1992 Vol. 9, No. 2
ANALYTICAL-GENERALIZED VARIATIONAL METHOD OF SOLUTION FOR DELAMINATION OF LAMINATES IN PLANE WARPING
1992, 9(2): 1-12.
Abstract:
In this paper,the delamination solution of the angularly and symmetrically stacked composite laminates is given for the plane warping condition.First of all,the eigen function expansions of stress and displacement.fields are derived,for which all of the basic equations,boundary conditions on crack surfaces and conditions of continuities between different plies are satisfied.Furthermore,the govcring parameters of the singular stress fields as the coefficient of singular terms in the above expansions are determined by the generalized variational principle for multi-regions,to satisfy the boundary conditions.,excluding those along the craclt surfaces.There are only line integrals in the variational equations duc to the previous satisfactions of all basic equations.The computations show that this method of solution has the advantages of simple preparation,rapid convergerrcy aid time-saving.
In this paper,the delamination solution of the angularly and symmetrically stacked composite laminates is given for the plane warping condition.First of all,the eigen function expansions of stress and displacement.fields are derived,for which all of the basic equations,boundary conditions on crack surfaces and conditions of continuities between different plies are satisfied.Furthermore,the govcring parameters of the singular stress fields as the coefficient of singular terms in the above expansions are determined by the generalized variational principle for multi-regions,to satisfy the boundary conditions.,excluding those along the craclt surfaces.There are only line integrals in the variational equations duc to the previous satisfactions of all basic equations.The computations show that this method of solution has the advantages of simple preparation,rapid convergerrcy aid time-saving.
1992, 9(2): 13-18.
Abstract:
A finite element model based on Mindlin's theory is used for the geometriclly nonlinear analysis of laminated stiffened plate.Using the total Lagrangian description the incremental equations and nonlinear stiffness matrix of the isoparametric stiffened plate element are formulated.The Newton-Raphson iteration procedure combined with the increment method is employed to trace the nonlinear equilibrium path.A variety of numerical examples are presented to demonstrate the precision and convergence of the method.All the results have a good agreement with those published.The effects of bounday condition,the size of transverse area of stiffener,the distribution of stiffener and the orientation angle of lamina on the geometricaly nonlinear strength of stiffened composite plates are investieated.
A finite element model based on Mindlin's theory is used for the geometriclly nonlinear analysis of laminated stiffened plate.Using the total Lagrangian description the incremental equations and nonlinear stiffness matrix of the isoparametric stiffened plate element are formulated.The Newton-Raphson iteration procedure combined with the increment method is employed to trace the nonlinear equilibrium path.A variety of numerical examples are presented to demonstrate the precision and convergence of the method.All the results have a good agreement with those published.The effects of bounday condition,the size of transverse area of stiffener,the distribution of stiffener and the orientation angle of lamina on the geometricaly nonlinear strength of stiffened composite plates are investieated.
1992, 9(2): 19-23.
Abstract:
A new finite element program was developed for analyzing the static strength of bolted joint in composite laminates.Based upon the failure characteristic ply by ply from circumference to inner region,Tsai-Wu tensor criterion was suggested in predicting the ply failure,and the reduced modulas of failed ply of elements was supposed to revalue its residual sustaining load capacity.Two fracture rnodels were also introduced in estimating the failure of mechanical joints.Theoretical results of ultimate stress as well as failure propagation or model were given for 21 different orintations of T300/648 Carbon/epoxy composite laminates.These results are of satisfactorv agreement with the testing data.
A new finite element program was developed for analyzing the static strength of bolted joint in composite laminates.Based upon the failure characteristic ply by ply from circumference to inner region,Tsai-Wu tensor criterion was suggested in predicting the ply failure,and the reduced modulas of failed ply of elements was supposed to revalue its residual sustaining load capacity.Two fracture rnodels were also introduced in estimating the failure of mechanical joints.Theoretical results of ultimate stress as well as failure propagation or model were given for 21 different orintations of T300/648 Carbon/epoxy composite laminates.These results are of satisfactorv agreement with the testing data.
1992, 9(2): 25-30.
Abstract:
The low-velocity impact response of composite laminated structures is very important.An accurate account of the contact problem of an elastic indenter and a laminated beam is given by using the mixed finite element method for solving elastic contact problems.The statical contact law is discussed.The effects of indenter elasticity,laminated beam lay-up and friction on the contact forces between the indenter and the laminated beam and the induced interlaminar stresses in the laminated beam are assessed.Based on the numerical results obtained.certain conclusions are drawm.
The low-velocity impact response of composite laminated structures is very important.An accurate account of the contact problem of an elastic indenter and a laminated beam is given by using the mixed finite element method for solving elastic contact problems.The statical contact law is discussed.The effects of indenter elasticity,laminated beam lay-up and friction on the contact forces between the indenter and the laminated beam and the induced interlaminar stresses in the laminated beam are assessed.Based on the numerical results obtained.certain conclusions are drawm.
1992, 9(2): 31-37.
Abstract:
Creep is one of the most important mechanical behaviors of composite material.The results of creep-recovery experiments show that under creep condition deformation can be divided into three parts:elastic deformation,viscoelastic deformation which can recover slowly and viscoplastic deformation which cannot when the load is removed.The thermodynamics of irreverible processes and concept of generalized variables can be used to derive creep constitutive equation in which strain is expressed observable variable.In this paper,the foundamental thermodynamics equationw arc reviewed.Based on the assumption,and idea of Schapery's equation,the common formula of mufti-dimensional creep constitutive equation is derived which includes elastic,viscoelastic and viscoplastic deformations.Considering that the generalized force is not unique,the authors proposed a principle for selecting variables so that the result is as simple as possible.According to such a principle,some special constitutive equations presented,which include the equations for one-dimensional problems,twodimensional problems of the isotropic material and the plane problems of fibre reinforced composite materials.
Creep is one of the most important mechanical behaviors of composite material.The results of creep-recovery experiments show that under creep condition deformation can be divided into three parts:elastic deformation,viscoelastic deformation which can recover slowly and viscoplastic deformation which cannot when the load is removed.The thermodynamics of irreverible processes and concept of generalized variables can be used to derive creep constitutive equation in which strain is expressed observable variable.In this paper,the foundamental thermodynamics equationw arc reviewed.Based on the assumption,and idea of Schapery's equation,the common formula of mufti-dimensional creep constitutive equation is derived which includes elastic,viscoelastic and viscoplastic deformations.Considering that the generalized force is not unique,the authors proposed a principle for selecting variables so that the result is as simple as possible.According to such a principle,some special constitutive equations presented,which include the equations for one-dimensional problems,twodimensional problems of the isotropic material and the plane problems of fibre reinforced composite materials.
1992, 9(2): 39-47.
Abstract:
In order to improva the accuracy of the shear deformation theory of thick laminated plates,an improved higher order theory is developed.The Legendre polynomials are introduced into the approximate displace ment distributions across the plate thickness,and a finite element model is suggested from the original equations.This theory has the same independent arguments as that in the second order shear deformation Yheory proposed by Whitney,Sun,and Engblom,etal.,but proposes the parabolic distribution of the transverse shear strains-through the thickness of the plate.The accuracy of the present theory is examined by applying it to bending problems of laminated plates which was solved exactly by Pagano.The results are compared with three-dimensional elasticity solutions,the second order shear deformation theory and some other higher order shear deformation theory solutions.The present theory shows the deflections and stress more accurately than that obtained from the previous works in the structural analysis of laminated plate with small apan with respect to thickness.
In order to improva the accuracy of the shear deformation theory of thick laminated plates,an improved higher order theory is developed.The Legendre polynomials are introduced into the approximate displace ment distributions across the plate thickness,and a finite element model is suggested from the original equations.This theory has the same independent arguments as that in the second order shear deformation Yheory proposed by Whitney,Sun,and Engblom,etal.,but proposes the parabolic distribution of the transverse shear strains-through the thickness of the plate.The accuracy of the present theory is examined by applying it to bending problems of laminated plates which was solved exactly by Pagano.The results are compared with three-dimensional elasticity solutions,the second order shear deformation theory and some other higher order shear deformation theory solutions.The present theory shows the deflections and stress more accurately than that obtained from the previous works in the structural analysis of laminated plate with small apan with respect to thickness.
1992, 9(2): 49-54.
Abstract:
Based on,the theory of nonlinear elasticity,the bending of laminated plates with the transverse shear defermation of each lamine are solved.Firstly,the analysie of anisotropic plates is presented,which is available for symmetrical laminated plates,then the method is extended to the asymmeiris laminated plates.
Based on,the theory of nonlinear elasticity,the bending of laminated plates with the transverse shear defermation of each lamine are solved.Firstly,the analysie of anisotropic plates is presented,which is available for symmetrical laminated plates,then the method is extended to the asymmeiris laminated plates.
1992, 9(2): 55-61.
Abstract:
A study was made to fracture characteristic of Graphite/Epoxy unbalanced liminates with inplane negative Poisson's ratio.These liminates have higher fracture toughness and notch fracture strength.lower notch sensitivity as compared with the balanced liminates.
A study was made to fracture characteristic of Graphite/Epoxy unbalanced liminates with inplane negative Poisson's ratio.These liminates have higher fracture toughness and notch fracture strength.lower notch sensitivity as compared with the balanced liminates.
1992, 9(2): 63-71.
Abstract:
With Takayanagi's two-phase blended model and Ziege's modified equation,and by taking composite interface as a medium phase (interphase),this paper derives a three-phase blended model of dynamic viscoelasticity from one-dimension FRP(fibcr reinforced polymer composite),and obtains the mixing parameters of geometric Structure in the interfacial layer (r,V,λ and medium parameter Band every dynamic viscoelastic parameter of interphase.Those parameters can be gained from the result of the dynamic viscoelastic experiment with FRP.Through the experiment of unidirectional fiber reinforced polyester with the given model,the result shoes that the thickness of interphaser and the fraction of volume V change with the temponature,and so do the dynamic viscoelastic parameters of interface.The interchange takes place between in1erphase and matrix phase.
With Takayanagi's two-phase blended model and Ziege's modified equation,and by taking composite interface as a medium phase (interphase),this paper derives a three-phase blended model of dynamic viscoelasticity from one-dimension FRP(fibcr reinforced polymer composite),and obtains the mixing parameters of geometric Structure in the interfacial layer (r,V,λ and medium parameter Band every dynamic viscoelastic parameter of interphase.Those parameters can be gained from the result of the dynamic viscoelastic experiment with FRP.Through the experiment of unidirectional fiber reinforced polyester with the given model,the result shoes that the thickness of interphaser and the fraction of volume V change with the temponature,and so do the dynamic viscoelastic parameters of interface.The interchange takes place between in1erphase and matrix phase.
1992, 9(2): 73-76.
Abstract:
This paper focuses on the research of the combination of Mg and carbon fibers coated with Ni,Cu and SiO2.C/Mg composite is formed by the liquid phase fabrication method.It is found that Ni,Cu and SiO2 are able to make liquid magnesium welt carbon fiber.Both Cu & Ni coatings disapperar after composite formed Ni shows a bad coexistance with carbon fiber at high temperature.SiO2 Coating is steady and it has a better protectivity towards carbon fiber.Different coating results in different distribution of fiber in matrix.
This paper focuses on the research of the combination of Mg and carbon fibers coated with Ni,Cu and SiO2.C/Mg composite is formed by the liquid phase fabrication method.It is found that Ni,Cu and SiO2 are able to make liquid magnesium welt carbon fiber.Both Cu & Ni coatings disapperar after composite formed Ni shows a bad coexistance with carbon fiber at high temperature.SiO2 Coating is steady and it has a better protectivity towards carbon fiber.Different coating results in different distribution of fiber in matrix.
1992, 9(2): 77-81.
Abstract:
The kinetic equation of interfacial reaction in simulating C/Al composite materials is established based on the theoretical analysis of diffusion limited interfacial reaction and experimental measurement.A set of reaction diffusion equations was analytically solved,and Scanning Auger Microprobe Depth Profile was applied to mersure the thickness of interfacial reaction zone.The results of experimental measurement verified well the kinetic equation of interfacial reaction proposed here,and gave the activation energy of interfacial reaction for the present specimens.
The kinetic equation of interfacial reaction in simulating C/Al composite materials is established based on the theoretical analysis of diffusion limited interfacial reaction and experimental measurement.A set of reaction diffusion equations was analytically solved,and Scanning Auger Microprobe Depth Profile was applied to mersure the thickness of interfacial reaction zone.The results of experimental measurement verified well the kinetic equation of interfacial reaction proposed here,and gave the activation energy of interfacial reaction for the present specimens.
1992, 9(2): 83-88.
Abstract:
The volume fraction (V) effect of SiC particles On fatigue crack propagation in SiCp/Al composites has been investigated by fatigue propaga tion rate examination,as well as fatigue crack path and fatigue fracture surface observation.The results indicate that fatigue craclt propagation resistance (FCPR) of the composites as V increases.However,the FCPR of composites is superior to that of matrix only when V is greater than 15%.
The volume fraction (V) effect of SiC particles On fatigue crack propagation in SiCp/Al composites has been investigated by fatigue propaga tion rate examination,as well as fatigue crack path and fatigue fracture surface observation.The results indicate that fatigue craclt propagation resistance (FCPR) of the composites as V increases.However,the FCPR of composites is superior to that of matrix only when V is greater than 15%.
1992, 9(2): 89-94.
Abstract:
The surface tensions of A.1-4.5Cu-Ce alloy and the wettability,stru- eture,bond type and bond strength of the interface of Al2O3/Al-4.5Cu-Ce alloy were researched by means of modem testing equipment,e.g.,sessile drop method and electronic microprobe etc..The results show that by adding Ce,the surface tension of Al-4.5Cu alloy can be reduced,the wettability and interfacial cut-off stress of Al2O3/.Al-4.5Cu alloy can be improved.The mechanism of Ce improving wettability is due to Ce accumulation on the interface.No interfacial reaction product is found.The interface belongs to direct bond type.
The surface tensions of A.1-4.5Cu-Ce alloy and the wettability,stru- eture,bond type and bond strength of the interface of Al2O3/Al-4.5Cu-Ce alloy were researched by means of modem testing equipment,e.g.,sessile drop method and electronic microprobe etc..The results show that by adding Ce,the surface tension of Al-4.5Cu alloy can be reduced,the wettability and interfacial cut-off stress of Al2O3/.Al-4.5Cu alloy can be improved.The mechanism of Ce improving wettability is due to Ce accumulation on the interface.No interfacial reaction product is found.The interface belongs to direct bond type.
1992, 9(2): 95-104.
Abstract:
In this paper,the structure,sod idif ication characterstic,mechanical properties,thermal-expansion coefficent and wear resistance of Zinc-Matrix/crystal silicon,ceramic particulate composites with Theological casting technology are investigated.The results show that SiC particles can be the nucleation basis of the primary phase of Zinc-matrix alloys containing high aluminum,disperse in grains and refine grains.The distribution of Si particles is related to the solidif ication of the alloys,and Al2O3 particles disperse on the grain boundary and coarsen the primary phase.Through the investigation to the inf luence of the particles on the mechanical properties it is found that the tensile strength is decreased slightly,but the hardness,the ductility and the toughness are increased with a suitable addition of particulate fraction.When particles being added,the thermal expansion coefficient of the alloy is decreased,and wear resistance is improved prominently.These properties may be suitable to the die and bearing materials.
In this paper,the structure,sod idif ication characterstic,mechanical properties,thermal-expansion coefficent and wear resistance of Zinc-Matrix/crystal silicon,ceramic particulate composites with Theological casting technology are investigated.The results show that SiC particles can be the nucleation basis of the primary phase of Zinc-matrix alloys containing high aluminum,disperse in grains and refine grains.The distribution of Si particles is related to the solidif ication of the alloys,and Al2O3 particles disperse on the grain boundary and coarsen the primary phase.Through the investigation to the inf luence of the particles on the mechanical properties it is found that the tensile strength is decreased slightly,but the hardness,the ductility and the toughness are increased with a suitable addition of particulate fraction.When particles being added,the thermal expansion coefficient of the alloy is decreased,and wear resistance is improved prominently.These properties may be suitable to the die and bearing materials.
1992, 9(2): 105-109.
Abstract:
On the base of analysing the behavior of fiber/matrix interface region and the demands to it in metal matrix composites,a functionally gradient coating idea was presented in this paper.The coating has many functions including wetting medium,resistatance to diffusion and reactions,and im proving properties of reinforced fibers.The functionally gradient coating on carbon fibers were developed with CVD and coated fibers were characterized.
On the base of analysing the behavior of fiber/matrix interface region and the demands to it in metal matrix composites,a functionally gradient coating idea was presented in this paper.The coating has many functions including wetting medium,resistatance to diffusion and reactions,and im proving properties of reinforced fibers.The functionally gradient coating on carbon fibers were developed with CVD and coated fibers were characterized.
