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We establish an exact equivalence of the non-interaction approximation (NIA) and Gassmann theory in describing the changes in effective elasticity due to variations in the bulk modulus of fluid infill of isolated inclusions that have identical shapes and orientations. If the sizes of inclusions (pores or fractures) are equal, the fluid pressures in all inclusionsare equal too regardless of their hydraulic connectivity. This fact makes Gassmann theory rigorous; therefore, other effective media schemes should comply with it when applied to such microstructures. While the NIA satisfies this requirement, other effective media schemes (e.g., self-consistent and differential) do not. [ABSTRACT FROM AUTHOR]

A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy. [ABSTRACT FROM AUTHOR]

For evolutionary processes of material remodelling and growth, a comparison is drawn between a conventional formulation and one that postulates the existence of additional balance laws for the configurational forces. [ABSTRACT FROM AUTHOR]

The distributed dislocation technique proved to be in the past an effective approach in studying crack problems within classical elasticity. The present work aims at extending this technique in studying crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. As a first step, the technique is introduced to study finite-length cracks under remotely applied shear loadings (mode II and mode III cases). The mode II and mode III cracks are modeled by a continuous distribution of glide and screw dislocations, respectively, that create both standard stresses and couple stresses in the body. In particular, it is shown that the mode II case is governed by a singular integral equation with a more complicated kernel than that in classical elasticity. The numerical solution of this equation shows that a cracked material governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a material governed by classical elasticity. Also, the stress level at the crack-tip region is appreciably higher than the one predicted by classical elasticity. Finally, in the mode III case the corresponding governing integral equation is hypersingular with a cubic singularity. A new mechanical quadrature is introduced here for the numerical solution of this equation. The results in the mode III case for the crack-face displacement and the near-tip stress show significant departure from the predictions of classical fracture mechanics. [ABSTRACT FROM AUTHOR]

In this note we study a basic propagation criterion for quasi-static crack evolution in Mode III. Using classical techniques of complex analysis, the assumption of stable growth is expressed in terms of the parameters defining the elastic field around the tip. We explore the consequences of the local condition obtained and analyse its role as a crack propagation law. In particular, we herein extend to bounded domains a number of results previously obtained for the whole plane. [ABSTRACT FROM AUTHOR]

The problem of finding effective elastic moduli of media with spheroid inclusions in case of small concentration of these inclusions is addressed. A number of particular solutions, both known and new, were obtained as limit transitions and asymptotical expansion of the general solution, based on Eshelby’s approach. A special attention was paid to determining the ranges of applicability of the obtained asymptotical solutions. It was shown that for spheroid inclusions the areas of applicability of the asymptotic solutions are determined by two parameters: the ratio of elastic moduli of the inclusion and the matrix and aspect ratio of the inclusions. [ABSTRACT FROM AUTHOR]

A crack is steadily running in an elastic isotropic fluid-saturated porous solid at an intersonic constant speed c. The crack tip speeds of interest are bounded below by the slower between the slow longitudinal wave-speed and the shear wave-speed, and above by the fast longitudinal wave-speed. Biot’s theory of poroelasticity with inertia forces governs the motion of the mixture. The poroelastic moduli depend on the porosity, and the complete range of porosities n ∈ [0, 1] is investigated. Solids are obtained as the limit case n = 0, and the continuity of the energy release rate as the porosity vanishes is addressed. Three characteristic regions in the plane ( n, c) are delineated, depending on the relative order of the body wave-speeds. Mode II loading conditions are considered, with a permeable crack surface. Cracks with and without process zones are envisaged. In each region, the analytical solution to a Riemann–Hilbert problem provides the stress, pore pressure and velocity fields near the tip of the crack. For subsonic propagation, the asymptotic crack tip fields are known to be continuous in the body [Loret and Radi (2001) J Mech Phys Solids 49(5):995–1020]. In contrast, for intersonic crack propagation without a process zone, the asymptotic stress and pore pressure might display a discontinuity across two or four symmetric rays emanating from the moving crack tip. Under Mode II loading condition, the singularity exponent for energetically admissible tip speeds turns out to be weaker than 1/2, except at a special point and along special curves of the ( n, c)-plane. The introduction of a finite length process zone is required so that 1. the energy release rate at the crack tip is strictly positive and finite; 2. the relative sliding of the crack surfaces has the same direction as the applied loading. The presence of the process zone is shown to wipe out possible first order discontinuities. [ABSTRACT FROM AUTHOR]

The title problem is considered for an elastic circular tube of inner radius A and outer radius B. The tube is made of a single component solid with vacancies as its second component. The mole fraction of the massive species is denoted by x 1, while that of the vacancies by x 0 = 1 – x 1. The tube is completely surrounded by vacuum, serving as a reservoir of vacancies. One of the standard elasticity boundary conditions is applied at time t = 0, when the composition is uniform. The ensuing coupled deformation and diffusion leads to the evolving of A( t), B( t) and x 1( R, t) as functions of time. Since the single component solid is not in contact with its vapor or liquid, the diffusion boundary condition is always tied to the elasticity problem through a surface condition that involves the normal configurational traction. Our chemical potential has an energy density term that serves as a source in the interior and the boundary conditions for the diffusion problem are such that the time rates of boundary accretion Ȧ( t) and Ḃ( t) must simultaneously satisfy two dissipative inequalities, one governed by the gradient of the internal chemical potential and the other by the normal configurational traction. [ABSTRACT FROM AUTHOR]

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem. [ABSTRACT FROM AUTHOR]

New numerical methods were presented for stress intensity factor analyses of two-dimensional interfacial crack between dissimilar anisotropic materials subjected to thermal stress. The virtual crack extension method and the thermal M-integral method for a crack along the interface between two different materials were applied to the thermoelastic interfacial crack in anisotropic bimaterials. The moving least-squares approximation was used to calculate the value of the thermal M-integral. The thermal M-integral in conjunction with the moving least-squares approximation can calculate the stress intensity factors from only nodal displacements obtained by the finite element analysis. The stress intensity factors analyses of double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load were demonstrated. Excellent agreement was achieved between the numerical results obtained by the present methods and the exact solution. In addition, the stress intensity factors of double edge cracks in jointed dissimilar anisotropic semi-infinite plates subjected to thermal loads were analyzed. Their results appear reasonable. [ABSTRACT FROM AUTHOR]

The accurate computation of stress intensity factors (SIFs) plays a decisive role in the determination of crack paths. The calculation of SIFs with the help of singular weight functions leads to pure Neumann problem for anisotropic elasticity in a plane domain with a crack. Here a method is presented to overcome the specific numerical difficulties which arises while calculating these solutions with Finite Element methods. The accuracy and advantage of this method are shown by a numerical example, the calculation of SIFs of a compact tension specimen. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to a comment made on an article about the effective elastic properties of cracked solids published in a previous issue of the periodical.

The averaged value of the strain energy density over a well-defined volume is used to predict the static strength of U-notched specimens under mixed-mode conditions due to combined bending and shear loads. The volume is centered in relation to the maximum principal stress present on the notch edge, by rigidly rotating the crescent-shaped volume already used in the literature to analyse U- and V-shaped notches subject to mode I loading. The volume size depends on the ultimate tensile strength σ u and the fracture toughness K IC of the material. In parallel, an experimental programme was performed. All specimens are made of polymethyl-metacrylate (PMMA), a material which exhibits quasi-brittle behaviour at -60°C. Good agreement is found between experimental data for the critical loads to failure and theoretical predictions based on the constancy of the mean strain energy density over the control volume. [ABSTRACT FROM AUTHOR]

The non-interaction approximation (NIA) formulated in compliances and the differential effective media (DEM) schemes are believed to be the most accurate theories for predicting the effective elasticity of fractured solids. While their predictions are always plausible, the DEM yields consistently softer effective properties than does the NIA. Here I compare these two theories with the finite element (FE) modeling for arrays of randomly located, parallel, penny-shaped cracks. I perform FE simulations by applying the homogeneous strain and homogeneous stress boundary conditions that establish the upper and lower bounds for the effective stiffness tensor. These numerically derived bounds demonstrate that the NIA is more accurate than the DEM. [ABSTRACT FROM AUTHOR]

By using direct calculation of the gradient and divergence of the Lagrangian of any quasicrystal, its dynamic conservation integrals are derived. These conservation integrals can be reduced to J- and M-integrals for plane and antiplane problems, which are calculated around the tip of an interfacial crack of antiplane sliding mode between a crystal and a quasicrystal. [ABSTRACT FROM AUTHOR]

In order to predict the fatigue limit of a specimen with an axisymmetric complex surface, a practical method to estimate a stress concentration factor (SCF) of its surface was proposed. The roughness is coarse-grained by removing high frequency components and approximated with a parallel row of a local notch and innumerable average notches. Then, the notches are each approximated with the elliptical holes in the infinite plate, and the SCF is calculated approximately by superposing the elastic solutions of the holes. Moreover, FEM analyses were carried out on the various notch models which consist of the local notch and innumerable average notches to examine the application limit of the present method. Then, the validity of the application limit was examined by using the real roughness and the infinite parallel row of the various notches, and it was shown that the present method was available for the real roughness. [ABSTRACT FROM AUTHOR]

We consider connections between microstructure and elastic properties of porous/microcracked materials on the example of Fontainebleau sandstone. The microstructural information (average shapes of pores) required for adequate modeling of the isotropic elastic properties is identified. It is shown that, if this information is utilized, the usual effective media schemes provide satisfactory predictions of the effective elastic properties. [ABSTRACT FROM AUTHOR]

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis–Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis–Menten kinetics. [ABSTRACT FROM AUTHOR]

The solution to elastic isotropic problems in three-dimensional (3-D) polyhedral domains in the vicinity of an edge is provided in an explicit form. It involves a family of eigen-functions with their shadows, and the associated edge stress intensity functions (ESIFs), which are functions along the edges. Utilizing the explicit structure of the solution in the vicinity of the edge we use the quasidual function method, recently presented in [Omer et al. (2004). International Journal of Fracture 129:97–130] for scalar elliptic problems and in [Costabel et al. (2004). SIAM Journal of Mathematical Analysis 35(5), 1177–1202] in a general theoretical framework, for the extraction of ESIFs. This method provides a polynomial approximation of the ESIF along the edge whose order is adaptively increased so to approximate the exact ESIF. It is implemented as a post-solution operation in conjunction with the p-version finite element method. Numerical examples are provided in which we extract ESIFs associated with traction free or homogeneous Dirichlet boundary conditions in 3-D cracked domains or 3-D V-Notched domains. These demonstrate the efficiency, robustness and high accuracy of the proposed quasi-dual function method. [ABSTRACT FROM AUTHOR]

An analytical model is developed to study various ‘system effects’ during impact of a flat-faced, cylindrical projectile into a flexible, multi-layered target with no bonding between layers. Each thin layer is assumed to have in-plane, isotropic, elastic mechanical properties. The model allows variation of the mechanical properties from layer to layer as well as the spacings between the layers in order to study their combined effects on the ballistic performance of the system. In particular, we consider such performance measures as the V 50 limit velocity, the number of layers penetrated when impacting below this limit, and the residual projectile velocity after complete penetration above this limit. The V 50 performance of the target is found to degrade progressively as the spacings between layers are increased relative to the sum of layer thicknesses without spacing. A second finding is that for a given set of layers with differing mechanical properties, both the V 50 and the residual velocity depend on the order of layer placement. A third finding is that among systems with identical layers of a given in-plane tensile strength, the V 50 velocity increases with increasing strain-to-failure of the layers. However the relative magnitude of this increase diminishes with increasing target-to-projectile areal density ratio. The model builds on the authors’ previous analysis for impact into a single elastic membrane and the results have important design implications for armor design especially for hybrid material configurations. [ABSTRACT FROM AUTHOR]

A numerical method is presented here to determine stress intensity factors for interface cracks in plane, isotropic, elastic bimaterial fracture problems. The method relies on considering a companion problem wherein a very thin elastic interlayer with a crack, is artificially inserted between the two material regions of the original bimaterial problem. Modes I and II stress intensity factors are obtained for the companion problem using the modified virtual crack closure method. These stress intensity factors for the companion problem are then converted to the stress intensity factors for the original interface crack problem with the help of a universal relation. This universal relation between the stress intensity factors of the two problems is established by considering an asymptotic problem where the thickness of the interlayer is small compared with all other length scales. Two benchmark problems are considered to demonstrate the effectiveness of the interlayer approach for determining interface stress intensity factors. [ABSTRACT FROM AUTHOR]

The problem of multi-material junctions composed of angularly nonhomogeneous elastic wedges in plane elasticity is addressed. For this new type of grading the governing equation for the Airy stress function is derived and, by applying the eigenfunction expansion method, a fourth-order ODE with nonconstant coefficients for the eigenequation is obtained. The solution to this ODE permits the formulation of an eigenvalue problem similar to that valid for material junctions between homogenous different materials. It is mathematically demonstrated that the angular grading influences the order of the stress-singularity. The potentials of the use of this new class of materials in joining technology are carefully investigated and some illustrative examples are deeply discussed. Comparisons with the corresponding results obtained from homogeneous materials are made. [ABSTRACT FROM AUTHOR]

A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models. [ABSTRACT FROM AUTHOR]

A solution scheme based on the fundamental solution for a generalized edge dislocation in an infinite magnetoelectroelastic solid is presented to analyze problems involving single, multiple and slowly growing impermeable cracks. The fundamental solution for a generalized dislocation is obtained by extending the complex potential function formulation used for anisotropic elasticity. The solution for a continuously distributed dislocation is derived by integrating the solution for an edge dislocation. The problem of a system of cracks subjected to remote mechanical, electric and magnetic loading is formulated in terms of set of singular integral equations by applying the principle of superposition and the solution for a continuously distributed dislocation. The singular integral equation system is solved by using a numerical integration technique based on Chebyshev polynomials. TheJ i andM-integrals for single crack and multi-cracks problems are derived and their dependence on the coordinate system is investigated. Selected numerical results for theM-integral, total energy release rate and mechanical energy release rate are presented for single, double and multiple crack problems. The case of a slowly growing crack interacting with a stationary crack is also considered. It is found thatM-integral presents a reliable and physically acceptable measure for assessment of fracture behaviour and damage of magnetoelectroelastic materials. [ABSTRACT FROM AUTHOR]

Debonding of two different solids made of power law hardening materials is studied for the case of anti-plane shear loading mode by using an interface crack model. The stresses and the stress intensity factor at the interface crack are determined analytically. Using these analytical results, the constitutive equations by Hencky-Ilyushin and the general equation of energy in the neighborhood of the crack tip, the adhesion energy for the loading mode under consideration is found analytically. It can be observed that for the particular case of two linearly elastic materials and a homogeneous linearly elastic material the solution found here is in excellent agreement with the solutions found in the literature. [ABSTRACT FROM AUTHOR]

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann-Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poisson’s ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poisson’s ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material. [ABSTRACT FROM AUTHOR]

The out-of-plane constraintsT z around the semi-elliptical surface cracks in an elastic plate subjected to uniform tension loading have been investigated through detailed three-dimensional (3D) finite element (FE) analyses. The distributions ofT z are obtained in the vicinity of the crack border with aspect ratios of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0.T z drops from Poisson’s ratio at the crack tip to approximate zero beyond certain radial distance in the normal plane of the crack front line, and increases gradually from the free surface to the mid-plane at the same radial distance. By fitting the numerical results, empirical formulae are obtained to describe the 3D distributions ofT z for semi-elliptical surface cracks with a sufficient accuracy in the wide aspect ratio range of 0.2=a/c =1.0 except very near the free surface, whereT z is extremely low.T z, combining with the correspondingKandTorJandQ, can be applied to establish the three-parameter dominated stress field, which can characterize the 3D crack front field completely as an attempt. [ABSTRACT FROM AUTHOR]

A new method is proposed for shape sensitivity analysis of a crack in a homogeneous, isotropic, and nonlinearly elastic body subject to mode I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of theJ-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is required in the proposed method. Since the governing variational equation is differentiated before the process of discretization, the resulting sensitivity equations are independent of any approximate numerical techniques. Based on the continuum sensitivities, the first-order reliability method was employed to perform probabilistic analysis. Numerical examples are presented to illustrate both the sensitivity and reliability analyses. The maximum difference between the sensitivity of stress-intensity factors calculated using the proposed method and the finite-difference method is less than four percent. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently. [ABSTRACT FROM AUTHOR]

Micropolar elasticity laws provide a possibility to describe constitutive properties of materials for which internal length scales may become important. They are characterized by the presence of couple stresses and nonsymmetric Cauchy stress tensor. Beyond the classical displacement field, the kinematical variables are augmented by a so-called microrotation field and its gradient, the latter introducing an internal length scale in the theory. For an isotropic, linear micropolar elastic material, the near-tip asymptotic field solutions for mode I and mode II cracks are derived. It is shown that these solutions behave similar to those according to the so-called couple stress theory, which has been investigated by Huang et al. (1997a), or similar to those derived for cellular materials by Chen et al. (1998). In particular, the singular fields have an order of singularityr-1/2 and are governed by some amplitude factors, having the meaning of stress intensity factors as in the classical linear elastic theory. The effect of material parameters on the stress intensity factors is studied by applying the finite element method to calculate the values of the stress intensity factors for an edge-cracked specimen of finite width. [ABSTRACT FROM AUTHOR]

The asymptotics of solutions to scalar second order elliptic boundary value problems in three-dimensional polyhedral domains in the vicinity of an edge is provided in an explicit form. It involves a family of eigen-functions with their shadows, and the associated edge flux intensity functions (EFIFs), which are functions along the edges. Utilizing the explicit structure of the solution in the vicinity of the edge we present a new method for the extraction of the EFIFs called quasidual function method. It can be interpreted as an extension of the dual function contour integral method in 2-D domains, and involves the computation of a surface integral J[R] along a cylindrical surface of radius R away from the edge as presented in a general framework in (Costabel et al., 2004). The surface integral J[R] utilizes special constructed extraction polynomials together with the dual eigen-functions for extracting EFIFs. This accurate and efficient method provides a polynomial approximation of the EFIF along the edge whose order is adaptively increased so to approximate the exact EFIF. It is implemented as a post-solution operation in conjunction with the p-version finite element method. Numerical realization of some of the anticipated properties of the J[R] are provided, and it is used for extracting EFIFs associated with different scalar elliptic equations in 3-D domains, including domains having edge and vertex singularities. The numerical examples demonstrate the efficiency, robustness and high accuracy of the proposed quasi-dual function method, hence its potential extension to elasticity problems. [ABSTRACT FROM AUTHOR]

Localized deformation band formation and crack generation in elastic brittle-plastic materials were simulated numerically in various loading conditions. Cracking patterns for a specimen with a failed inclusion and for a damaged layer of a geomedium in shear, as well as for a sandstone specimen in compression, were obtained. To describe deformation, a complex approach was used. According to this approach, in the course of plastic deformation damages are accumulated and govern bulk plastic deformation. Due to damage accumulation, strength decreases and material degradation occurs, while macrocrack opening and material fracture take place only under the action of tensile stresses. [ABSTRACT FROM AUTHOR]

The results of 2D computer simulations of crack trajectories in an elastic material under a superposition of external uniaxial or biaxial tension and spatially random stress fluctuations are presented. The initial crack is straight. The criterion of maximum tensile stress near the crack tip is used to determine the crack trajectory. It is assumed that crack propagates in linear segments, step by step from either left or right tip depending on where the local circumferential stress is higher. Each segment is subjected to randomly-generated uniform tractions whose values are normally distributed with zero mean, independent of loads on previous segments. It is shown that the deflection of the actual crack paths from the trend increases with the crack length; its standard deviation grows stronger than predicted by the `random walk' model. [ABSTRACT FROM AUTHOR]

The size effects on the mean values of the mechanical properties of condensed matter and on the related variances are analysed by means of a unified approach based on the multiscale character of energy dissipation. In particular, the scaling law for fragmentation energy density is obtained taking into account the self-similarity of fragments. It is based on a generalization of the three classical comminution laws that has been performed to evaluate the energy dissipation, computing volume and surface area of the particles for one- two- and three-dimensional fragmented objects. The result is general and can be applied to different fractal energy dissipation mechanisms, e.g., plasticity. Based on this approach, the scaling laws for mean and standard deviation values of the main mechanical properties of materials can be derived, like Young's and shear elastic moduli, ultimate normal and shear stresses and strains, fracture energy and toughness. [ABSTRACT FROM AUTHOR]

In the evaluation of accurate weight functions for the coefficients of first few terms of the linear elastic crack tip fields and the crack opening displacement (COD) using the finite element method (FEM), singularities at the crack tip and the loading point need to be properly considered. The crack tip singularity can be well captured by a hybrid crack element (HCE), which directly predicts accurate coefficients of first few terms of the linear elastic crack tip fields. A penalty function technique is introduced to handle the point load. With the use of these methods numerical results of a typical wedge splitting (WS) specimen subjected to wedge forces at arbitrary locations on the crack faces are obtained. With the help of appropriate interpolation techniques, these results can be used as weight functions. The range of validity of the so-called Paris equation, which is widely used in the evaluation of the COD from the stress intensity factors (SIFs), is established. [ABSTRACT FROM AUTHOR]

Steady-state tunneling and plane-strain delamination of an H-shape crack are examined for elastic, isotropic multi-layers. Both tunneling and delamination are analysed by employing linear elastic fracture mechanics within a 2D finite element framework. Failure maps are produced to reveal the sensitivity of cracking path to the relative toughness of layer and interface, and to the stiffness mismatch of layers. Closed-form expressions are derived for the critical stress level for steady-state plane-strain delamination. By means of a comparison with experimental results taken from the literature, it is demonstrated that these expressions serve as useful design criteria for elastic multilayers. [ABSTRACT FROM AUTHOR]

In this investigation, the conservative M-integral is extended to treat thermal-elastic, mixed mode problems. With it, stress intensity factors are obtained for cracks in homogeneous, isotropic materials, as well as isotropic and anisotropic, bimaterials. Excellent agreement is found between results determined in this study and those found in the literature. In addition, new results are obtained for interface cracks for a wide range of material properties and for a delamination in a composite material. [ABSTRACT FROM AUTHOR]

A method to determine constitutive properties of thin adhesive layers loaded in shear is presented. The test specimen consists of two adherends joined by the adhesive layer. By loading the specimen antisymmetrically with respect to the adhesive layer a state of pure shear is ensured. To avoid instability the test specimen is designed to give a non-uniform stress distribution in the adhesive layer. This is achieved by using a long specimen loaded at one side. The method is based on an exact inverse solution which is derived utilizing the balance of the energetic forces of the applied loads and of the adhesive at the start of the adhesive layer. The method is intended for determination of both hardening and softening behaviour of adhesives but is confined to monotonic loading. [ABSTRACT FROM AUTHOR]

Carbon fiducial marks are formed during thin film local delamination processes induced either by superlayer indentation forming circular blisters, or by residual stress relief through telephone cord blister formations. Hydrocarbons are sucked into the crack tip during the delamination process, outlining the crack tip opening angle (CTOA), which can be used to back calculate thin film adhesion using either elastic or plastic analyses presented here. Fiducial marks have been observed in two different thin films systems, namely Cu/SiO2 and TiWXNY/GaAs. TiWXNY/GaAs system also exhibited biaxial compressive stress-induced phone cord buckling delaminations. Surface AFM CTOA measurement approach is used to estimate the strain energy release rate increase along these phone cords delaminations. [ABSTRACT FROM AUTHOR]

The characteristics of stress singularities near the free edge of the interface of bonded dissimilar materials subjected to change in temperature are investigated. The thermal stresses are represented by the sum of the singular terms of types r and log r, no singular ones and the particular ones. The functions, K × F (j=1,2,3), associated with the terms except the particular terms contributing to the thermal stresses are described as new stress intensity factors. The K is obtained from the technique of the Mellin transform and the F is calculated by numerical analysis such as finite element analysis. The emphasis here is placed on clarifying material combinations with arbitrary wedge angles and elastic properties yielding K = 0. The results can be used to determine material/geometry which ensures that interface residual stresses will be in compressive. [ABSTRACT FROM AUTHOR]

The dynamic stress intensity factors for a semi-infinite crack in an otherwise unbounded elastic body is investigated. The crack is subjected to a pair of suddenly-applied shear point loads on its faces at a distance l away from the crack tip. This problem is treated as the superposition of two problems. The first problem considers the disturbance by a concentrated shear force acting on the surface of an elastic half space, while the second problem discusses a half space with its surface subjected to the negative of the tangential surface displacements induced by the first problem in the front of the crack edge. A fundamental problem is proposed and solved by means of integral transforms together with the application of the Wiener–Hopf technique and Cagniard–de Hoop method. Exact expressions are then derived for the mode II and III dynamic stress intensity factors by taking integration over the fundamental solution. Some features of the solutions are discussed. [ABSTRACT FROM AUTHOR]

This study investigates the stress singularities in the neighborhood of the tip of a sliding crack with Coulomb-type frictional contact surfaces, and applies the boundary integral equation method to solve some frictional crack problems in plane elasticity. A universal approach to the determination of the complex order of stress singularity is established analytically by using the series expansion of the complex stress functions. When the cracks are open, or when no friction exists between the upper and lower crack faces, our results agree with those given by Williams. When displacement and traction are prescribed on the upper and lower crack surfaces (or vice versa), our result agrees with those by Muskhelishvili. For the case of a closed crack with frictional contact, the only nonzero stress intensity factor is that for pure shear or sliding mode. By using the boundary integral equation method, we derive analytically that the stress intensity factor due to the interaction of two colinear frictional cracks under far field biaxial compression can be expressed in terms of E(k) and K(k) (the complete elliptic integrals of the first and second kinds), where k=[1-(a/b)2]1/2 with 2a the distance between the two inner crack tips and b- a the length of the cracks. For the case of an infinite periodic colinear crack array under remote biaxial compression, the mode II stress intensity factor is found to be proportional to [2b tan(π a/2b)]1/2 where 2a and 2b are the crack length and period of the crack array. [ABSTRACT FROM AUTHOR]