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Y Z Chen - One of the best experts on this subject based on the ideXlab platform.

  • numerical solution for curved Crack Problem in elastic half plane using hypersingular integral equation
    Philosophical Magazine, 2009
    Co-Authors: Y Z Chen, X Y Lin, X Z Wang
    Abstract:

    A hypersingular integral equation for the curved Crack Problems of an elastic half-plane is introduced. Formulation of the equation is based on the usage of a modified complex potential. The potential is generally expressed in the form of a Cauchy-type integral. The modified complex potential is composed of the principal part and the complementary part. The principal part of the complex potential is actually equivalent to the original complex potential for the curved Crack in an infinite plate. The role of the complementary part is to eliminate the boundary traction along the boundary of the half-plane caused by the principal part. From the assumed boundary traction condition, a hypersingular integral equation is obtained for the curved Crack Problems of an elastic half-plane. The curve length coordinate method is used to obtain a final solution. Several numerical examples are presented that prove the efficiency of the suggested method.

  • t stress in the zener stroh arc Crack Problem in plane elasticity
    Engineering Fracture Mechanics, 2008
    Co-Authors: Y Z Chen, Z. X. Wang, X Y Lin
    Abstract:

    Abstract A Zener–Stroh curved Crack is defined such that the Crack undergoes an initial displacement discontinuity. A singular integral equation is suggested to solve the Zener–Stroh curved Crack Problem. General formulation for evaluating the stress intensity factors and the T-stresses at the Crack tips of a Zener–Stroh curved Crack is carried out. For the Zener–Stroh arc Crack, T-stresses at the Crack tips can be evaluated in a closed form.

  • collinear zener stroh Crack Problem in plane elasticity
    Engineering Fracture Mechanics, 2008
    Co-Authors: Y Z Chen, X Y Lin
    Abstract:

    Abstract This paper investigates the collinear Zener–Stroh Crack Problem in plane elasticity. Two Cracks in series are chosen as an example in analysis. Different to the Griffith Crack Problem, an initial displacement discontinuity exists in the Zener–Stroh Crack Problem, which in turn is the increment of displacement when a moving point goes around the Crack in a closed loop. From the traction free condition along the Cracks, the dislocation distribution function as well as the complex potential with undetermined coefficients is suggested. The involved undetermined coefficients can be evaluated from the condition of the assumed initial displacement discontinuity. Finally, a closed form solution for the Problem is obtained and the calculated stress intensity factors at Crack tips are presented. A Problem for two collinear Zener–Stroh Cracks with different lengths is also studied.

  • Periodic group edge Crack Problem of half-plane in antiplane elasticity
    Communications in Numerical Methods in Engineering, 2007
    Co-Authors: Y Z Chen, Z. X. Wang
    Abstract:

    Using complex variable function, an elementary solution of a single-edge Crack Problem for half-plane is proposed. The elementary solution is obtained by distributing the dislocation density along the prospective place of Crack, and it is composed of the principal part and the complementary part. Based on the elementary solution and the principle of superposition, a system of Cauchy singular integral equations for periodic group edge Crack Problems of half-plane in antiplane elasticity can be formulated. In the solution of the singular integral equation, the influences of many neighbouring groups on the central group are evaluated exactly. In addition, the influences on the central group by the many remote groups are considered approximately. By using a semi-open quadrature rule, the singular integral equations are solved and the stress intensity factors at the Crack tips are evaluated. Several numerical examples are given. Copyright © 2007 John Wiley & Sons, Ltd.

  • solution of zener stroh arc Crack Problem in plane elasticity
    Mechanics Research Communications, 2005
    Co-Authors: Y Z Chen, X Y Lin, Z. X. Wang
    Abstract:

    Abstract In this paper, solution of the Zener–Stroh arc Crack in plane elasticity is present. The Problem is reduced to a solution of singular integral equation. After using some formulae and equations in complex variable function a closed form solution is obtained.

Licheng Guo - One of the best experts on this subject based on the ideXlab platform.

  • the interface Crack Problem for a functionally graded coating substrate structure with general coating properties
    International Journal of Solids and Structures, 2018
    Co-Authors: Licheng Guo, Shanqiao Huang, Li Zhang, Pengfei Jia
    Abstract:

    Abstract A piecewise-exponential model (PE model) is developed for the interface Crack Problem of a functionally graded coating-substrate structure in which the coating mechanical properties are generally continuous while the substrate is homogeneous. By this way, the coating properties can be approached by a series of exponential functions without losing the continuity. Through a series of mathematical manipulations, the Problem is reduced into a group of singular integral equations that can be solved by numerical methods. After analyzing the mix-mode stress intensity factors (SIFs) and the strain energy release rates (SERRs) of some typical examples under plane loadings, the influences of the geometric parameters and coating properties variations on the fracture behaviors of the interface Crack are presented. Those analyses can greatly benefit the designs and the manufactures of FGM coating-substrate structures.

  • a fracture mechanics model for a Crack Problem of functionally graded materials with stochastic mechanical properties
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2012
    Co-Authors: Licheng Guo, Zhihai Wang, Naotake Noda
    Abstract:

    This study aimed to develop a method to build a ‘bridge’ between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics Problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the Crack Problems of FGMs with stochastic properties.

  • mode i Crack Problem for a functionally graded orthotropic strip
    European Journal of Mechanics A-solids, 2004
    Co-Authors: Licheng Guo, Tao Zeng
    Abstract:

    A theoretical treatment of mode I Crack Problem is put forward for a functionally graded orthotropic strip. The internal Crack and edge Crack perpendicular to the boundaries are investigated, respectively. The elastic property of the material is assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. The singular integral equation for solving the Problem and the corresponding asymptotic expression of the singular kernel are obtained. Three different loading conditions, namely Crack surface pressure, fixed-grip loading and bending, are considered during the analysis. The influences of parameters such as the material constants and the geometry parameters on the stress intensity factors (SIFs) are studied.

  • the interface Crack Problem under a concentrated load for a functionally graded coating substrate composite system
    Composite Structures, 2004
    Co-Authors: Licheng Guo
    Abstract:

    Abstract The plane Crack Problem for a functionally graded coating–substrate system under a concentrated load is studied in this paper. The medium consists of a functionally graded coating bonded to a homogeneous substrate of finite thickness, containing an interface Crack of finite length. With use of the integration transform and differential factor methods, the displacement form can be obtained. By introducing auxiliary functions, the present Problem can be turned into solving a group of singular integral equations. The mixed-mode stress intensity factors (SIFs) and strain energy release rates (SERRs) are obtained. The influences of the parameters such as the load location, nonhomogeneity constants and the geometry parameters on the SIFs and SERRs are studied.

F. Erdogan - One of the best experts on this subject based on the ideXlab platform.

  • the mixed mode Crack Problem in an inhomogeneous orthotropic medium
    International Journal of Fracture, 1999
    Co-Authors: Murat Ozturk, F. Erdogan
    Abstract:

    The mixed mode Crack Problem in plane elasticity for a graded and oriented material is considered. The material property grading is intentional, whereas the property orientation or orthotropy is usually the consequence of material processing. It is assumed that the Crack is located in a plane perpendicular to the direction of property grading and the principal axes of orthotropy are parallel and perpendicular to the Crack. The four independent engineering constants E11, E22, G12, and ν12 are replaced by a stiffness parameter, E = √E11 E22, a stiffness ratio, δ = (E11/E22)1/4, a Poisson's ratio, ν = √ν12 ν21, and a shear parameter κ0 = (E/2G12) - ν. The corresponding mixed boundary value Problem is reduced to a system of integral equations which is solved for various loading conditions and material parameters. The results presented consist of the strain energy release rate, the stress intensity factors and the Crack opening displacements. It is found that generally the stress intensity factors increase with increasing material inhomogeneity parameter and shear parameter and with decreasing stiffness ratio.

  • the surface Crack Problem for a plate with functionally graded properties
    Journal of Applied Mechanics, 1997
    Co-Authors: F. Erdogan, B H Wu
    Abstract:

    In this study the plane elasticity Problem for a nonhomogeneous layer containing a Crack perpendicular to the boundaries is considered. It is assumed that the Young's modulus of the medium varies continuously in the thickness direction. The Problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the Crack region. Mode I stress intensity factors are presented for embedded as well as edge Cracks for various values of dimensionless parameters representing the size and the location of the Crack and the material nonhomogeneity. Some sample results are also given for the Crack-opening displacement and the stress distribution.

  • mode i Crack Problem in an inhomogeneous orthotropic medium
    International Journal of Engineering Science, 1997
    Co-Authors: Murat Ozturk, F. Erdogan
    Abstract:

    In the symmetric Crack Problem considered the material is both oriented and graded. The properties of the medium is assumed to vary monotonously in the x1-direction, x1 and x2 are the principal axes of orthotropy, and the Crack is located along the x1-axis. The loading is such that x2=0 is a plane of symmetry. The mode I Crack Problem for the inhomogeneous orthotropic plane is formulated and the solution is obtained for various loading conditions and material parameters. In the formulation four independent engineering constants, E11, E22, G12 and ν12, are replaced by a stiffness parameter E = √E11E22, a stiffness ratio c = (E11/E22)1/4, a Poisson's ratio ν = √ν12ν21 and a shear parameter κ = E/2G12 − ν. The results show that the stress intensity factors are independent of E and c and generally the effect of κ and ν on the stress intensity factors is not very significant. The exception is the values of κ approaching − 1, where the physical range of κ is − 1κ < ∞. In the isotropic case the kernel of the related integral equation is evaluated in closed form, which simplifies the numerical solution and improves the accuracy of the results.

  • the interface Crack Problem for a nonhomogeneous coating bonded to a homogeneous substrate
    Journal of The Mechanics and Physics of Solids, 1996
    Co-Authors: Y F Chen, F. Erdogan
    Abstract:

    Abstract The debonding Problem for a composite layer that consists of a homogeneous substrate and a non-homogeneous coating is considered. It is assumed that the Problem is one of plane strain or generalized plane stress and the elastic medium contains a Crack along the interface. It is further assumed that the thermomechanical properties of the medium are continuous functions of the thickness coordinate with discontinuous derivatives and the kink line of the property distributions corresponds to the “interface”. The mixed-mode Crack Problem is formulated for arbitrary Crack surface tractions and sample results are given for uniform normal and shear tractions. The main variables in the Problem are two dimensionless length parameters and a nonhmogeneity constant. Calculated results consist of primarily the stress intensity factors and the strain energy release rate and are partly intended to provide benchmark solutions for further numerical studies.

  • axsiymmetric Crack Problem in bonded materials with a graded interfacial region
    International Journal of Solids and Structures, 1996
    Co-Authors: Murat Ozturk, F. Erdogan
    Abstract:

    Abstract The Problem of a penny-shaped Crack in homogeneous dissimilar materials bonded through an interfacial region with graded mechanical properties is considered. The applied loads are assumed to be axisymmetric but otherwise arbitrary. The shear modulus of the interfacial region is assumed to be μ2(z) = μ1exp (αz) and that of the adherents μ1, and μ3 = μ1, μ1exp(αh), h being the thickness of the region. A Crack of radius α is located at the z = 0 plane. The axisymmetric mode III torsion Problem is separated and treated elsewhere. Because of material nonhomogeneity, the deformation modes I and II considered in this study are always coupled. The related mixed boundary value Problem is reduced to a system of singular integral equations. The asymptotic behavior of the stress state near the Crack tip is examined, and the influence of the thickness ratio h a and the material nonhomogeneity parameter α on the stress intensity factors and the strain energy release rate is investigated. The results show that the stress state near the Crack tip would always have standard square-root singularity provided h > 0 or the material properties are continuous but not necessarily differentiable functions of z.

Radhi Abdelmoula - One of the best experts on this subject based on the ideXlab platform.

  • Mode III Crack Problem in a functionally graded magneto-electro-elastic strip
    International Journal of Solids and Structures, 2007
    Co-Authors: Radhi Abdelmoula
    Abstract:

    Considering the material properties to be one-dimensionally dependent, this paper studied an anti-plane Problem for an embedded Crack and edge Crack perpendicular to the boundary of a functionally graded magneto-electro-elastic strip. The Crack is assumed to be either magneto-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. Numerical results show the effects of the loading combination parameter, material gradient parameter and Crack configuration on the field intensity factors and the energy release rates of the functionally graded magneto-electro-elastic strip.

W.j. Feng - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic internal Crack Problem of a functionally graded magneto-electro-elastic strip
    International Journal of Solids and Structures, 2006
    Co-Authors: W.j. Feng
    Abstract:

    In this paper the dynamic anti-plane Problem for a functionally graded magneto-electro-elastic strip containing an internal Crack perpendicular to the boundary is investigated. The Crack is assumed to be either magneto-electrically impermeable or permeable. Integral transforms and dislocation density functions are employed to reduce the Problem to Cauchy singular integral equations. Numerical results show the effects of loading combination parameter, material gradient parameter and Crack configuration on the dynamic response. With the magneto-electrically permeable assumption, both the magnetical and electrical impacts have no contribution to the Crack tip field singularity. However, with the impermeable assumption, both the applied magnetical loads and electrical loads play a dominant role in the dynamic fracture behavior of Crack tips. And for the two kinds of Crack surface conditions, increasing the graded index can all retard the Crack extension.