W.J. Feng

Stress Analysis of a Penny-Shaped Crack in a Magneto-Electro-Thermo-Elastic Layer Under Uniform Heat Flow and Shear Loads

This article analyzes the mechanical behavior induced by a penny-shaped crack in a magneto-electro-thermal-elastic layer that is subjected to a heat flow. The surfaces of the magneto-electro-thermal-elastic layer are subjected to radial shear loads, and the crack is assumed to be thermally insulated. The Hankel transform technique is employed to reduce the problem to a Fredholm integral equation, which is then solved numerically. Shear stress intensity factors (SIFs) are obtained and discussed in detail. Numerical results reveals that in the case of only applied shear loads, the layer height has insignificant effects on the SIF when the ratio of the half-layer height h to crack radius a is larger than 2, and that in the case of only applied heat flow, the layer height also has insignificant effects on the crack extension force when h/a > 8. It is further interesting to note that for the magneto-electro-thermo-elastic layer under only applied heat flow, there exists a critical height as far as the stability of the crack is concerned.

Fracture analysis of bounded magnetoelectroelastic layers with interfacial cracks under magnetoelectromechanical loads: Plane problem

Fracture behaviors of multiple interfacial cracks between dissimilar magnetoelectroelastic layers subjected to in-plane magnetoelectromechanical loads are investigated by using integral transform method and singular integral equation technique. The number of the interfacial cracks is arbitrary, and the crack surfaces are assumed to be magnetoelectrically impermeable. The field intensity factors including stress, electric displacement and magnetic induction intensity factors as well as the energy release rates (ERRs) are derived. The effects of loading combinations, crack configurations and material property parameters on the fracture behaviors are evaluated according to energy release rate criterion. Numerical results show that both negative electrical and magnetic loads inhibit crack extension, and that the material constants have different and important effects on the ERRs. The results presented here should have potential applications to the design of multilayered magnetoelectroelastic structures.

Dynamic stress field for torsional impact of a penny-shaped crack in a transversely isotropic functional graded strip

Abstract The torsional impact response of a penny-shaped crack in a transversely isotropic strip is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Investigated are the effects of material nonhomogeneity and orthotropy and strip’s highness on the dynamic stress intensity factor. The peak of the dynamic stress intensity factor can be suppressed by increasing the shear moduli’s gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface. The dynamic behavior varies little with the increasing of the strip’s highness.

Fracture assessment of an interface crack between two dissimilar magnetoelectroelastic materials under heat flow and magnetoelectromechanical loadings

A magnetoelectrically permeable interface crack between two semi-infinite magnetoelectroelastic planes under the action of a heat flow and remote magnetoelectromechanical loadings is considered, where the assumption of frictionless contact between two dissimilar halfplanes is adopted. Not only the solutions of the interface crack problem are presented in an explicit form, but also the general condition for the transition from a perfect thermal contact of two magnetoelectroelastic bodies to their separation is given.

A second-order theory for magnetoelectroelastic materials with transverse isotropy

In this paper, we concentrate on the basic governing equations of three-dimensional problems in transversely isotropic and nonlinear magnetoelectroelastic materials (i.e., 6m m magnetic crystals). We place emphasis on developing the nonlinear and fully coupled constitutive relations between extended traction (including elastic stress, polarization and magnetization) and extended strain (including elastic strain, electric field and magnetic induction). Simplified results are also presented for the corresponding small deformation problems in the case of both strong magnetic and electric fields and in the case of both weak magnetic and electric fields. The derived concise equations are important in investigating the nonlinear magnetoelectric effects of novel magnetoelectroelastic materials.

A second-order theory for piezoelectricity with 6mm and m3 crystal classes

The present paper concentrates on the basic equations of three-dimensional problems for nonlinear piezoelectric materials of hexagonal systems with symmetry class 6mm and of cubic systems with symmetry class m3. Emphasis is placed on developing the nonlinear constitutive relations between extended traction (including elastic stress and polarization) and extended strain (including elastic strain and electric field). The corresponding one-dimensional mathematical models for piezoelectric ceramic with symmetry classes 6mm and m3 are also given. Numerical examples are also carried out for the impact problem to show the important effect of the piezoelectric nonlinearity on the stress wave. Therefore, the derived concise equations can directly be applied to evaluate the nonlinear piezoelectric effects of piezoelectricity by the nonlinear finite element method.

Dynamic Response of Multiple Coplanar Interface Cracks between Two Dissimilar Piezoelectric Materials

The linear piezoelectricity theory is applied to investigate the dynamic response of coplanar interface cracks between two dissimilar piezoelectric materials subjected to the mechanical and electrical impacts. The number of cracks is arbitrary, and the interface cracks are assumed to be permeable for electric field. Integral transforms and dislocation density function are employed to reduce the problem to Cauchy singular integral equations. Numerical examples are given to show the effects of crack relative position and material property parameters on the variations of dynamic energy release rate.

Fracture Failure Prediction of a Mode III Crack in Orthotropic Functionally Graded Strip

Mode III fracture failure of a through crack in an orthotropic functionally graded strip is investigated. The shear moduli in two directions of the material are respectively assumed to vary proportionately as a definite gradient. Fourier cosine transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Energy density factor criterion is applied to obtain the maximum of the minimum energy density and direction of crack initiation. Numerical results are given graphically to illustrate the effects of the material property parameters and geometry criterion on the energy density factor.

Transient thermal fracture analysis of a penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder

ABSTRACT The problem of penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder is investigated under thermal shock load. The problem is reduced to solve three coupled Fredholm integral equations. The field intensity factors are derived. Numerical results of crack opening displacement intensity factors are presented, and the effects of thermal shock time, crack configuration, and magnetoelectrical crack surface conditions on crack propagation and growth are evaluated. Among others, the larger cylinders radius, the easier to propagate the crack is. For a fixed crack configuration, magnetoelectrical crack surface conditions have different effects on crack propagation as well.

Analysis of symmetric and skew-symmetric weight functions for a semi-infinite interfacial crack in transversely isotropic piezoelectric bimaterials

This paper presents an analysis of symmetric and skew-symmetric weight functions for in-plane interfacial crack problems in piezoelectric bimaterials. The symmetric weight function matrix is obtained by means of the solution of a Wiener–Hopf functional equation and the skew-symmetric weight function matrix is developed by the construction of a corresponding full field solution. The explicit expressions for the symmetric and skew-symmetric weight functions are given and applied to in-plane deformation problems for a semi-infinite crack between two dissimilar piezoelectric materials. The validity of the present method in the determination of the field intensity factors is demonstrated by illustrative examples, in which both piezoelectric bimaterials and piezoelectric/elastic bimaterials are considered. It is shown that, for the present interfacial crack problem, both symmetric and skew-symmetric weight function matrices are necessary in the general integral formula for the evaluation of field intensity factors, and that the contribution of the skew-symmetric element of the applied load is not negligible in fracture analysis.