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Steady-state cracking in ceramic matrix composites
Literature survey Prepared by M.R. Alexander, J. Collins, J.D. Hague and A.J. Hosty, University of Sheffield, UK CERAMIC MA TRICES Steady-state cracking in ceramic matrix composites Dharani, L.R., Chai, L. and Pagano, N.J. Composites Science and Technology Vol 39 No I (1990) pp 29-43 The problem of steady state cracking, in which the crack extends under a constant load, is investigated for two interface conditions: elastic (no slip) and frictional interface. The fibre, matrix and interface stresses in the cracked and uncracked regions of a unidirectional composite subjected to a remote axial stress are obtained using an improved shearlag theory that accounts for the axial and transverse load-carrying capacity of the matrix. The fibre axial stresses are the same as those of previous models. However, the matrix shear and transverse normal stresses predicted in the present model for the interface conditions are different, as are the critical cracking conditions considered. The critical cracking conditions are established using a generalized energy release rate formulation, and critical stresses are obtained in terms of microstructural properties of the constituents and the interface.
GENERAL An analytical model for the elastic properties of fibrous composites with anisotropic constituents Zhang, W.-C. and Evans, K.E. Composites Science and Technology Vol 38 No 3 (1990) pp 229-246 The concept of the energy equivalence principle is used to develop an analytical model for the determination of the mechanical properties of composite materials with anisotropic constituents. This model, unlike energy variational analyses, produces a unique solution, with closed-form analytical expressions for a composite material. The model uses a representative volume containing a single fibre surrounded by a cylindrical matrix together with an interracial sheath between them. All three phases may be assumed to be isotropic. Using this model, the effects of constituent anisotropy and of the interface on the resultant mechanical properties of the composite are studied. An approximate method of determination of shear stresses due to flexure in composite beams Segura, J.M. International Journal o f Engineering Science Vol 28 No 8 (1990) pp 735750 A potential-energy theorem associated with a finite set of statistically admissible fields was used as an approximation for the normal method of determining shear stresses due to flexure in composite beams--solving a series of 'Neumann-Poisson' problems. The construction of fields was explained and was
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applied to multilayered cross-sections and circular cross-sections with two concentric layers. Assessment of computational models for muitilayered anisotropic plates Noor, A.K. and Burton, S. Composite Structures Vo114 No 3 (1990) pp 233-265 The effect of variation in the lamination and geometric parameters of multilayered anisotropic (non-orthotropic) plates on the accuracy of static and vibrational responses predicted by eight different 2D sheardeformation-based theories was investigated. The standard comparison was taken to the exact 3D elastic solutions and the quantities compared were not just gross response characteristics but detailed through-thickness distributions. The numerical studies carried out suggested the predictor-corrector approach to be the most effective of the eight approaches considered. Axisymmetric buckling of an annular sandwich plate of varying thickness Payar, N. Composite Structures Vol 15 No 2 (1990) pp 149-159 This paper presents the governing equations for axisymmetric buckling analysis of an annular sandwich plate of varying thickness, the plate being symmetric with respect to its middle surface. The core was assumed to be inextensible in the thickness direction and deformable in transverse shear with the face sheets as membranes. The face sheets carry all the compressive force. Results for a clamped-free plate were obtained using a numerical technique and plots of critical buckling load as a function of plate shear stiffness were presented. Bending analysis of thick bimodular laminates by higher-order individual-layer theory Cho, K.N., Striz, A.G. and Bert, C.W. Composite Structures Vol 15 No 1 (1990) pp 1-24 The stress, deflection and neutral surface behaviour is investigated for cylindrical bending and rectangular plate bending of thick laminates of composite materials having soft transverse shear modulus and different elastic properties depending on whether the fibre-direction strains are tensile or compressive. The higher-order individual-layer laminate theory, previously developed by the authors, treats each layer separately using an independent higher-order displacement field. Numerical results for single-layer plates and laminates having all edges simply supported and subjected to sinusoidally distributed normal pressure are obtained and compared with results obtained from Pagano's elasticity theory and other approximate plate theories. The predictions of the present theory show better agreement with the elasticity theory results than any of the other approximate theories. Bending of cross-ply laminated plates using Lagrange multipliers Chandrashekhara, K., Yahyavi, A.H. and
Rao, P.R. Composite Structures Vol 15 No 2 (1990) pp 169-179 The bending analysis of cross-ply clamped plates incorporating the Lagrange multiplier method was reported. The energy function included transverse shear deformation effects with boundary conditions not satisfied by the assumed series expressions being enforced by Lagrange multipliers. To demonstrate the effect of anisotropy, plate geometry and span-to-depth ratios on the deflections, results for symmetric and antisymmetric cross-ply plates with clamped boundary conditions were presented. The buckling of delaminated rings subjected to hydrostatic pressure Marshall, J.M. and Moshaiov, A. Composite Structures Vo114 No 3 (1990) pp 193-211 The buckling strength of a detaminated ring under hydrostatic pressure was investigated by applying a weighted residual solution technique to the equation of the second variation of the potential energy for the ring. The effect of the position and shape of the delamination is addressed along with the contact problem between adjacent layers. A comparison of solution techniques for impact response of composite plates Ouian, Y. and Swanson, R. Composite Structures Vo114 No 3 (1990) pp 177-192 In this paper the results of different solution techniques for the impact response of composite plates were compared to assess the accuracy of the calculation. One technique used was based on the Rayleigh-Ritz approach with numerical integration in time, another being an analytical approach using Laplace transformation of the governing differential equations, but requiring linearization of the contact deformation. Finite element calculations and experimental calculations were also compared with these methods. The results show the range of numerical parameters required to give a good accuracy of solution. Deflections and free vibrations of laminated plates--Levy type solutions Chen, W.C. and Liu, W.H. International Journal o f Mechanical Science Vol 32 No 9 (1990) pp 779-794 Poisson-Kirchoff plate theory, which neglects the effects of transverse shear strain, underpredicts deflections and overpredicts natural frequencies for moderately thick composite plates. To overcome this, Mindlin plate theory was used in conjunction with a state space concept to obtain a Levy-type solution. The effects of fibre orientation, modulus ratios, laminate arrangements, aspect ratios and thickness/length ratios were investigated. Good agreement was found with published results. l)elamination energy release rates under thermal loading in fiber-reinforced composite laminates Aoki, T. and Kondo, K. Composite Structures Vo114 No 3 (1990) pp 213-231
GENERAL An analytical model for the elastic properties of fibrous composites with anisotropic constituents Zhang, W.-C. and Evans, K.E. Composites Science and Technology Vol 38 No 3 (1990) pp 229-246 The concept of the energy equivalence principle is used to develop an analytical model for the determination of the mechanical properties of composite materials with anisotropic constituents. This model, unlike energy variational analyses, produces a unique solution, with closed-form analytical expressions for a composite material. The model uses a representative volume containing a single fibre surrounded by a cylindrical matrix together with an interracial sheath between them. All three phases may be assumed to be isotropic. Using this model, the effects of constituent anisotropy and of the interface on the resultant mechanical properties of the composite are studied. An approximate method of determination of shear stresses due to flexure in composite beams Segura, J.M. International Journal o f Engineering Science Vol 28 No 8 (1990) pp 735750 A potential-energy theorem associated with a finite set of statistically admissible fields was used as an approximation for the normal method of determining shear stresses due to flexure in composite beams--solving a series of 'Neumann-Poisson' problems. The construction of fields was explained and was
68
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applied to multilayered cross-sections and circular cross-sections with two concentric layers. Assessment of computational models for muitilayered anisotropic plates Noor, A.K. and Burton, S. Composite Structures Vo114 No 3 (1990) pp 233-265 The effect of variation in the lamination and geometric parameters of multilayered anisotropic (non-orthotropic) plates on the accuracy of static and vibrational responses predicted by eight different 2D sheardeformation-based theories was investigated. The standard comparison was taken to the exact 3D elastic solutions and the quantities compared were not just gross response characteristics but detailed through-thickness distributions. The numerical studies carried out suggested the predictor-corrector approach to be the most effective of the eight approaches considered. Axisymmetric buckling of an annular sandwich plate of varying thickness Payar, N. Composite Structures Vol 15 No 2 (1990) pp 149-159 This paper presents the governing equations for axisymmetric buckling analysis of an annular sandwich plate of varying thickness, the plate being symmetric with respect to its middle surface. The core was assumed to be inextensible in the thickness direction and deformable in transverse shear with the face sheets as membranes. The face sheets carry all the compressive force. Results for a clamped-free plate were obtained using a numerical technique and plots of critical buckling load as a function of plate shear stiffness were presented. Bending analysis of thick bimodular laminates by higher-order individual-layer theory Cho, K.N., Striz, A.G. and Bert, C.W. Composite Structures Vol 15 No 1 (1990) pp 1-24 The stress, deflection and neutral surface behaviour is investigated for cylindrical bending and rectangular plate bending of thick laminates of composite materials having soft transverse shear modulus and different elastic properties depending on whether the fibre-direction strains are tensile or compressive. The higher-order individual-layer laminate theory, previously developed by the authors, treats each layer separately using an independent higher-order displacement field. Numerical results for single-layer plates and laminates having all edges simply supported and subjected to sinusoidally distributed normal pressure are obtained and compared with results obtained from Pagano's elasticity theory and other approximate plate theories. The predictions of the present theory show better agreement with the elasticity theory results than any of the other approximate theories. Bending of cross-ply laminated plates using Lagrange multipliers Chandrashekhara, K., Yahyavi, A.H. and
Rao, P.R. Composite Structures Vol 15 No 2 (1990) pp 169-179 The bending analysis of cross-ply clamped plates incorporating the Lagrange multiplier method was reported. The energy function included transverse shear deformation effects with boundary conditions not satisfied by the assumed series expressions being enforced by Lagrange multipliers. To demonstrate the effect of anisotropy, plate geometry and span-to-depth ratios on the deflections, results for symmetric and antisymmetric cross-ply plates with clamped boundary conditions were presented. The buckling of delaminated rings subjected to hydrostatic pressure Marshall, J.M. and Moshaiov, A. Composite Structures Vo114 No 3 (1990) pp 193-211 The buckling strength of a detaminated ring under hydrostatic pressure was investigated by applying a weighted residual solution technique to the equation of the second variation of the potential energy for the ring. The effect of the position and shape of the delamination is addressed along with the contact problem between adjacent layers. A comparison of solution techniques for impact response of composite plates Ouian, Y. and Swanson, R. Composite Structures Vo114 No 3 (1990) pp 177-192 In this paper the results of different solution techniques for the impact response of composite plates were compared to assess the accuracy of the calculation. One technique used was based on the Rayleigh-Ritz approach with numerical integration in time, another being an analytical approach using Laplace transformation of the governing differential equations, but requiring linearization of the contact deformation. Finite element calculations and experimental calculations were also compared with these methods. The results show the range of numerical parameters required to give a good accuracy of solution. Deflections and free vibrations of laminated plates--Levy type solutions Chen, W.C. and Liu, W.H. International Journal o f Mechanical Science Vol 32 No 9 (1990) pp 779-794 Poisson-Kirchoff plate theory, which neglects the effects of transverse shear strain, underpredicts deflections and overpredicts natural frequencies for moderately thick composite plates. To overcome this, Mindlin plate theory was used in conjunction with a state space concept to obtain a Levy-type solution. The effects of fibre orientation, modulus ratios, laminate arrangements, aspect ratios and thickness/length ratios were investigated. Good agreement was found with published results. l)elamination energy release rates under thermal loading in fiber-reinforced composite laminates Aoki, T. and Kondo, K. Composite Structures Vo114 No 3 (1990) pp 213-231