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Zhen-gong Zhou - One of the best experts on this subject based on the ideXlab platform.
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investigation of anti plane shear behavior of a Griffith permeable Crack in functionally graded piezoelectric materials by use of the non local theory
Composite Structures, 2007Co-Authors: Zhen-gong ZhouAbstract:In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith Crack in functionally graded piezoelectric materials under the anti-plane shear loading for the permeable electric boundary conditions. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the Crack. By means of the Fourier transform, the problem can be solved with the help of a pair of dual-integral equations that the unknown variable is the jump of the displacement across the Crack surfaces. These equations are solved by use of the Schmidt method. Numerical examples are provided. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present near the Crack tips. The non-local elastic solutions yield a finite hoop stress at the Crack tips, thus allows us to using the maximum stress as a fracture criterion. The finite hoop stresses at the Crack tips depend on the Crack length, the functionally graded parameter and the lattice parameter of the materials, respectively.
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On the moving Griffith Crack in a non-homogeneous orthotropic medium
European Journal of Mechanics A-solids, 2005Co-Authors: Li Ma, Linzhi Wu, Zhen-gong ZhouAbstract:A finite Crack with constant length (Yoffe type Crack) propagating in the functionally graded orthotropic medium under the plane loading is investigated by means of the Schmidt method. By using the Fourier transform and defining the jumps of displacement components across the Crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the Crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties and the speed of the Crack propagating upon the dynamic fracture behavior.
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investigation of the dynamic behavior of a Griffith Crack in a piezoelectric material strip subjected to the harmonic elastic anti plane shear waves by use of the non local theory
Meccanica, 2004Co-Authors: Zhen-gong Zhou, Yu-guo Sun, Biao WangAbstract:In this paper, the dynamic behavior of a Griffith Crack in a piezoelectric material strip subjected to the harmonic anti-plane shear waves is investigated by use of the non-local theory for impermeable Crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near at the Crack tip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical solution, it is found that no stress and electric displacement singularity is present near the Crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the Crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the Crack tip depends on the Crack length, the thickness of the strip, the circular frequency of incident wave and the lattice parameter.
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investigation of a Griffith Crack subject to anti plane shear by using the non local theory
International Journal of Solids and Structures, 1999Co-Authors: Zhen-gong Zhou, Jiecai HanAbstract:Abstract Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith Crack subject to the anti-plane shear. Then a set of dual-integral equations is solved using Schmidts method. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the Crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales.
Z M Xiao - One of the best experts on this subject based on the ideXlab platform.
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plastic zone correction on a zener stroh Crack interacting with a circular inclusion in ductile materials
Fatigue & Fracture of Engineering Materials & Structures, 2016Co-Authors: M Fan, Z M XiaoAbstract:Elastic–plastic stress analysis on a matrix Zener–Stroh Crack interacting with a circular inclusion (fibre) in fibre-reinforced composites has been carried out. The Zener–Stroh Crack is initiated near the fibre in the pure matrix. Plastic zone correction is introduced the first time for such a Crack–inclusion interaction problem so that the fracture behaviour can be analysed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode problem where the Von Mises stress yielding criterion is employed. Different to a Griffith Crack, a Zener–Stroh Crack propagation always occurs from the sharp tip whose relative position to the inclusion has great effect on the elastic–plastic fracture behaviour of the Crack. In our study, the plastic zone size (PZS), Crack tip opening displacement (CTOD) and effective stress intensity factor (SIF) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fibre) shear modulus, Crack–inclusion distance and the Crack sharp tip position on the fracture behaviour of the Crack is discussed. It is found that the shear modulus ratio and the Crack–inclusion distance have great effect on the normalized values of PZS and CTOD, but the effects highly depend on the Crack sharp tip position.
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generalized irwin plastic zone correction for a Griffith Crack near a coated circular inclusion
International Journal of Damage Mechanics, 2015Co-Authors: M Fan, Z M XiaoAbstract:Elastic-plastic stress analysis on a radial Crack interacting with a coated-circular inclusion in a matrix has been carried out with the aid of a generalized Irwin plastic zone correction. The Crack line is assumed to be at the angle of 90° − θ from a remote tensile loading. In the mathematical formulation, the distributed dislocation method is used to simulate the Crack. By solving a set of singular integral equations, three quantities, the effective stress intensity factor, the plastic zone size and the Crack tip opening displacement (CTOD), are evaluated with the generalized Irwin model proposed. Numerical examples are given to show the influence of the key parameters such as the Crack orientation angle θ, the normalized Crack distance, the normalized coating phase thickness and the shear modulus ratio (μ2/μ3, coating phase/matrix) on the fracture behavior. The results indicate that the influence of angle θ is the greatest, while the effect of shear modulus ratio μ2/μ3 is relatively small. A validation...
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a zener stroh Crack in fiber reinforced composites with generalized irwin plastic zone correction
International Journal of Mechanical Sciences, 2014Co-Authors: M Fan, Z M XiaoAbstract:Abstract Elastic–plastic stress analysis on a matrix Zener–Stroh Crack interacting with nearby inclusions (the fibers) in fiber-reinforced composites has been carried out. The Zener-Stroh Crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. Plastic zone correction is introduced the first time for such a Crack-inclusion interaction problem so that the fracture behavior can be analyzed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode loading problem where the Von Mises stress yielding criterion is employed. Different to a Griffith Crack, a Zener–Stroh Crack propagation always occurs from the sharp tip whose relative position to the near-by fiber has great effect on the fracture behavior of the Crack. In our study, the effective stress intensity factor (SIF), plastic zone size (PZS) and Crack tip opening displacement (CTOD) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fiber) shear modulus, inclusion volume fraction and the Crack sharp tip position on the fracture behavior of the Crack is discussed. It is found that the shear modulus ratio has great effect on the normalized values of PZS and CTOD, while the effect of fiber volume fraction depends highly on the conditions of the inclusion/matrix properties and the Crack sharp tip position.
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stress investigation on a Griffith Crack initiated from an eccentric disclination in a cylinder
Acta Mechanica, 2009Co-Authors: J. Luo, Kun Zhou, Z M XiaoAbstract:Disclinations are rotational line defects which may be introduced in metal wires during the manufacturing process. In this work, the relaxation of an eccentric (off-center) negative wedge disclination in a cylinder by nucleation of a Griffith Crack is investigated. The nucleated Crack is simulated with distributed edge dislocations. The stress intensity factors (SIFs) of the Crack are evaluated by solving a set of singular integral equations. By enforcing the condition that the SIFs at the two Crack tips should keep the same value in the nucleation process, the Crack length growth on each side of the wedge disclination is determined. The critical disclination power and equilibrium Crack lengths are then numerically determined. Some important characteristics of the Griffith Crack nucleation are revealed. (1) The two tips of the nucleated Griffith Crack grow asymmetrically when the disclination locates eccentrically. The tip closer to the cylinder edge travels a shorter length. This asymmetry is getting more severe as the normalized off-center distance increases. (2) The critical disclination power increases monotonically with the normalized off-center distance. (3) The normalized stable equilibrium Crack length decreases as the normalized off-center distance increases while the normalized unstable equilibrium Crack length shows an opposite dependence. The dependence of the critical disclination power and the equilibrium Crack lengths on the disclination power and cylinder radius is also discussed in this work. It is believed that this work helps to predict the strength of disclinated metal wires at various length scales.
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a line dislocation interacting with a semi infinite Crack in piezoelectric solid
International Journal of Engineering Science, 2004Co-Authors: B J Chen, Z M Xiao, K M LiewAbstract:Closed-form analytical solutions are presented for the physical problem of a semi-infinite Crack interacting with a line dislocation under the loading of a line force and a line charge in two-dimensional infinite anisotropic piezoelectric medium. The Crack can be a conventional Griffith Crack or an anti-Crack (a rigid line inhomogeneity). Using the extended Stroh formalism and perturbation technique, the explicit expressions of the field intensity factors and the image force on the dislocation are computed as functions of dislocation location and material constants. The results are discussed and compared with those from special cases existed in the literature. The analytical solutions obtained can be applied to studying interacting Cracks and Crack branching problems in piezoelectric solids.
J N Reddy - One of the best experts on this subject based on the ideXlab platform.
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laminated anisotropic thin plate with an elliptic inhomogeneity
Mechanics of Materials, 2004Co-Authors: Zhenqiang Cheng, J N ReddyAbstract:This work is concerned with a through-thickness elliptic elastic inhomogeneity in a laminated anisotropic elastic thin plate within the context of the Kirchhoff theory. By means of the octet formalism recently established by the authors, an exact closed-form solution is obtained, for the first time, for coupled stretching and bending deformations of the plate subjected to remote uniform membrane stress resultants and bending moments. The stress resultants inside the elastic elliptic inhomogeneity are uniform, which is consistent with the uniformity property of the Eshelby inclusion solution in three-dimensional elasticity. In two special limit cases where the elliptic inhomogeneity becomes an elliptic rigid inclusion or hole, the corresponding solutions are also obtained. A relation between the rotational moment and the rotation is given for the elliptic rigid inclusion problem. The concentration factors of hoop membrane stress resultants and hoop bending moments are given for the elliptic hole problem. The intensity factors of membrane stress resultants and moments are obtained for a Griffith Crack. Displacements, slopes, membrane stress resultants and bending moments along the elliptic boundary for the elliptic inhomogeneity, rigid inclusion and hole problems are all presented in a real form.
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green s functions for an anisotropic thin plate with a Crack or an antiCrack
International Journal of Engineering Science, 2004Co-Authors: Zhenqiang Cheng, J N ReddyAbstract:Abstract Based on the octet formalism established by the authors, Green’s functions for an infinite anisotropic elastic thin plate with a Griffith Crack or an antiCrack (rigid line inclusion) are studied. The plate can be laminated or consist of a continuously inhomogeneous material in the thickness direction. Two systems of problems of the plate under non-self-equilibrated loads are solved. The first is associated with discontinuous in-plane displacements and slopes, in-plane concentrated forces and out-of-plane concentrated moments. The second is associated with a transverse concentrated force. The Green functions for an infinite plate with a Crack or an antiCrack and the surface Green functions for an infinite plate with a Crack are obtained in an exact closed form. The surface Green functions and associated stress resultants at any point throughout the line where the Crack is located are presented in a real form. The intensity factor of membrane stress resultants and bending moments are obtained in a real form for the Griffith Crack subjected to concentrated loads.
S. Itou - One of the best experts on this subject based on the ideXlab platform.
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stresses around a moving Griffith Crack at an interface between a nonhomogeneous bonding layer and two dissimilar orthotropic half spaces
International Journal of Mechanical Sciences, 2017Co-Authors: S. ItouAbstract:Abstract In this study, stresses were estimated for a moving interface Crack located on the lower interface between a nonhomogeneous elastic layer and a lower orthotropic elastic half-space while the upper interface between the layer and the upper orthotropic elastic half-space was not weakened by any Cracks. It was assumed that the moving Crack was open at one end and closed at the other and moved at a constant speed. The material properties of the bonding layer were assumed to vary continuously from the lower half-space to the upper half-space. A self-equilibrated system of pressure was applied to the Crack surfaces. The mixed boundary value conditions with respect to the Crack were reduced to dual integral equations. To solve the equations, the differences in the Crack surface displacements were expanded to a series of functions that equal zero outside the Crack. The unknown coefficients in the series were solved using the Schmidt method. The stress intensity factors were calculated numerically for the case in which the lower and upper half-spaces are made of unidirectional glass fiber-reinforced epoxy composites.
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Stress intensity factors around a moving Griffith Crack in a non-homogeneous layer between two dissimilar elastic half-planes
Acta Mechanica, 2004Co-Authors: S. ItouAbstract:Stresses are determined in the vicinity of a propagating finite Crack having a constant velocity in a non-homogeneous elastic layer sandwiched between two dissimilar elastic half-planes. The self-equilibrated system of pressure is applied to the Crack surfaces. Application of the Fourier transform technique reduces the problem to that of solving dual integral equations. In order to solve the equations, the differences in the Crack surface displacements are expanded in a series of functions that are equal to zero outside the Crack. The unknown coefficients in the series are solved by the Schmidt method. The stress intensity factors are calculated numerically for a Crack in a non-homogeneous layer between a half-plane made of epoxy resin and a half-plane made of aluminum.
Jiecai Han - One of the best experts on this subject based on the ideXlab platform.
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investigation of a Griffith Crack subject to anti plane shear by using the non local theory
International Journal of Solids and Structures, 1999Co-Authors: Zhen-gong Zhou, Jiecai HanAbstract:Abstract Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith Crack subject to the anti-plane shear. Then a set of dual-integral equations is solved using Schmidts method. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the Crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales.
