FEM Mo delling of Elastically Strained Interfacial Microstructures in Cu-Al-Ni Single Crystals

Abstract

Abstract. In this paper, a construction of FEM models of particular microstructures forming between austenite and mechanically stabilised 2H-martensite of the Cu-Al-Ni shape memory alloy is presented. Since these microstructures appearing during the shape recovery process (the so-called X-interfaces or the Xmicrostructures) are not global minimisers of the free energy, their mesoscopic morphology cannot be determined from any known thermodynamic extremal criterion, but must be taken directly from the experimental observations. For the elastic coefficients of both austenite and martensite phase of this alloy known from the ultrasonic measurements, such model enables determination of elastic strains within the microstructure and, thus, evaluation of the stored elastic energy in the microstructure. The model (implemented in COMSOL Multiphysics FEM environment) is applied to analyse interfacial microstructures observed experimentally in a prismatic bar of a single crystal of the examined alloy, and to find optimal morphology of this microstructure by means of the free energy (local) minimisation.

A finite element analysis of the morphology of the twinned-to-detwinned interface observed in microstructure of the Cu–Al–Ni shape memory alloy

“…In this paper we adopt a slightly different approach to incorporate the elastic strains into the model. This approach has been successfully used by Balandraud and Zanzotto (2007) for the analysis of the elastic strains for the wedge microstructure in the Cu-Zn-Al alloy and for the X-interface microstructure in Cu-Al-Ni alloy by the current authors Glatz et al, 2009;Glatz et al, 2010). More details on this approach will be given within the description of the finite elements model.…”

Almost compatible X-microstructures in CuAlNi shape memory alloy

“…The analysis of Seiner et al [21] and Glatz et al [9] indicates that the X-microstructure formed within a bar (as observed experimentally) does not correspond to a local minimum of elastic strain energy. Accordingly, formation and propagation of the X-microstructure cannot be explained by the tendency of the material to minimize its free energy only.…”

“…Compared with the approach of Glatz et al [9], the present model is a simplification in the sense that the effect of boundary conditions is neglected. However, being considerably simpler, the present approach is suitable for a systematic study of all 528 crystallographically distinct candidate X-microstructures.…”

“…They have also carried out a finite element analysis of the X-microstructure formed within the specimen by assuming specific geometrical arrangement of the interfaces. The analysis has been further refined in [9] where optimal interface orientations have been determined that minimize the elastic strain energy. An important conclusion of the analysis in [9,21] is that the observed X-microstructures are not local energy minimizers as in all analyzed cases the energy can be reduced by moving the intersection line toward the specimen boundary (when the intersection line is on the boundary, the X-microstructure degenerates to the V-microstructure introduced in Sect.…”

“…However, being considerably simpler, the present approach is suitable for a systematic study of all 528 crystallographically distinct candidate X-microstructures. Furthermore, the volume fractions of martensite variants in the twinned domains are considered here as additional unknown parameters in the energy minimization scheme, while, in [9], the fixed values of the twin fractions are taken from the crystallographic theory.…”