Tong-Yi Zhang

Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic

Abstract Structural reliability concerns of various electromechanical devices call for a better understanding of the mechanisms of fracture in piezoelectric ceramics subjected to combined mechanical and electrical loading. For these materials, due to unexplained discrepancies between theory and experiments, even the basic criterion of fracture remains a point of controversy. A viewpoint adopted in this paper is to model piezoelectric ceramics as a class of mechanically brittle and electrically ductile solids. As a first step toward understanding the effects of electric yielding, a strip saturation model is developed for a finite crack perpendicular or parallel to the poling axis of an infinite poled piezoelectric ceramics medium with electrical polarization reaching a saturation limit along a line segment in front of the crack. This model may be considered as a generalization of the classical Dugdale model for plastic yielding near cracks in thin metal sheets. The essential features of the strip saturation model are analyzed via a simplified electroelasticity formulation. Two energy release rates emerge from this analysis. An “apparent” or global energy release rate appears when evaluating J-integral along a contour surrounding both the electrical yielding strip and the crack tip. Under small scale yielding conditions, this energy release rate is equal to that of a linear piezoelectric crack without electrical yielding. A “local” energy release rate is obtained by evaluating J along an infinitesimal contour near the crack tip. The local energy release rate gives predictions which seem to be in broad agreement with experimental observations. It is also interesting that the local energy release rate is independent of the strength and size of electrical yielding.

Fracture of piezoelectric ceramics

Publisher Summary Piezoelectric ceramics can sense and actuate by rapidly converting mechanical and thermal signals into electrical ones, the reverse also being true. The piezoelectric properties and quick response characteristics have made piezoelectric ceramics one of the most commonly used smart materials. The intrinsic brittleness of piezoelectric ceramics and damageability of the materials under electric field — making the materials prone to fracture — are of major concern for product reliability. The fracture of piezoelectric ceramics under combined electrical and mechanical loading has been among the most prevalent research topics. The chapter describes piezoelectricity, ferroelectrics, spontaneous polarization, and electric domains; and discusses the poling process, the hysteresis loop of polarization versus the electric field strength, and the butterfly loop of strain versus the electric field. The chapter focuses on the basic equations commonly used in the study of the fracture behavior of piezoelectric ceramics within the thermodynamics framework, the general solution based on Strohs formalism (a powerful tool for solving two-dimensional electroelastic problems), analysis of Greens functions for insulating elliptical cavities and cracks, study of conductive elliptical cavities and cracks, study of piezoelectric interface cracks, and three-dimensional electroelastic problems. The four types of nonlinear approaches considered are: electrostriction, domain switching, domain wall kinetics, and polarization saturation at a crack tip. The polarization saturation model that treats piezoelectric ceramics as mechanically brittle and electrically ductile materials is also discussed. The chapter provides an overview of experimental observations whose results show that microstructure and temperature have a profound influence on the fracture behaviors of piezoelectric ceramics under purely mechanical loads, and also discusses the commonly used failure criteria, the electric saturation model, the stress intensity factor criterion and the stress criterion.

Fracture mechanics for a mode III crack in a piezoelectric material

Abstract The mechanical and electric fields in a piezoelectric material around an elliptical cylinder cavity and the electric field within the cavity are formulated by complex potentials. The electric field inside the cavity is uniform and varies with the shape of the ellipse. When the cavity is reduced to a slit crack, the electric field strength inside the cavity is inversely proportional to the permittivity of the cavity. When the ratio of the short semi axis of the ellipse over the long semi-axis is much smaller than the ratio of the permittivity of the cavity over that of the material, it can be used as the electric boundary condition that the electric field strength along the crack faces equals the remote one. In this case, the energy release rate for crack propagation depends only on the applied stress and can be represented in terms of the stress intensity factor as in a pure elastic body without coupling with the electric field. Electric loading may promote or retard crack propagation depending on whether it increases or decreases the applied stress.

Electrochemical synthesis of silver polyhedrons and dendritic films with superhydrophobic surfaces.

Single-crystalline Ag dendrites are grown on a Ni/Cu substrate by using a simple templateless, surfactantless electrochemical technique. Controlling only the applied potential causes a change in the deposited silver morphology from polyhedrons to dendrites. Microstructure characterization suggests that preferential growth along the 211 directions by the oriented attachment of Ag nanocrystals leads to the formation of Ag dendrites, which are composed of trunks, branches, and leaves. Modifying as-grown Ag dendritic film with a thickness of about 10 microm with a self-assembled monolayer of n-dodecanethiol yields a superhydrophobic surface with a contact angle of 154.5 +/- 1.0 degrees and a tilt angle lower than 2 degrees.

Interfacial crack problems in magneto-electroelastic solids

Abstract In this paper, we present an explicitly analytic solution for an electrically permeable interface crack between two dissimilar magneto-electroelastic solids. Using the Stroh formalism, we first derive the general solution under arbitrary loads by reducing the generalized 2D problem to an equivalent interface crack problem in two-elastic anisotropic media, which can be solved with well-established methods. With the analytic solution, we then study the interface crack loaded by remote uniform loads, by a generalized line force or/and by a generalized line dislocation. The results show the singular and oscillatory fields ahead of the crack tips. The electric–magnetic field within the crack has a similar singularity at the crack tip as the electric–magnetic field within the solids. In particular, when uniform mechanical–electric–magnetic loads are applied at infinity, the singular intensity depends on the material properties and the mechanical loads, but not on the electric–magnetic loads.

Microbridge testing of silicon nitride thin films deposited on silicon wafers

Abstract A novel microbridge testing method for thin films is proposed. Theoretic analysis and finite element calculation are conducted on microbridge deformation to provide a closed formula of deflection vs load, considering both substrate deformation and residual stress in the film. Using the formula, one can simultaneously evaluate the Youngs modulus, residual stress and bending strength of thin films from experimental load–deflection curves. The microbridge test is conducted with a load and displacement sensing nanoindenter system equipped with a microwedge probe. Samples for the microbridge test are prepared by the microelectromechanical fabrication technique such that they are easy to handle. Silicon nitride films fabricated by low pressure chemical vapor deposition on silicon substrates are tested to demonstrate the proposed method. The present work shows that the Youngs modulus, residual stress and bending strength for the annealed silicon nitride films are 202.57±15.80 GPa , 291.07±56.17 MPa , and 12.26±1.69 GPa , respectively.

Surface Effects on Nanoindentation

In this paper, we report on a study of the surface effect on nanoindentation and introduce the apparent surface stress that represents the energy dissipated per unit area of a solid surface in a nanoindentation test. The work done by an applied indentation load contains both bulk and surface work. Surface work, which is related to the apparent surface stress and the size and geometry of an indenter tip, is necessary in the deformation of a solid surface. Good agreement is found between theoretical first-order approximations and empirical data on depth-dependent hardness, indicating that the apparent surface stress plays an important role in depth-dependent hardness. In addition, we introduce a critical indentation depth. The surface deformation predominates if the indentation depth is shallower than the critical depth, while the bulk deformation predominates when the indentation depth is deeper than the critical depth.

Mode‐III cracks in piezoelectric materials

The stress and electric fields around a mode‐III crack containing a dielectric medium are formulated. Mechanical equilibrium requires that the crack surfaces be traction free. Previous solutions have used the electrical boundary condition that the electric displacement component perpendicular to the crack surfaces should be zero. However, cracks that are filled with a dielectric medium, such as vacuum or air, require that the electric displacement be continuous across the crack faces. Using the boundary condition appropriate for an insulating crack, the stress, strain, and electric‐field strength are found to exhibit r−1/2 singularities while the electric displacement does not. The singularity in the electric‐field strength arises from piezoelectricity. The driving force for crack growth is only related to the effective level of applied stress. Under constant displacement, the applied field may increase or decrease the effective applied stress depending on its direction. As a result the electric field may...

Measurements of residual stresses in thin films using micro-rotating-structures

Abstract In the present study, micro-rotating-structures for local measurements of residual stresses in a thin film were simulated by the finite element method (FEM). A sensitivity factor – the ratio of the deflection of the micro-structure to the normalized residual stress is introduced and tabulated from the FEM results. Thereafter, a formula to calculate the residual stress is given so that the residual stress can be easily evaluated from the deflection of the rotating beam. A variety of optimized micro-rotating-structures were then designed and fabricated to verify the FEM results. Residual stresses in both silicon nitride and polysilicon thin films were determined by this technique and compared with measurements by the wafer-curvature method. The two methods lead to comparable results. In addition, the micro-rotating-structures have the ability to measure spatially and locally a large range of residual tensile or compressive stresses.

Size-dependent surface stress, surface stiffness, and Young’s modulus of hexagonal prism [111] β-SiC nanowires

The present work studies the size-dependent surface stress, surface stiffness, and Young’s modulus of a prism crystalline nanowire, which is theoretically treated to be composed of a hypothetical nanowire phase, a true two-dimensional geometric surface phase, and a true one-dimensional geometric edge phase. The hypothetical nanowire phase could be elastically deformed due to relaxation of a free-standing nanowire, without any applied load, with respect to its bulk counterpart. The initially deformed nanowire phase is taken as reference in the present work in the determination of excess surface and edge energies. The theoretical results indicate that the edge phase causes the nominal specific surface energy, surface stress, and surface stiffness to be size dependent, and the surface phase and the edge phase make the nominal Young’s modulus size dependent. The edge and surface effects are more significant as the cross-sectional area of a nanowire becomes smaller. Molecular dynamics simulations on hexagonal ...