A micromechanics-inspired constitutive model for shape-memory alloys

This paper presents a three-dimensional constitutive model for shape-memory alloys that generalizes the one-dimensional model presented earlier (Sadjadpour and Bhattacharya 2007 Smart Mater. Struct. 16 S51–62). These models build on recent micromechanical studies of the underlying microstructure of shape-memory alloys, and a key idea is that of an effective transformation strain of the martensitic microstructure. This paper explains the thermodynamic setting of the model, demonstrates it through examples involving proportional and non-proportional loading, and shows that the model can be fitted to incorporate the effect of texture in polycrystalline shape-memory alloys

Strain intermittency in shape-memory alloys

We study experimentally the intermittent progress of the mechanically induced martensitic transformation in a Cu-Al-Be single crystal through a full-field measurement technique: the grid method. We utilize an in- house, specially designed gravity-based device, wherein a system controlled by water pumps applies a perfectly monotonic uniaxial load through very small force increments. The sample exhibits hysteretic superelastic behavior during the forward and reverse cubic-monoclinic transformation, produced by the evolution of the strain field of the phase microstructures. The in-plane linear strain components are measured on the sample surface during the loading cycle, and we characterize the strain intermittency in a number of ways, showing the emergence of power-law behavior for the strain avalanching over almost six decades of magnitude. We also describe the nonstationarity and the asymmetry observed in the forward versus reverse transformation. The present experimental approach, which allows for the monitoring of the reversible martensitic transformation both locally and globally in the crystal, proves useful and enhances our capabilities in the analysis and possible control of transition-related phenomena in shape-memory alloys.Comment: Four supplementary video

Homogenization in magnetic-shape-memory polymer composites

Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult to manifacture single crystal of these alloys we study composite materials in which small magnetic-shape-memory particles are embedded in a polymer matrix. The macroscopic properties of the composite depend strongly on the geometry of the microstructure and on the characteristics of the particles and the polymer. We present a variational model based on micromagnetism and elasticity, and derive via homogenization an effective macroscopic model under the assumption that the microstructure is periodic. We then study numerically the resulting cell problem, and discuss the effect of the microstructure on the macroscopic material behavior. Our results may be used to optimize the shape of the particles and the microstructure.Comment: 17 pages, 4 figure

Theoretical prediction and experimental study of a ferromagnetic shape memory alloy: Ga_2MnNi

We predict the existence of a new ferromagnetic shape memory alloy Ga_2MnNi using density functional theory. The martensitic start temperature (T_M) is found to be approximately proportional to the stabilization energy of the martensitic phase (deltaE_tot) for different shape memory alloys. Experimental studies performed to verify the theoretical results show that Ga_2MnNi is ferromagnetic at room temperature and the T_M and T_C are 780K and 330K, respectively. Both from theory and experiment, the martensitic transition is found to be volume conserving that is indicative of shape memory behavior.Comment: 11 pages, 3 figure

Collisions in shape memory alloys

We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by an hammer stroke

Crystallographic attributes of a shape-memory alloy

Shape-memory Alloys are attractive for many potential applications. In an attempt to provide ideas and guidelines for the development of new shape-memory alloys, this paper reports on a series of investigations that examine the reasons in the crystallography that make (i) shape-memory alloys special amongst martensites and (ii) Nickel-Titanium special among shape-memory alloys