J.G. Williams

The peeling of flexible laminates

The present work has defined an adhesive fracture energy Ga for the peel testing of flexible laminates. The value of Ga characterises the fracture of the laminate and is considered to be a ‘geometry-independent’ parameter which reflects (i) the energy to break the interfacial bonding forces and (ii) the energy dissipated locally ahead of the peel front in the plastic or viscoelastic zone. We have shown that in order to determine this true adhesive fracture energy Ga that the following energy terms must be considered: (i) the stored strain-energy in the peeling arm, (ii) the energy dissipated during tensile deformation of the peeling arm, and (iii) the energy dissipated due to bending of the peeling arm. The analysis proposed yields quantitative expressions for these various energy dissipation terms and, in particular, considers the energy dissipated due to bending of the peeling arm. Another important feature of the analysis is the modelling of the region below the peel front as an elastic beam on an elastic foundation; such that the peeling arm does not act as a truly built-in beam and root rotation at the peel front is allowed. The analysis described in the present paper has been employed for four different laminates. The values of the local angle θ0 at the peel front from the theoretical calculations have been shown to be in excellent agreement with the experimentally measured values; a small-scale peel test rig having been built so that the peel test, as a function of applied peel angle θ, thickness h of peeling arm and rate of test, could be observed and photographed using a stereo-optical microscope. The value of the adhesive fracture energy Ga (i.e the ‘fully corrected’ value) for each laminate is indeed shown to be a ‘material parameter’.

End corrections for orthotropic DCB specimens

Abstract An extension of the beam on an elastic foundation model for estimating the end rotation correction for orthotropic double cantilever beam specimens is described. The solutions are compared with finite element results and a small empirical modification to the analytical result gives a simple formula for calculating an effective crack length correction of the form (a + χh), where h is the thickness. Values of χ for orthotropic materials are about 2·5 compared with 0·67 for isotropic materials. Such large corrections are likely to be important in data analysis.

The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints

Analytical solutions for beam specimens used in fracture-mechanics testing of composites and adhesively-bonded joints typically use a beam on an elastic foundation model which assumes that a non-infinite, linear-elastic stiffness exists for the beam on the elastic foundation in the region ahead of the crack tip. Such an approach therefore assumes an elastic-stiffness model but without the need to assume a critical, limiting value of the stress,σmax, for the crack tip region. Hence, they yield asingle fracture parameter, namely the fracture energy,Gc. However, the corresponding value ofσmax that results can, of course, be calculated from knowledge of the value ofGc. On the other hand, fracture models and criteria have been developed which are based on the approach thattwo parameters exist to describe the fracture process: namelyGcandσmax. Hereσmax is assumed to be a critical,limiting maximum value of the stress in the damage zone ahead of the crack and is often assumed to have some physical significance. A general representation of the two-parameter failure criteria approach is that of the cohesive zone model (CZM). In the present paper, the two-parameter CZM approach has been coupled mainly with finite-element analysis (FEA) methods. The main aims of the present work are to explore whether the value ofσmax has a unique value for a given problem and whether any physical significance can be ascribed to this parameter. In some instances, both FEA and analytical methods are used to provide a useful crosscheck of the two different approaches and the two different analysis methods.

Temperature effects in the fracture of PMMA

Experiments are described in which the fracture toughness,Kc, of PMMA has been determined in the temperature range −190 to + 80° C and over the crack speed range of 10−2 to 102 mm sec−1. Single edge notch tension was used for instability measurements but the other data were obtained using the double torsion method. In the range −80 to + 80°C the variations inKc may be described in terms of modulus changes and a constant crack opening displacement criterion. Crack instabilities are correlated with isothermal-adiabatic transitions at the crack tip. Below −80° C there is an inverted rate dependence associated with thermal effects during post-instability crack propagation.

Corrections for mode II fracture toughness specimens of composites materials

Abstract A correction factor for the end-loaded-split (ELS) and end-notch-flexure (ENF) Mode II fracture toughness tests is described. This takes the form of correcting the crack length a , by a length χh , where h is the half thickness and χ is a constant that depends on the elastic parameters of the material. The predictions obtained by using this correction are compared with G II results from several numerical schemes, and good agreement is achieved.

The mixed-mode delamination of fibre composite materials

Abstract The present paper is concerned with an investigation of the mixed-mode delamination of polymeric fibre composite materials. Various test geometries have been used to measure the interlaminar fracture energy, G c , of both thermoplastic and thermosetting carbon fibre composites when subjected to various ratios of mode I to mode II loadings. In particular, the mixed-mode bending (MMB) delamination test has been studied in detail and the results from this test method compared to those obtained from the fixed-ratio mixed-mode (FRMM) test method. Further, for the FRMM results, two methods of partitioning the measured interlaminar fracture energy, G c , have been employed: namely, by way of a local singular-field approach and by a global method based on a consideration of the applied energy release rates. It is shown that the latter approach is the more appropriate method. Finally, a general criterion for mixed-mode failure is proposed which assumes that a crack loaded with G I and G II will have an induced mode I component equal to the failure value, termed G 0 , such that: G 0 = G c [( cos 2 ( Ψ − Ψ 0 ) + sin 2 ω sin 2 ( Ψ − Ψ 0 )] where G c is the measured fracture energy, Ψ is the phase angle of the applied loads, Ψ 0 is the phase angle which arises from the elastic mismatch across a bimaterial interface (e.g. the fibre/matrix interface) and where ω can be regarded as the slope of the fracture surface roughness.

Mechanics and mechanisms of delamination in a poly(ether sulphone)—Fibre composite

Abstract The interlaminar fracture behaviour of AS4/PES (poly(ether sulphone)) composite has been investigated in Mode I, Mode II and for fixed Mode I to Mode II ratios of 0·84, 1·33 and 2·13. The data obtained from these tests have been analysed using several different analytical approaches. The results obtained show that in Mode I the interlaminar crack growth in double cantilever beam (DCB) specimens is accompanied by fibre bridging behind the crack tip and by splitting at the crack tip, and in Mode II by the formation of a damage zone at the crack tip. These failure mechanisms are shown to increase the value of the interlaminar fracture energy considerably as the crack propagates through the composite, i.e. a rising ‘R-curve’ is measured. It is shown also that the value of the interlaminar fracture energy at crack initiation in Mode I, G CI (init), increases as the length of the initial precrack is increased. The lowest G IC (init) value obtained for the poly(ether sulphone) (PES) composite in this study is 0·8 kJm−2, and this value was ascertained from a specimen with the precrack being grown by about 2 mm ahead of the initial crack ( a 0 = 23 mm, a p = 25 mm ). The typical Mode II steady-state propagation energy, G IIC (s/s-prop), value obtained for the specimens was about 2·0 kJm−2. The length of the initial precrack had no significant effect on the G IIC (init) and G I/IIC (init) values. The Mode II tests gave values of G IIC (init) = 1·25 kJm −2 and of G IIC (s/s-prop) = 1·85 kJm −2 . Finally, the failure loci for the PES composite have been constructed and theoretical expressions to describe these data considered.

On the analysis of mixed-mode failure

The present paper is concerned with the problem of mixed-mode fracture, especially where such failure occurs along a plane of weakness at a bimaterial interface or by interlaminar failure in polymer fibre-composite materials. Firstly, two different schemes for analysing such mixed-mode failures are discussed. These schemes are: (i) a method based upon a consideration of the local singular field ahead of a crack tip, and (ii) a global method based upon a consideration of the applied energy release rates. Secondly, experimental data taken from the literature are reviewed and it is concluded that the latter scheme results in a more consistent interpretation of the data. Indeed, in several cases the global method clearly gives far better agreement between the theoretical predictions and the observed results. The reasons for this are suggested to be the very localised nature of the singular-dominated region ahead of a crack tip in many test specimens and the relatively large damage zone in the materials studied. Finally, the present work has led to the proposal of a general criterion for fracture under mixed-mode loading.

Delamination Fracture of Multidirectional Carbon-Fiber/Epoxy Composites under Mode I, Mode II and Mixed-Mode I/II Loading

The purpose of the present study was to characterize the delamination fracture of continuous carbon fiber/epoxy multidirectional-laminates under Mode I, Mode II and Mixed-Mode I/II loading conditions. The present study considers the variation of the interlaminar failure energy, G C , with the extent of crack jumping, and ensuing fiber bridging, which arises during the growth of the delamination in the multidirectional-laminates under the various modes of loading. The main type of laminate which was studied was a multidirectional fiber composite prepared from 24 ply lay-ups of (-45°/0°/+45°)2S (+45°/0°/-45°)2S. The initial delamination was located at the +45°/-45° mid-plane of the specimen. It has been found that when the values of the interlaminar fracture energy, G c , are ascertained as a function of the length of the propagating crack, a, then very complex relationships are observed. This was the case for all the different modes of loading, and these observations reflected the complex failure paths which occurred as the delamination propagated through the multidirectional fiber composites. It was, however, possible to define clearly the onset of crack initiation. These results also revealed that the values for the interlaminar fracture energy, G C -(initiation), at crack initiation for the (-45°/O°/+45°)2S (+45°/O°/-45°)2S multidirectional laminates were always significantly greater than that for the corresponding unidirectional (i.e., 0°/0°) laminates.

European group on fracture: Kc and Gc methods for polymers

Abstract This short paper summarises the curren status of reseach initiated by the European Group on Fracture (EGF) Polymers and Composites Task Group on the standardisation of K c and G c methods for polymers. The work is based on ASTM Standard E399 for metals and has led to a testing protocol which takes account of the major difficulties imposed by polymers. The special features of the current testing protocol are described.