Model Tracking of Stress and Temperature Induced Martensitic Transformations for Assessing Superelasticity and Shape Mem
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the phase fraction internal variables; the linking of these internal variables to thermomechanical response; and the algorithms given for the evolution of these variables. Specifically, we indicate how a model presented in [7] for high temperature austenite/martensite transformations can be extended to the low temperature regime so as to treat direct martensite/martensite transformations. The most important of these is a generic stress-assisted detwinning transformation starting from a strain-free "random" martensite, i.e., martensite consisting of balanced opposing variant fractions, typically in some self-accommodated arrangement. Under load this then transforms to a "biased" martensite in which certain variants predominate. We consider a relatively simple version of the model for single direction response in which the material is characterized by only two martensite variants. Seven parameters then characterize the material: the four transformation temperatures M. Ms, As, A. the austenite/martensite transformation strain y*, the elastic modulus E, and the latent heat of the austenite/martensite transformation AH. An interesting aspect of this model is that the stresses associated with detwinning start and detwinning finish are determined in terms of the other material parameters. This is due to the simplified form of the model. A more sophisticated treatment is possible in which: these stresses are specified independently; the martensite and austenite have different moduli; and conventional thermal expansion is present. However, these extensions require a discussion of various thermodynamic issues with respect to the construction of thermodynamic phase diagrams in stresstemperature space. The version of the model presented here is free of these details, at the expense of increased generality. The nature of the complications associated with these additional extensions 431 Mat. Res. Soc. Symp. Proc. Vol. 459 01997 Materials Research Society
is briefly discussed, although a complete development will be given elsewhere. The theory is presented in the context of uniaxial tension, and material parameters are chosen on the basis of experimental work on TiNi as given in [8]. These values are: My = 235 K, M, = 263 K, A, = 295 K, 6 3 Af= 308 K, y* = 0.06, E = 38 GPa, AH = 116x10 J/m . After presenting the underlying theory in
the following section, we apply it to various isothermal loading situations. We also examine path dependence as it pertains to the production of biased martensite. THEORY Following [7], consider two martensitic variants M' and M- whose crystallographic lattice strains are complementary shears from the base austenite state A. Transformations are triggered by changes in temperature T and stress 'r, and may involve: M*-A, A-M-, or M--4M÷. At each instant there are 3 possibilities for AM+ neutrality curve that is on the T-axis in the simple phase diagram. In the unfolding of Figure lb, two of the four unfolded M-"M' curves connect to the high T construction at the termination of the two M -"A curves th
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