1988 Vol. 5, No. 4
1988, 5(4): 1-Ⅰ.
Abstract:
This plates paper proposed a new displacement model for laminated composite on the bases of the model in Reference (4).The assumptions are introduced as following: a)The material ef each Iayer is homogenous and has a plane of elastic symmetry; b) Every layer is stuck to each other perfectly; c) The tranverse-stress σz and .strain εz are negligible; d) The tranverse shear stresses and τxz are quadratic functions of z. With these assumptions and the continuity of the displacements,the displacment expressions are obtained,Obviously,this model satisfies the continuitis of displacements and stress on the interfaces of layers.Then the. equilibrium equations and the boundary conditions are derived from Hellinger-Reissner's principle. This model has five unknowns uo, vo, ζx, ζy, and w.The plane-stress state and bending state in the model in the model is uncoupled only in the case that the plate has a symmetric plane and the material is orthotropic in Euclid coordinate system. Some examples show that this model. has high precission compared with the model in Reference (4).
This plates paper proposed a new displacement model for laminated composite on the bases of the model in Reference (4).The assumptions are introduced as following: a)The material ef each Iayer is homogenous and has a plane of elastic symmetry; b) Every layer is stuck to each other perfectly; c) The tranverse-stress σz and .strain εz are negligible; d) The tranverse shear stresses and τxz are quadratic functions of z. With these assumptions and the continuity of the displacements,the displacment expressions are obtained,Obviously,this model satisfies the continuitis of displacements and stress on the interfaces of layers.Then the. equilibrium equations and the boundary conditions are derived from Hellinger-Reissner's principle. This model has five unknowns uo, vo, ζx, ζy, and w.The plane-stress state and bending state in the model in the model is uncoupled only in the case that the plate has a symmetric plane and the material is orthotropic in Euclid coordinate system. Some examples show that this model. has high precission compared with the model in Reference (4).
1988, 5(4): 10-Ⅲ.
Abstract:
A model for the computation of the complex moduli iu the fiver direction of aligned short fiber reinforced composites is suggested in this paper. The usual model for such purpose is based on an analysis of an isolated elastic fiber embeded in the matrix.The pr went model takes into account the mutual effects of the transversely neighboring fibers and of the longitudinally adjacent fibers.The packing georr.etry of fiber is shown in Fig. 1. By solving the basic equations (4)-(6) under conditions (1)-(7),the stresses in the fiber and in the gap (filled with matrix) between the adjacent fibers can be determined. It can be shown that the average of the stress in an fiber (or in a gap) and the stress in any one of neighbors does not change with x.This average can then be used as the macroscopic Stress of fiber to calculate the elastic modulus of the composite .According to the correspondence priniple of viscoelasticity by replacing the elastic moduli of the fiber and the matrix by complex ones the above procedure will give the complex modulus of the compo site Feig,2 shows another packing geometry which is more close to that of test specimens made with prepregs. The. numerical results are depicted in Figs. 3-7,from which the following conclusions can be drawn 1)The storage modulus Eć decreases and the loss modulusEć increases rapidly with the gap size when the gap size is about or less than the size of fiber cross-section.The variations become slow when the gap size exceeds that range. 2) Aa shown in Fig. 6,when the fiber is long the gap size has no significant effect on the moduli.This means that the breakage of scme fibers in a continuous fiber reinforced composite has very little effect on the stiffness of the composite if the breakages do not occur on the sane crosssection. 3) The curves 4 in Fig.7 show that the packing geometry in Fig.2 gives an appreciably better agreement with experimental resuits.It proves the present model is an improvement upon the existing ones represented by the curves 1 and 2.
A model for the computation of the complex moduli iu the fiver direction of aligned short fiber reinforced composites is suggested in this paper. The usual model for such purpose is based on an analysis of an isolated elastic fiber embeded in the matrix.The pr went model takes into account the mutual effects of the transversely neighboring fibers and of the longitudinally adjacent fibers.The packing georr.etry of fiber is shown in Fig. 1. By solving the basic equations (4)-(6) under conditions (1)-(7),the stresses in the fiber and in the gap (filled with matrix) between the adjacent fibers can be determined. It can be shown that the average of the stress in an fiber (or in a gap) and the stress in any one of neighbors does not change with x.This average can then be used as the macroscopic Stress of fiber to calculate the elastic modulus of the composite .According to the correspondence priniple of viscoelasticity by replacing the elastic moduli of the fiber and the matrix by complex ones the above procedure will give the complex modulus of the compo site Feig,2 shows another packing geometry which is more close to that of test specimens made with prepregs. The. numerical results are depicted in Figs. 3-7,from which the following conclusions can be drawn 1)The storage modulus Eć decreases and the loss modulusEć increases rapidly with the gap size when the gap size is about or less than the size of fiber cross-section.The variations become slow when the gap size exceeds that range. 2) Aa shown in Fig. 6,when the fiber is long the gap size has no significant effect on the moduli.This means that the breakage of scme fibers in a continuous fiber reinforced composite has very little effect on the stiffness of the composite if the breakages do not occur on the sane crosssection. 3) The curves 4 in Fig.7 show that the packing geometry in Fig.2 gives an appreciably better agreement with experimental resuits.It proves the present model is an improvement upon the existing ones represented by the curves 1 and 2.
1988, 5(4): 21-27,55.
Abstract:
1988, 5(4): 28-Ⅳ.
Abstract:
A quasi-3D finite element and Virtzual Crack Extension Method of Hellen (1) are used to investigate the energy release rate for delaminated composite with various laminate parameters. The numerical results have shown that this method presents an effective approach ti predict the initistion and propagation mechanism of delamination.Ccrnparing the theoretical results with experimental evidence, it can be seen that for a given angle between the crack front and the fiber orientation of lateral delaminatod layers the eritical energy release rate could be considered as the material behavior for controlling the delamination growth of composite laminate.
A quasi-3D finite element and Virtzual Crack Extension Method of Hellen (1) are used to investigate the energy release rate for delaminated composite with various laminate parameters. The numerical results have shown that this method presents an effective approach ti predict the initistion and propagation mechanism of delamination.Ccrnparing the theoretical results with experimental evidence, it can be seen that for a given angle between the crack front and the fiber orientation of lateral delaminatod layers the eritical energy release rate could be considered as the material behavior for controlling the delamination growth of composite laminate.
1988, 5(4): 37-Ⅴ.
Abstract:
Stress distributions around a no-lcadiing hole in composites is theore tically and experimentally investigated by the use of photoelastic-coating method. Governing equationa in the method are developed accerding to the essential principles in photoelasting method and the mechanies of composite. materials-Correction factors for unmatched Possion's ratios and coating reinforcement effects are added to the governing equations Experimental results for carbon fiber reinforced epoxy and glass fiber reinforced epoxy composites show that there exists good agreement between the experimental results and theoretical results introducing the correction factors to the unmatched Possion}s ratios It is also found that thereinforcement effect of the coatincs is very small and can be neglected.
Stress distributions around a no-lcadiing hole in composites is theore tically and experimentally investigated by the use of photoelastic-coating method. Governing equationa in the method are developed accerding to the essential principles in photoelasting method and the mechanies of composite. materials-Correction factors for unmatched Possion's ratios and coating reinforcement effects are added to the governing equations Experimental results for carbon fiber reinforced epoxy and glass fiber reinforced epoxy composites show that there exists good agreement between the experimental results and theoretical results introducing the correction factors to the unmatched Possion}s ratios It is also found that thereinforcement effect of the coatincs is very small and can be neglected.
1988, 5(4): 49-Ⅵ.
Abstract:
Nosetip is an axisymmterical structure.Three. Dimensional Carbon-Carbon (3D C-C) is orthotropic,nonlinear material with different moduli in tension and in compression.SAAS III,which is usually used for thermal stress analvs.is of nosetiu made of 3D C-C, was modified in this paper.The modification consists of follow-ing aspects.The tensile or compressive modulus used for complex stress state is determined with the signs of fiber bundle stress instead of the sins of the principal stresses. Nonlinear shear stress-strain relationship is taken into consideration, Integrity check is also included in computation based on strength criterion established in authors' previous paper.Graphic plotting function is also improved. Influence of different weave on thermal stress distribution is also discussed in this paper.
Nosetip is an axisymmterical structure.Three. Dimensional Carbon-Carbon (3D C-C) is orthotropic,nonlinear material with different moduli in tension and in compression.SAAS III,which is usually used for thermal stress analvs.is of nosetiu made of 3D C-C, was modified in this paper.The modification consists of follow-ing aspects.The tensile or compressive modulus used for complex stress state is determined with the signs of fiber bundle stress instead of the sins of the principal stresses. Nonlinear shear stress-strain relationship is taken into consideration, Integrity check is also included in computation based on strength criterion established in authors' previous paper.Graphic plotting function is also improved. Influence of different weave on thermal stress distribution is also discussed in this paper.
1988, 5(4): 56-Ⅶ.
Abstract:
In the elasto-plastic analysis, much more atte'ntion has been paid to bifurcation behaviour of the governing equation which always predicts various mechanism of failure or fractures In reference (5), an infinite plate a thin layer sandwiched was considered for its interface insta bilities and it was shown that the innerbuckling could appear Before the emergence of shear bands.Unfortunately, the analytical derivation of this bifureation is quite tedious about complex function calculus. Hence, the extention of this analytical scheme to the laminated plate will be even difficult and troublesome as we tasted.
In the elasto-plastic analysis, much more atte'ntion has been paid to bifurcation behaviour of the governing equation which always predicts various mechanism of failure or fractures In reference (5), an infinite plate a thin layer sandwiched was considered for its interface insta bilities and it was shown that the innerbuckling could appear Before the emergence of shear bands.Unfortunately, the analytical derivation of this bifureation is quite tedious about complex function calculus. Hence, the extention of this analytical scheme to the laminated plate will be even difficult and troublesome as we tasted.
1988, 5(4): 66-Ⅶ.
Abstract:
A function of displacement is developed to the bending analysis of antisymmetrical angle-ply laminates reinforced with ribs, and the governing equations for the laminates is reduced to one equation whice caa be easily solved by the use of the fourier series theory, the reliability of the function of displacement is checked by calculating a special example in which all the parameters refered to the ribs are neglected and the deflection for antisymmetrical angle-ply laminates is calculateed.
A function of displacement is developed to the bending analysis of antisymmetrical angle-ply laminates reinforced with ribs, and the governing equations for the laminates is reduced to one equation whice caa be easily solved by the use of the fourier series theory, the reliability of the function of displacement is checked by calculating a special example in which all the parameters refered to the ribs are neglected and the deflection for antisymmetrical angle-ply laminates is calculateed.
THE BENDING ANALYSIS OF COMPOSITE LAMINATES BY THE COMBINED INITIAL FUNCTION AND VIRTUAL LOAD METHOD
1988, 5(4): 74-Ⅷ.
Abstract:
The bending analysis for laminatsd composite materials is performed by using the combined, initial function and virtual load method. The method of the initial function theory developed by Vlassov is generalized to anisotropic laminated plates.The virtual load method is developed and combined with the initial function, theory to solve the elstic bending problems of the laminates.Three numerical examples presented show that the method advanced herein has high accuracy and promising potency of application.
The bending analysis for laminatsd composite materials is performed by using the combined, initial function and virtual load method. The method of the initial function theory developed by Vlassov is generalized to anisotropic laminated plates.The virtual load method is developed and combined with the initial function, theory to solve the elstic bending problems of the laminates.Three numerical examples presented show that the method advanced herein has high accuracy and promising potency of application.
1988, 5(4): 84-Ⅸ.
Abstract:
The large deflection problems of the symmetrically laminated cross-ply circular places of fiber reinforced composites are investigated in this paper by using Galekins procedure. One axisymmetric term and two nonaxisymmetric terms are involved in the selected deflection function. The stress function is selected as a form of power functions, and determined through satisfying condition of compatibility.
The large deflection problems of the symmetrically laminated cross-ply circular places of fiber reinforced composites are investigated in this paper by using Galekins procedure. One axisymmetric term and two nonaxisymmetric terms are involved in the selected deflection function. The stress function is selected as a form of power functions, and determined through satisfying condition of compatibility.
1988, 5(4)
Abstract:
An experimental investigation of the stability of rectangular carbon/epoxy composite laminated plates simply supported under uniaxial compression is presented.The specimens are made of four kinds of cardon/epoxy laminates and one aluminum specimen is used to check the experi-mental plan, The critical buckling loads of the plates are determined by three methods load-shortening (p-Δ),load-strain (p-ε) and load-deflection (p-f) curves.
An experimental investigation of the stability of rectangular carbon/epoxy composite laminated plates simply supported under uniaxial compression is presented.The specimens are made of four kinds of cardon/epoxy laminates and one aluminum specimen is used to check the experi-mental plan, The critical buckling loads of the plates are determined by three methods load-shortening (p-Δ),load-strain (p-ε) and load-deflection (p-f) curves.
