L. Távara

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.

Mixed-mode failure of interfaces studied by the 2D Linear Elastic-Brittle Interface Model: macro- and micro-mechanical finite element applications in composites

ABSTRACT Macro-scale delamination and micro-scale fiber–matrix debonding events may notably affect the mechanical performance of fibrous composite elements. This article presents a two-dimensional finite-element (FE)-based formulation of interface of a small but finite thickness relying on the so-called linear elastic-brittle interface model (LEBIM) to be applied for simulation of an adhesive interface debonding and fiber–matrix decohesion failures. This modeling strategy is implemented in the commercial FE package ABAQUS by means of the user-defined subroutine UMAT. The practicability of the developed interface model is assessed through the comparison of the computational results with experimental data and with previous boundary element method (BEM) analyses using the LEBIM formulation. Specifically, LEBIM results for the interlaminar fracture toughness test showed an excellent agreement with experimental results (adhesive saw-tooth post-peak response was captured). Besides, studies of several micro-mechanical fiber–matrix configurations showed that fiber–matrix debonding events are the predominant failure mechanisms for moderate transverse loading values. The developed tool will certainly contribute to elucidate several open aspects regarding the interface crack behavior in fiber-reinforced composite materials.

Symmetrical or Non-Symmetrical Debonds at Fiber–Matrix Interfaces: A Study by BEM and Finite Fracture Mechanics on Elastic Interfaces

A recently proposed criterion is used to study the behavior of debonds produced at a fiber–matrix interface. The criterion is based on the Linear Elastic–(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Special attention is given to the discussion about the symmetry of the debond onset and growth in an isolated single fiber specimen under uniaxial transverse tension. A common composite material system, glass fiber–epoxy matrix, is considered. The present methodology uses a two-dimensional (2D) Boundary Element Method (BEM) code to carry out the analysis of interface failure. The present results show that a non-symmetrical interface crack configuration (debonds at one side only) is produced by a lower critical remote load than the symmetrical case (debonds at both sides). Thus, the non-symmetrical solution is the preferred one, which agrees with the experimental evidences found in the literature.

Revisiting the Problem of Debond Initiation at Fibre-Matrix Interface under Transversal Biaxial Loads - A Comparison of Several Non-Classical Fracture Mechanics Approaches

Understanding matrix failure in LFRP composites is one of the main challenges when developing failure criteria for these materials. This work aims to study the influence of the secondary transverse load on the crack initiation at micro-scale. Four non-classical approaches of fracture mechanics are used to model the onset of fibre-matrix interface debonds: Linear Elastic Brittle Interface Model (LEBIM), an Energetic Approach for the Linear Elastic Brittle Interface Model (EA-LEBIM), an Energetic Approach for the bilinear Cohesive Zone Model (EA-CZM) and the Coupled Criterion of the Finite Fracture Mechanics (CC-FFM). Results obtained by these approaches predict that, for brittle fibre-matrix configurations, a secondary transverse compression reduces the critical value of the main transverse tension leading to the debond onset. This fact is not taken into account by the currently used failure criteria

SGBEM for Cohesive Cracks in Homogeneous Media

In this paper, the Symmetric Galerkin Boundary Element Method for Linear Elastic Fracture Mechanics is extended to non-linear cohesive cracks propagating through homogeneous linear elastic isotropic media. The cohesive model adopted is based on the concept of free energy density per unit undeformed area. The corresponding constitutive cohesive equations present a softening branch which induces a potential instability. Thus, a suitable solution algorithm capable of following the growth of the cohesive zone is needed, and in the present work the numerical simulation is controlled by an arc-length method combined with a Newton-Raphson algorithm for the iterative solution of nonlinear equations. The Boundary ElementMethod is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries of linear elastic domains. Moreover a Galerkin approximation scheme, applied to a suitable symmetric boundary integral equation formulation, ensures an easy and efficient treatment of cracks in homogeneous media and an excellent convergence behavior of the numerical solution. The cohesive zone model is applied to simulate a pure mode I crack propagation in concrete. Numerical results for three-point bending test are used to check the numerical results for mode I and are compared with some numerical results obtained by FEM analysis found in the literature.

2.16 Micromechanics of Interfacial Damage in Composites

One of the reasons for the application of composites to mobile structures is their capacity to absorb energy under impact. As their components have a very reduced interval of deformation till breakage, the mechanism of absorption of energy cannot be based on plasticity but on the capacity of generating free surfaces inside the material, the debonding between fibers and matrix being the most direct materialization of the mechanism of absortion of energy in composites. In this chapter the onset and propagation of damage in between fiber and matrix in a fibrous composite, particularly under transverse loading is studied and characterized. The tools to apply are interfacial fracture mechanics (IFM), linear elastic brittle interface model, finite fracture mechanics (FFM), and cohesive zone model (CZM), combined with a numerical tool, in this case the boundary element method (BEM). Different loading situations are analyzed, single tension and compression, bi-dimensional loading as well as curing effects. Finally single fiber, two fibers, and multi-fiber configurations are considered in this chapter, the key being the evolution of the energy released by the debonding crack representing damage in between fiber and matrix. Numerical predictions are compared with experimental evidence to support the adequacy of the approaches followed.

Convergence of the BEM Solution Applied to the CCFFM for LEBIM

A procedure based on the Linear Elastic Brittle Interface Model (LEBIM) combined with the Coupled Criterion of Finite Fracture Mechanics (CCFFM) is successfully implemented in a 2D Boundary Element Method (BEM) code. In the original LEBIM formulation, the values of the interface strength, fracture toughness and stiffness are dependent on each other. Therefore, for a large interface stiffness, when the elastic interface tends to a perfect (infinitely stiff) interface, LEBIM is not able to properly characterize the crack propagation. The use of the CCFFM applied to LEBIM, with both the stress and energy criteria imposed as independent fracture conditions, allows to uncouple the interface fracture toughness and strength, obtaining realistic predictions for crack propagation even for stiff interfaces. This code is successfully applied to the problem of debond onset and growth in the pull push test. A benchmark problem is solved, focusing on the convergence of the load-displacement curve and crack-tip solution for h-refinements of BE meshes.