Elastic Deformation of Polycrystals

We propose a framework to model elastic properties of polycrystals by coupling crystal orientational degrees of freedom with elastic strains. Our model encodes crystal symmetries and takes into account explicitly the strain compatibility induced long-range interaction between grains. The coupling of crystal orientation and elastic interactions allows for the rotation of individual grains by an external load. We apply the model to simulate uniaxial tensile loading of a 2D polycrystal within linear elasticity and a system with elastic anharmonicities that describe structural phase transformations. We investigate the constitutive response of the polycrystal and compare it to that of single crystals with crystallographic orientations that form the polycrystal.Comment: 4 pages, 4 ps figure

Stress-Induced Phase Transformations in Shape-Memory Polycrystals

Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress–strain relations of the general problem using Milton–Serkov bounds

Advances in martensitic transformations in Cu-based shape memory alloys achieved by in situ neutron and synchrotron X-ray diffraction methods

This article deals with the application of several X-ray and neutron diffraction methods to investigate the mechanics of a stress induced martensitic transformation in Cu-based shape memory alloy polycrystals. It puts experimental results obtained by two different research groups on different length scales into context with the mechanics of stress induced martensitic transformation in polycrystalline environment

Irreversible flow of vortex matter: polycrystal and amorphous phases

We investigate the microscopic mechanisms giving rise to plastic depinning and irreversible flow in vortex matter. The topology of the vortex array crucially determines the flow response of this system. To illustrate this claim, two limiting cases are considered: weak and strong pinning interactions. In the first case disorder is strong enough to introduce plastic effects in the vortex lattice. Diffraction patterns unveil polycrystalline lattice topology with dislocations and grain boundaries determining the electromagnetic response of the system. Filamentary flow is found to arise as a consequence of dislocation dynamics. We analize the stability of vortex lattices against the formation of grain boundaries, as well as the steady state dynamics for currents approaching the depinning critical current from above, when vortex motion is mainly localized at the grain boundaries. On the contrary, a dislocation description proves no longer adequate in the second limiting case examined. For strong pinning interactions, the vortex array appears completely amorphous and no remnant of the Abrikosov lattice order is left. Here we obtain the critical current as a function of impurity density, its scaling properties, and characterize the steady state dynamics above depinning. The plastic depinning observed in the amorphous phase is tightly connected with the emergence of channel-like flow. Our results suggest the possibility of establishing a clear distinction between two topologically disordered vortex phases: the vortex polycrystal and the amorphous vortex matter.Comment: 13 pages, 16 figure

Optimal configuration of microstructure in ferroelectric materials by stochastic optimization

An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterised by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. Apparent enhancement of piezoelectric coefficient $d_{33}$ is observed in an optimally oriented BaTiO$_3$ single crystal. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO$_{3}$ is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centred around ${45^\circ}$. The piezoelectric coefficient in such a ceramic is found to be nearly three times as that of the single crystal.Comment: 11 pages, 7 figure

Domain Patterns, Texture and Macroscopic Electro-mechanical Behavior of Ferroelectrics

This paper examines the domain patterns and its relation to the macroscopic electromechanical behavior of ferroelectric solids using a theory based on homogenization and energy minimization. The domain patterns in different crystalline systems are classified, the spontaneous strain and polarization for single crystals and polycrystals are characterized, and the optimal texture of polycrystals for high-strain actuation is identified. The results also reveal why it is easy to pole PZT at compositions close to the 'morphotropic phase boundary'