Interaction Surface of Phase Transformation Stress by Constitutive Model for Accommodation of Transformation Strain

Abstract

The phase transformation behavior of polycrystalline shape memory alloys is investigated by a constitutive model under multi-axial stress states of tension and shear. The constitutive model used here was developed by the authors to describe the accommodation mechanism acting on the phase transformation phenomenon. The transformation occurs in microscopic transformation systems of crystals and is calculated by the constitutive model. The transformation stress is introduced here as an indicator to describe the macroscopic transformation start. Transformation stresses are obtained from calculated stress-strain curves for various loading paths. The interaction surface of macroscopic transformation stresses obtained is revealed to be very similar to the Mises yield surface in the stress space. Discussions are also made on the relation between the equivalent stress and the equivalent transformation strain of Mises type. , etc. which can successfully describe transformation behavior of shape memory alloys. But most of them are phenomenological ones with internal variables through which accommodation mechanism is reflected in the models indirectly and there are few models that can directly treat the accommodation mechanism which controls transformation behaviors of micro structures of shape memory alloys. The accommodation mechanism automatically chooses transformation planes and directions which should be active so that the internal stress caused by transformation becomes smallest. One of such models that can treat accommodation mechanism directly was developed by the authors [5] [6] where the equal strain assumption is introduced to describe the accommodation behavior in microscopic transformation systems of crystals.In the present paper, the outline of the constitutive model proposed by the authors is described first and results from sample calculations by the constitutive model are given next in order to demonstrate the ability of the model for describing the deformation behavior of shape memory alloys. Though it is demonstrated from results of sample calculations that the model is applicable for describing deformation behavior of shape memory alloys, a great

Influence of Plastic Strain on Transformation Behavior of Shape Memory Alloys

“…To demonstrate the validity of the constitutive model mentioned above, several calculations are conducted [1,2] . Figure 3 and 4 show an example of those results depicting the shape memory effect of the material.…”

“…A constitutive model was proposed by the authors [1,2] to describe the inelastic behavior of shape memory alloys such as Ti-Ni alloys where the main mechanism of the inelastic behavior is the phase transformation under thermo-mechanical conditions. In the constitutive model, a material point is treated as an aggregate of many crystal micro grains with arbitrary crystal orientations.…”

“…The authors proposed before a constitutive model named as the "accommodation model" for the transformation behavior of the shape memory alloy considering the accommodation behavior of the transformation strain and showed this model can successfully predict the super elastic behavior, the shape memory effect and so forth of shape memory alloys under various mechanical and thermal loadings [1,2] . It is necessary to think about the transformation behavior primarily in the engineering application of shape memory alloys.…”

Transformation Behavior of Shape Memory Alloys in Multiaxial Stress State

“…Outline of the Constitutive model. Figure 1 shows the conceptional image of the constitutive model proposed by the authors [5,6]. A parallel structure of micro crystal grains with arbitrary crystal orientations shown in Fig.…”

“…The accommodation mechanism automatically chooses transformation planes and directions which should be active so that the internal stress caused by transformation becomes smallest. One of such models that can treat the accommodation mechanism directly was developed by the authors [5,6] and named as "accommodation model" where the equal strain assumption is employed to describe the accommodation behavior in microscopic transformation systems of crystals. An extended version of the model was also presented to incorporate the plastic deformation in addition to the transformation strain [7].…”