Simple Solutions of the Free-Edge Stresses in Composite Laminates under Thermal and Mechanical Loads

1994 ◽  
Vol 28 (6) ◽  
pp. 573-586 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Composite Laminates ◽  
Constitutive Relations ◽  
Free Edge ◽  
Normal Derivative ◽  
Boundary Region ◽  
Material Behavior ◽  
Interlaminar Stresses ◽  
Inelastic Material ◽  
Stress Functions ◽  
Temperature Loads

Intense and localized interlaminar stresses generally occur in a narrow boundary region near the free edge of a multilayered anisotropic laminate under mechanical and temperature loads. Quantitative measures of interlaminar action across interfaces may be readily obtained through purely algebraic operations, even if nonlinear and inelastic material behavior becomes significant in the boundary region due to severe strain concentration. These measures are the limiting values of the Lekhnitskii stress functions F and $$ (and of the normal derivative of F) along interfaces and toward the interior region of the laminate. In the present work, they are used as the basis of an exceedingly simple and efficient method of interlaminar stress analysis that is potentially applicable to free-edge problems involving nonlinear thermoelastic constitutive relations. Example solutions are obtained for symmetric, four-layer, cross-ply and angle-ply laminates under a temperature load and two different types of strain loads, and the results are found to be in reasonable agreement with the existing numerical and analytical solutions based on elaborate analysis methods.

The Effects of Adhesive Nonlinearity on Thermal Stress in Layered Components

1994 ◽  
Vol 116 (2) ◽  
pp. 105-109 ◽  
Author(s):  
Wan-Lee Yin ◽  
James L. Dale
Keyword(s):  
Thermal Stress ◽  
Middle Layer ◽  
Free Edge ◽  
Boundary Region ◽  
Local Concentration ◽  
Interlaminar Stresses ◽  
Softening Behavior ◽  
Stress Strain Relation ◽  
Inelastic Material ◽  
Stress Functions

Interlaminar stresses near the free edge of a multi-layered structure under thermal and mechanical loads are significantly affected by nonlinear and inelastic material properties. Most previous studies of the subject ignored such effects and obtained singular or extremely severe and localized stress fields in boundary regions based strictly on the assumption of linearly elastic stress-strain relation. In the present paper, a variational method, using approximate stress functions and the principle of complementary energy, is developed to study the thermal stress in a three-layer beam including a thin, compliant, non-linearly elastic middle layer. It is found that the elastic softening behavior of the thin layer results in dispersion of the interlaminar stresses and widening of the boundary region. Hence the use of toughened, compliant bonding layers may produce a beneficial effect by alleviating local concentration of interlaminar stresses.

The Effects of Inclined Free Edges on the Thermal Stresses in a Layered Beam

1993 ◽  
Vol 115 (2) ◽  
pp. 208-213 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Thermal Stresses ◽  
Stress Singularity ◽  
Approximate Solutions ◽  
Free Edge ◽  
Local Concentration ◽  
Interlaminar Stresses ◽  
Beneficial Effects ◽  
Stress Functions ◽  
Layered Beam ◽  
Free Edges

A stress-function-based variational method is used to determine the thermal stresses in a layered beam with inclined free edges at the two ends. The stress functions are expressed in terms of oblique cartesian coordinates, and polynomial expansions of the stress functions with respect to the thickness coordinate are used to obtain approximate solutions. Severe interlaminar stresses act across end segments of the layer interfaces. Local concentration of such stresses may be significantly affected by the inclination angle of the end planes. Variational solutions for a two-layer beam show generally beneficial effects of free-edge inclination in dispersing the concentration of interlaminar stresses. The significance of these effects is generally not indicated by the power of the stress singularity as computed from an elasticity analysis of a bimaterial wedge.

Free-Edge Effects in Anisotropic Laminates Under Extension, Bending, and Twisting, Part II: Eigenfunction Analysis and the Results for Symmetric Laminates

1994 ◽  
Vol 61 (2) ◽  
pp. 416-421 ◽  
Author(s):  
W.-L. Yin
Keyword(s):  
Eigenvalue Problem ◽  
Edge Effects ◽  
Free Edge ◽  
Interlaminar Stresses ◽  
Particular Solutions ◽  
Variational Solutions ◽  
Stress Functions ◽  
Polynomial Expansions ◽  
Eigenfunction Analysis

The eigenvalue problem associated with the determination of the interlaminar stresses in a laminated strip is examined and physical interpretations are given to the (constant) particular solutions and the complementary solutions of the problem. The case of symmetric laminates is considered in detail, and variational solutions are computed for four-layer, symmetric, cross-ply, and angle-ply laminates subjected to the three fundamental types of strain loads. Solutions based on two sets of stress functions with polynomial expansions of different degrees are compared with each other and with the existing solutions to assess the accuracy. The interfacial values of the stress functions and their derivatives are identified as the resultant peeling and shearing forces over end intervals of the interface.

scholarly journals Analysis of Free Edge Stresses in Composite Laminates Using Higher Order Theories

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hamidreza Yazdani Sarvestani ◽  
Ali Naghashpour
Keyword(s):  
Composite Laminates ◽  
High Efficiency ◽  
Single Layer ◽  
Free Edge ◽  
Higher Order ◽  
Design Guidelines ◽  
Computational Time ◽  
Interlaminar Stresses ◽  
Layerwise Theory ◽  
Free Edges

This paper presents the determination of the interlaminar stresses close to the free edges of general cross-ply composite laminates based on higher order equivalent single-layer theory (HESL). The laminates with finite dimensions were subjected to a bending moment, an axial force, and/or a torque for investigation. Full three-dimensional stresses in the interior and the boundary-layer regions were determined. The computed results were compared with those obtained from Reddy’s layerwise theory. It was found that HESL theory predicts precisely the interlaminar stresses near the free edges of laminates. Besides, high efficiency in terms of computational time is obtainable when HESL theory is used as compared with layerwise theory. Finally, various numerical results were presented for the cross-ply laminates. Also design guidelines were proposed to minimize the edge-effect problems in composite laminates.

Refined Variational Solutions of the Interfacial Thermal Stresses in a Laminated Beam

1992 ◽  
Vol 114 (2) ◽  
pp. 193-198 ◽  
Author(s):  
W.-L. Yin
Keyword(s):  
Thermal Stresses ◽  
Virtual Work ◽  
Free Edge ◽  
Interlaminar Stresses ◽  
Laminated Beam ◽  
Variational Solutions ◽  
Stress Functions ◽  
Polynomial Expansions ◽  
Resultant Forces ◽  
Derivatives Of

Efficient and accurate solutions of the interlaminar stresses in a layered beam under a temperature loading are obtained by a variational method using stress functions and the principle of complementary virtual work. Polynomial expansions of the fifth or lower degrees are used to approximate the variation of the stress functions in the thickness direction of each layer. Comparison of the solutions of the various orders with the existing numerical and analytical solutions indicates that the variational solutions converge rapidly as the degree of the polynomial expansion increases and that even the lowest-order variational solutions yield satisfactory results for the interlaminar stresses. Over short segments of the interface adjacent to the free edge, the resultant forces of the interlaminar normal and shearing stresses are given by the first-order derivatives of the stress functions. These global measures of the severity of interlaminar peeling and shearing action are predicted accurately by the lowest-order variational solution.

scholarly journals Investigation of the Free Edge Interlaminar Stresses Dependence on the PLY Thickness and Orientation

2006 ◽  
Vol 15 (1) ◽  
pp. 096369350601500
Author(s):  
Dionisios T. G. Katerelos
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Composite Laminates ◽  
Free Edge ◽  
Thermomechanical Loading ◽  
Interlaminar Stresses ◽  
Element Analysis ◽  
3 Dimensional ◽  
Out Of Plane ◽  
Dimensional Finite Element

Among the principal damage modes in composite laminates, is delamination. Design details, such as free, straight or curved, edges, induce large local out-of-plane loads, generating interlaminar stresses. In the present work, the effect of ply thickness and the angle between two adjacent layers on the interlaminar stresses developed at the vicinity of straight and curved free edges in composite laminates under thermomechanical loading is examined. The results are obtained by the application of a 3-dimensional Finite Element Analysis.

Free Edge Stresses in Elastic and Viscoelastic Composites Under Uniaxial Extension, Bending, and Twisting Loadings

1997 ◽  
Vol 119 (3) ◽  
pp. 266-272 ◽  
Author(s):  
Sung Yi ◽  
H. H. Hilton
Keyword(s):  
Stress Relaxation ◽  
Constitutive Relations ◽  
Plane Deformation ◽  
Uniaxial Extension ◽  
Free Edge ◽  
Time Dependent ◽  
Interlaminar Stresses ◽  
Shear Moduli ◽  
Deformation State ◽  
Interlaminar Shear

Time-dependent interlaminar stresses in elastic and viscoelastic laminated composites subjected to arbitrary combinations of axial extension, bending and/or twisting loads are obtained based on integral constitutive relations and Pipes and Pagano’s displacement field for laminates under a generalized plane deformation state. Numerical results obtained from the present formulation are compared against experimental data and excellent agreement within two percent was obtained between these results. Time-dependent interlaminar stresses for cross-ply and angle-ply laminates subjected to uniaxial extension, bending and twisting are also presented. Appreciable stress relaxation occurred during the loading period resulting in decreased magnitudes of residual stresses. It is seen that the rate of interlaminar shear stress relaxation is greater than the normal one, since the relaxation of shear moduli is larger than that of the normal moduli.

scholarly journals The effect of edge interlaminar stresses on the strength of carbon/epoxy laminates of different stacking geometry

2006 ◽  
Vol 71 (4) ◽  
pp. 421-431 ◽  
Author(s):  
Momcilo Stevanovic ◽  
Milan Gordic ◽  
Daniela Sekulic ◽  
Isidor Djordjevic
Keyword(s):  
Tensile Strength ◽  
Normal Stress ◽  
Edge Effect ◽  
Edge Effects ◽  
Free Edge ◽  
Tensile Tests ◽  
Boundary Region ◽  
Stacking Sequence ◽  
Interlaminar Stresses ◽  
Static Tensile

The effect of edge interlaminar stresses on strength of carbon/epoxy laminates of different stacking geometry: cross-ply, quasi-isotropic and angle-ply laminates with additional 0? and 90? ply was studied. Coupons with two widths of laminates with an inverse stacking sequence were tested in static tensile tests. The effect of edge interlaminar stresses on strength was studied, by comparing the values of the tensile strength of laminate coupons of the same width with an inverse stacking sequence, as well as, by comparing the values of the tensile strength of the same lay-up laminate coupons but of different widths. The edge effects were analyzed by observing failure, identifying the interlayer where axial cracks at the free edge were initiated or inhibited and by computing interlaminar stresses and strains in the interlayer near the free edge of the coupon. The established edge effect was first correlated to the sign of the normal edge interlaminar stress. The extent of the edge effect was then successfully correlated to the edge interlaminar normal stress normalized to the size of the edge boundary region in which the stress appeared.

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