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

Abstract

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.

Revisiting the problem of a crack impinging on an interface:A modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model

“…(4) is assumed to be decomposed in the sum of the Mode I and Mode II energy release rates, G I and G II , based on the considered cohesive zone model. In the present study, without loss of generality, we adopt a linear Mode I cohesive zone model with tension cut-off upon failure, see previous applications in [78,79,80]. Moreover, the same traction-separation profile is used for the cohesive zone relation corresponding to Mode II fracture, see Fig.3.…”

Two adhesive-contact models for quasistatic mixed-mode delamination problems

“…A standard engineering approach, as e.g. in [5,13,14,15], is that A is diagonal in a local coordinate system associated to Γ C , writing e.g. A = diag(κ n , κ t , κ t ) for n C = (1, 0, 0) at some x ∈ Γ C , and the activation energy denoted here by α, whereas in engineering typically referred to as fracture energy and denoted by G c , depends on the so-called energetic fracturemode-mixity angle ψ G defined as…”

“…respectively. Here, we will not use any of the phenomenological laws for G c (ψ G ) well-known in engineering (see [13]) but rather fit it with the plasticity-inspired model described in the following section.…”

“…Two models developed in the literature that allow for rigorous mathematical and numerical analysis (as far as existence of solutions and numerically stable, implementable, and convergent approximation schemes) are studied here. Both have a bit different character: LEBIM: Linear Elastic -(perfectly) Brittle Interface Model (like [11,12,13,14,15,16]): + It allows for incorporation of arbitrary phenomenological dependence of dissipation (or activation) energy on the fracture mode mixity. The state q in (1.1) is a couple (u, z) and the "elasticity domain" of the adhesive varies depending on the state, which is sometimes called "non-associative", cf.…”

“…Such computations and the models themselves are thus unjustified so far from the mathematical point of view, although in particular cases the launched computational simulations may be physically relevant; see e.g. [26,27,13,14,15,16] and references therein. Let us still mention that the LEBIM was rigorously analyzed already in [28] even in a full thermodynamical context but exploiting the concept of non-simple materials (see e.g.…”