E. Correa

Kinking of Transversal Interface Cracks Between Fiber and Matrix

Under loads normal to the direction of the fibers, composites suffer failures that are known as matrix or interfiber failures, typically involving interface cracks between matrix and fibers, the coalescence of which originates macrocracks in the composite. The purpose of this paper is to develop a micromechanical model, using the boundary element method, to generate information aiming to explain and support the mechanism of appearance and propagation of the damage. To this end, a single fiber surrounded by the matrix and with a partial debonding is studied. It has been found that under uniaxial loading transversal to the fibers direction the most significant phenomena appear for semidebonding angles in the interval between 60 deg and 70 deg. After this interval the growth of the crack along the interface is stable (energy release rate (ERR) decreasing) in pure Mode II, whereas it is plausibly unstable in mixed mode (dominated by Mode I for semidebondings smaller than 30 deg) until it reaches the interval. At this interval the direction of maximum circumferential stress at the neighborhood of the crack tip is approximately normal to the applied load. If a crack corresponding to a debonding in this interval leaves the interface and penetrates into the matrix then: (a) the growth through the matrix is unstable in pure Mode I; (b) the value of the ERR reaches a maximum (in comparison with other debonding angles); and (c) the ERR is greater than that released if the crack continued growing along the interface. All this suggests that it is in this interval of semidebondings (60-70 deg) that conditions are most appropriate for an interface crack to kink. Experiments developed by the authors show an excellent agreement between the predictions generated in this paper and the evolution of the damage in an actual composite.

BEM analysis of inter-fibre failure under compression in composites: comparison between carbon and glass fibre systems

Abstract The heterogeneous character of fibrous composite materials implies mechanisms of damage that are frequently associated, at least at the micromechanical level, with the generation of interface cracks and, thus, with interfacial fracture mechanics. The particular case of matrix/interfibre failure, typically appearing in impact problems and in cross-ply laminates, and caused by a dominant traction acting transversely to the fibres, is directly associated to the appearance and growth of cracks at the fibre/matrix interfaces that eventually lead to macrofailure. The present work studies the evolution of this mechanism of damage under compression and compares the results obtained for two different bimaterial systems: glass fibre–epoxy matrix and carbon fibre–epoxy matrix. To this end, a boundary element model of a single fibre cell is performed, and its results are analysed using the concepts derived from interfacial fracture mechanics. The conclusions obtained establish the morphological differences existing in the generation of this mechanism for both material systems, supporting the idea of a weak dependence of the development of the interfibre failure under compression on fibre elastic properties.

Fiber–matrix debonding in composite materials: Transverse loading

The objective of this chapter is the study of the interfiber–matrix failure under tension. The initial micromechanical stages of this damage mechanism are identified and studied. The boundary elements method is employed and interfacial fracture mechanics concepts are used for the analysis of the results. Two complementary studies are also presented: The first analyzes the influence of the presence of a secondary transverse load (perpendicular to the transverse tension nominally responsible for the failure) on the micromechanical stages previously identified, and the second focuses on the effect of thermal residual stresses (originated in the cooling-down step associated with the curing process).Abstract The objective of this chapter is the study of the interfiber–matrix failure under tension. The initial micromechanical stages of this damage mechanism are identified and studied. The boundary elements method is employed and interfacial fracture mechanics concepts are used for the analysis of the results. Two complementary studies are also presented: The first analyzes the influence of the presence of a secondary transverse load (perpendicular to the transverse tension nominally responsible for the failure) on the micromechanical stages previously identified, and the second focuses on the effect of thermal residual stresses (originated in the cooling-down step associated with the curing process).

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.

Numerical Study of the Progression of the Micromechanical Debonding Damage in Composites

This paper deals with the study of the actual progression of the damage in the 90 degrees lamina of a composite. It has been proved and observed that isolated debondings between fibres and matrix are the first manifestation of damage in the weakest lamina, the 90 degrees lamina in a [0,90]S laminate. It was also numerically supported that this first phase was independent of the thickness of the 90 degrees lamina, not being then affected by the “scale effect”. The continuation of this first phase of damage is the objective of the present paper. To this end, a multiscale model is created involving the debonding between fibre and matrix and studying the kink of this crack, abandoning the fibre-matrix interface and entering into the matrix to produce a meso-transverse crack in the 90 degrees ply. The study is based on the application of Fracture Mechanics to an incipient kinked crack that starts from a debonding between fibre and matrix. It is concluded that this second phase of damage, playing with the thickness of the 90 degrees lamina, is not affected by the scale effect, as the variation of the energy release rate of the kinked crack is not significantly influenced by the variation of the thickness of the lamina.

Micromechanical Evidences on Interfibre Failure of Composites

Micromechanics has been widely used in the link in between an actual non-homogeneous composite ply involving fibre and matrix and an equivalent homogeneous ply with non-isotropic behaviour, connecting stiffness and strength properties of the equivalent lamina with the properties of fibre and matrix. The authors believe that beyond this, Micromechanics is the key tool to understand the behaviour of composites, to be able, among many other things, to propose physically based failure criteria that obviously are established at meso- or macro-level of a composite. Thus, the role of Micromechanics in the understanding of the interfibre failure mechanisms of composites is presented in this chapter. Different loading conditions (single tension, single compression, bidirectional loads and fatigue) are studied based on a simple single fibre model. The role of residual curing stresses at micromechanical level in the strength of a ply in the direction normal to the fibres is also studied. Finally, more refined models cover two questions of interest as the effect of a nearby fibre in the debonding of a primary fibre, and the scale effect in composites at micromechanical level, considering the debonding between fibre and matrix. In all cases the approach is to develop a BEM model and apply the tools derived from Interfacial Fracture Mechanics to deal with the debonds between fibre and matrix and Linear Elastic Fracture Mechanics to deal with cracks running into the matrix. It is noticeable that no material or fitting parameters are used in the developments carried out. In all cases studied, experimental evidences are presented to support numerical predictions.

MICROMECHANICAL BASES FOR THE PREDICTION OF FAILURE OF THE MATRIX IN FIBROUS COMPOSITES

Prediction of the failure of the matrix (also called inter-fiber failure) has been assigned in many proposals to a certain interaction (typically quadratic) between the components of the stress vector associated to the plane of failure. In this paper, a numerical micromechanical study is conducted considering, based on failure observations, that the mechanism of failure is first of all produced by a crack running between the fiber and the matrix, and secondly by the kinking of these interface cracks whose coalescence produces a crack of macromechanical relevance associated to the inter-fiber failure. The study is carried out by means of several micromechanical models, whose numerical analysis is performed using the Boundary Element Method, allowing contact between the lips of the cracks under consideration. With reference to the first step, which is considered the one determinant of the inter-fiber failure, the objective of the micromechanical analysis is to elucidate the adequacy of the assumption that the stress vector associated to a plane controls the failure of the plane. The results obtained prove numerically that stresses not associated to the macromechanical plane of failure play an important role in the micromechanism of failure of fibrous composites. This conclusion is based on the influence that normal stresses not associated to the plane of failure have in the energy release rate of the interfacial crack between fiber and matrix, this having been considered to be the parameter that characterizes the damage at this first step. With reference to the second step, i.e. the coalescence of the interfacial cracks to generate a crack of macromechanical meaning, it has been found that the most significant phenomena appear for debonding angles between fiber and matrix in the interval between 60 and 70 degrees. First, it has been found that the growth of the crack along the interface is plausibly unstable in mixed mode until it reaches the interval and unconditionally stable in mode II for greater debondings. Second, it is at this interval that the direction of maximum circumferential stress at the neighbourhood of the crack tip is approximately normal to the applied load. Third, if a crack corresponding to a debonding in this interval leaves the interface and penetrates into the matrix: the growth through the matrix is unstable, the value of the energy release rate reaches a maximum (in comparison with other debonding angles), and the energy released is greater than that released for the crack continuing to grow along the interface. All this suggests that it is in this interval of debondings that conditions are most appropriate for a crack to kink. All the aforementioned facts create a micromechanical basis to generate proposals of inter-fiber failure of fibrous composites.