Michael R Wisnom

Size effects in the testing of fibre-composite materials

Abstract The effect of test specimen size on the unnotched strength of continuous fibre reinforced composites is considered. The different fundamental failure mechanisms of fibre direction tension, fibre direction compression, and matrix dominated transverse tension and shear are discussed in turn. The available experimental data is reviewed, concentrating on tests on unidirectional carbon and glass fibre/epoxy materials. The results show a tendency for the strength to decrease with increasing specimen volume for all failure modes. Size effects in tensile failure have been found in both tensile and flexural tests, and from higher strengths in bending than in tension. The magnitude of the effect is consistent with Weibull moduli in the range 13–29 for the materials considered. There are some indications that the size effect in tension diminishes with increasing scale. Lower compressive strengths have been found in large components than in small test coupons, and attributed to defects. Size effects observed in compressive failure in bending are believed to be mainly due to the stress gradient through the thickness. There are large size effects for matrix dominated failures, and Weibull strength theory fits the data reasonably well. It is important to consider the effect of specimen size on strength when carrying out tests on composites, and to take account of it when using strength data from small coupons in the design of large structures.

A Combined Stress Based and Fracture Mechanics Based Model for Predicting Delamination in Composites

Abstract An interface model for delamination using spring elements is introduced. The advantages of the model are that it is very simple and can handle singular and non-singular problems in a unified way. Furthermore, it requires no assumption of the existence of initial defects and no knowledge of the direction of crack growth. By applying it to two example problems of three-point bending and specimens with cut central plies, it is shown that this model is able to predict the onset and growth of delamination in both types of problem very well.

Experimental Investigation of Progressive Damage and the Effect of Layup in Notched Tensile Tests

The presence of subcritical damage in notched composites significantly affects the ultimate failure mode and strength. This article presents a detailed study of four different layups of E-glass/913 tested using a double-edge-notched specimen loaded in tension. For each layup three different in-plane dimensions are tested. Results are presented in terms of failure mode, strength, and subcritical damage development. Subcritical damage development is consistent between the layups and between scaled specimens of a single layup. Ultimate failure, however, shows some variations both with layup and size and this is examined in some detail. The trend of decreasing strength with increasing specimen size is observed for all cases except those where there is a change in failure mode between different size tests. The strengths are compared with predictions from two analytical techniques, which show some ability to achieve correlation across a subset of the test data. Correlation is not possible where variations in failure mode occur for a single layup.

In-situ measurement of chemical shrinkage of MY750 epoxy resin by a novel gravimetric method

A novel approach has been developed to measure in-situ chemical shrinkage of epoxy resins at the temperature of cure, during which the epoxy resins pass through liquid, rubbery and glassy states. A small sample of MY750/HY917/DY073 epoxy resin system, sealed in a thin-walled silicone bag, was suspended in a pot of silicone fluid and weighed independently of the silicone bath. The buoyancy of the sample was monitored as its density increases with respect to the constant density fluid during isothermal cures at three different temperatures. The relationship between the chemical shrinkage and degree of cure was deduced from a cure kinetics model for the resin. The good match of the results for the three different cure cycles suggests that chemical shrinkage is only a function of degree of cure regardless of time and temperature. A bi-linear relationship was fitted to the experimental data. The break point is at a degree of cure of about 28%, with corresponding chemical shrinkage of 3%. This point is linked to the gel point of the resin, which was measured as approximately 25% degree of cure in previous work. Total cure shrinkage of 6.9% for the MY750 resin system was obtained by extrapolating the results to a degree of cure of 100%. The method is sensitive, reliable and keeps the resin stress-free; therefore it should be applicable to a wide range of materials.

Reduction in interlaminar shear strength by discrete and distributed voids

Discrete voids of different sizes were simulated by embedding PTFE monofilaments, tubes and strips at the mid-plane of unidirectional glass fibre and carbon-fibre/epoxy plates. Short-beam shear tests were carried out to determine the effect of the defects on interlaminar shear strength. For those specimens where failure initiated from the defect, linear elastic fracture mechanics was not able to predict the reduction in strength. However, excellent correlation was obtained with a previous finite element analysis which used non-linear springs to model the interfaces between plies. In other specimens failure initiated above and below the defect. For these failures, the main factor appears to be the increase in stress due to the reduction in net cross-section. Failure of specimens with high levels of distributed voidage was also consistent with failure being controlled mainly by the reduction in net section. It is suggested that the commonly observed decrease in interlaminar shear strength with voidage is due to a combination of the reduction of cross-sectional area due to distributed voidage and initiation of failure from larger discrete voids.

Modelling of splitting and delamination in notched cross-ply laminates

A finite-element approach has been developed for modelling the detailed damage development in notched composites. Separate elements are used for each ply, connected together with interface elements to allow delamination between the plies. Interface elements are also used to model splitting at the notch. The approach is applied to a cross-ply laminate with a centre crack loaded in tension, and the results compared with experimental measurements. The model accurately predicts the development of a narrow triangular delamination zone, and the extent of splitting as a function of applied tensile stress. The approach offers scope for improved simulation and understanding of the complex failure processes in notched composites.

Three Dimensional Finite Element Analysis of the Stress Concentration at a Single Fibre Break

Abstract A linear elastic analysis is performed of a single broken fibre surrounded by six equally spaced fibres. These fibres and the surrounding epoxy matrix are modelled separately whilst the rest of the composite is treated as a homogeneous, orthotropic material. The distance of the adjacent fibres is fixed based on an assumed fibre volume fraction of 0·60. The analysis shows that the stress concentration in the adjacent fibres is 1·058, much lower than the value of 1·104 predicted by Hedgepeth and van Dyke (J. Comp. Mater., 1 (1967) 294–309). The positively affected length where there is an increase in stress is only about half the ineffective length of the broken fibre. Further away from the break the axial stress in the adjacent fibres actually drops below the nominal axial stress. This results in a very small enhanced probability of failure in the adjacent fibres. Very close local fibre spacing around the broken fibre increases the maximum stress in the adjacent fibres by less than 3%.

Prediction of delamination initiation and growth from discontinuous plies using interface elements

Abstract A special type of interface element was created to represent the resin-rich layers between plies in a finite element model of a composite structure. Yielding of the element depended on an interactive stress-based criterion and final failure depended on a mixed-mode fracture mechanics criterion. Both perfectly plastic and work softening types of damage behaviour were modelled. The interface elements were inserted into finite element models of two different straight specimens and two different curved specimens at all possible delamination sites. The specimens contained a group of discontinuous plies which produced a similar stress concentration to that at a ply-drop. Failure was due to multiple delaminations initiating at the cut. The interface elements successfully predicted the locations of the delaminations and were able to account for the changing mode ratio as damage progressed. The predicted failure loads using ‘perfectly plastic’ interface elements were very good for the straight specimens but unconservative for the curved specimens. On the other hand, the predictions using the ‘work softening’ interface elements were reasonable for all four types of specimen.

Development of curvature during the cure of AS4/8552 [0/90] unsymmetric composite plates

Abstract The development of residual stresses in [0/90] unsymmetric flat laminates (AS4/8552 composite system) was monitored by stopping the cure cycle at pre-determined points and evaluating the related level of deformation. Cylindrical shapes of consistent curvature are obtained and the “cured” curvature can be eliminated by re-heating samples up to a certain temperature, designated as the stress free temperature, T sf . The stress free temperature has also been measured after the interrupted cure cycles: the evolution of the stress free temperature during the cure cycle allowed the vitrification point to be estimated. Both curvature and T sf increase with increasing cure but level off after the vitrification point, attaining a constant value. The stress free temperature of samples cured beyond vitrification is systematically higher than their cure temperature. It is evident that a certain percentage of non-thermoelastic stress is present in the structure, possibly due to resin chemical shrinkage. The “cured” curvature is mostly driven by the transverse coefficient of thermal expansion, α 2 . From curvature–temperature profiles, it is found that α 2 is almost constant during the cycle, below T g . Post-cure of laminates that have not been fully cured tends to increase their “residual” curvature, but the effect of the post-cure is relatively small for specimens cured beyond the vitrification point.

The effect of fibre misalignment on the compressive strength of unidirectional carbon fibre/epoxy

Abstract The effect of a misalignment angle between the fibres and loading axis of a unidirectional composite is analysed by considering the shear strains induced by the misalignment. It is shown that shear instability in the matrix drastically reduces the predicted compressive strength even for very small misalignments. The same trend is predicted for composites with initial fibre curvatures due to the misalignment angle associated with the curvature. The reduction in compressive strength often attributed to initial fibre curvature may therefore actually be due to fibre misalignment angles. Small misalignments are hard to avoid during the manufacture and testing of unidirectional composites and so these results cast serious doubts on the possibility of measuring a true ultimate compressive strength for this kind of material.