On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

Abstract

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.Keywords SMA · NiTi alloys · Adaptive composite · Macroscopic free energy functions · Gibbs energy · Micromechanics · Coherence energy · Stored coherency energy · Ultimate phase transformation eigenstrains · Self-equilibrated eigenstrains influence moduli · SEIM · Effective property estimates · Martensitic phase transformationThe coming into existence of the present paper would not be possible without contributions and long discussions with Professor Bogdan Raniecki who passed away suddenly on August 2014. I dedicate this work to his memory. dx is an average of a local field over a region occupied by volume V α . When volume V α is occupied by phase α then A α denotes α phase average.It is accepted that internal energy and internal entropy of all kinds of martensitic phases at microscopic thermodynamic reference state (m.t.r.s.)-i.e., at zero local stresses ( σ (x) = 0) and reference temperature (T = T 0 ), are the same, e.g., (u 0 α, α =1 = u M α = u A − u 0 , u A ≡ u 0 1 ) and (s 0 α, α =1 = s M α = s A − s 0 , s A ≡...