SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅱ)- INSTABILITY

Based on the (Ⅰ) of the present work, the behavior of shear beam model at crack initiation stage and at instable propagation stage was studied. The prime results include: 1) discriminant equation which clarifies the mode of instability, snap-back or snap-through, was established; 2) analytical solution was given out for the double shear beam and the load-displacement diagram for monotonic loading was presented for a full process; and 3) the problem of the energy release induced by instability was discussed.     

Boundary element analysis of interaction between an elastic rectangular inclusion and a crack

The interaction between an elastic rectangular inclusion and a kinked crack inan infinite elastic body was considered by using boundary element method. The new complexboundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundaryintegral equation was obtained on interface and involves only singularity of order l/ r. Toverify the validity and effectiveness of the present boundary element method, some typicalexamples were calculated. The obtained results show that the crack stress intensity factorsdecrease as the shear modulus of inclusion increases. Thus, the crack propagation is easiernear a softer inclusion and the harder inclusion is helpful for crack arrest.     

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.     

Investigation on behavior of crack penetration/deflection at interfaces in intelligent coating system

Based on the three-phase model, the propagation behavior of a matrix crack in an intelligent coating system is investigated by an energy criterion. The effect of the elastic mismatch parameters and the thickness of the interface layer on the ratio of the energy release rate for infinitesimal deflected and penetrated crack is evaluated with the finite element method. The results show that the ratio of the energy release rates strongly depends on the elastic mismatch α1between the substrate and the driving layer.It also strongly depends on the elastic mismatch α2between the driving layer and the sensing layer for a thinner driving layer when a primary crack reaches an interface between the substrate and the driving layer. Moreover, with the increase in the thickness of the driving layer, the dependence on α2gradually decreases. The experimental observation on aluminum alloys monitored with intelligent coating shows that the established model can better explain the behavior of matrix crack penetration and can be used in optimization design of intelligent coating.     

Analysis on the cohesive stress at half infinite crack tip

The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function . The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are give     

THEORETICAL MODEL ON INTERFACE FAILURE MECHANISM OF REINFORCED CONCRETE CONTINUOUS BEAM STRENGTHENED BY FRP

Fiber reinforced polymer （FRP） composites are increasingly being used for the re-pair and strengthening of deteriorated concrete structural components through adhesive bonding of prefabricated strips/plates and the wet lay-up of fabric. Interfacial bond failure modes have attracted the attention of researchers because of the importance. The objective of the present study is to analyse the interface failure mechanism of reinforced concrete continuous beam strength-ened by FRP. An analytical solution has been firstly presented to predict the entire debonding process of the model. The realistic bi-linear bond-slip interfacial law was adopted to study this problem. The crack propagation process of the loaded model was divided into four stages （elastic,elastic-softening,elastic-softening-debonded and softening-debonded stage）. Among them,elastic-softening-debonded stage has four sub-stages. The equations are solved by adding suitable stress and displacement boundary conditions. Finally,critical value of bond length is determined to make the failure mechanism in the paper effective by solving the simultaneously linear algebraic equations. The interaction between the upper and lower FRP plates can be neglected if axial stiffness ratio of the concrete-to-plate prism is large enough.     

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.     

QUASI-STATIC ANALYSIS FOR VISCOELASTIC TIMOSHENKO BEAMS WITH DAMAGE

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.     

A PENNY-SHAPED CRACK IN A MAGNETOELECTROELASTIC LAYER UNDER RADIAL SHEAR IMPACT LOADING

This paper analyzes the dynamic magnetoelectroelastic behavior induced by a penny- shaped crack in a magnetoelectroelastic layer.The crack surfaces are subjected to only radial shear impact loading.The Laplace and Hankel transform techniques are employed to reduce the prob- lem to solving a Fredholm integral equation.The dynamic stress intensity factor is obtained and numerically calculated for different layer heights.And the corresponding static solution is given by simple analysis.It is seen that the dynamic stress intensity factor for cracks in a magnetoelec- troelastic layer has the same expression as that in a purely elastic material.And the influences of layer height on both the dynamic and static stress intensity factors are insignificant as h/a>2.     

INVESTIGATION OF BEHAVIOR OF MODE-I INTERFACE CRACK IN PIEZOELECTRIC MATERIALS BY USING SCHMIDT METHOD

The behavior of a Mode-Ⅰinterface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.     

INVESTIGATION OF BEHAVIOR OF MODE-Ⅰ INTERFACE CRACK IN PIEZOELECTRIC MATERIALS BY USING SCHMIDT METHOD

The behavior of a Mode-Ⅰ interface crack in piezoelectric materials was investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips was negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. It is found that the stress and the electric displacement singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. The solution of the present paper can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.     

SCATTERING OF ANTI-PLANE SHEAR WAVES BY A SINGLE CRACK IN AN UNBOUNDED TRANSVERSELY ISOTROPIC ELECTRO-MAGNETO-ELASTIC MEDIUM

A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform, the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto imperme ableboundary conditions. The closed form expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor.     

Dynamic fracture analysis of adhesive bonded material under normal loading

Dynamic fracture behavior of a Griffith crack along the interface of an adhesive bonded material under normal loading is studied. The singular integral equations are obtained by employing integral transformation and introducing dislocation density functions. By adopting Gauss-Jacobi integration formula, the problem is reduced to the solution of algebraic equations, and by collocation dots method. their solutions can be obtained Based on the parametric discussions presented in the paper, the following conclusions can be drawn： （1） Mode I dynamic stress intensity factor （DSIF） increases with increasing initial crack length and decreasing visco-elastic layer thickness, revealing distinct size effect; （2） The influence of the visco-elastic adhesive relaxation time on the DSIF should not be ignored.     

FINITE ELEMENT MODELLING OF COMPLEX 3D STATIC AND DYNAMIC CRACK PROPAGATION BY EMBEDDING COHESIVE ELEMENTS IN ABAQUS

<正>This study proposes an algorithm of embedding cohesive elements in Abaqus and develops the computer code to model 3D complex crack propagation in quasi-brittle materials in a relatively easy and efficient manner.The cohesive elements with softening traction-separation relations and damage initiation and evolution laws are embedded between solid elements in regions of interest in the initial mesh to model potential cracks.The initial mesh can consist of tetrahedrons,wedges,bricks or a mixture of these elements.Neither remeshing nor objective crack propagation criteria are needed.Four examples of concrete specimens,including a wedge-splitting test,a notched beam under torsion,a pull-out test of an anchored cylinder and a notched beam under impact,were modelled and analysed.The simulated crack propagation processes and load-displacement curves agreed well with test results or other numerical simulations for all the examples using initial meshes with reasonable densities.Making use of Abaqus's rich pre/post-processing functionalities and powerful standard/explicit solvers,the developed method offers a practical tool for engineering analysts to model complex 3D fracture problems.     

EXACT ANALYSIS OF WAVE PROPAGATION IN AN INFINITE RECTANGULAR BEAM

The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam. Initially, by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam. And then for the beam with stress-free boundaries, the propagation characteristics of elastic waves were presented. This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.     

STOCHASTIC ELASTO-PLASTIC FRACTURE ANALYSIS OF ALUMINUM FOAMS

Model I quasi-static nonlinear fracture of aluminum foams is analyzed by considering the effect of microscopic heterogeneity. Firstly, a continuum constitutive model is adopted to account for the plastic compressibility of the metallic foams. The yield strain modeled by a two- parameter Weibull-type function is adopted in the constitutive model. Then, a modified cohesive zone model is established to characterize the fracture behavior of aluminum foams with a cohesive zone ahead of the initial crack. The tensile traction versus local crack opening displacement relation is employed to describe the softening characteristics of the material. And a Weibull statistical model for peak bridging stress within the fracture process zone is used for considering microscopic heterogeneity of aluminum foams. Lastly, the influence of stochastic parameters on the curve of stress-strain is given. Numerical examples are given to illustrate the numerical model presented in this paper and the effects of Weibull parameters and material properties on J-integral are discussed.     

SCATTERING OF ANTI-PLANE SHEAR WAVES IN A FUNCTIONALLY GRADED MATERIAL STRIP WITH AN OFF-CENTER VERTICAL CRACK

The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using 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. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.     

FRACTURE ANALYSIS OF AN ANNULAR CRACK IN A PIEZOELECTRIC LAYER

A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of Gauss-Chebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. Numerical results reveal the effects of electric loadings and crack configuration on crack propagation and growth. The results seem useful for design of the piezoelectric structures and devices of high performance.     

Electroelastic interaction between a piezoelectric screw dislocation and a circular inhomogeneity with interfacial cracks

A piezoelectric screw dislocation in the matrix interacting with a circular inhomogeneity with interfacial cracks under antiplane shear and in-plane electric loading at infinity was dealt with. Using complex variable method, a general solution to the problem was presented. For a typical case, the closed form expressions of complex potentials in the inhomogeneity and the matrix regions and derived explicitly when the interface containsthe electroelastic field intensity factors weresingle crack. The image force acting on the piezoelectric screw dislocation was calculated by using the perturbation technique and the generalized Peach-Koehler formula. As a result, numerical analysis and discussion show that the perturbation influence of the interfacial crack on the interaction effects of the dislocation and the inhomogeneity is significant which indicates the presence of the interfacial crack will change the interaction mechanism when the length of the crack goes up to a critical value. It is also shown that soft inhomogeneity can repel the dislocation due to their intrinsic electromechanical coupling behavior.     

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.