1987 Vol. 4, No. 1
1987, 4(1): 1-Ⅱ.
Abstract:
In engineering practice,the following questions are often raised about laminated constructions made of fiber reinforced bimodular composites:(1)Under what circumstances do we need to make nonlinear analysisp?(2)How much do bimodular properties affect the displacernents,force and moment resultanEs in,large deflection analysis?How is the effect different from that in linear analysisy However,the problem becomes very complex if the effects of physically bi-linear and geometrically nonlinear behaviors are all taken into account and the exact solutions are difficult to obtain.Hence selecting an effewive and simple approximate method is necessary.In this paper Dynamic-Relaxation Method(DRM) is adopted to investigate the large deflection beading of rectangular plates laminated of bimorlular composite materials.The basic,formulae of iterations and the main steps of solving this subject are outlined.The numerical results are given for simply supported,two-layer cross-ply square plates made of mildly bimodular material(Boron/Epoxy (B/E)) and highly bimodnlar material(Aramid/Rubber(A/R)) under sinusoidally distributed and uniformly distributed transverse loads.The results obtained are compared with linear results and those obtained for laminates fabricated from conventional composite materials,the elastic moduli of which are identical with the tensile moduli or the compressive moduli of the bimodular materials.The necessity of large deflection analysis and the effects of bimodnlar properties on the large deflection analysis are discussed.The main conclusions of this paper are as following:(1) The DRM proves an effective numerical method for solving the problem taking into account the effects of physically bilinear and geometrically nonlinear behavior.(2)The relative error between linear theory solution and nonlinear theory solution of normalized center deflection w increases with increasing of the load.When w=1.0 It is about 75% for the A/R laminate,and about 40% for the B/E laminate.Therefore,it is necessary to consider nonlinear effect when the load gets greater.(3) When w=1.0 the relative error between tensile moduli solutions and bimodular solutions of the B/E laminate is below 500 for w,whereas it is below 1500 for force and moment resultants.The relative error,in general,decreases with increasing of the load.This implies that the tensile moduli become predominant for large deflections.(4) For the A/R laminate,even though the relative error between tensile moduli solutions and bimodular solutions of w decreases somewhat with increasing load parameter,the effect of bimodularity on deflection,force and moment resultants is very significant.Therefore,it is necessary to consider the influence of bimodular properties in large deflction analysis for highly bimodular materials.
In engineering practice,the following questions are often raised about laminated constructions made of fiber reinforced bimodular composites:(1)Under what circumstances do we need to make nonlinear analysisp?(2)How much do bimodular properties affect the displacernents,force and moment resultanEs in,large deflection analysis?How is the effect different from that in linear analysisy However,the problem becomes very complex if the effects of physically bi-linear and geometrically nonlinear behaviors are all taken into account and the exact solutions are difficult to obtain.Hence selecting an effewive and simple approximate method is necessary.In this paper Dynamic-Relaxation Method(DRM) is adopted to investigate the large deflection beading of rectangular plates laminated of bimorlular composite materials.The basic,formulae of iterations and the main steps of solving this subject are outlined.The numerical results are given for simply supported,two-layer cross-ply square plates made of mildly bimodular material(Boron/Epoxy (B/E)) and highly bimodnlar material(Aramid/Rubber(A/R)) under sinusoidally distributed and uniformly distributed transverse loads.The results obtained are compared with linear results and those obtained for laminates fabricated from conventional composite materials,the elastic moduli of which are identical with the tensile moduli or the compressive moduli of the bimodular materials.The necessity of large deflection analysis and the effects of bimodnlar properties on the large deflection analysis are discussed.The main conclusions of this paper are as following:(1) The DRM proves an effective numerical method for solving the problem taking into account the effects of physically bilinear and geometrically nonlinear behavior.(2)The relative error between linear theory solution and nonlinear theory solution of normalized center deflection w increases with increasing of the load.When w=1.0 It is about 75% for the A/R laminate,and about 40% for the B/E laminate.Therefore,it is necessary to consider nonlinear effect when the load gets greater.(3) When w=1.0 the relative error between tensile moduli solutions and bimodular solutions of the B/E laminate is below 500 for w,whereas it is below 1500 for force and moment resultants.The relative error,in general,decreases with increasing of the load.This implies that the tensile moduli become predominant for large deflections.(4) For the A/R laminate,even though the relative error between tensile moduli solutions and bimodular solutions of w decreases somewhat with increasing load parameter,the effect of bimodularity on deflection,force and moment resultants is very significant.Therefore,it is necessary to consider the influence of bimodular properties in large deflction analysis for highly bimodular materials.
1987, 4(1): 8-Ⅲ.
Abstract:
It has been demonstrated in previous studies that nitrite rubber toughened epoxy can increase the fracture tourghness of composites,but little has been done on the effect of various nitrite rubber additive proportions of matrix on other important mechanical properties of composites,such as interlaminar shear strength which proved fatal to laminate composites.Exprimental study is made to determine and compare the interlaminar shear,tensile,bending and vibration-damping properties of high modulus carbon/epoxy unidirectional composites with various contents of nitrite rubber(0,1000,15%,20%).Acoustic,emission(AE) technique is used to detect the formation and propagation of the damage zone in the composite specimens,The micro-structure failure modes of specimens are investigated by means of a scanning electron microscope(SEM).Comparison is made among the four types of specimens,and the optimal proportion,10%,of the nitrile rubber additive is determined.Based on these results,toughening and strengthening mechanism of the composite is discussed.
It has been demonstrated in previous studies that nitrite rubber toughened epoxy can increase the fracture tourghness of composites,but little has been done on the effect of various nitrite rubber additive proportions of matrix on other important mechanical properties of composites,such as interlaminar shear strength which proved fatal to laminate composites.Exprimental study is made to determine and compare the interlaminar shear,tensile,bending and vibration-damping properties of high modulus carbon/epoxy unidirectional composites with various contents of nitrite rubber(0,1000,15%,20%).Acoustic,emission(AE) technique is used to detect the formation and propagation of the damage zone in the composite specimens,The micro-structure failure modes of specimens are investigated by means of a scanning electron microscope(SEM).Comparison is made among the four types of specimens,and the optimal proportion,10%,of the nitrile rubber additive is determined.Based on these results,toughening and strengthening mechanism of the composite is discussed.
1987, 4(1): 16-Ⅳ.
Abstract:
Fatigue life prediction on composite materials is studied analytically using degradation and damage models,resultant strain and fatigue modulus.Definition of fatigue modulus,new damage models using fatigue modulus and resultant strain,and prediction of fatiguelife on composite materials using degradation and damage models are discussed.This approach can accurately predict the multi-stress level fatigue life as well as single-stress level fatigue life of composite materials.Defining fatigue damage on composite materials is not a simple problem.Common variables used to define damage of composite materials are secant modulus,residual strength,strain,compliance,amount of acoustic emission,crack densitv,crack length,and number of debonded or failed fibers.These damage models are tabulated in Table 1.However,one variable can not be used universally to represent the degree of damage in various composite materials.Fatigue modulus is defined using secant modulus and resultant strain during fatigue cycle.Fatigue modulus represents the physical damage in composites with different orientation and materials.,specially metal-matrix and ceramic-matrix composites for high temperature applications.Damage model Ⅰ (D=[F0-F(n)]/[F0-Ff]),model Ⅱ (D=ε(n)-εf) and model Ⅲ (D=[ε(n)-ε0]/[εf-ε0]) are defined as functions of fatigue modulus and resultant strain.The structure of damage model,boundary conditions and physical meanings are inserted in order to interpret the proposed damage models.Also the effect of applied stress on the accumulated damage is studied analytically using proposed damage models.Fatigue life is predicted by the following procedures:(1)establish the fatigue modulus degradation,(2) find fatigue life equation as a function of fatigue modulus,(3)calculate the fatigue life using strain failure criterion.Degradation models for composite damage are generalized and found that three-pare meter degradation model (dF/dn=ACnC-1/BFB-1) and two-parameter power function model(dF/dn=-ACnC-1) are most suitable to predicting fatigue life of composites.Also the predicted two-stress.level fatigue life using the proposed damage models are reasonably close to the experimental data.
Fatigue life prediction on composite materials is studied analytically using degradation and damage models,resultant strain and fatigue modulus.Definition of fatigue modulus,new damage models using fatigue modulus and resultant strain,and prediction of fatiguelife on composite materials using degradation and damage models are discussed.This approach can accurately predict the multi-stress level fatigue life as well as single-stress level fatigue life of composite materials.Defining fatigue damage on composite materials is not a simple problem.Common variables used to define damage of composite materials are secant modulus,residual strength,strain,compliance,amount of acoustic emission,crack densitv,crack length,and number of debonded or failed fibers.These damage models are tabulated in Table 1.However,one variable can not be used universally to represent the degree of damage in various composite materials.Fatigue modulus is defined using secant modulus and resultant strain during fatigue cycle.Fatigue modulus represents the physical damage in composites with different orientation and materials.,specially metal-matrix and ceramic-matrix composites for high temperature applications.Damage model Ⅰ (D=[F0-F(n)]/[F0-Ff]),model Ⅱ (D=ε(n)-εf) and model Ⅲ (D=[ε(n)-ε0]/[εf-ε0]) are defined as functions of fatigue modulus and resultant strain.The structure of damage model,boundary conditions and physical meanings are inserted in order to interpret the proposed damage models.Also the effect of applied stress on the accumulated damage is studied analytically using proposed damage models.Fatigue life is predicted by the following procedures:(1)establish the fatigue modulus degradation,(2) find fatigue life equation as a function of fatigue modulus,(3)calculate the fatigue life using strain failure criterion.Degradation models for composite damage are generalized and found that three-pare meter degradation model (dF/dn=ACnC-1/BFB-1) and two-parameter power function model(dF/dn=-ACnC-1) are most suitable to predicting fatigue life of composites.Also the predicted two-stress.level fatigue life using the proposed damage models are reasonably close to the experimental data.
1987, 4(1): 25-Ⅳ.
Abstract:
A laminate of composite material with equilateral triangular patten of ribs is concetned.The ribs are equal in width and depth.The skin is braided to (0,±60)configuration.It behaves in a gross sense as a transversely isotropic material.The extentional and flexural stiffness matrix,the transverse shear stiffness and its coefficient of modification for this laminate aie devised.For a circular cylindrical shell manufactured by this laminate,design analysis in general instability is discussed and a simple formula for buckling is obtained.Numerical results agree well with experimental data.Computational example shows that the effect of the transverse shear deformation on the critical load is not significant.
A laminate of composite material with equilateral triangular patten of ribs is concetned.The ribs are equal in width and depth.The skin is braided to (0,±60)configuration.It behaves in a gross sense as a transversely isotropic material.The extentional and flexural stiffness matrix,the transverse shear stiffness and its coefficient of modification for this laminate aie devised.For a circular cylindrical shell manufactured by this laminate,design analysis in general instability is discussed and a simple formula for buckling is obtained.Numerical results agree well with experimental data.Computational example shows that the effect of the transverse shear deformation on the critical load is not significant.
1987, 4(1): 32-Ⅵ.
Abstract:
The stability of laminated and reinforced composite plate structures,subjected to combination of axial compression and thermal loading is studied.According to updated hagrangian Forrriulation,nonlinear governing equations are established for.laminated structures by means of finite.elerirent method.The equations are mixedly solved with the help of Newton's and incremental methods.The computational results show that the effrects of changes of Experimental results show that the intestigation method is suitable for FRP laminales with different lay-up,hole diameter and thickness.The designed fixtures according to the loaded manner can be freely chosen for better accnracy and convenience.
The stability of laminated and reinforced composite plate structures,subjected to combination of axial compression and thermal loading is studied.According to updated hagrangian Forrriulation,nonlinear governing equations are established for.laminated structures by means of finite.elerirent method.The equations are mixedly solved with the help of Newton's and incremental methods.The computational results show that the effrects of changes of Experimental results show that the intestigation method is suitable for FRP laminales with different lay-up,hole diameter and thickness.The designed fixtures according to the loaded manner can be freely chosen for better accnracy and convenience.
1987, 4(1): 59-Ⅵ.
Abstract:
Filament winding is one significant technological melhnd for making high-strength composite materials and it can be widely employed for making,rocket generators,tubes and pressure vessels etc.in various industrial field (e.g.spacecrafl,aviation,building mantrteraals,chemical).The moving regularity of winding curved tube on a computer controlled filament winding machine is discussed in this paper.A enred tube represents a section of a torus.If point P (Fig.2) shows a position of the filameot.control and point M is a corresponding payout yarn point on the products,the line MP is the tangent to,the curve LM on the products at M,of which the tangents ventors is T.In consideratiow of geometrie relations of the differential element on the nerved.tube and change of the coordinate axes,we obtain the kinematic equations of the filament control for geodesic winding and non-geo-desic stable winding.The equations can be solved with the Runge-Kuttta method.The winding pattern design of the winding curved tube is,analyzed and the base for winding carved tube (for example 45 pipe,90 pipe,…) on a computer.controlled filameul winding machine is discussed.
Filament winding is one significant technological melhnd for making high-strength composite materials and it can be widely employed for making,rocket generators,tubes and pressure vessels etc.in various industrial field (e.g.spacecrafl,aviation,building mantrteraals,chemical).The moving regularity of winding curved tube on a computer controlled filament winding machine is discussed in this paper.A enred tube represents a section of a torus.If point P (Fig.2) shows a position of the filameot.control and point M is a corresponding payout yarn point on the products,the line MP is the tangent to,the curve LM on the products at M,of which the tangents ventors is T.In consideratiow of geometrie relations of the differential element on the nerved.tube and change of the coordinate axes,we obtain the kinematic equations of the filament control for geodesic winding and non-geo-desic stable winding.The equations can be solved with the Runge-Kuttta method.The winding pattern design of the winding curved tube is,analyzed and the base for winding carved tube (for example 45 pipe,90 pipe,…) on a computer.controlled filameul winding machine is discussed.
1987, 4(1): 67-Ⅷ.
Abstract:
Mindlin-type elements have been widely used to stress analysis for laminated composite classical thin and moderately thick plates and/or shells.However,as the ratio of thickness to span of the plates and/or shells increases,so-called "shear lockingn" becomes noticeable.To overcome the shortcoming,the present paper,by using Tang's multi-variable quasi-con-forming and penalty elements technique (QCPE) estabilished a general propose shear flexible triangular finite element for laminated composite plate,which can be afforded for practical usea.The element consists of two rotation and three displacements as generalized degrees of freedom per node.Numerical examples for bending problem are presented for plates of isotropic as well as laminated composite.From examination and discussion on numerical results,the following conclusions are given:(1) QCPE is a element with good behaviour.As the mesh is refined，the finite element solutions for both thin and/or modertely thick plates rapidly converge towanl the exact solutions.(2) The shear effect on the deflection W of laminated composite plate would be gradually strengthened as the ratio of thickness to span of the plates increases.For Graphite/Epoxy material,the shear effect becomes nonelimiable when h/a≥30.(3) The shear effect on the deflection W of laminated composite plates would be gradually strengthened as the numbers of layer decreases or the ratio of moduli E1/E2 increases.This pmject was supported by science fund of the Chinese Academy of Sciences.
Mindlin-type elements have been widely used to stress analysis for laminated composite classical thin and moderately thick plates and/or shells.However,as the ratio of thickness to span of the plates and/or shells increases,so-called "shear lockingn" becomes noticeable.To overcome the shortcoming,the present paper,by using Tang's multi-variable quasi-con-forming and penalty elements technique (QCPE) estabilished a general propose shear flexible triangular finite element for laminated composite plate,which can be afforded for practical usea.The element consists of two rotation and three displacements as generalized degrees of freedom per node.Numerical examples for bending problem are presented for plates of isotropic as well as laminated composite.From examination and discussion on numerical results,the following conclusions are given:(1) QCPE is a element with good behaviour.As the mesh is refined，the finite element solutions for both thin and/or modertely thick plates rapidly converge towanl the exact solutions.(2) The shear effect on the deflection W of laminated composite plate would be gradually strengthened as the ratio of thickness to span of the plates increases.For Graphite/Epoxy material,the shear effect becomes nonelimiable when h/a≥30.(3) The shear effect on the deflection W of laminated composite plates would be gradually strengthened as the numbers of layer decreases or the ratio of moduli E1/E2 increases.This pmject was supported by science fund of the Chinese Academy of Sciences.
1987, 4(1): 73-Ⅸ.
Abstract:
The deflection of symmetric angle-ply laminated plates is expressed by a series which exactly satisifies the bending governing equation and,in a common simply connected region,can uniformly approximate any solution of the equation.The coefficients of the series are determined by the use of the boundary collocation method.For nonsymmetric laminates,if the reduced bending stiffness is introduced,the method can also be applied.A number of examples are presented in order to investigate the convergency of the deflection and the internal forces.For clamped round laminates,aeeurate results can be obtained by taking only 6 undetermined coefficients and 3 collocations.For simply supported ±45°angle-ply regular rhombic laminates,when 13 coefficients and 7 collocations are taken,the deviation of results from the double trigonometric series is very small.For simply supported square anisotropic plates,the difference between the results obtained by the isotropic skew plate analogy and those by the semi-analytic method with 13 coefficients and 10 collocations is less than 1.7%.For clamped ±45°square laminates for which no exact solution exists,the results are obtained by taking 13 coefficients and 7 collocations and by taking 33 coefficents and 25 collocations,and it is found that there is little differency between them.
The deflection of symmetric angle-ply laminated plates is expressed by a series which exactly satisifies the bending governing equation and,in a common simply connected region,can uniformly approximate any solution of the equation.The coefficients of the series are determined by the use of the boundary collocation method.For nonsymmetric laminates,if the reduced bending stiffness is introduced,the method can also be applied.A number of examples are presented in order to investigate the convergency of the deflection and the internal forces.For clamped round laminates,aeeurate results can be obtained by taking only 6 undetermined coefficients and 3 collocations.For simply supported ±45°angle-ply regular rhombic laminates,when 13 coefficients and 7 collocations are taken,the deviation of results from the double trigonometric series is very small.For simply supported square anisotropic plates,the difference between the results obtained by the isotropic skew plate analogy and those by the semi-analytic method with 13 coefficients and 10 collocations is less than 1.7%.For clamped ±45°square laminates for which no exact solution exists,the results are obtained by taking 13 coefficients and 7 collocations and by taking 33 coefficents and 25 collocations,and it is found that there is little differency between them.
1987, 4(1): 79-Ⅹ.
Abstract:
This paper reviews the characteristics of Narmco 5208 resin matrix.Emphasis is given to the formula of the resin system,mechanism of cure reaction,kinetics of cure reaction and processing characteristics of Narmco 5208.The formulation of 5208 consists of mainly MY-720 (TGDDM) as epoxy resrn,EPORAL (DPS) as curing agent and EpiRea SU-8 (polyglyuidyl ether of bisphenol A novalac ream) as minor epoxy component.The principal cure reactions are the primary amine-epoxide,the secondary amine-epoxide,hydroxyl-epoxide and epoxide-epoxide.The kinetics analysis of 5208 shows that the lemtion order,n,is substantially affected by heating rate.n is equal to 2 at slow scan rate but is reduced to 1.5 at higher scan rate.The activation energy,E,is not affeced by the sean rate,and the average value of E is 25.6±1.8keal/mole.Enviromental effeces during a process cure cycle and resin advattcemenC effects of 5208 are evaluated.some suggedtions are proposed for developing TGDDM-DDS resin matrices in China.
This paper reviews the characteristics of Narmco 5208 resin matrix.Emphasis is given to the formula of the resin system,mechanism of cure reaction,kinetics of cure reaction and processing characteristics of Narmco 5208.The formulation of 5208 consists of mainly MY-720 (TGDDM) as epoxy resrn,EPORAL (DPS) as curing agent and EpiRea SU-8 (polyglyuidyl ether of bisphenol A novalac ream) as minor epoxy component.The principal cure reactions are the primary amine-epoxide,the secondary amine-epoxide,hydroxyl-epoxide and epoxide-epoxide.The kinetics analysis of 5208 shows that the lemtion order,n,is substantially affected by heating rate.n is equal to 2 at slow scan rate but is reduced to 1.5 at higher scan rate.The activation energy,E,is not affeced by the sean rate,and the average value of E is 25.6±1.8keal/mole.Enviromental effeces during a process cure cycle and resin advattcemenC effects of 5208 are evaluated.some suggedtions are proposed for developing TGDDM-DDS resin matrices in China.
