Dominique Leguillon

Strength or toughness? A criterion for crack onset at a notch

Both energy and stress criteria are necessary conditions for fracture but neither one nor the other are sufficient. Experiments by Parvizi et al. on transverse cracking in cross-ply laminates corroborate this assumption. Thanks to the singularity at the tip of the notch, the incremental form of the energy criterion gives a lower bound of admissible crack lengths. On the contrary, the stress criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation. It enjoys the desirable property of coinciding with the usual Griffith criterion to study the crack growth and with the stress criterion for the uniform traction along a straight edge. Comparisons with experiments carried out on homogeneous notched materials and on bimaterial structures show a good agreement.

A revisited criterion for crack deflection at an interface in a brittle bimaterial

Abstract An asymptotic analysis is carried out to model the mechanism of deflection of a crack at an interface in a brittle bimaterial. Necessary conditions are derived from an energy analysis based on seeking the path which provides the maximum of additional energy released by the fracture process. In the case of a stationary crack impinging perpendicularly on the interface and submitted to progressive loading, the energy criterion depends on the elastic mismatch of the bimaterial constituents and the ratio of the crack extensions in the deflected and the penetrated directions. The criterion reveals high sensitivity to the value of this ratio. Applying this criterion thus requires an arbitrary assumption concerning the value of the crack extension ratio, as was proposed by He and Hutchinson (He, MY, Hutchinson JW. Crack deflection at an interface between dissimilar elastic materials. Int J Solids Structures 1989;25:1053–67). Considering now a crack propagating towards the interface, an improved criterion which does not require any assumption concerning the extension ratio is established by using a quasi-static approximation and assuming that the deflection mechanism occurs under constant loading.

Interface debonding ahead of a primary crack

Abstract The debonding of an interface between two elastic materials is assumed to occur ahead of a primary crack lying in material 1. Conditions for such a mechanism are derived from an asymptotic analysis and depend on the elastic mismatch between the two materials as well as on material 1 and interface toughnesses. The ligament width between the primary crack tip and the interface and the debond nucleation length can be determined if the interface strength is known. A similar mechanism involving a crack nucleation ahead of the primary crack in material 2 is also examined. Deflection prediction is derived from an energetic criterion which is in general more favourable to deflection than the He and Hutchinson one. The former decreases asymptotically towards the latter. Moreover, if the crack lies in the stiffest material, results show that these nucleation mechanisms are highly improbable. If material 2 and interface strengths are known, a stress criterion is naturally derived. The presented analysis is independent of the applied loads and of the geometry of the specimen.

A criterion for crack nucleation at a notch in homogeneous materials

Abstract Experiments of Parvizi et al. on transverse fracture of cross-ply laminates showed that both energy (Griffith) and strength criteria are necessary conditions for fracture but neither one nor the other are sufficient. Thanks to the singularity at the tip of the notch, the incremental form of the Griffith criterion gives a lower bound of admissible crack lengths. On the contrary, the strength criterion leads to an upper bound. The consistency between these two conditions provides a general form of a criterion for crack nucleation.

Failure initiation in an epoxy joint between two steel plates

An Irwin-like criterion, initially developed to predict crack initiation in monolithic v-notched specimens, is used to examine the failure of two steel plates bonded together by an epoxy joint. It is based on an estimate of the critical value of the intensity factor of the elastic singular fields appearing in some regions of the structure, due to the geometry and to the elastic mismatch of the components. The analysis is worked out at two scales: a macroscopic one ignoring the thin epoxy layer and considering the two plates as perfectly bonded along an idealized interface and a microscopic one taking into account the elastic fields within the joint. It is shown that these two approaches are equivalent and that a macroscopic failure criterion can be developed. The characteristic failure parameter is a macroscopic critical intensity factor. It can be derived from the knowledge of microscopic data such as the strength and the toughness of the epoxy.

The onset of delamination at stress-free edges in angle-ply laminates — analysis of two criteria

Abstract Prediction of delamination onset in ±θ s angle-ply carbon-fiber/epoxy-resin laminates is proposed by means of two approaches. Both are based on a preliminary analysis of the boundary effects. In the first, more classical, case, an ‘average stress’ criterion retaining only the interface shear component of the stress field is used. Layer-thickness influence is taken into account to estimate the averaging length. The second case takes advantage of the stress concentrations caused by singularities to put to work an incremental Griffith-like criterion. Initiation is considered to be a locally unstable process. It requires us to account for the existence of surface flaws to explain the influence of layer thickness on the critical delamination stress.

A method based on singularity theory to predict edge delamination of laminates

Delamination starting from a stress free edge is the main mode of failure of cross-ply laminates. The analysis of singularities and resulting stress concentrations at interfaces along these edges are not sufficient to provide a satisfying model of onset mechanisms. In particular, the model is by far less sensitive to the layers thickness than observed in traction experiments. A refined asymptotic process is proposed which takes into account the existence of surface flaws (micro-cracks or notches). Numerical results prove that this model is much more in agreement with the experiments. Moreover, the knowledge of the interface toughness, in addition with the experiments, allows to estimate a characteristic fracture length, a kind of process zone. It is a material property and in a first approximation it arises to be of the same order of magnitude than the characteristic inhomogeneity length of the components, i.e. the fibers diameter.

The influence of an interphase on the deflection of a matrix crack in a ceramic-matrix composite

The main purpose of this paper is to develop a criterion which is able to predict a particular mechanism of matrix crack deflection which often occurs in brittle-matrix composites: an interface debonding ahead of the matrix crack. The problem is solved with the help of an energetic approach which couples an asymptotic and a numerical analysis. It is further extended by taking into account the presence of an interphase introduced between the fibre and the matrix. Numerical results are then used to describe a crack deflection mechanism within a model bi-material (consisting of two dense alumina substrates separated by a porous alumina interlayer) and a SiC/SiC composite.

The strengthening effect caused by an elastic contrast—part I: the bimaterial case

The final aim of the two parts of this study is to quantify the gain in strength of a layered heterogeneous structure caused by the elastic contrast between the layers, especially if no crack deflection is observed at the interface. In part I, the analysis focus on an example, the 3 point-bending of a bimaterial made of a compliant and a stiff layer; whereas part II is dedicated to the 3-point bending of a homogeneous beam embedding a thin stiff film. Baptized “step-over” and “jump-through”, two original mechanisms of crack crossing the interface are proposed herein. They rely on a coupled criterion involving both energy requirement and stress condition. It is established from asymptotic expansions and the theory of singularities. This criterion is able to respond to the paradox posed by the traditional tools of brittle fracture mechanics which might carelessly conclude to a quasi infinite strength enhancement. The subtitle of this first part might be: can a crack pass through an interface?

Crack deflection by an interface – asymptotics of the residual thermal stresses

The He and Hutchinson (1989) criterion allows to predict a matrix crack deflection by an interface under mechanical loadings. It has been improved by the same authors and Evans (1994) to take into account the residual thermal stresses. This criterion is revisited here from an asymptotic point of view. A first-order (local) and second-order (non-local) forms of this criterion are proposed for mechanical loadings. Next, the same approach is carried out for a pure thermal loading, i.e. for a cooling process for instance. It is shown that residual thermal stresses do not intervene at the leading order but play a role at the second one. When combined loadings are considered, the first-order criterion is still unchanged but the second-order one becomes quite illusory since it makes an explicit reference to the critical mechanical loading triggering the deflection. Nevertheless, some trends on the deflection promotion or inhibition are derived for a notched bimaterial under four-point bend loading. In the light of these results, criticisms to the He et al. (1994) expressions are brought.