Thermodynamic Driving Forces for Martensitic Phase Transformations in Shape-Memory Alloys
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Thermodynamic Driving Forces for Martensitic Phase Transformations in Shape-Memory Alloys C. Jannetti1, J.L. Bassani1, S. Turteltaub2 1
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 2 Department of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
Abstract A macroscopic constitutive model for the martensitic phase transformations in single-crystal shape-memory alloys (SMAs) is developed in the framework of irreversible thermodynamics with internal variables. Central to the model is the notion that the rate of progression of structural rearrangements on the microscale depends on the stress state through the thermodynamic forces conjugate to the rearrangements. These thermodynamic forces, i.e. the driving forces for the phase transitions, are shown to have an important contribution that arises from changes in the effective elastic response of the SMA, which in turn depend upon the state of transformation. This contribution is shown to have a significant effect on the overall macroscopic stress-strain response. Introduction In this paper, the setting of irreversible thermodynamics [1] is adopted to develop a 3D, continuum-level material model that describes the inelastic deformation associated with evolution of martensitic transformations. Specifically, we address how the dependence of material properties on the transformation state affects the expression for the thermodynamic driving force and, consequently, the macroscopic stress-strain-temperature response1. This work has some similarities to the recent study of Anand and co-workers [2] [3], where the latter paper focuses on thermal effects, which we have neglected. However, their work ignored important implications that microstructural evolution has on the constitutive response, in particular on expressions for the thermodynamic driving forces for transformations. In these models the force thermodynamically conjugate to the transformation is taken to drive the phase transformation. Our work builds upon the notion of a composite-type representative volume element to describe the underlying microstructure. Constitutive model and driving forces The evolving microstructure of shape-memory alloys comprises austenite and martensite crystal phases, which macroscopically can be thought of as a multi-phase composite. At the macroscopic scale, the latter corresponds to continuum material point in a single crystal that is capable of undergoing microstructural rearrangements arising from multiple transformations as well as from elastic deformation. Therefore, we introduce the notion of a representative volume element (RVE) as a composite with martensite phases (inclusions) embedded in austenite2, where the phases are characterized by specified transformation deformation gradients and their volume fractions that evolve with straining. The transformation strains are moderately large. 1
The implications discussed here can be extended to acco
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