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Nonlinear behaviour of woven fabric composites
nates with circular holes were discussed and the application of the model to other notch geometries and multiple notched laminates is proposed.
Journal of the Mechanics and Physics of Solids Vol 32 No 1 (1984) p 21 The effective linear elastic behaviour of random media subjected to inhomogeneous m e a n fields is considered. The authors used the well-known Hashin-Shtrikman bounds for the Lame parameters of isotropic multi-phase mixtures; these bounds involve two-point correlations of random elastic moduli. The interest was focussed on composites with a cell structure and on binary mixtures. It is concluded that improved bounds could be obtained from the incorporation of more information, although this would lead to more involved and tedious calculations.
Compressive and torsional behuviour of Kevlar 49 fibre Deteresa, S.J., Allen, S.A., Farris, RJ. and Porter, R.S. Journal of Materials Science Vol 19 (1984) pp57-72 The behaviour of Kevlar 49 fibre under tensile, compressive, and torsional loading was investigated. In compression, fibres embedded in a plastic matrix showed no sinusoidal buckling, as observed for glass fibres. Instead, a kinking along the fibre surface occurred, which is associated with compressive yield failure of the fibre. In the authors' opinion it is the absence of fibre buckling which is responsible for the differences between measured and calculated compressive strengths of Kevlar/epoxy composites. The compressive strain needed to induce kinking was measured using a new technique, in which the fibre was bonded to the compressive face of a plastic beam and tested in 3-point bend. In this way accurate compressive loads could be applied to single fibres. The strain needed to induce kinking was found to be -0.53%; upon repeated loading, the length of fibre subjected to compressive strains greater than this showed an increase in the n u m b e r of kink bands.
Effective behaviour of inelastic fibre-reinforced composites Aboudi, J. International Journal of Engineering Science Vo122 (1984) p 439 The prediction of average composite mechanical properties for unidirectionally reinforced laminates is discussed. The author further extends an earlier theory to take account of anisotropie constituents in the elastic region. The resulting theory is particularly applicable to carbon reinforced composites, as these fibres are strongly anisotropic. Comparison of the theoretical predictions with those obtained from numerical methods, and previously published data, show good agreement with both. Work hardening in the viscoplastic range is also considered.
Failure strength of notched composite laminates Lo, K.H., Wu, E.M. and Konishi, D.Y.Journalof Composite Materials Iiol 17 (September 1983) p 384 An alternative approach to assessing the effects of stress raisers on the strength degradation of composite laminates is proposed. The approach was made using an analytical model developed using the principle of mechanics, and avoids a cost ineffective empirical investigation. The proposed model is capable of predicting the sequential failure of laminates and good correlation with experimental data is obtained for fibre-dominant laminates in tension. Lami-
COMPOSITES. JULY 1984
Impact loading in filamentary structural composites Sierakowski, R.L and Chatuvedi, S.K. The Shock and Vibration Digest Vo115 No 10 (October 1983) pp 13-33 A s u m m a r y of tests which have been carried out to determine the impact dynamics and impact loading response of filamentary type composite materials is given. The composite materials studied include boron fibre, glass fibre, chopped fibre, graphite or carbon fibre, hybrids and Kevlar fibre in epoxy, polyester, aluminium and titanium alloy matrices. An extensive appendix gives details of tests in tabular form and relevant references from the literature.
,
Improved rigorous bounds on the effective elastic moduli of a composite material Kantor, Y. and Bergman, D J . Journal of the Mechanics and Physics of Solids Vo132 No 1 (1984) p 41 A new method for deriving rigorous bounds on the effective elastic constants of a composite is presented and used to derive a n u m b e r of known, as well as some new, bounds. The basis of the new approach is the presentation of those constants as a sum of poles, the locations and strengths of which are treated as variational parameters. The results include an extension of the range of validity of the existing bounds to the case of composites made from isotropic materials but with an arbitrary microgeometry.
Load transfer from a pin to a wound fibre composite strip Mansfield, E.H. Journal of Composite Materials Vol 17 (September 1983) p 414 A simplified analysis is given of the stresses caused by load transfer into a U-shaped fibrereinforced strip wound round a pin. It is shown that the peak stresses vary markedly with the rates of the longitudinal to transverse modulus of the composite. The method of load transfer described has m a n y attractions in the context of glass fibre composites, but the high ratio of longitudinal to transverse modulus in carbon fibre composites is shown to be of less use.
Mechanical property enhancement in short fiber composites through the control of fiber orientation during fabrication Goettler, L.A. Polymer Composites Vol 5 No 1 (January 1984) pp 60-71 A study of fibre orientation during fabrication of composite materials was made. Observation of the behaviour of short glass fibres through runners, gates and dies has lead to the development of a kinetic model which indicates recommendations for optimizing directional strength and stiffness of the final product. Performance data on components fabricated from various short-fibre composite materials bear out these projections.
A model of couple stress effect upon the transverse stiffness of a fibre-reinforced material Lukhanpal, S.K. and Hackett, R.M. Journal of
Reinforced Plastics and Composites Vol 2 (October 1983) p 256 The model considered was a uniaxially loaded, infinitely long rectangular cell of composite material with a circular fibre located at the centre. A numerical solution for the transverse elastic stiffness of the composite material as a function of the elastic constants, including the moduli of curvature, of the fibre and the matrix was developed. A discussion of the characteristic length of the fibre to that of the matrix is included. It was concluded that the couple stresses can be predicted from the moduli of curvature for each material; however, these moduli are not readily available in the literature.
Nonlinear behaviour of woven fabric composites Ishikawa, T. and Chou, T.W. Journal of Composite Materials Vol 17 (September 1983) p 399 Three types of stress/strain non-linearity are taken into consideration in this study; the shear deformation of fill threads, the extensional deformation of pure matrix regions and the transverse cracking in the warp regions. An analysis combining the Hahn-Tsai non-linear constitutive relation and the Ishikura-Chou fibre undulation and bridging models is used and is observed to compare well with a practical system. The analysis shows that the non-linear effects are less pronounced for fabric composites with larger repeat units due to the increased bridging effect. Shear deformation is observed to contribute more than matrix extensional deformation to the non-linearity and is combined with the transverse cracking phenomenon.
A note on the solution of a time-dependent crack problem in an elastic composite George, O.D. International Journal of Engineering Science Vol 22 (1984) pp 311-317 The author, in an earlier paper, dealt with the interaction of a forced transient torsional wave and a penny-shaped crack at a bi-material interface. The solution given assumed that the square of the shear wave speed of the outer member of the composite was less than twice the square of the shear wave speed of the inner member. In this note, it is shown how the problem can be solved if this constraint is removed.
Probabilistic aspects of strength of unidirectional fibre-reinforced composites with matrix failure Suemasu, H. Journal of Materials Science Vol 19 (1984) pp 574-584 Using a three-dimensional hexagonal array shear lag model, the author calculates the stress distribution around a fibre break. The concept of a damaged matrix region, where a uniform shear force exists, is used in the calculation of successive fibre breakages and the fibre flaw population is assumed to follow a Poisson distribution. The results obtained show that generally the strains in the fibres, expressed in terms of non-dimensionality, decrease as the size of the damaged matrix region increases, and that the m a x i m u m shear force is almost independent of the damaged area size. The expected n u m b e r of fibre breaks around a broken fibre increases with increasing size of the damaged matrix region. However at large sizes, there is a decrease in the expected n u m b e r of fibre breaks due to a decrease in the m a x i m u m strains.
241
Journal of the Mechanics and Physics of Solids Vol 32 No 1 (1984) p 21 The effective linear elastic behaviour of random media subjected to inhomogeneous m e a n fields is considered. The authors used the well-known Hashin-Shtrikman bounds for the Lame parameters of isotropic multi-phase mixtures; these bounds involve two-point correlations of random elastic moduli. The interest was focussed on composites with a cell structure and on binary mixtures. It is concluded that improved bounds could be obtained from the incorporation of more information, although this would lead to more involved and tedious calculations.
Compressive and torsional behuviour of Kevlar 49 fibre Deteresa, S.J., Allen, S.A., Farris, RJ. and Porter, R.S. Journal of Materials Science Vol 19 (1984) pp57-72 The behaviour of Kevlar 49 fibre under tensile, compressive, and torsional loading was investigated. In compression, fibres embedded in a plastic matrix showed no sinusoidal buckling, as observed for glass fibres. Instead, a kinking along the fibre surface occurred, which is associated with compressive yield failure of the fibre. In the authors' opinion it is the absence of fibre buckling which is responsible for the differences between measured and calculated compressive strengths of Kevlar/epoxy composites. The compressive strain needed to induce kinking was measured using a new technique, in which the fibre was bonded to the compressive face of a plastic beam and tested in 3-point bend. In this way accurate compressive loads could be applied to single fibres. The strain needed to induce kinking was found to be -0.53%; upon repeated loading, the length of fibre subjected to compressive strains greater than this showed an increase in the n u m b e r of kink bands.
Effective behaviour of inelastic fibre-reinforced composites Aboudi, J. International Journal of Engineering Science Vo122 (1984) p 439 The prediction of average composite mechanical properties for unidirectionally reinforced laminates is discussed. The author further extends an earlier theory to take account of anisotropie constituents in the elastic region. The resulting theory is particularly applicable to carbon reinforced composites, as these fibres are strongly anisotropic. Comparison of the theoretical predictions with those obtained from numerical methods, and previously published data, show good agreement with both. Work hardening in the viscoplastic range is also considered.
Failure strength of notched composite laminates Lo, K.H., Wu, E.M. and Konishi, D.Y.Journalof Composite Materials Iiol 17 (September 1983) p 384 An alternative approach to assessing the effects of stress raisers on the strength degradation of composite laminates is proposed. The approach was made using an analytical model developed using the principle of mechanics, and avoids a cost ineffective empirical investigation. The proposed model is capable of predicting the sequential failure of laminates and good correlation with experimental data is obtained for fibre-dominant laminates in tension. Lami-
COMPOSITES. JULY 1984
Impact loading in filamentary structural composites Sierakowski, R.L and Chatuvedi, S.K. The Shock and Vibration Digest Vo115 No 10 (October 1983) pp 13-33 A s u m m a r y of tests which have been carried out to determine the impact dynamics and impact loading response of filamentary type composite materials is given. The composite materials studied include boron fibre, glass fibre, chopped fibre, graphite or carbon fibre, hybrids and Kevlar fibre in epoxy, polyester, aluminium and titanium alloy matrices. An extensive appendix gives details of tests in tabular form and relevant references from the literature.
,
Improved rigorous bounds on the effective elastic moduli of a composite material Kantor, Y. and Bergman, D J . Journal of the Mechanics and Physics of Solids Vo132 No 1 (1984) p 41 A new method for deriving rigorous bounds on the effective elastic constants of a composite is presented and used to derive a n u m b e r of known, as well as some new, bounds. The basis of the new approach is the presentation of those constants as a sum of poles, the locations and strengths of which are treated as variational parameters. The results include an extension of the range of validity of the existing bounds to the case of composites made from isotropic materials but with an arbitrary microgeometry.
Load transfer from a pin to a wound fibre composite strip Mansfield, E.H. Journal of Composite Materials Vol 17 (September 1983) p 414 A simplified analysis is given of the stresses caused by load transfer into a U-shaped fibrereinforced strip wound round a pin. It is shown that the peak stresses vary markedly with the rates of the longitudinal to transverse modulus of the composite. The method of load transfer described has m a n y attractions in the context of glass fibre composites, but the high ratio of longitudinal to transverse modulus in carbon fibre composites is shown to be of less use.
Mechanical property enhancement in short fiber composites through the control of fiber orientation during fabrication Goettler, L.A. Polymer Composites Vol 5 No 1 (January 1984) pp 60-71 A study of fibre orientation during fabrication of composite materials was made. Observation of the behaviour of short glass fibres through runners, gates and dies has lead to the development of a kinetic model which indicates recommendations for optimizing directional strength and stiffness of the final product. Performance data on components fabricated from various short-fibre composite materials bear out these projections.
A model of couple stress effect upon the transverse stiffness of a fibre-reinforced material Lukhanpal, S.K. and Hackett, R.M. Journal of
Reinforced Plastics and Composites Vol 2 (October 1983) p 256 The model considered was a uniaxially loaded, infinitely long rectangular cell of composite material with a circular fibre located at the centre. A numerical solution for the transverse elastic stiffness of the composite material as a function of the elastic constants, including the moduli of curvature, of the fibre and the matrix was developed. A discussion of the characteristic length of the fibre to that of the matrix is included. It was concluded that the couple stresses can be predicted from the moduli of curvature for each material; however, these moduli are not readily available in the literature.
Nonlinear behaviour of woven fabric composites Ishikawa, T. and Chou, T.W. Journal of Composite Materials Vol 17 (September 1983) p 399 Three types of stress/strain non-linearity are taken into consideration in this study; the shear deformation of fill threads, the extensional deformation of pure matrix regions and the transverse cracking in the warp regions. An analysis combining the Hahn-Tsai non-linear constitutive relation and the Ishikura-Chou fibre undulation and bridging models is used and is observed to compare well with a practical system. The analysis shows that the non-linear effects are less pronounced for fabric composites with larger repeat units due to the increased bridging effect. Shear deformation is observed to contribute more than matrix extensional deformation to the non-linearity and is combined with the transverse cracking phenomenon.
A note on the solution of a time-dependent crack problem in an elastic composite George, O.D. International Journal of Engineering Science Vol 22 (1984) pp 311-317 The author, in an earlier paper, dealt with the interaction of a forced transient torsional wave and a penny-shaped crack at a bi-material interface. The solution given assumed that the square of the shear wave speed of the outer member of the composite was less than twice the square of the shear wave speed of the inner member. In this note, it is shown how the problem can be solved if this constraint is removed.
Probabilistic aspects of strength of unidirectional fibre-reinforced composites with matrix failure Suemasu, H. Journal of Materials Science Vol 19 (1984) pp 574-584 Using a three-dimensional hexagonal array shear lag model, the author calculates the stress distribution around a fibre break. The concept of a damaged matrix region, where a uniform shear force exists, is used in the calculation of successive fibre breakages and the fibre flaw population is assumed to follow a Poisson distribution. The results obtained show that generally the strains in the fibres, expressed in terms of non-dimensionality, decrease as the size of the damaged matrix region increases, and that the m a x i m u m shear force is almost independent of the damaged area size. The expected n u m b e r of fibre breaks around a broken fibre increases with increasing size of the damaged matrix region. However at large sizes, there is a decrease in the expected n u m b e r of fibre breaks due to a decrease in the m a x i m u m strains.
241