P. W. R. Beaumont

A model for the toughness of epoxy-rubber particulate composites

Epoxy resins are toughened significantly by a dispersion of rubber precipitates. Microscopic examinations of propagating cracks in epoxy-rubber composites reveal that the brittle epoxy matrix cracks, leaving ligaments of rubber attached to the two crack surfaces. The rubber particles are stretched as the crack opens and fail by tearing at large, critical extensions. This fracture mechanism is the basis of a new analytical model for toughening. An increase in toughness (ΔGIC) of the composite is identified with the amount of elastic energy stored in the rubber during stretching which is dissipated irreversibly (e.g. as heat) when the particles fail. The model predicts the failure strain of the particles in terms of their size. It also relates the toughness increase to the volume fraction and tearing energy of the rubber particles. Direct measurements of the tearing strains of rubber particles, and toughness data obtained from epoxy-rubber composites, are in good agreement with the model. The particle-stretching model provides a quantitative explanation, in contribution to existing qualitative theories, for the toughening of epoxy-rubber composites.

R-curve behaviour of Al2O3 ceramics

Abstract The fracture micromechanics and underlying physical processes of fracture in Al2O3-based ceramic specimens have been studied as a function of grain size by instrumented in situ dynamic scanning electron microscopy (SEM) using the double torsion technique. The toughness is found to increase with grain size. Crack bridging is found to extend over hundreds of grain diameters behind the crack tip, resulting in R-curve behaviour. Evidence is amassed which points to frictional energy dissipation, rather than distrubuted microcracking or crack-closure due to elastic ligaments, as the dominant contribution to toughening. The friction occurs at grains which bridge the crack faces and are pulled out as the faces separate. Restraining stresses, which constrain the bridging grains in their sockets, are believed to be the result of both grain morphology and the thermal expansion anisotropy of the material. Simple modelling indicates that only a few percent of the grains need be involved in the frictional process to account for the toughening. The conclusion is supported by hysteresis measurements.

Debonding and pull-out processes in fibrous composites

The processes of debonding and pull-out in fibrous composites are described. Models predicting the debond length and the probability distribution of pull-out lengths of fibres and bundles are derived. These lengths are functions of the fibre, matrix and interface properties. Prediction is then compared with experiment and a simple relationship between pull-out and debond lengths is found. An understanding of the debonding and pull-out processes is important because they affect the fracture toughness of fibre composites.

Damage mechanics of composite materials: I— Measurements of damage and strength

Abstract A new approach for modelling the strength of notched composites has been developed. The approach is based on the assumption that subcritical damage modifies the notch-tip stress field and that the state of subcritical damage just before failure, referred to as the terminal damage state (TDS), must have a significant influence on notched strength. The TDS was monitored for a wide range of cross-ply graphite reinforced epoxy specimens using real-time radiography. A finite element model incorporating the TDS was used to determine the modified notch-tip stress field. A simple tensile stress failure criterion has been found to predict failure very well provided that the effect of subcritical damage is considered in this way. The effect of both layup and notch size on strength can be entirely accounted for by the effect these parameters have on the terminal damage state. In the first paper of a four-part series, radiographs of c. 60 specimens have been used to characterize the notch-tip damage zone and to establish a qualitative relationship between terminal damage and notched strength.

Mechanisms of toughening in rubber toughened polymers

Abstract A method is presented whereby various potential contributions to the toughness of rubber toughened polymers can be quantified. The tendencies toward either synergism or additivity amongst mechanisms is emphasised for rubber stretching, cavitation and shear banding. The method reveals that specific experimental measurements of microstructural changes near a crack tip, in the crack wake, are needed to unequivocally ascertain the dominant toughening mechanisms.

On the toughness of particulate filled polymers

An approach for predicting trends in the toughness of particulate filled polymers has been presented. The approach is based on independent knowledge of the constitutive law that describes the non-linear behaviour in the process zone. An idealized law is used to demonstrate expected trends with particulate volume fraction and size. The trends are correlated with experimental data. Some discussion of the non-linear process zone mechanisms, such as debonding and microcracking, is presented as a basis for developing more realistic constitutive laws and hence, providing superior predictions of toughness.

The fatigue damage mechanics of a carbon fibre composite laminate: I—development of the model

Abstract The mechanics of fatigue damage of a carbon fibre composite laminate is developed. In this system, damage consists of a delamination front, with associated matrix cracking, which propagates inwards from the sample edges. The elastic stiffness of the laminate is related to the current level of damage, and is used to measure it. The damage growth rate is a power function of the stress amplitude and of the mean stress, and is independent of damage when cycling is at constant stress amplitude. Failure occurs when the damage reaches a critical level which depends on the maximum stress seen in the loading cycle. The results are applied to life prediction in Part II of this work.

Low-temperature behaviour of epoxy-rubber particulate composites

Toughness and mechanical property data are presented for a carboxyl-terminated acrylonitrile butadiene (CTBN) rubber-modified epoxy resin in the temperature range 20 to − 110° C. A toughening model based on ultimate strain capability and tear energy dissipation of the rubber, present as dispersed microscopic particles in an epoxy matrix, is used to explain the suppression of composite toughness (GIc) below − 20° C. The toughness loss is attributed to a glass transition in the rubber particles, and to a secondary transition in the epoxy resin, both occurring in the range − 40 to − 80° C. Strain-tofailure and modulus measurements on bulk rubber-epoxy compounds, formulated to simulate rubber particle compositions, confirm a decrease in rubber ductility coincident with the onset of composite toughness loss. An increase in rubber tear energy associated with its transition to a rigid state can explain the observation that even at low temperatures composite toughness generally remains significantly higher than that of pure epoxy. Although the low-temperature epoxy transition reduces molecular mobility in the matrix phase, residual ductility in, and energy dissipation by, the rubber particles determine the extent of composite toughness suppression. The low-temperature data bear out the particle stretching-tearing model for toughening.

Damage mechanics of composite materials. II: A damaged-based notched strength model

Abstract A new model of the notched strength of graphite-epoxy composites has been developed. In this second paper of a four-part series, a finite element model has been used to simulate observed subcritical notch tip cracking patterns in cross-ply laminates. The model produced maps displaying tensile stress contours in the 0° ply, and it was found that all specimens failed when the maximum tensile stress in the 0° ply exceeded the strength of that ply. The strength of the 0° ply in the vicinity of the notch tip was determined independently using a Weibull statistical strength model.

The fatigue damage mechanics of a carbon fibre composite laminate: II — life prediction

Abstract The equations of fatigue damage mechanics for a carbon fibre composite laminate, developed in Part I of this paper, are applied to life prediction under constant and varying stress amplitudes. The S-N curves predicted for constant stress amplitude at various mean stresses are in good agreement with experiments. Life prediction for various block and random loadings are less satisfactory: there is an acceleration in damage growth caused by load-block interaction which is not, at present, well modelled, but can be included empirically. However, the predictions are far better than those of Miners Rule, which is seriously non-conservative.