E. Graciani

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.

A simple local smoothing scheme in strongly singular boundary integral representation of potential gradient

Abstract A new approach for computation of potential gradient at and near boundary is introduced. A strongly singular boundary integral representation of potential gradient, whose integral density is the potential gradient, is derived and analysed. Applying the concept of the osculating circle, a local smoothing procedure which computes a continuous approximation of potential gradient from the results of a 2D Boundary Element Method (BEM) analysis using linear elements is proposed and evaluated. This approximation is used in the integral representation derived as an integral density which fulfills the continuity requirements. Numerical experiments demonstrate, for quasiuniform meshes, an O( h 2 ) accuracy of potential gradient computed by both the local smoothing procedure on smooth parts of the boundary and by the integral representation on smooth boundary parts and near smooth boundary parts for points inside the domain. A consequence of the latter result is that no significant increase in the error appears near the boundary, boundary layer effect thus being eliminated in this approach.

SINGLE FIBER FRAGMENTATION TEST. A BEM ANALYSIS

Numerical analysis was performed with the aid of the Boundary Element Method (BEM). Contact conditions were taken into account using a weak formulation of the equilibrium compatibility equations al ...

Potential gradient recovery using a local smoothing procedure in the Cauchy integral

A new approach for evaluation of the potential gradient in the 2D boundary element method is presented. The two key elements of the procedure developed are, firstly, a new Strongly Singular Boundary Integral Representation of Potential Gradient in complex variable formulation (equivalent to the Cauchy integral representation of analytic functions), and secondly a continuous approximation of the integral density of this representation determined by a local smoothing procedure applied to the data obtained from BEM analysis. Numerical tests show the high accuracy of the recovered value of the tangential derivative of the potential on smooth and non-smooth boundaries. Copyright

Effect of Friction on the Size of the Near-Tip Contact Zone in a Penny-Shaped Interface Crack

Relations between different solutions of an interface crack in a neighborhood of the crack tip given by the open model, frictionless and frictional contact models of interface cracks are analyzed numerically for a penny-shaped interface crack subjected to remote tension. A new analytic expression for the size of the near-tip contact zone in presence of Coulomb friction between crack faces is proposed in the so-called case of the contact zone field embedded in the oscillatory field.

On the Thickness Dependence of ILTS in Curved Composite Laminates

A test campaign has been carried out to determine the interlaminar tensile strength (ILTS) in AS4/8552 composite laminates with different thicknesses, following AITM 1-0069 and ASTM D6415/D6415M-06a standards. Results show that L-shaped samples with low thicknesses present lower values of the ILTS. Numerical finite element (FE) models of the samples have been carried out and the results of the numerical analyses have been compared with the experimental measurements, showing that a loss of stiffness has taken place in the samples. Optical inspection of the samples has shown up a significant misalignment of the fibers in the curved part that justifies the loss of stiffness in all samples and the loss of strength in the thinner samples.

Boundary integral formulation of frictionless contact problems based on an energetic approach and its numerical implementation by the collocation BEM

A unified methodology to solve problems of frictionless unilateral contact as well as adhesive contact between linear elastic solids is presented. This methodology is based on energetic principles and is casted to a minimization problem of the total potential energy. Appropriate boundary integral forms of the energy are defined and the quadratic problem form of the contact problem is proposed. The problem is solved by the collocation boundary element method (BEM). To solve the quadratic problem two algorithms are developed, both being variants of the well-known conjugate gradient algorithm. The difference between them is given by an explicit construction or not of the quadratic-problem matrix. This matrix has the same physical meaning as the stiffness matrix commonly used in the context of the finite element method (FEM). Both symmetric and non-symmetric formulations of this matrix are presented and discussed, showing that the non-symmetric one provides more accurate results. The present procedure, in addition to its interest by itself, can also be extended to problems where dissipative phenomena take place such as friction, damage and plasticity. Elements of the numerical implementation are briefly presented and the numerical solution of some standard problems of frictionless contact are given and compared to those obtained by other well-known BEM and FEM procedures for contact problems.

Fiber–matrix debonding in composite materials : Axial loading

The propagation of fiber–matrix interfacial debonding under axial loading is analyzed, using the single-fiber fragmentation test as a reference, in order to determine fiber–matrix failure properties. A data reduction technique is presented in which the fiber–matrix Mode II interfacial fracture toughness is obtained from the measurements of the average debond crack growth. A set of boundary element models are employed to evaluate the energy release rate associated with interfacial crack propagation. The interfacial friction coefficient is parametrically varied until a constant value of the energy release rate (which is then equal to the fiber–matrix Mode II interfacial fracture toughness) is obtained. The applicability of the properties evaluated is demonstrated using a set of finite element models with cohesive elements.