Multilayered Composite Laminates Research Articles

Modeling of the progressive failure behavior of multilayer knitted fabric-reinforced composite laminates

This paper deals with the characterization and modeling of the failure behavior of laminates with application to multilayer plain weft-knitted-fabric-reinforced composites. Experiments have been performed to measure the uniaxial tensile strengths of eight knitted-fabric laminates with lay-ups of [0/0/0/0], [0/+30/−30/0], [0/45/−45/0], [0/+60/−60/0], [0/90/90/0], [+30/−30/−30/+30], [+60/−60/−60/+60], and [90/90/90/90], where 0 refers to the fabric wale direction and 90 to the course direction. A theoretical modeling procedure for the progressive failure process in the laminate is presented. The simulation, made at the lamina ply level, is based on the classical thin-laminate theory and a recently developed bridging micromechanics model. Only material properties of constituent fiber and matrix as well as fabric geometric parameters are necessary. The internal stress increments generated in the fiber and the matrix of each lamina are directly related to the overall applied load increment on the laminate. Whenever any constituent material attains its ultimate stress state, according to the maximum normal stress criterion, the corresponding lamina fails, and a stiffness discount is applied to the remaining laminate. An angle-ply laminate subjected to in-plane biaxial load combinations together with the eight knitted-fabric laminates under uniaxial tension has been analyzed. The predicted ultimate failure strengths or strength envelope of the laminates agree well with our or available experimental data. Furthermore, the influence of different fabric lay-up configurations on the first and the last-ply failure strengths of the knitted-fabric laminates has been investigated, and the failure envelopes of several knitted-fabric laminates subjected to bi-axial loads are also shown in the paper.

Free vibration analysis of multi-layered composite laminates based on an accurate higher-order theory

This paper deals with an accurate higher-order theory employing finite element procedure for the free vibration analysis of multi-layered thick composite plates. The theory accounts for the realistic variation of in-plane and transverse displacements through the thickness. The accuracy of the present model is verified by comparison with three-dimensional elasticity solutions for the vibration study of the composite laminates. The performance and the applicability of the proposed discrete model are also discussed among developed elements and alternate models, considering different parameters such as ply-angle, degree of orthotropicity, aspect ratio and boundary conditions.

Initial strain effects in multilayer composite laminates

A boundary integral formulation for the analysis of stress fields induced in composite laminates by initial strains, such as may be due to temperature changes and moisture absorption is presented. The study is formulated on the basis of the theory of generalized orthotropic thermo-elasticity and the governing integral equations are directly deduced through the generalized reciprocity theorem. A suitable expression of the problem fundamental solutions is given for use in computations. The resulting linear system of algebraic equations is obtained by the boundary element method and stress interlaminar distributions in the boundary-layer are calculated by using a boundary only discretization. The approach is general and it does not require a priori assumptions. Numerical results are presented to show the potential of the proposed approach.

Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses

Natural frequencies and buckling stresses of angle-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the fundamental natural frequency are examined in detail. Numerical results are compared with those of the published existing theories. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. The present global higher-order approximate theories can predict the natural frequencies, buckling stresses and modal stresses of thick multilayered angle-ply composite laminates accurately within small number of unknowns which is not dependent on the number of layers.

Singular full-field stresses in composite laminates with open holes

A method of the superposition of a hybrid and displacement approximation was developed to provide the accurate stress fields in a multilayered composite laminate, including the singular neighborhood of the ply interface and the hole edge. Asymptotic analysis was used to derive the hybrid stress functions. The displacement approximation is based on the polynomial B-spline functions. The method provides the determination of the coefficient of the singular term along with convergent stress components including the singular regions. Reissner’s variational principle was employed. Simple [45/−45] s and quasi-isotropic IM7/5250 [45/90/−45/0] s laminates were analyzed. Uniaxial loading and residual stress calculation (quasi-isotropic laminate) were considered. A convergence study showed that accurate values of the coefficient of the singular term of the asymptotic stress expansion could be obtained with coarse out-of-plane and in-plane subdivisions. The interaction between the singular terms on the neighboring interfaces was found to be important for the convergence with coarse subdivisions. Converged transverse interlaminar stress components as a function of the distance from the hole edge, were shown for all examples.

Asymptotically exact stresses in laminates with a rigid fastener

A method of superposition of a hybrid and displacement approximation has been extended to provide accurate stress fields in a multilayered composite laminate including the singular neighborhood of the ply interface and the edge of a hole containing a rigid fastener. Asymptotic analysis was used to derive the hybrid stress functions. Multiple singular terms at each interface were incorporated. The displacement approximation is based on polynomial B-spline functions. The method provides determination of the coefficient of the singular term along with convergent stress components, including the singular regions. Reissner's variational principle was employed. Coefficients of the singular term of the asymptotic expansion were determined for a [45/-45] s laminate under bearing loading introduced through a rigid fastener.

Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory

Natural frequencies and buckling stresses of cross-ply laminated composite plates are analyzed by taking into account the effects of shear deformation, thickness change and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for thick rectangular laminates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported thick laminated plate. In order to assure the accuracy of the present theory, convergence properties of the lowest natural frequency and buckling stress are examined in detail. Numerical results are compared with those of the published existing theories and FEM solutions. The modal displacement and stress distributions in the thickness direction are obtained and plotted in figures. It is noticed that the present global higher-order approximate theories can predict the natural frequencies, buckling stresses and stresses of thick multilayered composite laminates as accurately as three-dimensional solutions.

Curing simulation of thermoset composites

Abstract This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composite laminates during processing in an autoclave. Darcy's Law and Stokes’ slow-flow equations are used for the flow model and, for approximately isothermal flows, a similarity solution is developed. This permits the decoupling of the velocity and thermal fields. A two-dimensional convection–diffusion heat equation with an internal heat generation term is then solved numerically, together with the equation for the rate of cure, using a finite difference scheme on a moving grid. The simulations are performed with varying composite thicknesses, and a comparison of numerical results with known experimental data confirms the approximate validity of the model.

Prediction of failure envelopes and stress/strain behaviour of composite laminates

Failure envelopes for unidirectional composites and multi-layered composite laminates have been predicted by linear laminate theory. The ply-by-ply discount method with parallel spring stiffness reduction model was used in the prediction. The stress/strain behavior of four laminates under uniaxial or biaxial loading were predicted by considering both material non-linearity and progressive matrix cracking. Material non-linearity was considered by using a one-parameter plasticity model for fiber-reinforced composites. Progressive matrix cracking and the corresponding stiffness reduction were predicted by use of a simplified shear-lag analysis and finite element analysis.

DELAMINATION: LAMINATE ANALYSIS AND FRACTURE MECHANICS

In the analysis of a multilayered composite laminate with an arbitrarily shaped delamination, accurate non‐linear laminate analysis is required to obtain the kinematic and kinetic variables which characterize the local state of deformation at a generic point of the delamination front. These variables provide the strain/curvature parameters and the boundary tractions for the local analysis model of a multimaterial region containing an interfacial crack. The singular elasticity solution in the vicinity of the crack tip is obtained by an eigenfunction expansion, where the coefficients of the eigenfunctions are evaluated by boundary collocation. The accuracy of the present solution is indicated by the computed energy release rate, which is in close agreement with the result based on path‐independent integrals.

Boundary Element Solution for Free Edge Stresses in Composite Laminates

The edge-stress problem in multilayered composite laminates under uniform axial extension is analyzed through an alternative method based on a boundary integral formulation. The basic equations of the formulation are discussed and solved by the multiregion boundary element method. Generalized orthotropic elasticity analytic fundamental solutions are employed to establish the integral equations governing the problem. The formulation is absolutely general with regard to the laminate stacking sequence and the section geometry and it does not require any aprioristic assumption on the elastic response nature. This makes the formulation suitable for an investigation of the singular behavior of the stress field at the free edge in composite laminates. The interlaminar normal and shear stress distributions are examined in detail with the aim of calculating the stress singularity at the interlaminar free edge. The singularity parameters, i.e., power and strength, are determined for two family of laminates in order to ascertain the effectiveness of the method for the free edge-stress problem.

Stress fields in general composite laminates

A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The interlaminar stress field near the free edge of generally stacked composite laminates subjected to uniaxial extension is investigated through this boundary integral equation formulation. The numerical applications show good agreement with those already available in literature, and they demonstrate the accuracy and the efficiency of the proposed method. approach where a complete three-dimensional analysis is performed was presented by Pipes and Pagano,1 who employed the finite dif- ference technique to obtain the solution of the governing elastic- ity equations. Many solutions obtained by using the finite element method are available.21() These differ from each other in the formu- lation, in the kind of employed elements, and in the discretization schemes. In the literature analytical solutions of approximate the- ories are also present. The techniques employed to achieve these solutions include the perturbation method,11 series solution,12'13 Lekhintskii's complex stress potentials coupled with an eigenfunc- tion expansion14'15 or a polynomial expansion,16'll the extension of Reissner's variational principle,18'19 and the force balance method coupled with the minimum complementary energy principle.20'21 The stress distributions obtained with these approaches show good agreement between them for points away from the free edge. Con- siderable disagreement exists instead for points near the free edge location among the various numerical and analytical solutions. This is to be expected as a result of a priori assumptions or because the boundary conditions of the continuum problem have been trans- formed into conditions on the generalized data. Actually the numer- ical solution techniques are not able to predict the singular trend in the stress field at the free edge, and hence, to achieve satisfactory solutions a lengthy extrapolation procedure is required. On the other hand, the analytical approximate solutions often rest on assumptions about the problem unknowns that enforce the free edge stress field structure. In the present paper, the stress field in multilayered composite laminates under uniform axial extension is analyzed on the basis of the integral equation theory.22'23 The laminate is considered as composed by prismatic elements having different elastic proper- ties. The generic element or ply is treated as homogeneous, and in terms of constitutive equations it is described by a generalized orthotropic law. The integral equations governing the exact elastic- ity solution of the problem are directly obtained by applying the reciprocity theorem with the fundamental solutions of the general- ized orthotropic elasticity.2427 The

Response of multilayered composite laminates to dynamic surface loads

A theoretical investigation of the response of multilayered composite laminates to concentrated and distributed dynamic surface loads is carried out. Each layer of the laminate is assumed to be transversely isotropic and dissipative with arbitrarily oriented symmetry axis. The dissipative property of the material is modeled approximately through the introduction of a frequency-dependent damping function. A multiple transform technique is used to calculate the spectra and time histories of the displacements and stresses produced by a variety of dynamic loads, and the quantitative features of the waves produced in the laminate are determined. The methodology developed in this work is expected to be useful in the prediction of the response of composite laminates to impact loads and also in the characterization of acoustic emission (AE) sources in these materials under static and dynamic loads.

A mixed finite element for interlaminar stress computation

A mixed finite element method (MFEM) aiming at solving the problem of three-dimensional stress analysis of multi-layer composite laminates with a high accuracy is presented. The approach, which is based on the global-local laminate variational model, proposes a mixed use of a hibrid stress element within a high precision stress solution region in the thickness direction of the laminate and a conventional displacement finite element in the remaining. This results in a reduction of the overall computation time while maintaining the solution precision in the area(s) of interest, normally being certain interface(s) within a laminate. A formulation of a 49 stress parameter hybrid stress element in conjunction with a 42 degree of freedom iso-parametric displacement element is given. The quality of the hybrid stress element is assured by a stiffness matrix eigenvalue analysis. Example computations of laminate cylindrical bending and the classical free-edge problem have shown the feasibility of the MFEM approach and the convergence of the specific 49β-42 q formulation.

AXISYMMETRIC TRANSIENT THERMAL STRESS ANALYSIS OF A MULTILAYERED COMPOSITE HOLLOW CYLINDER

This article is concerned with axisymmetric, transient, thermal stress analysis of a hollow cylinder composed of multilayered composite laminates with temperature changes in the radial and axial directions due to axisymmetric heating from the outer and/or the inner surfaces. For analysis, we apply the methods of Fourier cosine transform and Laplace transform to the temperature field and the thermo-eiastic potential function and apply Love's displacement function to the thermo-etastic field. We then obtain the exact solutions for the temperature and thermal stress distributions in a transient state. Moreover, we apply the theoretical developments proposed in our present article into the analysis of a hollow cylinder with nonhomogeneous material properties such as a functionally gradient material.

Stochastic Material Design of Composite Material. Selection of Effective Failure Path and Approximated Failure Probability of MultiLayer Laminates.

A method of evaluating an effective failure path of multilayer composite laminates under the off-axial load condition is presented. It is necessary to select the failure path whose occurrence probabilities are greater than others, since the combinations of failure paths of multilayer composite laminates are too numerous to evaluate. The proposed method of selecting an effective failure path depends upon the heuristic procedure based on the branch and bound rule which enables one to estimate the effective failure path whose occurrence probabilities are greater than others. An extended study is carried out in order to calculate the failure probability of a multilayer laminate using the resultant effective failure path. Some numerical analysis based on the proposed algorithm are represented for graphite/epoxy composite laminates.

Effects of Interleaves on Fracture of Laminated Composites: Part I—Analysis

The influence of placing interleaves between fiber-reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as a two-dimensional, isotropic, linearly elastic media consisting of a damaged layer bonded between two half-planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. Fourier integral transform techniques are used to develop the solutions in terms of singular integral equations.

Dynamic behavior of delamination and transverse cracks in fiber reinforced laminated composites

In this paper a numerical method is developed to study the dynamic behavior of delamination and transverse cracks in lamianted fiber-reinforced composite plates of finite dimension. The plate is subjected to time dependent antiplane shear stress field which is acting on the plate surfaces. The interaction of waves diffracted at the crack tip with those reflected at the plate boundaries and transmitted at the material interface makes the problem very complicated, so analytical study of this problem cannot be carried out with our present state of knowledge. Hence the problem is solved numerically. A versatile functional is developed which can handle delamination and transverse cracks with any orientation in multilayered composite laminates. The variational principle is adopted in frequency domain to obtain the finite element equations. The numerical difficulty associated with the singular behavior of the stress field near the crack tip has been avoided by using quarter point elements.

Transient thermal stress analysis of a multilayered composite laminate cylinder with a uniformly distributed heat suply and [its analytical development to nonhomogeneous materials

As one of the analytical models of the thermal stress problem for composite materials, we consider a hollow circular cylinder composed of multilayered composite laminate and discuss the transient thermal stress problems of a hollow cylinder with a uniform heat supply from the outer or inner surface. In studying the analytical developments for a multilayered composite cylinder, we introduce the method of Laplace transform for the temperature field and Airy's stress function method for the thermoelastic field. and then evaluate the temperature and thermal stress distributions in a transient state. Extending the theoretical developments proposed in the present paper to the analysis of a hollow cylinder with nonhomogeneous material properties, we examine the thermal stress distributions and the effect of relaxation of stresss values in nonhomogeneous cylinders made of functionally gradient material.

An integrated micromechanical and macromechanical approach to fracture behavior of fiber-reinforced composites

An integrated micromechanical and macromechanical fracture criterion (IMMFC) has been developed for the fracture characterization of fiber-reinforced composites. The Griffith's energy balance equation has been modified to include the energy absorption due to physical failure processes, characteristic of the heterogeneous and anisotropic nature of these materials. A local elastic energy release rate in the presence of plasticity has been defined and used as a criterion for the onset and growth of cracks in both micromechanics and macromechanies analyses. A crack growth simulation technique based on the virtual crack extension method has been developed for a three-dimensional (3-D) finite element analysis. A 3-D finite element micromechanical model is used to study the effects of broken fibers, cracked matrix and fiber-matrix debond on the fracture toughness of the unidirectional composite. The crack growth resistance curves ( R-curves) concept has been used to bridge the micromechanics and macromechanics approaches. The energy release rates at the onset of the unstable crack growth in the micromechanics analysis are used as critical energy release rates in the macromechanics analysis. The approach has been shown to be very effective in predicting the onset and growth of cracks in general multilayered composite laminates by applying the criterion to predict the initiation and growth of cracks and associated damages in a single-edged notched [ ± 45 0 ] s graphite/epoxy laminate subjected to inplane tension normal to the notch.