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End fixity effects on the buckling and post-buckling of delaminated composites
investigation concerns the effects test temperature and environment have on the tensile behaviour of simple crossply laminates by testing in tension, fatigue and stress rupture modes. Results indicate that under an inert argon atmosphere tensile strength is maintained to 1300°C. However in air, poor strength and a change in failure mode are observed at high temperature due to an alteration in fibre-matrix bond. Fatigue testing in air causes a further loss in strength which is explained by matrix cracks allowing air to enter the fibre-matrix interfacial region.
GENERAL Acoustoelastic response of unidirectional fiber composites Chatterjee, S. N., Journal of Composite Materials Vol 23 No 1 (January 1989) pp 58-76 The theory of acoustoelasticity, relating the change in wave speeds to initial stresses, has been widely applied to homogeneous materials. This paper considers the analytical relationship between wave speeds in a unidirectional composite, the second and third order moduli of the constituents and the residual stresses and applied stresses. The authors obtain acoustoelastic equations of motion for in-plane waves by simple averaging of stress and displacement gradients over a representative volume element and define effective moduli in order to estimate the change in potential energy of the system. They examine published experimental data on wave velocity changes due to thermal cycling in graphite/aluminium composite and obtain reasonable agreement between computed wave velocities and test data after thermal cycling. Analysis of delamination in compressively loaded laminates Shaw, D. and Tsai, M. Y. Composites Science and Technology Vol 34 No 1 (1989) pp 1-17 A combination of post-buckling theory and fracture mechanics is used to present a model describing delamination in one direction. Classical plate theory is used to determine stress distribution and then a finite element model for the crack tip region is used to evaluate the strain energy release rate. It is shown that the influence of fibre orientation on delamination behaviour is significant. Application of reflection orthotropic photoelasticity to laminated composites Friere, J. L. F., Antonelli, R. A., Dror, Y. and Voloshin, A. S. Journal of Composite Materials Vol 23 No 1 (January 1989) pp 42-57 Qualitative observations of fringe patterns in glass/polyester composites are made using a reflection photoelastic technique to obtain information on stress fields in multilayered composites. The technique involves application of a layer of aluminium paint between plies of different orientations in a + 3 0 / - 3 0 / +30 laminate under tensile loading and discs of 0/0/0 and 0/45/0 configuration under diametrical compression. Isochromatic fringes in the surface plies are distorted according to the underlying fibre orientation. Good agreement is obtained between experimental
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observations of fringe order and predictions made using orthotropic photomechanics combined with finite element analysis to calculate the stress state in the laminate. A continuum damage model of fatigueinduced damage in laminated composites Harris, C. E. and Allen, D. H. S A M P E Journal Vol 24 No 4 (July~August 1988) pp 43-50 A model (based on the concept of continuum damage mechanics) which will predict stress/ strain behaviour of continuous fibrereinforced laminated composites in the presence of microstructural damage is presented. It is shown that predictions from the model are in close agreement with results of fatigue tests obtained experimentally on laminate panels of graphite fibre-reinforced epoxy with different fibre orientations. Decomposition of strain energy density in fiber reinforced composites Theocaris, P. S. Engineering Fracture Mechanics Vol 33 No 3 (1989) pp 335-344 The elliptic paraboloidal failure surface (EPFS) criterion is proposed as a suitable criterion for yielding and failure of heterogeneous composite materials. The criterion is first reviewed in general and then applied to the case of a transtropic composite, the elastic strain energy density, defined as corresponding to a point on the EPFS, can be divided into two independent parts derived from orthogonal state of stress. Expressions for the decomposition of the strain energy density are presented. Delamination from surface cracks in composite materials Thouless, M. D., Cao, H. C. and Mataga, Journal of Materials Science Vo124 (1989)pp 1406-1412 The mechanism for delamination in laminated composite materials normally occurs by the differing elastic properties of the constituent plies inducing interlaminar shear and normal stresses. However for a different type of delamination caused by discontinuities in sample geometry such as surface flaws, a system of an elastically homogeneous material containing aligned interfaces may be used as a model, which is the subject for the present paper. It is shown that when the interface is sufficiently weak the delamination crack will propagate along the interface under simple and mixed loading conditions when considering the fracture mechanics of the process. An explanation is offered based on statistical effects for cracks observed to deviate from the interface. Driving forces for composite interface fatigue cracks Chan, K. S. and Davidson, D. L. Engineering Fracture Mechanics Vo133 No 3 (1989. pp 451-466 Fatigue crack growth at the fibre/matrix interface in a composite material is considered both experimentally and analytically. The local stress intensity factor range (AK) at the crack tip is derived by two methods: by plotting experimentally determined crack opening displacement (COD) as a function of r the distance ahead of the crack tip, or by using a J-integral approach based on the experimental crack tip opening displacement. These methods are compared for fatigue cracks in SEN specimens of compo-
sites containing alumina fibres in Mg alloy and boron fibres in Ti alloy. Crack opening displacements are measured by a stereoimaging technique for the alumina/Mg composite. Observations indicate that interpenetrating crack surfaces just behind the crack tip can be ignored and small scale yielding in the interface zone is also indicated by good agreement between the COD and AJ methods. The equivalent AK (defined in terms of the cyclic J-integral or strain energy release rate) is found to be the crack growth driving force for these interface fatigue cracks. Crack growth is slower than predicted for the Ti/B composite due to crack branching which reduces the effective AK. Effect of transverse cracks on the thermomechanical properties of cross-ply laminated composites Lim, S. G. and Hong, C. S. Composites Science and Technology Vol 34 No 2 (1989) pp 145-162 A modified shear lag analysis (which takes into account the concept of an interlaminar shear layer) to evaluate the effect of transverse cracks on the stiffness and coefficient of thermal expansion in cross-ply laminated composites is presented. Predictions of the thermomechanical property changes due to transverse cracks are compared with numerical results and existing experimental data. It is shown that the model represents well the dependence of the degradation of thermomechanical properties on the laminate configuration. Effective fracture toughness of a marbleepoxy two phase composite Sachan, A. K. and Kamesawara Rao, C. V. S. The International Journal of Cement Composites and Lightweight Concrete Vo110 No 3 (August 1988) pp 167-169 The effective fracture roughness of a composite material comprising marble particles distributed in an epoxy sand mortar matrix was determined by testing notched beam specimens of varying volume fractions. It is shown that if the phases are of the same fracture toughness then the resulting composite will have the same fracture toughness irrespective of the volume fractions. End fixity effects on the buckling and post-buckling of delaminated composites Kardomateas, G. A. Composites Science and Technology Vol 34 No 2 (1989) pp 113-128 The effects of end fixity (clamped-clamped versus simply-supported) on the buckling and post-buckling of delaminated composites under compressive loads were investigated. An analytical solution for the case of post-buckling behaviour of delaminated composites with simply-supported ends is presented and the results are compared with the characteristics of the clamped-clamped case. The end-fixity effects were found to be more pronounced for lower values of the foundation modulus. Flexible composites (review) Tsu-Wei Chou Journal of Materials Science Vol 24 (1989) pp 761-783 To examine the current knowledge regarding the modelling of elastic behaviour in flexible composites, this review article considers three categories of materials. These are pneumatic tyres, coated fabrics and flexible composites containing wavy fibres, and are
COMPOSITES. SEPTEMBER 1989
GENERAL Acoustoelastic response of unidirectional fiber composites Chatterjee, S. N., Journal of Composite Materials Vol 23 No 1 (January 1989) pp 58-76 The theory of acoustoelasticity, relating the change in wave speeds to initial stresses, has been widely applied to homogeneous materials. This paper considers the analytical relationship between wave speeds in a unidirectional composite, the second and third order moduli of the constituents and the residual stresses and applied stresses. The authors obtain acoustoelastic equations of motion for in-plane waves by simple averaging of stress and displacement gradients over a representative volume element and define effective moduli in order to estimate the change in potential energy of the system. They examine published experimental data on wave velocity changes due to thermal cycling in graphite/aluminium composite and obtain reasonable agreement between computed wave velocities and test data after thermal cycling. Analysis of delamination in compressively loaded laminates Shaw, D. and Tsai, M. Y. Composites Science and Technology Vol 34 No 1 (1989) pp 1-17 A combination of post-buckling theory and fracture mechanics is used to present a model describing delamination in one direction. Classical plate theory is used to determine stress distribution and then a finite element model for the crack tip region is used to evaluate the strain energy release rate. It is shown that the influence of fibre orientation on delamination behaviour is significant. Application of reflection orthotropic photoelasticity to laminated composites Friere, J. L. F., Antonelli, R. A., Dror, Y. and Voloshin, A. S. Journal of Composite Materials Vol 23 No 1 (January 1989) pp 42-57 Qualitative observations of fringe patterns in glass/polyester composites are made using a reflection photoelastic technique to obtain information on stress fields in multilayered composites. The technique involves application of a layer of aluminium paint between plies of different orientations in a + 3 0 / - 3 0 / +30 laminate under tensile loading and discs of 0/0/0 and 0/45/0 configuration under diametrical compression. Isochromatic fringes in the surface plies are distorted according to the underlying fibre orientation. Good agreement is obtained between experimental
494
observations of fringe order and predictions made using orthotropic photomechanics combined with finite element analysis to calculate the stress state in the laminate. A continuum damage model of fatigueinduced damage in laminated composites Harris, C. E. and Allen, D. H. S A M P E Journal Vol 24 No 4 (July~August 1988) pp 43-50 A model (based on the concept of continuum damage mechanics) which will predict stress/ strain behaviour of continuous fibrereinforced laminated composites in the presence of microstructural damage is presented. It is shown that predictions from the model are in close agreement with results of fatigue tests obtained experimentally on laminate panels of graphite fibre-reinforced epoxy with different fibre orientations. Decomposition of strain energy density in fiber reinforced composites Theocaris, P. S. Engineering Fracture Mechanics Vol 33 No 3 (1989) pp 335-344 The elliptic paraboloidal failure surface (EPFS) criterion is proposed as a suitable criterion for yielding and failure of heterogeneous composite materials. The criterion is first reviewed in general and then applied to the case of a transtropic composite, the elastic strain energy density, defined as corresponding to a point on the EPFS, can be divided into two independent parts derived from orthogonal state of stress. Expressions for the decomposition of the strain energy density are presented. Delamination from surface cracks in composite materials Thouless, M. D., Cao, H. C. and Mataga, Journal of Materials Science Vo124 (1989)pp 1406-1412 The mechanism for delamination in laminated composite materials normally occurs by the differing elastic properties of the constituent plies inducing interlaminar shear and normal stresses. However for a different type of delamination caused by discontinuities in sample geometry such as surface flaws, a system of an elastically homogeneous material containing aligned interfaces may be used as a model, which is the subject for the present paper. It is shown that when the interface is sufficiently weak the delamination crack will propagate along the interface under simple and mixed loading conditions when considering the fracture mechanics of the process. An explanation is offered based on statistical effects for cracks observed to deviate from the interface. Driving forces for composite interface fatigue cracks Chan, K. S. and Davidson, D. L. Engineering Fracture Mechanics Vo133 No 3 (1989. pp 451-466 Fatigue crack growth at the fibre/matrix interface in a composite material is considered both experimentally and analytically. The local stress intensity factor range (AK) at the crack tip is derived by two methods: by plotting experimentally determined crack opening displacement (COD) as a function of r the distance ahead of the crack tip, or by using a J-integral approach based on the experimental crack tip opening displacement. These methods are compared for fatigue cracks in SEN specimens of compo-
sites containing alumina fibres in Mg alloy and boron fibres in Ti alloy. Crack opening displacements are measured by a stereoimaging technique for the alumina/Mg composite. Observations indicate that interpenetrating crack surfaces just behind the crack tip can be ignored and small scale yielding in the interface zone is also indicated by good agreement between the COD and AJ methods. The equivalent AK (defined in terms of the cyclic J-integral or strain energy release rate) is found to be the crack growth driving force for these interface fatigue cracks. Crack growth is slower than predicted for the Ti/B composite due to crack branching which reduces the effective AK. Effect of transverse cracks on the thermomechanical properties of cross-ply laminated composites Lim, S. G. and Hong, C. S. Composites Science and Technology Vol 34 No 2 (1989) pp 145-162 A modified shear lag analysis (which takes into account the concept of an interlaminar shear layer) to evaluate the effect of transverse cracks on the stiffness and coefficient of thermal expansion in cross-ply laminated composites is presented. Predictions of the thermomechanical property changes due to transverse cracks are compared with numerical results and existing experimental data. It is shown that the model represents well the dependence of the degradation of thermomechanical properties on the laminate configuration. Effective fracture toughness of a marbleepoxy two phase composite Sachan, A. K. and Kamesawara Rao, C. V. S. The International Journal of Cement Composites and Lightweight Concrete Vo110 No 3 (August 1988) pp 167-169 The effective fracture roughness of a composite material comprising marble particles distributed in an epoxy sand mortar matrix was determined by testing notched beam specimens of varying volume fractions. It is shown that if the phases are of the same fracture toughness then the resulting composite will have the same fracture toughness irrespective of the volume fractions. End fixity effects on the buckling and post-buckling of delaminated composites Kardomateas, G. A. Composites Science and Technology Vol 34 No 2 (1989) pp 113-128 The effects of end fixity (clamped-clamped versus simply-supported) on the buckling and post-buckling of delaminated composites under compressive loads were investigated. An analytical solution for the case of post-buckling behaviour of delaminated composites with simply-supported ends is presented and the results are compared with the characteristics of the clamped-clamped case. The end-fixity effects were found to be more pronounced for lower values of the foundation modulus. Flexible composites (review) Tsu-Wei Chou Journal of Materials Science Vol 24 (1989) pp 761-783 To examine the current knowledge regarding the modelling of elastic behaviour in flexible composites, this review article considers three categories of materials. These are pneumatic tyres, coated fabrics and flexible composites containing wavy fibres, and are
COMPOSITES. SEPTEMBER 1989