Asymptotic analysis of a wedge crack in an anisotropic dielectric material

The asymptotic problem of a conducting crack emanating from the vertex of a wedge in an anisotropic dielectric material under purely electric loading is investigated. The wedge crack in an isotropic material is solved using a conformal mapping technique. The solution of the wedge crack in an anisotropic dielectric material is obtained from that for the transformed isotropic problem after applying a linear transformation method. The electric field intensity factor for the anisotropic wedge crack is obtained in the closed form. The effects of crack and wedge angles as well as anisotropic parameters on the electric field intensity factor are illustrated. The electric field intensity factor is numerically calculated by using the J integral and finite element analysis to validate the exact solution of the electric field intensity factor.     

Analysis of three collinear antiplane interfacial cracks in dissimilar piezoelectric materials under non-self equilibrated electromechanical loadings on a center crack

The problem of three collinear interfacial cracks between two dissimilar transversely isotropic piezoelectric materials is considered under electromechanical loadings. The crack surfaces are assumed to be impermeable to the electric field. A single antiplane mechanical and inplane electrical loads are applied at a point on centred crack surface. The problem is formulated by the complex function method, and reduced to the vector Hilbert problem. By solving the problem, a closed form solution for the stress intensity and electric displacement intensity factor is obtained. This solution can be used as a Green’s function for different loading conditions.     

Elastodynamic response of a crack perpendicular to the graded interfacial zone in bonded dissimilar materials under antiplane shear impact

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of antiplane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.     

Automated method for studying the deformation behavior of a material damaged by a thermal fatigue crack network

This paper presents a method for analyzing the fracture kinetics of a sample with multiple defects by calculating the change function of a crack image histogram. A method of automated identification of defect location is developed based on processing photo images of a surface with multiple defects taken at various stages of deformation of the investigated template. Experiments have confirmed that this method can be used to detect cracks whose direction coincides with one of the axes of the image.     

Analysis of a conducting crack in an electrostrictive ceramic under combined electric and mechanical loading

A conducting crack in an electrostrictive ceramic under combined electric and mechanical loading is investigated. Analysis based on linear dielectric model predicts that the surfaces of the crack are not open completely but they are contact near the crack tip. The complete solution for the crack with a contact zone in a linear electrostrictive ceramic under combined electric and mechanical loading is obtained by using the complex variable formula. The asymptotic problems for a semi-infinite crack with a partial opening zone as well as for a fully open semi-infinite crack in a nonlinear electrostrictive ceramic are analyzed in order to investigate the effect of the electrical nonlinearity on the stress intensity factor under small scale nonlinear conditions. Particular attention is devoted to a finite crack in the nonlinear electrostrictive ceramic subjected to combined electric and mechanical loading. The stress intensity factor for the finite crack under small scale nonlinear conditions is obtained from the asymptotic analysis.     

Analysis of a flat annular crack under shear loading

An annular crack in an infinite isotropic elastic solid under shear loading is analyzed. General solution to the Navier's equilibrium equation is expressed in terms of three harmonic functions. Employing the Hankel transform the harmonic functions are represented by the solution of a pair of triple integral equations. The triple integral equations are reduced to a pair of mixed Volterra-Fredholm integral equations, which are numerically solved. The stress intensity factors of the annular crack under various shear loadings such as uniform radial shear, linearly varying radial shear, uniform shear and linearly varying shear are calculated as the Poisson's ratio ν anda/b (a; inner radius,b; outer radius) vary.     

Characterisation of crack tip stresses in elastic-perfectly plastic material under mode-I loading

Asymptotic crack tip stress fields are developed for a stationary plane strain crack in incompressible elastic-perfectly plastic material under mode-I loading. Detailed investigations have revealed that in between the two extreme conditions of crack tip constraint, that is, between the fully plastic Prandtl [1] field and the uniform stress field the most general elastic-plastic crack tip fields can be completely described by the 5-sector stress solution proposed in this article. The 3-sector stress field proposed by Li and Hancock [2] and the 4-sector field proposed by Zhu and Chao [3] are subsets of the general elastic-plastic field proposed in this work. This study has revealed that cases arise where the severe loss of crack tip constraint can lead to compressive yielding of crack flank. This particular situation leads to 5-sector stress field. Detailed studies have revealed that, in the most general case of elastic-plastic crack tip fields, the T_π parameter proposed by Zhu and Chao [3] cannot be used as a constraint parameter to represent a unique state of stress at the crack tip. A new constraint-indexing parameter T_CS-2 is proposed, which along with T_p is capable of representing the entire elastic-plastic crack tip stress fields over all angles around a crack tip. Excellent agreement is obtained between the proposed asymptotic crack tip stress field and the full-field finite element results for constraint levels ranging from high to low. It is demonstrated that the proposed constraint parameters are adequate to represent the crack tip constraint arising due to specimen geometry and loading conditions as well as the additional constraint that arises due to weld strength mismatch.     

Analysis of a radial crack in cross-ply laminates under uniaxial tension

The problem of a radial crack in cross-ply laminates under uniaxial tension is investigated in this paper. The normalized stress intensity factors are obtained by the modified mapping collocation method which is based on analytic complex function theory of complex variables. The present results for an isotropic infinite plate show good agreement with existing solutions. In the range of small crack length, the stress intensity factor for a radial crack in cross-ply laminates under uniaxial tension becomes larger as the percentage of 0° plies increases. However in the range of large crack length, it is insensitive to the percentage of 0° plies.     

Analysis of an unsteadily propagating crack under mode I and II loading

Stress and displacement fields for an unsteadily propagating crack under mode I and II loading are developed through an asymptotic analysis. Dynamic equilibrium equations for the unsteady state are developed and the solution to the displacement fields and the stress fields for a crack propagating with high crack tip acceleration, deceleration and rapidly varying stress intensity factor. The influence of transients on the higher order terms of the stress fields are explicitly revealed. Using these stress components, isochromatic fringes around the propagating crack are generated for different crack speeds, crack tip accelerations and the time rate of change of stress intensity factor, and the effects of the transients on these fringes are discussed. The effects of the transients on the dynamic stress intensity factor are discussed when a crack propagates with high acceleration and deceleration. The effect of transient on the time rate of change of dynamic stress intensity factor below Rayleigh wave speed in an infinite body is also studied.     

Analysis of a crack approaching a circular hole in cross-ply laminates under biaxial loading

The problem of a crack approaching a circular hole in cross-ply laminates under uniaxial and biaxial loading is investigated in this paper. The effects of material orthotropy, geometry [R/d and a/d], and loading conditions on crack tip singularity are investigated. The stress intensity factors are obtained by the modified mapping collocation method. The present results for an isotropic infinite plate show good agreement with existing solutions. The results for cross-ply laminates show that the stress intensity factors strongly depend on material orthotropy, geometry, and loading condition. The stress intensity factors for cross-ply laminates exist between those for θ=0° and those for θ=90° in the whole range of crack length and decrease as the percentage of 0° plies increases. In the range of small crack length the stress intensity factors for biaxial tension are higher than those for uniaxial tension. In the range of large crack length the stress intensity factors for uniaxial tension are higher than those for biaxial tension.     

The effect of deformation anisotropy on the plastic zone at the tip of a crack under biaxial loading

A theoretical analysis for investigating the form and dimension of the plastic zone in the tip of a crack in a plate made from a material with deformation anisotropy is presented. The anisotropy is explained by the hardening process during plastic deformation caused by loading along a straight-line trajectory until a crack is formed in the plate plane. The idea of this method is to take into account the second term in the Williams’ series representation in eigenfunctions for stress components for the 2D case. The contribution of the second term in the Cartesian coordinate system is independent of the distance from the crack tip for the K ₁ − T concept. It is shown that for the case of anisotropy, the dimension of the plastic zone decreases. The stress along the crack’s axis changes the plastic zone significantly.     

Localization of plastic deformation along grain boundaries in a hardening material

The deformation characteristics of ductile polycrystalline materials at elevated temperatures were studied numerically by considering a square segment of material subjected to different stress modes. The initial polycrystalline microstructure was generated numerically. The micromechanical modeling of the deformation was performed using the material point method. The constitutive behavior was taken to be isotropic, elastic–plastic with linear hardening. To effectively simulate the deformation at high homologous temperatures, the grain boundary region was assumed to be a layer of finite thickness, bearing a lower yield strength than the interior of the grain. Complex deformation patterns were observed. The deformation is dominated by the formation of zones of concentrated instantaneous deformation along grain boundaries. These zones form paths that vary with time, and depend on the microstructure and macroscopic loading mode. The macroscopic stress, as well as the microscopic stresses at various locations within the grain boundary and grain interior, were seen to correlate with the instantaneous deformation pattern throughout the deformation history. For the sample analyzed, with a relatively small macroscopic strain of 0.01, the grain boundary region experienced plastic strains as large as 0.20, a result which provided a strong indication that failure will initiate in the grain boundaries. Implications of this modeling study to actual creep deformation and failure are discussed.     

Finite deformation of a fully fixed beam comprised of a non-linear material

The structural behaviour at finite deformation of a mild steel beam of rectangular cross-section, fully encastré at both ends and subjected to a concentrated load at mid-span, is examined in this paper. The axial tension, induced in the beam by virtue of its change in geometric configuration, gives rise to a load-carrying capacity of the beam in excess of that predicted by first-order flexural theory. Existing methods of analysis, assuming the beam to be composed solely of a linear elastic or a pure plastic material, are reviewed and an analysis is proposed for a beam composed of an elastic-plastic material. Experimental results are compared with theoretical predictions and the proposed elastic-plastic analysis is seen to give the most realistic prediction of the overall behaviour of the beam.     

Eccentric crack in a piezoelectric strip under electro-mechanical loading

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith eccentric crack off the center line under anti-plane shear loading with the theory of linear piezoelectricity. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate are obtained, and the influences of the electric fields for piezoelectric ceramics are discussed.     

弯管内拱壁含环向贯穿裂纹的极限载荷分析研究

含环向贯穿裂纹的弯管在受平面弯矩时明显地降低了其极限载荷,因此对含裂纹弯管的极限载荷研究是很有必要的。研究工作涉及了基于不同的裂纹角度、壁厚以及平均弯曲半径的弯管,进而比较了这些因素对弯管极限载荷的影响。利用ABAQUS软件对弯管进行三维有限元分析,得到了弯矩与末端转动曲线,以及用TES（Twice—elastic slope）方法得到每种情况的极限载荷值,该值与现有的部分工程方法进行了对比分析。结果表明,在大多数情况下工程法相对于有限元法保守。     

The process of the momentary arrest of a moving crack approaching a material discontinuity

The process of a moving transverse crack which coalesces with different types of material discontinuities (interfaces in multiphase specimens, longitudinal cracks, small holes, etc), and the related process of momentary crack-arrest was investigated. All momentary crack-arrest processes seem to belong to a specific type of crack arrest which depends mainly on the rapid transfer of the kinetic and strain energies stored at the propagating crack-tip, from the tip of the crack to the existing discontinuity, as the crack approaches it.     

镍基耐蚀材料结晶裂纹的研究综述

总结了解研究焊接结晶裂纹的几种主要试验方法，并简述了影响其焊接结晶裂纹的主要元素。     

Analysis of an anisotropic porous slider bearing considering slip velocity

A porous slider bearing with anisotropic permeability and slip velocity is considered. Expressions for the load-carrying capacity, friction, coefficient of friction and the position of the centre of pressure are obtained in integral form. Anisotropic permeability and slip affect these bearing characteristics.     

Experimental investigation of material deformation and failure regularities in a flat stressed state

Some problems of how to use modern experimental facilities—an Inston 8850 biaxial servohydraulic test system and Vic 3D Limess digital optical system—for analyzing the fields of deformation and displacements in order to investigate the regularities of material inelastic deformation and failure in a complicated stressed-deformed state are examined. Proportional loading with different ratios between the axial deformation and the shear angle is implemented. Diagrams of the material deformation for different stress states are generated. The diagrams of material deformation with a drop-down branch are obtained under uniaxial tension for samples with different ratios between the length and diameter. Information about the deformation fields taking place in the plates with stress concentrators determined by means of the correlation of digital images are presented.