International Journal of Fracture Mechanics

A discrete two-dimensional square-cell lattice with a steady propagating crack is considered. The lattice particles are connected by massless bonds, which obey a piecewise-linear double- humped stress–strain relation. Initially, Hooke’s law is valid as the first stable branch of the force–elongation diagram; then, as the elongation becomes critical, the transition to the other branch occurs. Further, when the strain reaches the next critical value, the bond breaks. This transition is assumed to occur only in a line of the breaking bonds; the bonds outside the crack line are assumed to be in the initial branch all the time. The formulation relates to the crack propagation with a ‘damage zone’ in front of the crack. An analytical solution is presented that allows to determine the crack speed as a function of the far-field energy release rate, to find the total speed-dependent dissipation, and to estimate the role of the damage zone. The analytical formulation and the solution present a development of the previous ones for the crack and localized phase transition dynamics in linear and bistable-bond lattices.

Based on discontinuous displacement approximation of the continuum and ‘shear band’ kinematics, two cohesive crack models are derived within the constitutive framework of coupled damage and plasticity. The models employ the Rankine fracture criterion, and the model parameters are determined from a uniaxial tension test (mode I cracking). Bifurcation analysis is used in order to diagnose critical directions along which the crack will gradually develop and propagate. These directions depend on the actual stress state and are kept fixed after fracture has initiated, whereby a ‘fixed crack’ model is obtained. A ‘discrete crack’ strategy is employed at the finite element implementation in the sense that interfaces (that represent the cohesive crack) are introduced along inter-element boundaries. This implementation strategy calls for gradual realignment of the mesh as a key feature of the algorithm. Numerical results from the analysis of mixed mode fracture in a notched concrete plate are presented.

This paper describes mechanisms that can lead to film channel cracking, even in scenarios when layer thickness is small. Computational models are used to illustrate conditions that lead to the introduction of channel cracks and their subsequent cycle- or time-dependent propagation. Results for elastic structures with periodic features are briefly reviewed to illustrate that small low-modulus sections promote cracking in adjacent layers because they allow for the release of strain energy in adjacent sections with high residual stress. Inelastic deformation in layers adjacent to the cracked layer may also act to increase the channel crack driving force, by allowing for increasing displacements that serve to release strain energy. Two inelastic mechanisms form the primary focus in this effort: rate-independent plasticity and creep. Analyses of a cracked film on an elastic-plastic layer reveal pronounced cyclic displacements (as known as ratcheting) when the misfit thermal strain amplitude in the ductile layer exceeds twice its yield strain. Similar behavior occurs in cracked films on layers susceptible to creep. Simulations are presented for both isolated cracks and periodic arrays of cracks, and illustrate that the likelihood of cracking grows dramatically with time. In both inelastic regimes, the upper limit on deformation is dictated by the residual stress in the elastic layer and the substrate dimensions. These results are discussed in the context of analytical models developed elsewhere and potential experiments.

The stress intensity factors are determined at the crack roots for a rectangular cutout with symmetric edge cracks in an infinite sheet under uniaxial tension. The stress analysis is carried out using conformal mapping and the Muskhelishvili formulation. Numerical results are obtained for varying crack length and selected length-to-width ratios for the rectangle. The stress intensity factors are compared to those for a single internal crack to illustrate the influence of the cutout effects.

Linear Elastic Fracture Mechanics (LEFM) provides a coherent framework to evaluate quantitatively the energy flux released at the tip of a growing crack. However, the way in which the crack chooses its path in response to this energy flux remains far from completely understood: the growing crack creates a structure on its own as conveyed by crack surface roughening even in brittle amorphous materials such as glass. We report here experiments designed to uncover the primary cause of surface roughening in brittle amorphous materials. Therefore, we investigate the response of a growing crack to local perturbation introduced as a shear wave pulse of controlled duration, amplitude, frequency and polarization. This pulse is shown to induce a local mode III perturbation in the loading of the crack front, which makes it twist locally, without fragmenting. This response is linear both in amplitude and frequency with respect to the perturbation, and disappears with it. We also show that shear wave pulses are emitted when the propagating crack encounters the heterogeneity. Implications of these observations for possible sources of roughening are finally discussed.

The high interlaminar stresses, which appear in laminated composites due to the boundary layer effect near the free edge, play an important role in the analysis and design of advanced structures. Moreover, they are also the dominant effect causing delamination. Even if the singular behavior of such structures is investigated in many works, most of them deal either with 2D, or with pseudo-3D problems, i.e. problems of two variables in a three-dimensional space. However, some numerical and experimental findings indicate that laminated plates exhibit a tendency to delaminate at corners, an effect impossible to be determined by a two-dimensional analysis. The aim of the present paper is to investigate stress singularities in a laminated composite wedge under consideration of real three-dimensional corner effects. A weak formulation, as well as a finite element approximation technique introduced in the past for isotropic problems is extended here to cover anisotropic material properties. This formulation leads to a quadratic eigenvalue problem, which is solved iteratively using the Arnoldi method. The first singular terms in the asymptotical expansion of the linear-elastic solution near the vertex of the wedge are obtained as eigenpairs of this eigenvalue problem. The order and mode of singularity are reported for all wedge angles and different fiber orientations for angle and cross-ply laminates. All calculations are based on a typical for some high modulus graphite-epoxy systems orthotropic material model.

The general problem of a straight crack near a rigid elliptical inclusion is solved. Complex potentials presented in a previous paper (Santare and Keer [6]) for the interaction of an edge dislocation with rigid ellipse are used to formulate the Green's function for this problem. The solution is written as a set of singular integral equations for crack opening displacement which are solved numerically. Stress intensity factors are presented for a variety of crack/inclusion geometries.