R. A. Duckett

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.

The strain-rate, temperature and pressure dependence of yield of isotropic poly(methylmethacrylate) and poly(ethylene terephthalate)

The yield behaviour of poly(methylmethacrylate) (PMMA) has been investigated in tension and compression over a range of testing temperatures and strain-rates. Both tensile and compressive yield stresses were found to increase monotonically with increasing strainrate and decreasing temperatures. Compressive yield stresses were in general found to be more dependent on strain-rate.The results of this investigation have been correlated with previous published data for the dependence of the torsional yield stress of PMMA on hydrostatic pressure. This was done by a modification of a theory proposed by Robertson which uses the internal viscosity approach to yield in glassy polymers. The modified theory clearly explains the temperature and strain-rate dependence of the yield stress and provides a quantitative explanation of the differences in behaviour between tension and compression in terms of the dependence of yield on the hydrostatic component of the applied stress.The tensile yield behaviour of isotropic amorphous poly(ethylene terephthalate) (PET) sheets has also been investigated over a wide range of temperatures and strain-rates. No torsion or compressive yield stresses are available because of the sheet form of the PET, but the results obtained in tension are shown to be fully consistent with the above theory, and with other published work.

Double yield points in polyethylene: Structural changes under tensile deformation

Abstract Previous work has shown that under mechanical deformation, three grades of polyethylene which differ mainly in terms of branch content exhibit two yield points. The first yield point occurs at low applied strains and marks the onset of temporary plastic deformation; the second yield point occurs at higher strains and marks the onset of permanent plastic deformation, and is associated with the development of a neck in tension. The present work describes structural measurements carried out on these three polyethylene samples before and subsequent to different levels of tensile deformation. X-ray diffraction, transmission electron microscopy, and optical microscopy were carried out on the isotropic materials and after the first and second yield points under tensile deformation. The results show that the first yield point marks the onset of a recoverable reorientation process of the lamellae within the spherulites, with little or no destruction of the lamellae themselves. This reorientation is explai...

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.

Temperature and strain‐rate dependence of yield stress of polyethylene

The yield stress behavior of a range of polyethylene materials which differ with respect to their short chain branch content has been studied. Measurements carried out over a wide range of temperatures have shown that there is a sudden transition in the behavior of the yield stress at a temperature which is dependent on both the grade of material and the applied strain rate. These results are in agreement with previous results found from analysis of the yield strain behavior. Above the transition temperature the materials all behave in a nonlinear viscoelastic manner, and the yield process is considered as being propagation controlled. Below the transition temperature the materials all behave in an elastic-plastic manner, and the yield process is considered as being nucleation controlled. Below the transition temperature the temperature dependence of the yield stress is determined by the thickness of the crystalline lamellae.

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.

An n.m.r. study of absorbed water in polybenzimidazole

Abstract Polybenzimidazole (PBI) is known to absorb 15 wt% water at equilibrium. This sorbed water greatly affects the mechanical properties of this polymer. Both FT i.r. and broadline n.m.r. have been used to study the interaction between water and PBI. The results clearly show that the water in PBI is mobile and therefore does not hydrogen bond to the polymer chain.

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.

The biaxial drawing behaviour of poly(ethylene terephthalate)

Abstract It is shown that the biaxial drawing of poly(ethylene terephthalate) at temperatures above the glass transition temperature Tg can be satisfactorily described by the Ball model of rubber elasticity (Polymer, 1981, 22, 1010), providing that the chain entanglement density is assumed to be a linear function of the logarithmic shear strain rate. With this assumption the behaviour for uniaxial, constant width and equibiaxial drawing can be fitted by a single set of model parameters. The validity of the network model has been confirmed by photoelastic studies, provided that the draw ratios do not reach a level where strain crystallization occurs to any significant extent.

Failure mechanisms in continuous carbon-fibre reinforced PEEK composites

Abstract The fracture behaviour of unidirectional carbon-fibre/poly(ether ether ketone) (PEEK) composites has been studied over the temperature range −60 to +100°C. Double cantilever beam tests were carried out for crack propagation parallel to the fibre direction, with the fracture plane either parallel (specimen DCB1) or perpendicular (specimen DCB2) to the plane of the pre-preg tapes. Stable crack propagation in the composite requires stable drawing of the PEEK matrix, and both depend similarly on strain rate and temperature. The fracture toughness can be related quantitatively to the failure mechanisms inferred from the fracture surface. The primary contribution is from matrix deformation and this is related to the energy of rupture of the unreinforced polymer, taking into account the volume of plastically deformed polymer seen on the fracture surface. Secondary contributions are from fibre bridging and the formation of large fibre bundles, which also increase the amount of matrix deformation. These are caused by misalignment of fibres with respect to the primary crack and are most important for the DCB2 geometry.