A tensorial description of the transformation kinetics of the martensitic phase transformation

Displacive stress and strain induced transformations are those transformations that occur when the formation of martensite or bainitic ferrite is promoted by the application of stress or strain. These transformations have been shown to be one of the mechanisms by which the mechanical properties of a microstructure can be improved, as they lead to a better ductility and strength by the transformation induced plasticity effect. This review aims to summarize the fundamental knowledge about them, both in fully austenitic or in multiphase structures, pointing out the issues that—according to the authors’ opinion—need further research. Knowing the mechanisms that govern the stress and strain induced transformation could enable to optimize the thermomechanical treatments and improve the final microstructure properties.

Future Trends on Displacive Stress and Strain Induced Transformations in Steels

Phenomenological models which describe phase transformation in solids often employ a single scalar variable, the mass (or volume) fraction of one of the phases involved. However, the orientation of the applied stress has a major influence on the microstructure developing during the phase transition and thus the overall mechanical behavior. Therefore, additional internal variables of higher order have to be introduced in order to capture this aspect.



The choice of these internal variables is often based on purely phenomenological considerations. In contrast to this, based on local observations at the phase boundary, a thermodynamically dual pair of second order tensors is introduced here.



Constitutive relations for shape menory alloys in the pseudoelastic and pseudoplastic range are proposed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

On the physically motivated choice of internal variables describing martensitic phase transformations

The transformation kinetics during phase transitions in solids are often described by a pair of scalar variables for both the thermodynamic force and flux. Based on the use of the Eshelby-Tensor as the thermodynamic driving force for the phase-transition, a tensorial measure is introduced which is used as the associated thermodynamic flux. Based on the assumption that the process maximizes the dissipation, these measures are used to describe the transformation kinetics during the phase transition. The tensorial description reduces to a description with the Gibbs-energy as the driving force and the mass change of the phases as the thermodynamic flux for a hydrostatic stress state.



These considerations serve as the base for a phenomenological material-law which describes the austenite-martensite transformation in steels. In order to incorporate the different behavior of the phases, they are modeled independently. The model have been implemented into a finite-element-code which allows thermodynamically coupled calculations. A quenching-test of a cylindrical specimen under biaxial mechanical load is simulated. The influence of the sequence of the change of the thermomechanical load in the stress-temperature space (temperaturestress vs. temperaturestress) is studied. Furthermore, the influence of the direction of the applied stress is presented.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.200310085

A unified tensorial driving force for phase transitions – calculation of the onset of the transformation

The description of the transformation kinetics during a martensitic 
phase transition in solids is usually performed by scalar variables for both the thermodynamic force and flux. In a local description at the phase boundary, the movement of the boundary during the martensitic transformation can be described in terms of the second order Eshelby Tensor (or asymmetric chemical potential tensor) and the local orientation of the phase boundary. Transferring this local consideration to a macroscopic description by applying appropriate homogenization techniques, the Eshelby Tensor is introduced as the 
macroscopic thermodynamic driving force for the phase transformation.
Consequently, a second order tensor is introduced as the associated thermodynamic flux. This tensorial description collapses to the classical case for a hydrostatic stress state. A constitutive relation between these tensorial variables is postulated
based upon the assumption of the maximization of the dissipation and
the existence of a threshold value for the thermodynamic force.
Considering shape memory alloys, the onset and progress of the 
transformation for various thermomechanical loading path is 
calculated. The influence of the direction and magnitude of the stress and the temperature on the transformation is investigated.
Furthermore, restrictions on the choice of the parameters of the model are derived.

Calculation of the onset and progress of the martenistic transformation using tensorial measures for transformation kinetics

The movement of a discontinuity in a continuum can usually be expressed in terms of the state in its direct vicinity. Thus, the knowledge of the local state around the discontinuity is vitally important in order to adequately describe its movement. Numerical schemes local to the discontinuity, as e.g. moving finite element methods, are appropriate approaches to describe its motion. However, for a large number of problems, the local state not only depends on measures of the discontinuity plane itself but also on measures related to the bulk behavior of the material, such as temperature or stress. For a complete description, the bulk behavior of the material has to be numerically modeled as well. In this contribution, the interface and its propagation is modeled explicitly by a two-dimensional discretization of the interface. The same discretization is utilized to describe the behavior of the bulk material employing the boundary element method. As an example, the movement of a phase transition front in a single crystal is presented. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

On the simulation of a moving discontinuity by boundary element methods

A coupling device for damping within a drive train is presented. For conventional damping couplings, damping is often realized by the dissipation of energy due to material damping or friction. In opposite to this, the damping effect of the presented coupling is based on the dissipated energy during the stress induced phase transformation of pseudoelastic NiTi shape memory alloys. In this contribution the design principles, experimental results, and a numerical simulation using the material law for shape memory alloys developed by Raniecki B. Lexcellent C. and Tanaka K. (Arch Mech 44(3:261–284)) are presented.

Claus Oberste-Brandenburg

Papers

A unified tensorial driving force for phase transitions – calculation of the onset of the transformation

Calculation of the onset and progress of the martenistic transformation using tensorial measures for transformation kinetics

On the simulation of a moving discontinuity by boundary element methods

Damping Couplings with Elements of Pseudoelastic NiTi Shape Memory Alloys

On the physically motivated choice of internal variables describing martensitic phase transformations