A STUDY ON STRESS INTENSITY FACTORS AND SINGULAR STRESS FIELDS OF THREE-DIMENSIONAL INTERFACE CRACK

By using the finite-part integral concepts and limit technique,the hypersingular inte- grodifferential equations ofthree-dimensional(3D)planar interface crack were obtained; then thedominant-part analysis of 2D hypersingular integral was further usedto investigate the stress fields near the crack front theoretically,and the accurate formulae were obtained for the singular stressfields and the complex stress intensity factors.

Theoretical analysis of three-dimensional interface crack

Using the fundamental solution of interface crack and the method of finite part integral, the problem of three dimensional interface crack is reduced to solve a set of two dimensional hypersingular integrodifferential equations with unknown displacement discontinuities of crack surface. Then a systematically theoretical analysis for solving these equations is presented.

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

INTERFACIAL CRACK ANALYSIS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC BI-MATERIALS BY BOUNDARY INTEGRAL EQUATION METHOD

The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.

The asymptotic field of mode Ⅰ quasi-static crack growth on the interface between a rigid and a pressure-sensitive material

A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering hi-materials. In the stable growth stage, stress and strain have the same singularity, ie （σ, ε） ∝ r^-1/（n-1）. The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy＇s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio v of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.

Effect of interface behaviour on damage and instability of PBX under combined tension-shear loading

To study the effect of interface behaviour on the mechanical properties and damage evolution of PBX under combined tension-shear loading, the present work establishes the numerical model of a PBX three-phase hybrid system, which introduces a nonlinear plastic damage cohesion model to study the mechanical response and damage process. The parameters in the model were fitted and calibrated.Taking the crack growth rate as the feature, the damage state in each stage was determined, and the damage instability criterion was given. The effects of interfacial tensile strength and shear strength on the damage process of PBX were studied. On this basis, serrated and hemispherical structures interface of PBX has been developed, which affects the damage process and instability during the loading process.The results indicate that damage state response of PBX experiences the process of stable load bearing,unstable propagation, and complete failure. At the critical moment of instability, the overall equivalent effective strain of material reaches 3024 με and instability loading displacement reaches 0.39 mm. The increase of interfacial tensile strength and shear strength significantly inhibits the damage of PBX. The effect of interfacial shear strength on critical instability of PBX is approximately 1.7 times that of the interfacial tensile strength. Further, interface opening along the normal direction is the main damage form at the interface. Serrated and hemispherical rough interfaces can significantly inhibit propagation of cracks, and the load bearing capacity is improved by 22% and 9.7%, respectively. Appropriate improvement of the roughness of the interface structure can effectively improve the mechanical properties. It is significantly important to have a better understanding of deformation, damage and failure mechanisms of PBX and to improve our predictive ability.

Fracture behaviors of columnar jointed rock mass using interface mechanics theorem

For a special geological structure of columnar jointed rock mass(CJRM),its mechanical properties are strongly affected by the columnar joints.To describe the fracture behaviors of CJRM using the basic theories of interface mechanics for composite materials,the interface stresses of the vertical and horizontal joints,which are the two primary joints in the CJRM under triaxial compression,are studied,and their mathematical expressions are derived based on the superposition principle.Based on the obtained interface stresses of the vertical and horizontal joints in the CJRM,the crack initiation of the joint interface in the CJRM is studied using the maximum circumferential stress theory in fracture mechanics.Moreover,based on this investigation,the fracture behaviors of CJRM are analyzed.According to the results of similar material physical model tests for the CJRM,the theoretical study is verified.Finally,the influence of the mechanical parameters of the CJRM on the joint interface stress is discussed comprehensively.

SCATTERING OF SH-WAVES BY AN INTERACTING INTERFACE LINEAR CRACK AND A CIRCULAR CAVITY NEAR BIMATERIAL INTERFACE

An analytical method is developed for scattering of SH-waves and dynamic stressconcentration by an interacting interface crack and a circular cavity near bimaterial interface.Asuitable Green’s function is contructed,which is the fundamental solution of the displacement fieldfor an elastic half space with a circular cavity impacted by an out-plane harmonic line source loadingat the horizontal surface.First,the bimaterial media is divided into two parts along the horizontalinterface,one is an elastic half space with a circular cavity and the other is a complete half space.Then the problem is solved according to the procedure of combination and by the Green’s functionmethod.The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forcesin order to satisfy continuity conditions at the linking section,or with some forces to recover cracks bymeans of crack-division technique.A series of Fredholm integral equations of first kind for determiningthe unknown forces can be set up through continuity conditions as expressed in terms of the Green’sfunction.Moreover,some expressions are given in this paper,such as dynamic stress intensity factor(DSIF)at the tip of the interface crack and dynamic stress concentration factor(DSCF)around thecircular cavity edge.Numerical examples are provided to show the influences of the wave numbers,the geometrical location of the interface crack and the circular cavity,and parameter combinations ofdifferent media upon DSIF and DSCF.

STRESS SINGULARITY ANALYSIS AT CRACK TIP ON BI-MATERIAL INTERFACES BASED ON HAMILTONIAN PRINCIPLE

In this paper, the stress singularity analysis at the crack tip on elastic bi-material interfaces is considered. The governing equations of plane elasticity In sectorial domain are derived to be in Hamiltonian form via variable substitution and variational principle. The methods of separation of variables and conjugate symplectic eigen-function expansion are developed to solve the equations in sectorial domain. The general formulae for the solution of stress singularities at the crack tip on bi-material interfaces are put forward, and a new solution technique for fracture problems is presented.

Fracture of two three-dimensional parallel internal cracks in brittle solid under ultrasonic fracturing

Similar to hydraulic fracturing(HF), the coalescence and fracture of cracks are induced within a rock under the action of an ultrasonic field, known as ultrasonic fracturing(UF). Investigating UF is important in both hard rock drilling and oil and gas recovery. A three-dimensional internal laser-engraved crack(3D-ILC) method was introduced to prefabricate two parallel internal cracks within the samples without any damage to the surface. The samples were subjected to UF. The mechanism of UF was elucidated by analyzing the characteristics of fracture surfaces. The crack propagation path under different ultrasonic parameters was obtained by numerical simulation based on the Paris fatigue model and compared to the experimental results of UF. The results show that the 3D-ILC method is a powerful tool for UF research.Under the action of an ultrasonic field, the fracture surface shows the characteristics of beach marks and contains powder locally, indicating that the UF mechanism includes high-cycle fatigue fracture, shear and friction, and temperature load. The two internal cracks become close under UF. The numerical result obtained by the Paris fatigue model also shows the attraction of the two cracks, consistent with the test results. The 3D-ILC method provides a new tool for the experimental study of UF. Compared to the conventional numerical methods based on the analysis of stress-strain and plastic zone, numerical simulation can be a good alternative method to obtain the crack path under UF.

Exact solution of plane isolated crack normal to a bimaterial interface of infinite extent

This paper presents an exact solution for the transverse interface crack in the plane strain case. The crack is perpendicular to the interface and in one material. The exact complex stress functions are first obtained with some unknown constants. The satisfactions of all boundary conditions are then checked, the condition at infinity is considered and the unknown constants are determined. Further study may focus on the case with different shear moduli and the influence of the large deformation.

Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods

The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors(SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method,whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials,but has to our knowledge not been used up to now for a bimaterial. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency(less time consuming and less spurious boundary effect).

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 al between the substrate and the driving layer. It also strongly depends on the elastic mismatch a2 between 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 a2 gradually 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.

Discrete Element Modeling of Asphalt Concrete Cracking Using a User-def ined Three-dimensional Micromechanical Approach

We established a user-defined micromechanical model using discrete element method （DEM） to investigate the cracking behavior of asphalt concrete （AC）. Using the ＂Fish＂ language provided in the particle flow code in 3-Demensions （PFC3D）, the air voids and mastics in asphalt concrete were realistically built as two distinct phases. With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes, the three-dimensional （3D） discrete element model was able to account for aggregate gradation and fraction. Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation. A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature, i e, -10 ℃ and 15 ℃. The predicted results of the numerical simulation were compared with laboratory experimental measurements. Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures. Based on the DEM model, the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.

Stress field near interface crack tip of double dissimilar orthotropic composite materials

In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations＇ discriminants △1 〉 0 and △2 〉0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and interembedding between the interfaces of the crack.

Analysis of a permeable interface crack in elastic dielectric/piezoelectric bimaterials

A permeable interface crack between elastic dielectric material and piezoelectric material is studied based on the extended Stroh＇s formalism. Motivated by strong engineering demands to design new composite materials, the authors perform numerical analysis of interface crack tip singularities and the crack tip energy release rates for 35 types of dissimilar bimaterials, respectively, which are constructed by five kinds of elastic dielectric materials： Epoxy, Polymer, Al2O3, SiC, and Si3N4 and seven kinds of practical piezoelectric ceramics： PZT-4, BaTiO3, PZT-5H, PZT-6B, PZT-TA, P-7, and PZT-PIC 151, respectively. The elastic dielectric material with much smaller permittivity than commercial piezoelectric ceramics is treated as a special transversely isotropic piezoelectric material with extremely small piezoelectricity. The present investigation shows that the structure of the singular field near the permeable interface crack tip consists of three singularities： r^-1/2±iε and r^-1/2, which is quite different from that in the impermeable interface crack. It can be concluded that different far field loading cases have significant influence on the near-tip fracture behaviors of the permeable interface crack. Based on the present theoretical treatment and numerical analysis, the electric field induced crack growth is well explained, which provides a better understanding of the failure mechanism induced from interface crack growth in elastic dielectric/piezoelectric bimaterials.

Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With con- sideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial dif- ferential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit, undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship be- tween the bi-material stress intensity factor and the ratio of bi-material Young＇s modulus are given in the numerical analysis.

ON THE PLANE PIEZOELECTRIC PROBLEM OF A LOADED CRACK TERMINATING AT A MATERIAL INTERFACE

The plane problem of a crack terminating at the interface of a bimaterial piezoelectric, and loaded on its faces, is treated. The emphasis is placed on how to transform this problem into a non-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conjugate is introduced and related to the complex conjugate. The angle between the crack line and the interface may be arbitrary. Numerical results are given to illustrate the stress singularity at crack tip.

Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case

Due to the incompatibility of the interlaminar deformations,the interface debonding or cracking usually happens in a layered magnetoelectric(ME)structure under an applied load.In this paper,the transient responses of the anti-plane interface cracks in piezoelectric(PE)-piezomagnetic(PM)sandwich structures are studied by the standard methods of the integral transform and singular integral equation.Discussion on the numerical examples indicates that the PE-PM-PE structure under electric impact is more likely to fracture than the PM-PE-PM structure under a magnetic impact.The dynamic stress intensity factors(DSIFs)are more sensitive to the variation of the active layer thickness.The effects of the material constants on the DSIFs are dependent on the roles played by PE and PM media during the deformation process.

Influence of interface crack on dynamic characteristics of CRTSⅢslab ballastless track on bridge

The damage of the self-compacting concrete in CRTSⅢslab ballastless track on bridge will lead to a partial void of the track slab,which will affect the comfort and safety of the train and the durability of the track slab and bridge structure.In order to study the impact of the interface crack on the dynamic response of CRTSⅢballastless track system on bridge,based on the principle of multi-body dynamics theory and ANSYS+SIMPACK co-simulation,the spatial model of vehicle-track-bridge integration considering the longitudinal stiffness of supports,the track structure and interlayer contact characteristics were established.The dynamic characteristics of the system under different conditions of the width,length and position of the interface crack were analysed,and the limited values of the length and width of the cracks at the track slab edge were proposed.The results show that when the self-compacting concrete does not completely void along the transverse direction of the track slab,the crack has little effect on the dynamic characteristics of the vehicle-track-bridge system.However,when the self-compacting concrete is completely hollowed out along the transverse direction of the track slab,the dynamic amplitudes of the system increase.When the crack length is 1.6 m,the wheel load reduction rate reaches 0.769,which exceeds the limit value and threatens the safety of train operation.The vertical acceleration of the track slab increases by 250.1%,which affects the service life of the track system under the train speed of 200 km/h.