Stuart Leigh Phoenix

Weibull strength statistics for graphite fibres measured from the break progression in a model graphite/glass/epoxy microcomposite

Recent statistical theories for the failure of fibrous composities focus on the initiation and growth of clusters of broken fibres within the composite. These theoreis require the probability distribution for fibre strength at the length scale of micromechanical load transfer around a cluster of broken fibres. Such lengths are of the order of 10 to 150 fibre diameters, and thus the associated strengths have previously been unmeasurable by direct means. Using Weilbull/weakest-link rules, researchers have resorted to extrapolation of tension test results from gauge lengths two orders of magnitude longer. In this paper, a technique is developed to study the break progression of a single graphite fibre in an epoxy microcomposite tape, where the graphite fibre is flanked by two, proof-tested, glass fibres. These results are interpreted using a Weibull/Poisson model of the break progression, the number of breaks in the graphite fibre as a function of applied strain, which accounts for stress decay at the fibre ends. It is shown that such extrapolations of tension test data are too optimistic. In addition, different fibres from the same yarn cross-section, apparently have different flaw populations, unlike that which occurs at longer gauge lengths.

MATRIX EFFECTS ON LIFETIME STATISTICS FOR CARBON FIBRE-EPOXY MICROCOMPOSITES IN CREEP RUPTURE

Experimental results are presented for the strength and lifetime in creep rupture of carbon-epoxy microcomposites consisting of seven carbon fibres (Hercules IM6) within an epoxy matrix (Dow DER 332 epoxy with Texaco Jeffamine T403 curing agent) in an approximately hexagonal configuration. Special attention was paid to clamping, specimen alignment, shock isolation and accurate lifetime measurement. The results were analysed using a previously developed model, which involves a Weibull distribution for fibre strength and micromechanical stress redistribution around fibre breaks where the matrix creeps in shear following a power law. The model yields Weibull distributions for both microcomposite strength and lifetime where the respective shape and scale parameters depend on model parameters such as the Weibull shape parameter for fibre strength, the exponent for matrix creep, and the effective load transfer length and critical cluster size for failed fibres. Experimental results were consistent with the theory, though a fractographic study suggested time-dependent debonding along the fibre-matrix interface as being a key mechanism. Arguments were given to suggest, however, that the overall analytical forms would essentially be preserved. The results were compared with earlier results using a different epoxy system (Dow DER 331 epoxy with DEH 26 curing agent). Values for the matrix creep exponent and the effective load transfer length were about double and triple respectively the values from the earlier study, leading to slightly reduced strength, about one-half the variability in lifetime, but almost one-half the value of the exponent for the power law relating microcomposite lifetime to stress level.

Experiments on shear deformation, debonding and local load transfer in a model graphite/glass/epoxy microcomposite

Recent statistical theories for the failure of polymer matrix composites depend heavily on details of the stress redistribution around fibre breaks. The magnitudes and length scales of fibre overloads as well as the extent of fibre/matrix debonding are key components in the development of longitudinal versus transverse crack propagation. While several theoretical studies have been conducted to investigate the roles of these mechanisms, little has been substantiated experimentally about the matrix constitutive behaviour and mechanisms of debonding at the length scale of a fibre break. In order to predict the growth of transverse and longitudinal cracks using the same micromechanical model, we microscopically observed the epoxy shear behaviour around a single fibre break in a three-fibre microcomposite tape. The planar specimens consisted of a single graphite fibre placed between two larger glass fibres in an epoxy matrix. The interfibre spacing was less than one fibre diameter (<6 μm) in order to reflect the spacing between fibres found in typical composites. The epoxy constitutive behaviour was modelled using shear-lag theory where the epoxy had elastic, plastic, and debond zones. The criteria for debonding were modified from conventional shear-lag approaches to reflect the orientational hardening in the epoxy network structure. The epoxy, which is brittle in bulk, locally underwent a shear strain of about 60% prior to debonding from the fibre.

Temperature dependence of lifetime statistics for single Kevlar 49 filaments in creep-rupture

Experimental data are presented for the strength and lifetime under constant stress of single Kevlar 49 aramid filaments at two elevated temperatures, 80 and 130° C. As seen in previously published work performed at room temperature (21 °C), the strength data could be fitted to a two-parameter Weibull distribution; increasing the temperature caused a decrease in the Weibull scale parameter while the shape parameter remained relatively constant, indicating a decrease in the mean strength but no change in strength variability. Lifetime experiments at both 80 and 130°C were performed at different filament stress levels, ranging from 55 to 92.5% of the Weibull scale parameter for short-term strength at that temperature. These data were fitted to a two-parameter Weibull distribution with large variability (scale parameter values ⩽ 1), and evaluated using an exponential kinetic breakdown model in the spirit of Eyring and Zhurkov. Using this model, activation energies in the neighbourhood of 80 kcal mol−1 (3.35 × 105 J mol−1 ) were obtained, suggesting that scission of the C-N bond plays the dominant role in fibre failure at longer times under constant stress.

Lifetime statistics for single graphite fibres in creep rupture

Experimental results are presented for the lifetime in creep rupture of single graphite fibres. The fibres were extracted from unsized, Hercules IM6 tows and were tested at a gauge length of 5 cm under standard ambient conditions (21°C, 50% r.h.). The results were analysed using a theoretical model which embodies Weibull distributions for both strength and lifetime, and a power-law relationship for lifetime against stress level. Using maximum likelihood techniques, the Weibull shape parameter values for strength and lifetime were found to be about 4.6 and 0.015, respectively, and the power-law exponent was about 300, but could be as low as 250. As expected, this exponent was close in value to the ratio of the respective Weibull shape parameter values. Using the Kaplan-Meier estimator for censored data, the goodness of fit of the model to the data was found to be excellent.

Effects of extreme transverse deformation on the strength of UHMWPE single filaments for ballistic applications

Fibers used in both soft and hard body armor have very high longitudinal tensile strength and stiffness, but differ drastically in their transverse mechanical properties. Glass and carbon fibers are stiff and brittle in the transverse direction and easily shatter upon projectile impact unless they are cushioned within a soft matrix to disperse the load. In contrast, aramid fibers (e.g., Kevlar 29 and Twaron) and ultra-high-molecular-weight polyethylene (UHMWPE) fibers (e.g., Dyneema and Spectra) have quasi-plastic transverse behavior, with a low yield strength, and thus tend to flatten upon projectile impact, yet retain much of their tensile load-carrying capability. Thus, these polymer fibers are especially suitable for ‘soft’ body armor consisting of stacked sheets or fabrics, whereas the former glass and carbon fibers are useful mainly when aligned in a strong polymer matrix to form a thick plate. In this work, we report on a study of the tensile mechanical properties of single UHMWPE fibers (i.e., single filaments) that have been transversely deformed from their original cylindrical shape to form thin flat micro-tapes with a width-to-thickness ratio of up to 60:1. The deformed, ribbon-like fibers show very high retention in fiber strength, though with increased variability resulting from locally induced defects. Because transverse deformation resulted in more than a factor of three increase in surface area per unit length, the stress transfer length necessary to fully load a fiber near a break was found also to decrease by the same factor, as the corresponding interfacial shear stress remained the same. A Weibull probability analysis revealed that the increase in variability in fiber strength was consistent with a more pronounced length effect. These changes in fiber strength properties were understood through an alteration of the crystalline domains within the fibers due to the extreme deformation.

Comparison of maximum likelihood approaches for analysis of composite stress rupture data

Stress rupture is a sudden, stochastic failure mode that occurs in continuous unidirectional fiber composites and in particular composite overwrapped pressure vessels subject to long-term, steady loads. A common approach for modeling stress rupture is the probabilistic classic power-law model for material breakdown within a Weibull framework (CPL-W). This model includes a number of parameters, which need to be estimated from real data. These parameters may be estimated in a variety of different ways. This paper investigates how best to estimate the parameters of the CPL-W model given a set of experimental data for both composite strength and composite lifetime obtained at multiple stress levels. Eight different maximum likelihood estimation approaches are investigated regarding their differing errors of estimation. The accuracy of each method is estimated by repeated Monte Carlo simulations of specific instances of the CPL-W model typical of various carbon/epoxy and aramid/epoxy fiber composite systems; no actual experimental data are analyzed. One particular approach stands out as having the least estimation error while a commonly used approach does very poorly.

Comparison of probabilistic models for stress rupture failure in continuous unidirectional fiber composite structures

Stress rupture is an important failure phenomenon in composite overwrapped pressure vessels, which is highly unpredictable other than on a statistical basis. Even then, there are several statistical models, with varying bases in composite micromechanics and molecular failure mechanisms. Choosing among these models is not trivial, even when micromechanical details of the failure process are reasonably well appreciated, and one has available a reasonably large database of strength and lifetime data. As a result, there is little in the way of guidance to choose the most appropriate model. One important issue is that accurate predictions are desired at relatively low service loads compared to the strength, and low probabilities of failure that are far less, e.g., 10−6, than can be directly confirmed using the data itself. In essence, one needs a robust and accurate statistical model free of inconsistencies associated with such low stress levels and probabilities of failure. This paper performs an in-depth comparison of several current models, which have varying physical bases. The models compared differ in the number of parameters to be estimated from data. The results of this study, however, show that over a broad range of parameter values these models give surprisingly similar failure probability predictions. While practitioners may have a preference for one model over another, the basis for such a choice is not easily established, given the fidelity of typical data.