Crack Growth Across a Strength Mismatched Bimaterial Interface

Crack growth across an interface between materials with different strength is examined by a cohesive zone model. The two materials have identical elastic properties but different fracture process properties, or different yield stresses, which is modeled by different cohesive stresses. The fracture criteria is a critical crack opening displacement. Load is represented by a stress intensity factor defining a remote square root singular stress field. The results show that the ratio between the cohesive stresses of the two materials primarily determines the behavior of the critical stress intensity factor. When the crack approaches a material with a higher cohesive stress the crack tip is shielded, but if the crack approaches a material with smaller critical crack opening displacement the maximum level of shielding is determined by the ratio between the critical crack opening displacements. When a crack approaches a material with a lower cohesive stress it is exposed to an amplified load. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bonded Cracked Half Planes with an Interface and an Interesting Crack

The solution of the plane elasticity problem of two bonded isotropic linearly elastic half-planes of different elastic properties having a crack L along the interface as well as a crack S in one of the half planes which intersects the interface crack, is given by using the Muskhelishvili's complex variable method with sectionally holomorphic functions. The initial problem is reduced to a Hilbert problem, the solution of which in the case of a dislocation existing in either half-planes constitutes the Green's functions of the problem. Finally, a singular integral equation is derived for the problem only along the crack S. The singular integral equation is solved numerically and results are presented for the stress intensity factors. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Novel Hexahedral Interface Element for Nonlinear Crack Analysis

Existence of a crack in structures would lead to a sudden failure and damage. Establishing a precise analytical model for the cracked element would be a powerful tool to achieve the right answers in the analysis of the structure. The main aim of this article is to formulate a hexahedral interface element for use in nonlinear crack analysis. In this investigation, the kinematics of the discontinuous displacement field along with the virtual work principle, for a body with an internal discontinuity, is utilized. Based on the suggested interpolation functions for the discrete segments, and also the element displacement field, the element stiffness matrix is calculated. The proposed element can be used for modeling of the discrete cracks in three-dimensional problems, such as a concrete dam. Several numerical examples are analyzed for the accuracy test and a few of them are presented here. The results indicated that utilizing sufficient elements yields suitable answers.     

Analytical-Numerical Solution of Elliptical Interface Crack Problem

The problem of elliptical interface crack, located between two bonded dissimilar elastic half spaces, is considered. To obtain a solution of the problem, the traction boundary pseudodifferential equations are used. An analytical-numerical method for solving these equations is proposed. Strain energy release rates along the crack contours are calculated for some examples. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of Biaxial Load on Crack Deflection/Penetration at Bi-material Ceramic Interface

The paper investigates the effect of the biaxial loading on crack deflection/penetration at a bi-material ceramic interface. A biaxially loaded geometry was numerically investigated using Finite Element Analysis in order to determine the energy release rate. The obtained results could be used in conjunction with a fracture criteria at interface for estimating the path of the crack after the interface was reached.     

Stress Intensity Factors for an Interface Kinked Crack in a Bi-Material Plate Loaded Normal to the Interface

Stress intensity factors for a kinked crack originating at interface of two bonded dissimilar materials subjected to normal tension are found by the finite element method.     

Application of Boundary Integral Equations to Elastodynamics of an Interface Crack

We considers application of boundary integral equations to the problem of an interface crack between two elastic half-spaces with different mechanical properties under dynamic loading. The derived system of equations allows evaluation of the displacements at the crack faces, and the traction and the displacements at the interface.     

Interface Edge Crack in a Bimaterial Elastic Half-Plane

The plane strain elastic half-plane problem of an edge crack lying along the interface of two perfectly bonded dissimilar quarter-planes is considered. Moreover, on the boundaries of the two quarter-planes concentrated forces are acting. For the correct formulation of the crack problem at hand, we consider the existence of a small slippage zone near the crack tip where closing stresses act. The mixed boundary value problem is subsequently reduced to a system of two functional equations of the Wiener–Hopf type which are effectively solved. The exact analytical solution of the problem is presented in series form. Numerical results, as well as asymptotic solutions for the most important physical quantities, are also presented. It is shown that there exist certain modes of surface loading of the homogeneous half-space, that result to the formation of two distinct zones at the crack tip region, one where the crack opening occurs and another adjacent to it, where frictionless contact of crack lips takes place. Also, it is demonstrated that in the case of high contrast of Young's moduli of the two quarter-planes, two opening-contact intervals appear consecutively along the crack. This revised version was published online in August 2006 with corrections to the Cover Date.     

Plane Stress Crack Tip Field Around a Rapidly Growing Ductile/Rigid Interface Crack

Plane stress dynamic crack growth along a ductile/rigid interface is investigated. The ductile material is taken to be ideally plastic and obey the J₂ flow theory of plasticity. Under steady-state conditions, the asymptotic structure of the crack-tip stress, velocity and strain fields has been obtained. The study reveals that two types of crack-tip sectors exist, namely uniform and nonuniform plastic sectors and that the stress, strain and velocity fields are bounded (nonsingular) in all sectors. In a uniform sector, the rectangular Cartesian components of the stress, strain and velocity fields are constant, and there is no plastic strain accumulation. In a nonuniform sector, the stress, strain and velocity components at a point depend on the angular position of the point in the crack-tip polar coordinate system and are governed by a system of simultaneous ordinary differential equations. This is a sector plastic strains can accumulate. A general crack-tip sector assembly is obtained for a practical range of crack growth speeds. Several nontrivial families of admissible solutions of the crack-tip fields based on this general assembly of uniform and nonuniform crack-tip sectors are presented and discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Plane Elastic Problem of a Crack Normal to and Terminating at Bimaterial Interface of Isotropic and Orthotropic Half Plates

In this paper, the displacement and stress fields for a crack normal to and terminating at a bimaterial interface of isotropic and orthotropic half planes are studied as a plane problem. The eigenequation, by which the order of stress singularity is determined, is given in an explicit form. A discriminant function is presented to judge whether the stress singularity at the crack tip is greater than -1/2 or not. An explicit closed form expression is derived for the displacement and stress distribution near the crack tip.     

Crack Extension at an Interface: Prediction of Fracture Toughness and Simulation of Crack Path Deviation

Ductile tearing of laser welded Al sheets is studied both experimentally and numerically. The mechanical behaviour and the microstructure of the various zones of the weld are characterised. Mechanical tests on compact tension (C(T))-specimen are carried out, with the position of the initial crack in the heat affected zone. Due to the asymmetry of the configuration, crack path deviation towards the softer fusion zone is observed. The topography of the non-planar fracture surface is measured using laser equipment. This work is focussed on the prediction of the fracture resistance and the simulation of crack path deviation for the respective configuration. The numerical simulations are based on two different models for ductile damage: the micromechanical Gurson–Tvergaard– Needleman (GTN) model and the phenomenological cohesive model. In the case of the GTN-model, the crack front may follow an arbitrary path. In contrast, the crack propagation direction for the cohesive model is prescribed by the morphology of the finite element mesh. The GTN-model is used to investigate crack path deviation and to derive limits for simplifications used together with the cohesive approach. The latter allows for a cost-efficient 2D simulation. Good agreement between experimental results and numerical simulations could be achieved in all cases     

Models of Interface Separation Accompanied by Plastic Dissipation at Multiple Scales

Two continuum mechanical models of interface fracture for interfaces joining materials where at least one undergoes plastic deformation are reviewed and examined critically. The embedded process zone model (EPZ model) has an adhesive zone, characterized by a work of separation and an interface strength, embedded within a continuum model of the adjoining materials. The SSV model imposes an elastic, plasticity-free layer of prescribed thickness between the interface and the surrounding elastic-plastic continuum. Crack advance requires the work of separation to be supplied by the local elastic crack tip field. The objective of each model is to provide the relation between the macroscopic interface toughness (the total work of fracture) and the work of separation. Under steady-state crack growth, the total work of fracture is the work of separation plus the work of plastic dissipation, the latter often far exceeding the former. It will be argued that each model has its own domain of validity, subject to the accuracy of conventional continuum plasticity at small scales, but neither is able to capture the dramatic trends which have been observed in macroscopic toughness measurements stemming from alterations in interface bonding conditions. A unified model is proposed which coincides with the two models in their respective domains of validity and provides a transition between them. Interface separation energy and interface strength (the peak separation stress) each play a central role in the unified model. Strain gradient plasticity is used to illustrate the effect of plastic deformation at the micron scale on the link between interface and macroscopic properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Intersonic Crack Propagation in an Orthotropic Material

Intersonic crack propagation is found to exhibit essentially the same features in orthotropic and isotropic materials, provided that the crack propagates along a plane of elastic symmetry. Thus the stress and strain singularity at the crack edge is weaker than the inverse square root singularity in the sub-Rayleigh case, except at one distinct velocity. The energy flux into the process region is determined by using the Barenblatt model. It depends on the crack velocity and on the size of the process region, approaching zero with this size. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crack opening conditions at ‘corner nodes’ in FE analysis with cracking along mesh lines

On the basis of a recent work proposed by the authors on a double-minimization method for evaluating inter-element forces and stresses transmitted across mesh lines, the crack opening conditions at a corner node of the FE mesh, from where several lines (potential cracks) emanate, is examined in this paper. The study is developed locally as a post-processing step of a standard displacement-based FE calculation, in terms of an always-increasing external (macroscopic) load factor μ. The cracking laws for each potential crack line are assumed rigid-plastic with hyperbolic failure criterion in terms of normal and shear components of the stress traction at that point. It is observed that, as μ increases, in general such point may undergo up to four phases of evolution until a crack can effectively open through it. First, while stress tractions across mesh lines at the point are all below cracking criterion, forces may be evaluated with the double minimization method recently proposed. Second, cracking criterion is reached for one of the lines only. Stress evaluation requires a modified minimization method with one (hyperbolic) constraint; however, crack still does not open at the node because of the lack of kinematic continuity. Third, cracking criterion is satisfied for a second of the lines converging at the nodal point. Stress tractions may then be calculated with a system of equations involving the two hyperbolic constraints alone and no minimization is needed. But in general the through crack cannot open yet at this stage because of non-coincident flow rules, until either (i) a third line reaches the cracking criterion, or (ii) these get reoriented to exhibit parallel directions in the global reference system. Two simple examples of application are provided which illustrates the development of the various cracking stages and shows different situations that may take place.     

Modelling on crack propagation behaviours at concrete matrix‐aggregate interface

A numerical model is proposed to simulate crack propagation at concrete matrix‐aggregate interface. One single aggregate surrounded by concrete matrix is taken to demonstrate the behaviours of crack penetration into concrete matrix and crack growth along the interface. Influences of side‐edge constraint, aggregate direction, and interface fracture energy on the crack propagation behaviours are respectively investigated. The results show that, tensile constraint on the side edge, a smaller angle between tensile axis and aggregate, and higher fracture energy lead to a higher rupture strength of the interface. Once the interface crack starts to grow, it propagates to the two ends of aggregate major axis drastically and further penetrates into the matrix. Nevertheless, these factors have no appreciable influence on crack propagation path. By mapping interface crack into major axis, ordinary crack is generated. Using the above simplification, modelling of multiple crack propagation in concrete is efficiently achieved.     

The effect of plasticity on dynamic crack growth across an interface

The effect of plasticity on the growth of a crack originating in an elastic solid across an interface and into an elastic-viscoplastic solid is analyzed numerically. The analyses are carried out within a framework where the continuum is characterized by two constitutive relations; one relating the stress and strain in the bulk material and the other relating the traction and separation across a specified set of cohesive surfaces. Crack initiation, crack growth and crack arrest arise naturally as a consequence of the imposed loading, without a priori assumptions concerning criteria for crack growth and for crack path selection. Full transient analyses are carried out. Various values of initial flow strength and cohesive strength of the elastic-viscoplastic solid and of cohesive strength of the interface are considered. With the ratio of cohesive strength of the elastic-viscoplastic solid to cohesive strength of the interface fixed, increasing the ratio of cohesive strength to initial flow strength for the elastic-viscoplastic solid is found to promote crack deflection into the interface.     

The Effect of Frequency in the Problem of Interface Crack Under Harmonic Loading

The breakage of a tiny tail on a head of solid glass just removed from a glass bath and treated by fluoric acid (a “Batavian tear") makes the tear explode into a cloud of dust with the sound like that of a shot. This explosion reminds that of TNT but TNT disintegrates into molecules of the order of 10⁻⁹ m while the glass particles of dust are of the order of 10⁻⁶ m and have the same chemical composition as the solid glass. Rock bursts in deep mines of South Africa and Russia represent another example of the sudden, explosive self-destruction. To explain this phenomenon the theory of self-sustaining fracture waves was suggested earlier by Galin and Cherepanov (1966). This theory was based on the analogy with detonation waves later criticized as insufficiently substantiated. The approach presented below is based only on the conservation laws and does not use any analogies. It proves that the self-sustaining fracture wave can propagate only in compressed structures at the speed of longitudinal elastic waves.     

Weight Function for an Inclined Edge Crack in a Semiplane

The matrix-like structure of the Weight Function (WF) for determining the Stress Intensity Factors (SIFs) in a nonsymmetric plane body is obtained from the general properties of the elastic field. General asymptotic and symmetric properties of the WF are discussed. By extending a previously proposed methodology, an analytical approximate WF is determined for an edge crack in a semiplane within the range of inclination (-75^–75^). Finite Element evaluations considering the minimum number of loading conditions were performed to this purpose. The accuracy of the SIFs obtained by the WF is found in the order of a few tenths of percent. The solution of a typical problem illustrates the practical usefulness of the WF. This revised version was published online in July 2006 with corrections to the Cover Date.     

橡胶夹层/复合材料粘接界面疲劳裂纹扩展行为的研究

用 型加载下的双悬臂夹层梁试样 ,以应变能释放率为裂纹扩展参量 ,研究橡胶夹层 /复合材料粘接界面疲劳裂纹的扩展行为。结果表明 ,循环载荷下的裂纹扩展速率对试验频率、载荷比、温度及橡胶夹层厚度反映较敏感。     

Invariant Points on Energy Contours Around a Crack Tip Under Mixed Mode Loading

The locus of points around a crack tip where the strain energy density is set equal to a critical value reveals interesting features. It is seen that, for certain cases, two points on this locus remain invariant with respect to the phase of the applied loads. The existence of these invariant points is examined for different configurations - a crack in a homogeneous isotropic medium, an interface crack and an inclined interface crack. This analysis is extended to the two components of strain energy density – volumetric (VSED) and distortional (DSED). This revised version was published online in August 2006 with corrections to the Cover Date.