P.J. Hine

Modelling of the energy absorption by polymer composites upon ballistic impact

Abstract In this paper we report on the development of a simple model for calculating the energy absorption by polymer composites upon ballistic impact. Three major components were identified as contributing to the energy lost by the projectile during ballistic impact, namely the energy absorbed in tensile failure of the composite, the energy converted into elastic deformation of the composite and the energy converted into the kinetic energy of the moving portion of the composite. These three contributions are combined in the model to determine a value for the ballistic limit of the composite, V0. The required input parameters for the model were determined by a combination of physical characterisation (for the physical and mechanical properties of the composites and the characteristics of the projectile) and from high-speed photography (for the size of the deformed region and the cone velocity). As the failure event usually occurred between two of a relatively small number of frames from the high-speed camera, the model predicted a range for V0. This range of V0 was compared with experimentally determined values for three composite systems: woven Nylon-66 fibres in a 50:50 mixture of phenol formaldehyde resin and polyvinyl butyral resin, woven aramid fibres in a similar matrix and Dyneema UD66 (straight gel-spun polyethylene fibres laid in a 0/90 fibre arrangement in a thermoplastic matrix). In all cases, the experimentally measured values of V0 were found to lie within the range predicted by the model. The size of the deformed region, formed through shear deformation, on the back face of the composite was found to relate directly to the in-plane shear modulus of the material. Perhaps the most surprising result was that the dominant energy absorbing mechanism was found to be the kinetic energy of the moving portion of the composites.

Fiber packing and elastic properties of a transversely random unidirectional glass/epoxy composite

Image analysis was used to characterize the microstructure of a unidirectional glass/epoxy composite which was found to be transversely randomly packed. Starting from a measured distribution of fiber diameter, a Monte Carlo procedure was employed to generate periodic computer models with unit cells comprising of random dispersion of a hundred non-overlapping parallel fibers of different diameter. The morphology generated in this way showed excellent agreement with that of the actual composite studied. An ultrasonic velocity method was used to measure a complete set of composite elastic constants and those of the epoxy matrix. On the basis of periodic three-dimensional meshes, the composite elastic constants of the Monte Carlo models were calculated numerically. Numerical and measured elastic constants were in good agreement. It was shown numerically that the randomness of the composite microstructure had a significant influence on the transverse composite elastic constants while the effect of fiber diameter distribution was small and unimportant. The predictive potential of the Halpin-Tsai and some other models commonly employed for predicting the elastic behavior of unidirectional composites was also assessed.

The hot compaction behaviour of woven oriented polypropylene fibres and tapes. I. Mechanical properties

Abstract The aim of this work was to establish the important parameters that control the hot compaction behaviour of woven oriented polypropylene. Five commercial woven cloths, based on four different polypropylene polymers, were selected so that the perceived important variables could be studied. These include the mechanical properties of the original oriented tapes or fibres, the geometry of the oriented reinforcement (fibres or tapes), the mechanical properties of the base polymer (which are crucially dependant on the molecular weight and morphology), and the weave style. The five cloths were chosen so as to explore the boundaries of these various parameters, i.e. low and high molecular weight: circular or rectangular reinforcement (fibres or tapes): low or high tape initial orientation: coarse or fine weave. A vital aspect of this study was the realisation that hot compacted polypropylene could be envisaged as a composite, comprising an oriented ‘reinforcement’ bound together by a matrix phase, formed by melting and recrystallisation of the original oriented material. We have established the crucial importance of the properties of the melted and recrystallised matrix phase, especially the level of ductility, in controlling the properties of the hot compacted composite.

Numerical simulation of the effects of volume fraction, aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites

In this paper a new numerical procedure by Gusev, for predicting the elastic and thermoelastic properties of short fibre reinforced composites, is described. Computer models, comprising 100 non-overlapping aligned spherocylinders, were generated using a Monte Carlo procedure to produce a random morphology. Periodic boundary conditions were used for all the generated structures. Where necessary, the generated microstructures were based on measurements of real materials: for example a measured fibre length distribution was used to seed the Monte Carlo generator to produce a computer model with an equivalent fibre length distribution (FLD). The generated morphologies were meshed using an intelligent 3 dimensional meshing technique, allowing the elastic and thermo-elastic properties of the microstructures to be calculated. The numerical predictions were compared with those from three commonly used micromechanical models, namely those attributed to Halpin/Tsai, Tandon/Weng and Cox (shear lag). Firstly, the effect of volume fraction and aspect ratio were investigated, and the numerical results were compared and contrasted with those of the chosen models. Secondly, the numerical approach was used to investigate what effect a distribution of fibre lengths, as seen in real materials, would have on the predicted mechanical properties. The results were compared with simulations carried out using a monodispersed fibre length, to ascertain if the distribution of lengths could be replaced with a single length, and whether this length corresponded to a particular characteristic of the distribution, for example the first moment or average length.

The hot compaction of SPECTRA gel-spun polyethylene fibre

The compaction of gel-spun high molecular weight polyethylene (PE) fibre, SPECTRA 1000, has been investigated for a range of compaction temperatures between 142 °–155 °C. Differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and broad-line nuclear magnetic resonance (NMR) techniques have been used to examine the structure of the compacted materials and to determine the compaction mechanisms. With increasing compaction temperature, the flexural properties of the compacted materials did not show any significant change up to 154 °C, but large changes were observed if the temperature was increased from 154 to 155 °C. DSC and SEM studies revealed that no evident surface melting and recrystallization occurred during hot compaction in the temperature range 144–154 °C, although the rigid crystalline fraction measured by NMR for all compacted materials is significantly lower than that for the original fibre. Significant transverse strength is also developed at the lower compaction temperatures, and this also only markedly increases on going from 154 to 155 °C. Structural investigations show how the fibres deform so as to interlock, and localized welding occurs, so as to bond each fibre to its neighbour. This is distinct from the melting and recrystallization at the surface of the fibres previously observed in melt spun fibres.

Direct numerical predictions for the elastic and thermoelastic properties of short fibre composites

Abstract In this paper we compare the predictions of the thermoelastic properties of misaligned short glass fibre reinforced composites, calculated using the finite-element-based numerical approach of Gusev, with experimental measurements. Characterisation of the microstructure of the two injection moulded materials chosen for examination, in particular the fibre length and fibre orientation distributions, were used to ensure that the computer models were built with the same microstructure as the ‘real’ materials. Agreement between the measurements, in particular for the longitudinal Youngs modulus E 11 and the longitudinal and transverse thermal expansion coefficients, α 1 and α 2 , and the numerical predictions was found to be excellent. A comparison was also made with the most commonly used micromechanical models available from the literature. The approaches of Tandon and Weng, Takao and Taya and McCullough [Polym Comp 5 (1984) 327; J Comp Mater 21 (1987) 140] were found to give good agreement with both the numerical and measured values, although only the numerical approach showed the same relationship between α 1 and the degree of orientation as shown by the real materials.

The hot compaction behaviour of woven oriented polypropylene fibres and tapes. II. Morphology of cloths before and after compaction

The morphology of woven oriented polypropylene tapes and fibres has been studied both before and after processing by hot compaction. In this technique bundles of oriented tapes or fibres are subjected to suitable conditions of temperature and pressure so that just sufficient of each tape or fibre is selectively melted; on cooling, this material recrystallizes to bind the whole structure together. Three different polymers were studied, woven into various individual weave styles, in relation to optimum processing conditions. The weave style, the adhesion between neighbouring interfaces after compaction and the direction of crack propagation along the neighbouring interfaces on peeling were examined leading to clear correlations between the observed morphology and mechanical peel strength data.

Measuring the fibre orientation and modelling the elastic properties of injection-moulded long-glass-fibre-reinforced nylon

Abstract This paper describes the characterisation of the 3D fibre orientation of a single-gated injection-moulded plaque of short-glass-fibre-reinforced Nylon by image analysis, and the use of this orientation data for the theoretical prediction of the composite elastic properties. Fibre orientations were measured by using a purpose built image analysis facility, which allows 3D data to be obtained. Composite elastic properties were measured by an ultrasonic velocity method and compared with theoretical predictions obtained from the modelling techniques of Wilczynski and Ward.

Negative Poisson's ratios in angle-ply laminates: theory and experiment

Abstract A series of composite panels has been prepared by laminating unidirectional prepreg tapes of epoxy resin reinforced with continuous carbon fibres. Each panel was a balanced, symmetrical laminate with the plies alternating at ± θ to a reference direction where θ = 0, 10, 15, 20, 25, 30 and 40°. The full set of nine elastic constants was determined for each panel using ultrasonic velocity measurements. The experimentally determined elastic constants were then compared with theoretical predictions obtained using standard laminate theory. The Poissons ratios of the composites were of particular interest in showing negative values for θ in the range between 15 and 30°, as predicted by the theory.

Modelling of the elastic properties of fibre reinforced composites. I: Orientation measurement

Abstract This paper describes the measurement of fibre orientation by means of a transputer-controlled image analysis system developed in house. The image analyser works directly from a polished section, and by employing transputers it can rapidly and accurately measure the orientation parameters of a large number of fibre images. The two composite materials used throughout this study were both well-aligned, one being a continuous carbon-fibre reinforced epoxy resin while the second was a novel short-carbon-fibre reinforced epoxy composite. Orientation distributions have been measured for both materials and this allowed various factors that affect the experimental accuracy of the orientation measurement of the distributions to be examined. These included the effects of fibre shape, sample orientation and manufacturing procedure.