D.M. Barnett

Fracture mechanics for piezoelectric ceramics

We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted—that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffiths energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r12±iϵand r12±iϵ, where ϵ. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.

Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate

A general theory is presented for the elastic interactions in a composite plate of layers with different relaxed planar dimensions. Solutions are obtained for the case of equivalent elastic properties and for the case of different elastic properties among the layers. Approximations for the case of thin films on a substrate lead to the governing equations for stresses in multilayered thin‐film systems. Finally, the experimental determination of the planar substrate strain, which is first order in the film/substrate thickness ratio, is presented as a rigorous test of the correctness of the theory.

An image force theorem for dislocations in anisotropic bicrystals

Using a formalism developed by Stroh (1962), a simple image force theorem for a dislocated anisotropic bicrystal is derived. An extension of the Stroh formalism, shows that the prelogarithmic energy factors depend only on the crystallographic directions of the dislocation line and its Burgers vector relative to each medium constituting the bicrystal. In addition, a formula is developed which allows one to obtain the prelogarithmic energy factor by simple numerical integration. A previous result of Dundurs and Sendeckyj (1965) for the net integrated tractions on any plane parallel to the interface of a dislocated bicrystal is extended to the anisotropic case. Finally, an intimate relation between dislocations moving parallel to the bicrystal interface and Stoneley waves in anisotropic bicrystals is developed.

On the existence of surface‐wave solutions for anisotropic elastic half‐spaces with free surface

A proof is developed that for a given direction of propagation on the free surface of a half‐infinite anisotropic crystal, a surface‐wave solution with a certain phase velocity vR<vL, where vL is the limiting velocity, will always exist, except in the special case when the bulk wave defining the limiting velocity satisfies the condition of a free surface. The proof is in terms of the surface impedance, which relates the amplitude at the surface of a surface wave with the external forces needed at the surface. The properties of the impedance as a function of phase velocity determines whether a surface wave not requiring external forces at the surface exists for a certain phase velocity. The proof is valid also in the case of degeneracies in the eigenvalue problem entering the analysis.

Thermal stresses and deposition patterns in layered manufacturing

In layered manufacturing, objects are constructed by sequential deposition of material layers. When the deposition process involves temperature gradients, thermal stresses develop. This paper examines the effect of deposition patterns on the resulting stresses and deflections in laser deposited metal parts. Finite element modeling of the deposition processes showed that the deposition pattern has a significant effect on the part stresses and deflections. Experiments performed using these same deposition patterns yielded sample deflections, which were in agreement with the finite element modeling predictions.

Free Surface (Rayleigh) Waves in Anisotropic Elastic Half-Spaces: The Surface Impedance Method

The questions of uniqueness and existence of free surface waves in anisotropic linear elastic half-spaces have been settled in previous investigations by appeal to the theory of uniformly moving dislocations. An alternative framework relying on the surface impedance tensor is capable of settling the same issues; that framework is developed and fully exploited in the present work. The same framework may be used to study thoroughly the existence of Stoneley waves in bonded anisotropic half-spaces, which is the subject of an accompanying paper.

Formation of chiral branched nanowires by the Eshelby Twist

Manipulating the morphology of inorganic nanostructures, such as their chirality and branching structure, has been actively pursued as a means of controlling their electrical, optical and mechanical properties. Notable examples of chiral inorganic nanostructures include carbon nanotubes, gold multishell nanowires, mesoporous nanowires and helical nanowires. Branched nanostructures have also been studied and been shown to have interesting properties for energy harvesting and nanoelectronics. Combining both chiral and branching motifs into nanostructures might provide new materials properties. Here we show a chiral branched PbSe nanowire structure, which is formed by a vapour-liquid-solid branching from a central nanowire with an axial screw dislocation. The chirality is caused by the elastic strain of the axial screw dislocation, which produces a corresponding Eshelby Twist in the nanowires. In addition to opening up new opportunities for tailoring the properties of nanomaterials, these chiral branched nanowires also provide a direct visualization of the Eshelby Twist.

Diffusionally modified dislocation-particle elastic interactions

Abstract The effects of diffusion on the elastic interactions between dislocations and incoherent second phase particles is examined. In the absence of diffusion, the particle-matrix interface is stressed in the presence of a dislocation. These stresses are related, in part, to the elastic requirements that both the tractions and displacements are continuous across the interface. Diffusion in the interface over length scales comparable to the width of the interface leads to a viscous-like relaxation of the shear tractions resulting in a sliding interface. When interfacial diffusion occurs over distances of order the particle radius, normal stress gradients along the particle-matrix interface may also be relaxed. A solution of the elastic problem of an edge dislocation interacting with a cylindrical particle is obtained in the limit that both of these diffusional relaxation processes have gone to completion. As a result of the diffusional relaxation, a dislocation on any glide plane that intersects the particle is always attracted toward the particle. These results differ from the diffusionless interaction, where attraction occurs only when the shear modulus of the matrix exceeds that of the particle.

The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion

Abstract T he problem of an anisotropic ellipsoidal inclusion which undergoes a stress-free transformation strain (in the sense of J.D. Eshelby) is considered, and the following theorem is proved: If an ellipsoidal region in an infinite anisotropic linear elastic medium undergoes, in the absence of its surroundings, a stress-free transformation strain which is a polynomial of degree M in the position coordinates x t , then the final stress and strain state in the transformed inclusion, when constrained by its surroundings, is also a polynomial of degree M in x t .

Integral formalism for surface waves in piezoelectric crystals. Existence considerations

An integral formalism for surface waves in piezoelectric half‐infinite solids valid up to the critical velocity is developed. Various boundary conditions are considered and, in particular, the problem of which boundary conditions allow surface‐wave solutions for velocities below the limiting velocity vL is discussed in detail. It is proved that (a) with a mechanically free surface and zero dielectric constant for adjoining medium, at most one solution is possible for v<vL, (b) with a mechanically clamped surface and zero dielectric constant for adjoining medium, no solution is possible for v<vL, (c) with a mechanically clamped surface and an infinitely conducting adjoining medium, no solution is possible for v<vL, and (d) with a mechanically free surface and an infinitely conducting adjoining medium, at least one and at most two solutions are possible for v<vL. When two solutions are possible, one solution is of the Bluestein‐Gulyaev type.