Finite-deformation crack in an infinite body under anti-plane simple shear

The anti-plane shear crack problem in an infinite body is studied within the context of finite-deformation elastostatics. The governing equations are found to be identical to those of certain previously studied small strain plastic problems under anti-plane shear. For a particular strain energy function, an exact solution of the problem is obtained through use of results in the literature.     

Fully plastic crack in an infinite body under anti-plane shear

The problem of a semi-infinite body with an edge crack subjected to far out-of-plane shear is solved by a transformation to a hodograph plane and the Wiener-Hopf technique. The material stress-strain behavior is governed by a pure power hardening relation and the results are valid for both deformation theory and flow theory of plasticity. Results are presented for crack opening displacement, path independent J integral and crack tip singularities for all finite values of the power hardening parameter.     

Scattering of harmonic anti-plane shear waves by an interface crack in magneto-electro-elastic composites

IntroductionCompositematerialconsistingofapiezoelectricphaseandapiezomagneticphasehasdrawnsignificantinterestinrecentyears,duetotherapiddevelopmentinadaptivematerialsystems .Itshowsaremarkablylargemagnetoelectriccoefficient,thecouplingcoefficientbetweenst…     

Layered piezoelectric medium with interface crack under anti-plane shear

The theory of linear piezoelectricity is applied to solve the anti-plane shear problem of a piezoelectric layer sandwiched by two dissimilar homogeneous materials with a crack at the interface. Both mechanical and electrical loads are applied to the piezoelectric laminate. By the use of Fourier transforms, the mixed boundary value problem is reduced to a singular integral equation which is solved numerically to determine the stress intensity factors for several layered piezoelectric media, and the results are presented in graphical form.     

Elastic-plastic analytical solutions for an eccentric crack loaded by two pairs of anti-plane point forces

IntroductionTheelastic_plasticanalysisforacrackedplatewithfinitedimensionsisoneofthemostdifficultfieldsofelastic_plasticmechanics .Thenearcracklineanalysismethod ,whichwasfirstproposedbyAchenbachetal.[1,2 ] ,hasbeenimprovedbyYiinRefs.[3,4 ].InRefs.[3,4 ],…     

Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading

The behaviour of a bi-piezoelectric ceramic layer with a centre interfacial crack subjected to anti-plane shear and in-plane electric loading has been studied. The dislocation density functions and the Fourier integral transform method have been employed to eliminate the problem of singular integral equations. The normalized energy release rate, stress and electrical displacement intensity factors, G/G₀,K_III/K_III0 and K_D/K_D0, respectively, were determined for different geometric and property parameters by use of two different crack surface electric boundary conditions, i.e. impermeable and permeable. It has been shown that the effects of the thickness and material constants of the piezoelectric layer on all the three parameters, i.e. G/G₀,K_III/K_III0 and K_D/K_D0 were significant.     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

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Electroelastic field for an impermeable anti-plane shear crack in a piezoelectric ceramics plate

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate are obtained. The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h → ∞. Biography: LI Xian-fang (1964-)     

A general solution method for an anti-plane shear crack dynamically accelerating along a bimaterial interface

We develop a general solution method for a dynamically accelerating crack under anti-plane shear conditions along the interface between two different homogeneous isotropic elastic materials. The crack is initially at rest, and after loading is applied the crack-tip speed which may accelerate up to the shear wave speed of the more compliant material. The analysis includes an exact, closed-form expression for the stress intensity factor for an arbitrary time-dependent crack-face traction, as well as expressions for computing the crack-face displacements and the stress in front of the crack. We also present some numerical examples for fixed loads and for loads moving with the crack tip, using a stress intensity factor fracture criterion, in order to examine the predicted effect of material mismatch on interfacial fracture.     

Analysis of bonded anisotropic wedges with interface crack under anti-plane shear loading

The antiplane stress analysis of two anisotropic finite wedges with arbitrary radii and apex angles that are bonded together along a common edge is investigated. The wedge radial boundaries can be subjected to displacement-displacement boundary condi- tions, and the circular boundary of the wedge is free from any traction. The new finite complex transforms are employed to solve the problem. These finite complex transforms have complex analogies to both kinds of standard finite Mellin transforms. The traction free condition on the crack faces is expressed as a singular integral equation by using the exact analytical method. The explicit terms for the strength of singularity are extracted, showing the dependence of the order of the stress singularity on the wedge angle, material constants, and boundary conditions. A numerical method is used for solving the resul- tant singular integral equations. The displacement boundary condition may be a general term of the Taylor series expansion for the displacement prescribed on the radial edge of the wedge. Thus, the analysis of every kind of displacement boundary conditions can be obtained by the achieved results from the foregoing general displacement boundary condition. The obtained stress intensity factors （SIFs） at the crack tips are plotted and compared with those obtained by the finite element analysis （FEA）.     

冲击载荷作用下裂纹动态响应的数值模拟

对垂直、剪切以及斜向等各种冲击载荷作用下裂纹的动态响应进行了数值模拟,得到了一系列随时间变化的动态应力场以及应变场图;根据其定义,计算出了相应的动态应力强度因子,进而分析了斜向载荷作用下裂纹起裂情况,并对最优断裂问题进行了阐述。     

The anti-plane shear field in an infinite slab of elasto-damaged material with a semi-infinite crack

This paper deals with an infinite slab with a semi-infinite crack, which is subjected to the anti-plane sheark _III field at infinity. The slab is made of an elasto-damaged material. Analytical solution is obtained by use of conformal mapping. The shape of damaged-zone, the dissipative energy, the shear opening displacement on the crack surface and several stress distribution curves are given. The far field condition is checked, The asymptotic behavior near the crack-tip is given. The project supported by National Natural Science Foundation of China     

Energy density and release rate study of an elliptic-arc interface crack in piezoelectric solid under anti-plane shear

The anti-plane problem of an elliptical inhomogeneity with an interfacial crack in piezoelectric materials is investigated. The system is subjected to arbitrary singularity loads (point charge and anti-plane concentrated force) and remote anti-plane mechanical and in-plane electrical loads. Using the complex variable method, the explicit series form solutions for the complex potentials in the matrix and the inclusion regions are derived. The electroelastic field intensity factors, the corresponding energy release rates and the generalized strain energy density at the cracks tips are then provided. The influence of the aspect ratio of the ellipse, the crack geometry and the electromechanical coupling coefficient on the energy release rate and the strain energy density is discussed and shown in graphs. The results indicate that the energy release rate increases with increment of the aspect ratio of the ellipse and the influence of electromechanical coupling coefficient on the energy release rate is significant. The strain energy density decreases with increment of the aspect radio of the ellipse and it is always positive for the cases discussed. The energy release rate, however, can be negative when both mechanical and fields are applied.     

Ⅲ型界面裂纹面受变载荷Pxmtn作用下的自相似解

通过复变函数论的方法,对Ⅲ型界面裂纹表面受变载荷$Px^mt^n$作用下的动态扩 展问题进行了研究. 采用自相似函数的方法可以获得解析解的一般表达式. 应用 该法可以很容易地将所讨论的问题转化为Riemann-Hilbert问题, 然后应 用Muskhelishvili方法就可以较简单地得到问题的闭合解. 利用这些解 并采用叠加原理,就可以求得任意复杂问题的解.     

Asymptotic analysis of an impermeable crack in an electrostrictive material subjected to electric loading

The simple asymptotic problem of an impermeable crack in an electrostrictive ceramic under electric loading is analyzed. Closed form solutions of elastic fields are obtained by using the complex function theory. It is found that the K_I-dominant region is very small compared to the electric saturation zone. A fracture parameter for an electrostrictive material subjected to electric loading is discussed. In order to investigate the influence of the transverse electric displacement on fracture behavior under the small-scale conditions, we also consider the modified boundary layer problem of a crack in an electrostrictive material. Analytic solutions of electric displacement fields for the asymptotic problem are obtained based on the nonlinear dielectric theory from a modified boundary layer analysis. The shape of the electric displacement saturation zone is shown to depend on the transverse electric displacement. Stress intensity factors induced by the electrostrictive strains are evaluated using the nonlinear solution of the electric displacements. It is found that the transverse electric displacement affects strongly the variation of the mode mixity.     

The singularity behavior of an interface crack under a dynamic load

The singularity behavior of a crack on the interface of two different media under dynamic load is investigated. By introducing a small region in which the crack faces make frictionless contact and making use of a kind of integral equations with moving boundaries, it is proved that there are only square-root singularities near the interface crack tips in case that a dynamic load acts on it. Numerical results show that the normal stress in the contact region remains negative. The results of the stress intensity factor and the length of the crack face contact region are given to illustrate the dynamic behavior of the interface crack.This work is supported by the National Natural Science Foundation of China.     

A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.     

Crack growth of an interface crack between two dissimilar magneto-electro-elastic materials under anti-plane mechanical and in-plane electric magnetic impact

This paper examines the dynamic response of an interface crack between two dissimilar magneto-electro-elastic materials subjected to the mechanical and electric magnetic impacts. The magneto-electric impermeable boundary conditions are adopted. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations in Laplace transform domain, which are solved numerically. Lots of numerical results are given graphically in time domain. The effects of electric impact loading and magnetic impact loading on dynamic energy density factors are discussed. Crack growth and propagation is predicted. The study of this problem is expected to have applications to the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks.     

Post-buckling analysis of slender elastic rods subjected to terminal forces

This paper presents formulation and solutions for the elastica of slender rods subjected to axial terminal forces and boundary conditions assumed hinged and elastically restrained with a rotational spring. The set of five first-order non-linear ordinary differential equations with boundary conditions specified at both ends constitutes a complex two-point boundary value problem. Solutions for buckling, initial post-buckling (perturbation), large loads (asymptotic) and numerical integration are developed. Results are presented in non-dimensional graphs for a range of rotational spring stiffness, tuning the analysis from double-hinged to hinged-built-in rods.