Dynamic stress intensity factors of multiple cracks in a functionally graded orthotropic half-plane

In the present paper dynamic stress intensity factor and strain energy density factor of multiple cracks in the functionally graded orthotropic half-plane under time-harmonic loading are investigated. By utilizing the Fourier transformation technique the stress fields are obtained for a functionally graded orthotropic half-plane containing a Volterra screw dislocation. The variations of the material properties are assumed to be exponential forms which the equilibrium has an analytical solution. The dislocation solution is utilized to formulate integral equation for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determined stress intensity factor and strain energy density factors (SEDFs) for multiple smooth cracks under anti-plane deformation. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded orthotropic half-plane with multiple curved cracks.     

Anti-plane analysis of a functionally graded strip with multiple cracks

The stress fields are obtained for a functionally graded strip containing a Volterra screw dislocation. The elastic shear modulus of the medium is considered to vary exponentially. The stress components exhibit Cauchy as well as logarithmic singularities at the dislocation location. The dislocation solution is utilized to formulate integral equations for the strip weakened by multiple smooth cracks under anti-plane deformation. Several examples are solved and stress intensity factors are obtained.     

Cracking in orthotropic half-plane with a functionally graded coating under anti-plane loading

This investigation evaluates, by the dislocation method, the dynamic stress intensity factors of cracked orthotropic half-plane and functionally graded material coating of a coating–substrate material due to the action of anti-plane traction on the crack surfaces. First, by using the complex Fourier transform, the dislocation problem can be solved and the stress fields are obtained with Cauchy singularity at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks in the orthotropic half-plane with functionally graded orthotropic coating. Several examples are solved and dynamic stress intensity factors are obtained.     

Periodic cracks in a functionally graded piezoelectric layer bonded to a piezoelectric half-plane

Studied is the problem of a periodic array of cracks in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric material. The properties of the functionally graded piezoelectric strip, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The crack surface condition is assumed to be electrically impermeable or permeable. Integral transform and dislocation density functions are employed to reduce the problem to the solution of a system of singular integral equations. The effects of the periodic crack spacing, material constants and the geometry parameters on the stress intensity factor, the energy release ratio and the energy density factor are studied.     

Anti-Plane stress analysis of orthotropic rectangular planes weakened by multiple defects

The solution of a Volterra type screw dislocation problem in an orthotropic rectangular plane with finite length and width and various boundary conditions is obtained by means of a separation of variables technique. A distributed dislocation method is employed to obtain integral equations of the plane with cracks and cavities under an anti-plane traction. The ensuing equations are of the Cauchy singular type and have been solved numerically. Several examples are presented to demonstrate the applicability of the proposed solution.     

考虑尺度影响的平面正交各向异性功能梯度微梁的屈曲分析

基于新修正偶应力理论,建立了能描述尺度效应的各向异性功能梯度微梁的屈曲分析模型。基于最小势能原理推导了控制方程及边界条件,并以简支梁为例分析了屈曲载荷及尺度效应受材料尺度参数和几何尺寸的影响。算例结果表明,在材料几何尺寸较小时,本文模型预测到的屈曲载荷明显大于传统理论的结果,有效地反映了尺度效应。几何尺寸较大时,尺度效应消失,本文模型将自动退化为传统宏观模型。模型反映出不同方向上的尺度参数对各向异性材料影响的效果不同。     

Three-dimensional analysis of doubly curved functionally graded magneto-electro-elastic shells

Three-dimensional (3D) solutions for the static analysis of doubly curved functionally graded (FG) magneto-electro-elastic shells are presented by an asymptotic approach. In the present formulation, the twenty-nine basic equations are firstly reduced to ten differential equations in terms of ten primary variables of elastic, electric and magnetic fields. After performing through the mathematical manipulation of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recurrent sets of two-dimensional (2D) governing equations for various order problems. These 2D governing equations are merely those derived in the classical shell theory (CST) based on the extended Love–Kirchhoffs' assumptions. Hence, the CST-type governing equations are derived as a first-order approximation to the 3D magneto-electro-elasticity. The leading-order solutions and higher-order corrections can be determined by treating the CST-type governing equations in a systematic and consistent way. The 3D solutions for the static analysis of doubly curved multilayered and FG magneto-electro-elastic shells are presented to demonstrate the performance of the present asymptotic formulation. The coupling magneto-electro-elastic effect on the structural behavior of the shells is studied.     

Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading and constraint conditions. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two- and three-dimensional mixed-mode fracture problems are selected from the literature for comparison. Two-dimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain and stress loadings, a slanted crack in a finite-size FGM plate under exponentially varying tensile stress loading and an edge crack in a finite-size plate under shear traction load. The three-dimensional example models a deflected surface crack in a finite-size FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs.     

In-plane analysis of a cracked orthotropic half-plane

The stress fields in an orthotropic half-plane containing Volterra type climb and glide edge dislocations under plane stress condition are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surface of smooth cracks embedded in the half-plane under in-plane loads. The integral equations are of Cauchy singular type which are solved numerically. The dislocation density functions are employed to evaluate modes I and II stress intensity factors for multiple cracks with different configurations.     

Analytical solution of multiple moving cracks in functionally graded piezoelectric strip

The dynamic behaviors of several moving cracks in a functionally graded piezoelectric (FGP) strip subjected to anti-plane mechanical loading and in-plane electrical loading are investigated. For the first time, the distributed dislocation technique is used to construct the integral equations for FGP materials, in which the unknown variables are the dislocation densities. With the dislocation densities, the field intensity factors are determined. Moreover, the effects of the speed of the crack propagation on the field intensity factors are studied. Several examples are solved, and the numerical results for the stress intensity factor and the electric displacement intensity factor are presented graphically finally.     

Limit equilibrium of an orthotropic plate weakened by a periodic row of collinear cracks

A modified δ_c-model is used to study the limiting state of an orthotropic plate weakened by a periodic row of collinear cracks and satisfying a general failure criterion. The failure mechanism of the plate is analyzed.Astudy is made of the effects of the degree of orthotropy, the biaxiality of external loading, and the geometrical parameters on the fracture process zones at the crack tips and the limiting state of the plate. The safe loading of an orthotropic viscoelastic plate with a periodic row of collinear cracks is examined. The effect of the rheological parameters on the safe-load region is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 126–135, August 2008.     

Thermoelastic contact instability of a functionally graded layer and a homogeneous half-plane

The conductive heat transfer between two elastic bodies in the static contact can cause the system to be unstable due to the interaction between the thermoelastic distortion and pressure-dependent thermal contact resistance. This paper investigates the thermoelastic contact instability of a functionally graded material (FGM) layer and a homogeneous half-plane using the perturbation method. The FGM layer and half-plane are exposed to a uniform heat flux and are pressed together by a uniform pressure. The material properties of the FGM layer vary exponentially along the thickness direction. The characteristic equation governing the thermoelastic stability behavior is obtained to determine the stability boundary. The effects of the gradient index, layer thickness and material combination on the critical heat flux are discussed in detail through a parametric study. Results indicate that the thermoelastic stability behavior can be modified by adjusting the gradient index of the FGM layer.     

Asymptotic analysis of transient curved crack in functionally graded materials

Transient mixed-mode elastodynamic crack growth along arbitrary smoothly varying paths in functionally graded materials (FGMs) is considered. The property gradation in FGMs is considered by varying shear modulus and mass density exponentially along the gradation direction. Crack tip out of plane displacement fields and their gradients are developed for propagating curved cracks of arbitrary velocity using asymptotic approach. The mode-mixity due to the inclination of curved crack with respect to property gradient is accommodated in the analysis through superposition of the opening and shear modes. The expansion of the displacement fields and their gradients around the crack-tip are derived in powers of radial coordinates with the coefficients of expansion depending on the instantaneous value of the local curvature of the crack path, time derivatives of crack-tip speed, and time derivative of mode-I and mode-II stress intensity factors. The effect of the transient terms instantaneous local curvature, crack-tip speed, time derivatives of crack-tip speed, and time derivative of mode-I and mode-II stress intensity factors on the contours of constant out of plane displacement are also discussed.     

Elastodynamic analysis of a plane weakened by several cracks

The stress fields in an infinite plane containing Volterra type climb and glide edge dislocations under time-harmonic excitation are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type which are solved numerically for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.     

An embedded mixed-mode crack in a functionally graded magnetoelectroelastic infinite medium

This paper focuses on the study of the influence of a mixed-mode crack on the coupled response of a functionally graded magnetoelectroelastic material (FGMEEM). The crack is embedded at the center of a 2D infinite medium subjected to magnetoelectromechanical loads. The material is graded in the direction orthogonal to the crack plane and is modeled as a nonhomogeneous medium with anisotropic constitutive laws. Using Fourier transform, the resulting plane magnetoelectroelasticity equations are converted analytically into singular integral equations which are solved numerically to yield the crack-tip mode I and II stress intensity factors, the electric displacement intensity factors and the magnetic induction intensity factors. The main objective of this paper is to study the influence of material nonhomogeneity on the fields’ intensity factors for the purpose of gaining better understanding on the behavior of graded magnetoelectroelastic materials.     

Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch

This paper investigates the two-dimensional frictionless contact problem of a functionally graded magneto-electro-elastic materials (FGMEEMs) layered half-plane under a rigid flat or a cylindrical punch. It is assumed that the punch is a perfect electro-magnetic conductor with a constant electric potential and a constant magnetic potential. The magneto-electro-elastic (MEE) properties of the FGMEEM layer vary exponentially along the thickness direction. Using the Fourier transform technique, the contact problem can be reduced to Cauchy singular integral equations, which are then solved numerically to determine the normal contact stress, electric displacement and magnetic induction on the contact surface. Numerical results show that the gradient index, punch geometry and magneto-electro-mechanical loads have a significant effect on the contact behavior of FGMEEMs.     

Thermo-stress concentration of an orthotropic plate weakened by multiple elliptical holes

A laminate weakened by multiple elliptical holes of arbitrary distribution, arbitrary orientation and arbitrary dimensions, is treated as an anisotropic, infinite, multiple connected thin plate. By Faber series expansion [1–6] and a complex potential method in the plane theory of thermo-elasticity of an anisotropic body, the general step to deduce the thermostress concentration in the laminate subjected to arbitrary mechanical and thermal loads is obtained.Supported by The Chinese Science Foundation of Aeronautics     

The dynamic response of an edge crack in a functionally graded orthotropic strip

The dynamic response of a functionally graded orthotropic strip with an edge crack perpendicular to the boundaries is studied. The material properties are assumed to vary continuously along the thickness direction. Laplace and Fourier transforms are applied to reduce the problem to a singular integral equation. Numerical results are presented to illustrate the influences of parameters such as the nonhomogeneity constant and geometry parameters on the dynamic stress intensity factors (SIFs).     

The mixed-mode fracture mechanics analysis of an embedded arbitrary oriented crack in a two-dimensional functionally graded material plate

Mixed-mode fracture mechanics analysis of an embedded arbitrarily oriented crack in a two-dimensional functionally graded material using plane elasticity theory is considered. The material properties are assumed to vary exponentially in two planar directions. Then, employing Fourier integral transforms with singular integral equation technique, the problem is solved. The stress intensity factors (SIFs) at the crack tips are calculated under in-plane mechanical loads. Finally, the effects of crack orientation, material non-homogeneity, and other parameters are discussed on the value of SIF in mode I and mode II fracture.     

On the screw dislocation in a functionally graded piezoelectric plane and half-plane

In this paper closed-form expressions of the electroelastic field induced by a piezoelectric screw dislocation in a functionally graded piezoelectric plane and half-plane are derived. The material properties are assumed to vary exponentially along the x and y-directions. The solution for a screw dislocation in a functionally graded piezoelectric plane is obtained through introduction of two generalized stress functions. The solution for a screw dislocation in a functionally graded piezoelectric half-plane is derived by using the method of image. It is also found that the interaction between a piezoelectric screw dislocation and a circular insulating hole in the functionally graded piezoelectric material can be solved by using series expansion method.