Elastic and Irreversible Energies of a Two-Stage Martensitic Transformation in NiTi Utilizing Calorimetric Measurements
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A thermoelastic martensitic transformation (MT) in shape memory alloys brings about a solid–solid phase transformation from a high-temperature austenite phase to a low-temperature martensite phase. The stress-free thermally induced MT is typically characterized using differential scanning calorimetry (DSC). During cooling, the forward transformation from austenite (A) fi martensite (M) brings about an exothermic peak in the DSC curve: the MT temperature at the start is designated Ms and that as the MT ends, Mf. An endothermic peak arises as a result of the reverse MT (A ‹ M) during heating which commences at As and ends at Af. In addition to Ms, Mf, As, and Af, DSC is implemented to establish the latent heat of transformation (see Figures 1(a) and (c)). In the current study, DSC measurements (see Figures 1(a) and (c)) are used to quantify the elastic energy and irreversible energy for a two-stage A () R () B19¢ phase transformation in NiTi. The two energetic contributions are determined based on thermodynamic analysis of a thermoelastic MT by Ortin and Planes[1] and Wollants et al.,[2] which is expounded upon in a review by Liu.[3] The material is studied in two conditions: after multiple thermal cycles that should stabilize transformation temperatures, and under virgin condition (or without stabilization).
ASHEESH LANBA, Ph.D. Student, and REGINALD F. HAMILTON, Assistant Professor, are with the Department of Engineering Science and Mechanics, The Pennsylvania State University, 212 Earth-Engineering Sciences Bldg., University Park, PA 16802-6812. Contact e-mail: [email protected] Manuscript submitted April 25, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS A
Phenomenological theories consider a balance between chemical and nonchemical contributions to the free energy in the reference frame of equilibrium thermodynamics. The chemical component is attributed to the free energy difference between the parent (austenite) and product (martensite) atomic crystal structures. The nonchemical component is due to elastic strain energy and irreversible energy. Interfacial energy and the elastic accommodation of the shape and volume changes make up the elastic strain energy. The irreversible contribution arises from the dissipation of energy; typically attributed to frictional work required to move interfaces and strain energy relaxation.[3] The governing formulation is the Gibbs free-energy:[3–6] DG ¼ DH TDS þ DEst þ DEir ;
½1
where H is the enthalpy, S is the entropy, Est is the elastic strain energy, and Eir represents the irreversible energy. It is generally accepted that the MT is athermal, and thus, the transformation is unaffected by thermally activated processes.[7] It is also well known that the MT is a diffusionless first-order transformation, which occurs via an atomic crystal structure alteration with a concomitant lattice invariant shear. In order for the transformation to occur, an energetic barrier (i.e., differential between free energy of parent and product phases due to their different atomic crystal s
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