-1591.
  3. Modeling of crack behavior in austenitic steel influenced by martensitic phase transformation, Håkan Hallberg and Matti Ristinmaa, Key Engineering Materials (2011), 452-453, 637-648.
  4. Crack tip transformation zones in austenitic stainless steel, Håkan Hallberg, Leslie Banks-Sills and Matti Ristinmaa, Engineering Fracture Mechanics (2012), 79, 266-280.

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