Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion

The plane strain problem of a single circular cylindrical inclusion embedded in an unbounded matrix subjected to a remote uniform uniaxial transverse tension is studied. A theoretical model for the simultaneous prediction of \emph{the initial size of a crack originated at the inclusion/matrix interface} (or equivalently the initial polar angle of this crack) and of \emph{the critical remote tension required to originate this crack} is developed. Isotropic and linear elastic behaviour of both materials, with the inclusion being stiffer than the matrix, is assumed. The interface is considered to be strong (providing continuity of displacements and tractions across the interface surface) and brittle. The model developed is based on the classical analytic solutions for the above-mentioned inclusion problem without and with a crack situated at the inclusion/matrix interface and a recently introduced coupled stress and energy criterion of failure by Leguillon (\emph{Eur. J. Mech. A/Solids, 21, pp. 61--72, 2002}). A new dimensionless structural parameter $\gamma$, depending on bimaterial and interface properties together with the inclusion radius $a$, which plays a key role in characterizing the interface crack onset, is introduced. Asymptotic behaviour of the predicted critical remote tension and the interface crack length/polar angle at the onset are characterized for small and large values of $\gamma$ and $a$. A size effect inherent to this problem is predicted and analysed. The following asymptotic characteristics of this size effect are noteworthy: \emph{i)} for small inclusion radii $a$, the polar angle of the crack at onset is constant (independent of $a$), whereas the critical remote tension increases with decreasing $a$, being inversely proportional to the square root of $a$; \emph{ii)} for large inclusion radii $a$, the length of the crack at onset and the critical remote tension are approximately constant.Ministerio de Educación, Cultura y DeporteJunta de Andalucí

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

A new linear elastic and perfectly brittle interface model for mixed mode is presented and analysed. In this model, the interface is represented by a continuous distribution of springs which simulates the presence of a thin elastic layer. The constitutive law for the continuous distribution of normal and tangential initially-linear-elastic springs takes into account possible frictionless elastic contact between adherents once a portion of the interface is broken. A perfectly brittle failure criterion is employed for the springs, which enables the study of crack onset and propagation. This interface failure criterion takes into account the variation of the interface fracture toughness with the fracture mode mixity. A unified way to represent several phenomenological both energy and stress based failure criteria is introduced. A proof relating the energy release rate and tractions at an interface point (not necessarily a crack tip point) is introduced for this interface model by adapting Irwin’s crack closure technique for the first time. The main advantages of the present interface model are its simplicity, robustness and computational efficiency, even in the presence of snap-back and snap-through instabilities, when the so-called sequentially linear (elastic) analysis is applied. This model is applied here in order to study crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads. Firstly, this model is used to obtain analytical predictions about interface crack onset, while investigating a single fibre embedded in a matrix which is subjected to uniform remote transverse loads. Then, numerical results provided by a 2D boundary element analysis show that a fibre-matrix interface failure is initiated by the onset of a finite debond in the neighbourhood of the interface point where the failure criterion is first reached (under increasing proportional load); this debond further propagates along the interface in mixed mode or even, in some configurations, with the crack tip under compression. The analytical predictions of the debond onset position and associated critical load are used for several parametric studies of the influence of load biaxiality, fracture-mode sensitivity and brittleness number, and for checking the computational procedure implemented.Ministerio de Educación y Ciencia TRA2006-08077 MAT2009-14022Ministerio de Economía y Competitividad (España) MAT2012-37387 DPI2012-37187Junta de Andalucía TEP-2045 TEP-4051 P12-TEP-105