Yu U. Wang

Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations

The first Phase Field model of evolution of a multi-dislocation system in elastically anisotropic crystal under applied stress is formulated. The model is a modification and extension of our Phase Field Microelasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations is calculated exactly and is explicitly incorporated in the Phase Field formalism. It also automatically takes into account the effects of “short-range interactions”, such as multiplication and annihilation of dislocations and a formation of various metastable microstructures involving dislocations and defects. The proposed 3-dimensional Phase Field model of dislocations does not impose a priori constraints on possible dislocation structures or their evolution paths. Examples of simulation of the FCC 3D system under applied stress are considered.

Adaptive ferroelectric states in systems with low domain wall energy: Tetragonal microdomains

Ferroelectric and ferroelastic phases with very low domain wall energies have been shown to form miniaturized microdomain structures. A theory of an adaptive ferroelectric phase has been developed to predict the microdomain-averaged crystal lattice parameters of this structurally inhomogeneous state. The theory is an extension of conventional martensite theory, applied to ferroelectric systems with very low domain wall energies. The case of ferroelectric microdomains of tetragonal symmetry is considered. It is shown for such a case that a nanoscale coherent mixture of microdomains can be interpreted as an adaptive ferroelectric phase, whose microdomain-averaged crystal lattice is monoclinic. The crystal lattice parameters of this monoclinic phase are self-adjusting parameters, which minimize the transformation stress. Self-adjustment is achieved by application of the invariant plane strain to the parent cubic lattice, and the value of the self-adjusted parameters is a linear superposition of the lattice c...

Full-field measurements of heterogeneous deformation patterns on polymeric foams using digital image correlation

The ability of a digital image correlation technique to capture the heterogeneous deformation fields appearing during compression of ultra-light open-cell foams is presented in this article. Quantitative characterization of these fields is of importance to understand the mechanical properties of the collapse process and the energy dissipation patterns in this type of materials. The present algorithm is formulated in the context of multi-variable non-linear optimization where a merit function based on a local average of the deformation mapping is minimized implicitly. A parallel implementation utilizing message passing interface for distributed-memory architectures is also discussed. Estimates for optimal size of the correlation window based on measurement accuracy and spatial resolution are provided. This technique is employed to reveal the evolution of the deformation texture on the surface of open-cell polyurethane foam samples of different relative densities. Histograms of the evolution of surface deformation are extracted, showing the transition from unimodal to bimodal and back to unimodal. These results support the interpretation that the collapse of light open-cell foams occurs as a phase transition phenomenon.

Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid

The phase field microelasticity theory of a three-dimensional elastically anisotropic solid of arbitrarily inhomogeneous modulus also containing arbitrary structural inhomogeneities is proposed. The theory is based on the equation for the strain energy of the elastically and structurally inhomogeneous system presented as a functional of the phase field, which is the effective stress-free strain of the “equivalent” homogeneous modulus system. It is proved that the stress-free strain minimizing this functional fully determines the exact elastic equilibrium in the elastically and structurally inhomogeneous solid. The stress-free strain minimizer is obtained as a steady state solution of the time-dependent Ginzburg–Landau equation. The long-range strain-induced interaction due to the elastic and structural inhomogeneities is explicitly taken into account. Systems with voids and cracks are the special cases covered by this theory since voids and cracks are elastic inhomogeneities that have zero modulus. Other ...

Phase field microelasticity theory and simulation of multiple voids and cracks in single crystals and polycrystals under applied stress

The phase field microelasticity theory of a three-dimensional elastically anisotropic single crystal with multiple voids and cracks is developed. It is extended to the case of elastically isotropic polycrystal. The theory is based on the exact equation for the strain energy of the “equivalent” continuous elastically homogeneous body presented as a functional of the phase field. This field is the equivalent stress-free strain. It is proved that the equivalent stress-free strain minimizing the strain energy of the elastically homogeneous body fully determines the elastic strain and displacement of the body with voids/cracks. The geometry and evolution of multiple voids and cracks are described by the phase field, which is a solution of the stochastic time-dependent Ginzburg–Landau equation. Other stress-generating defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on the configuration of multiple voids and cracks...

Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films

Abstract Dislocation dynamics near a free surface and in heteroepitaxial thin films are simulated using an extended version of the nanoscale Phase Field Microelasticity model of dislocations [Acta Mater. 49 (2001) 1847]. The model automatically takes into account the effect of image forces on dislocation motions. In particular, the operations of Frank–Read sources in epitaxial films grown on infinitely thick and relatively thin substrates are investigated. The simulation reveals different misfit dislocation behaviors at the interface. Its implication on the interface susceptibility to crack nucleation is discussed.

Three-dimensional nonlinear open-cell foams with large deformations

Abstract In this article, a hyperelastic formulation for light and compliant foams which accounts for nonlinear effects at material and kinematic levels is introduced. This theory is applicable to a large number of 2- and 3-D irregular open-cell structures. An expression for the strain-energy function is proposed which includes bending and stretching contributions. Although this description allows for irregularity in the structure at local or cell level, it also assumes that the macro structure is homogeneous, i.e. built by repetition of the same irregular unit cell. This micromechanical formulation has explicit correlation with the foam structure, and therefore it preserves in the constitutive relation the symmetries or directional properties of the corresponding structures, including the cases of re-entrant foams which exhibit negative Poisson’s ratio effects. Due to the introduction of nonlinear kinematics, the evolution of the structure during the loading process and its effects on the constitutive behavior can be traced, including the cases where configurational transformations are present leading to non-convex strain-energy functions. Several examples of the stress–strain behavior for arbitrary large homogeneous deformations in a diamond-like structure are presented. The effect of the structure reorientation on the transition of local deformation mechanisms is clearly shown. The development of texture and anisotropy induced by the deformation process is also demonstrated. Finally, the role of the deformation mechanisms on the relation between foam stiffness and foam density is analyzed.

Domain wall broadening mechanism for domain size effect of enhanced piezoelectricity in crystallographically engineered ferroelectric single crystals

Computer modeling and simulation reveal a domain wall broadening mechanism that explains the domain size effect of enhanced piezoelectric properties in domain engineered ferroelectric single crystals. The simulation shows that, under electric field applied along the nonpolar axis of single crystal without domain wall motion, the domain wall broadens and serves as embryo of field-induced new phase, producing large reversible strain free from hysteresis. This mechanism plays a significant role in the vicinity of interferroelectric transition temperature and morphotropic phase boundary, where energy difference between stable and metastable phases is small. Engineered domain configuration fully exploits this domain wall broadening mechanism.

Magnetic structure and hysteresis in hard magnetic nanocrystalline film: Computer simulation

Three-dimensional micromagnetic simulations are used to study the effect of crystallographic textures on the magnetic properties of uniaxial nanocrystalline films of hard magnetic materials with arbitrary grain shapes and size distributions. The correlation lengths (effective ferromagnetic exchange interaction radius and domain wall width) are assumed to be smaller than the typical grain size. The Landau–Lifshitz equations of magnetization dynamics are employed to describe the distribution of magnetization in ferromagnetic domains, domain evolution during magnetization switching, and the hysteresis curve. The equations are solved numerically in reciprocal space using the fast Fourier transform technique. Simulations are performed for films of different grain textures. The results show that magnetic coupling between grains in thin films significantly affects the morphology of the magnetic domains and their response to the magnetic field applied. The greater the deviation of the uniaxial directions of the g...

Electromechanical behavior of [001]-textured Pb(Mg1/3Nb2/3)O3-PbTiO3 ceramics

[001]-textured Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ceramics were synthesized by using templated grain growth method. Significantly high [001] texture degree corresponding to 0.98 Lotgering factor was achieved at 1 vol. % BaTiO3 template. Electromechanical properties for [001]-textured PMN-PT ceramics with 1 vol. % BaTiO3 were found to be d33 = 1000 pC/N, d31 = 371 pC/N, ɛr = 2591, and tanδ = ∼0.6%. Elastoelectric composite based modeling results showed that higher volume fraction of template reduces the overall dielectric constant and thus has adverse effect on the piezoelectric response. Clamping effect was modeled by deriving the changes in free energy as a function of applied electric field and microstructural boundary condition.