Stresses In Composite Laminates Research Articles

An accurate determination of stresses in thick laminates using a generalized plate theory

AbstractAnalytical solutions for displacements and stresses in composite laminates are developed using the laminate plate theory of Reddy. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the inplane deformation through individual laminae. The solutions are compared with the 3‐D elasticity solutions for the simply supported case and excellent agreement is found. Analytical solutions are also presented for other boundary conditions. The results indicate that the generalized shear deformation plate theory predicts accurate stress distributions in thick composite laminates.

Determination of Interlaminar Stresses in Composite Laminates under Combined Loads

A method to determine the complete state of stress at free edges of com posite laminates under combined loads (uniaxial tension or compression, moment, and out-of-plane shear) is presented. Based on the principle of minimum complementary en ergy, two coupled ordinary differential equations are derived with use of calculus of varia tions. The stresses are determined in closed form and are in good agreement with other solutions published in the literature for uniaxial tension and applied moment. This solu tion is applicable to general laminates with straight free edges and is computationally very efficient.

Elastic-plastic analysis of interlaminar stresses in composite laminates due to bending and torsion

The elastic-plastic response of interlaminar stresses in composite laminates due to bending and torsion is investigated using the finite element method. The plasticity model used is a general three-dimensional orthotropic yield criterion, which is quadratic in stresses, in conjunction with incremental flow theory. Linear and nonlinear studies are carried out with boron-aluminum metal-matrix composites. The results, including bending moment-curvature relations, growth of plastic zones, and distribution of interlaminar stresses, are presented. It is found that the free edge effect on interlaminar stresses is important in bending, but it is insignificant in torsion. It is also shown that the inclusion of plasticity could alter free edge interlaminar stresses significantly.

Variational principle of hybrid energy and the fundamentals of 3-D laminate theory—A new approach for the analysis of interlaminar stresses in composite laminates

This paper discusses the discontinuity of stresses and strains at interlaminar surfaces of the composue laminate and presents a 3-D laminate theory for composite materials. This paper also presents a new type of elastic energy based on the globally continuous variables in laminates, different from the traditional potential energy and complementary energy. Then, a variational principle corresponding to the 3-D laminate theory is developed. The theory and the principle could be a basis of verifying the 2-D laminate theory and determining the interlaminar stresses near the free edges.

Residual Stresses in Carbon Fibre-Thermoplastic Matrix Laminates

Residual stresses in composite laminates depend on thermoelastic properties of the material and processing temperatures. Their distribution in the various laminae is a func tion of stacking sequence and ply orientation. In this work residual stresses in APC-2 cross-ply laminates have been investigated. Predictions based on classical laminate theory are compared to measured levels of residual stress obtained from a number of experimen tal techniques. The analysis of the results shows that accurate predictions can be made pro vided that the changes in thermoelastic properties of the materials with temperature are taken into account.

A Boundary Layer Approach to Interlaminar Stresses in Composite Laminates with Curved Edges

A way for determining the interlaminar stresses in composite laminates with arbitrary curved edges is described using the boundary layer equations. A simple and efficient method for the calculation of interlaminar stresses is presented. The method gives a stress field that satisfies the zeroth order equilibrium equations and the stress boundary condi tions as well as the stress continuity between plies. Several laminates with a circular hole are dealt with by the present method. The results indicate that the method is of great versatility and has the ability to perform the analysis of thick laminates efficiently.

Effect of Plasticity on Free Edge Stresses in Boron-Aluminum Composite Laminates

A general orthotropic yield criterion that is quadratic in stresses in conjunction with the incremental flow theory of plasticity was used to analyze free edge interlaminar stresses in composite laminates. The growth of plastic zones and the distributions of interlaminar stresses were studied using a pseudo three-dimensional finite element method. Results for [0/90] s, [90/0] s, and [45/-45] s Boron-Aluminum metal matrix composites were pre sented. It was found that the inclusion of plasticity could significantly alter the inter laminar stresses.

On the effects of environmental conditioning on residual stresses in composite laminates

This study presents an experimental and theoretical investigation of moisture effects in graphite/epoxy composites. The experiments involved exposure of antisymmetric, cross-ply laminates to various levels of fixed and fluctuating humidity and measurements of the resulting, time-dependent curvatures. Those data were compared with computed values based upon linear elasticity and linear, Theologically simple, viscoelasticity. Good agreement was noted between data and viscoelastic predictions during the moisture absorption stage from the initially dry condition. However, increasing disparity between theory and experiment developed during subsequent drying and humidity cycling conditions. This disparity is attributed to the growth of moisture-induced damage, indicating that drying and moisture cycling are more detrimental to the integrity of composites than moisture absorption, even though they may be associated with a smaller total moisture content.

Optimally discretized finite elements for boundary-layer stresses incomposite laminates

Optimally discretized finite elements for boundary-layer stresses incomposite laminates

A singular hybrid finite element analysis of boundary-layer stresses in composite laminates

A singular hybrid finite element method for studying boundary-layer stresses in composite laminates is presented. The laminate elasticity basis and the fundamental solution structure for the boundary-layer field are briefly reviewed first. Formulation of a singular composite-edge element is based on the recently developed boundary-layer theory and the variational principle of a modified hybrid functional. The singular hybrid element is used conveniently in conjunction with displacement-based conventional elements. Numerical solutions for the well-known Pipes-Pagano problem are presented for illustration. Comparisons of the present solution with the laminate elasticity solution and conventional finite element results are made to demonstrate the accuracy and efficiency of the present approach. Influences of eigenfunction truncation, size and aspect ratio of the singular hybrid element as well as mesh configuration are studied.

Boundary-Layer Hygroscopic Stresses in Angle-Ply Composite Laminates

An investigation on hygroscopically- induced stress fields near g eometric b oundaries of finitewidth, a ngle-ply composite laminates is presented. The study is formulated on the b asis of the t heory of anisotropic hygroelasticity. By the i ntroduction of Lehknitskii's complex stress functions, governing partial differential equations of the sixth-order are established for composite laminates subjected to uniformly distributed moisture absorption. The hygroscopic stress singularity at the edges of a c omposite laminate is determined b y an eigenfunction expansion technique recently developed by the authors. Distributions of stresses and associated strain energy densities in the boundarylayer region of the composite laminate are obtained by using a boundary-colloca tion method. A symmetric, angle-ply (45°/-450/-450/4 50) graphitel epoxy is chosen for illustrative purposes in this study. The solution for the (+45), composite is presented to elucidate t he fundamental behavior of hygroscopic edge stresses in composite laminates. Of particular i nterest are the p resently introduced hygroscopic b oundary-layer stress intensity factors and their implications. Details of these are reported in the paper.

Reliability of the finite element method for calculating free edge stresses in composite laminates

The edge-stress problem for a [±45] s graphite/epoxy laminate was examined in detail. A review of the literature on this problem showed that the interlaminar normal stress σ z distributions along the interface between the +45° and -45° plies, obtained by various investigators, disagreed in magnitude and sign. In particular, a finite difference solution and a perturbation solution predicted a tensile σ z , whereas the finite element methods predicted a compressive stress. Since a stress singularity exists at the intersection of the interface and the free edge, the differences in magnitude of the peak stress were expected, but not the difference in the sign. This paper investigates the reliability of the displacement-formulated finite element method in analyzing the edge-stress problem. Analyses of two well-known elasticity problems, one involving a stress discontinuity and one a singularity, showed that the finite element analysis yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a [±45] s laminate showed the same behavior near the singularity as found in the well-known problems with exact solutions. The displacementformulated finite element method, therefore, appears to be a highly accurate technique for calculating interlaminar stresses in composite laminates. The disagreement among the numerical methods was attributed to the unsymmetric stress tensor at the singularity.

Edge Effects on Thermally Induced Stresses in Composite Laminates

Thermally induced stresses in fiber composite laminates play an important role in the strength and failure of such laminates as load carrying members. When laminates have free edges, cutouts or holes, interlaminar stress concentration will usually develop near the free-edge region under service loads. An accurate evaluation of thermally induced edge stresses will further the understanding of the laminates' behavior. The present paper examines the stress field of a finite-width, symmetrical laminate when subjected to a uniform temperature change. A finite-element proce dure employing advanced sparse matrix solution technique is employed to study the singular nature of stresses near the free-edge region. Edge effects on the overall response of the laminate under thermal loading are discussed.

Curing Stresses in Composite Laminates

Analysis of curing stresses in resin matrix composite laminates involves a temperature range over which variation of elastic moduli is appreciable. A method based on total stress-strain-temperature relations is formulated and applied to determine the curing stresses in boron/epoxy composite lam inates. This method is shown to be preferable to the incremental method because the former requires the thermal strains and the stress-strain rela tions only at the final temperature of interest. The use of incremental constitutive equations is also discussed, and it is shown that proper care must be exercised to insure inclusion of interaction terms that have no counterparts in linear theories.

The Influence of Stacking Sequence on Laminate Strength

Based upon considerations relating to the nature of the inter laminar stresses in composite laminates, an approach is presented to predict the detailed stacking sequence of specific layer orientations which leads to optimum protection against delamination under uniaxial static and fatigue loadings. In particular, it is argued that the interlaminar normal stress, as well as the interlaminar shear stress, is instrumental in precipitating delamination and subsequent strength degradation. Correlation with existing experimental evidence of the stacking sequence phenomenon is presented.