Experimental and analytical study of fatigue damage in notched graphite/epoxy laminates

Both tension and compression fatigue behaviors were investigated in four notched graphite/epoxy laminates. After fatigue loading, specimens were examined for damage type and location using visual inspection, light microscopy, scanning electron microscopy, ultrasonic C-scans, and X-radiography. Delamination and ply cracking were found to be the dominant types of fatigue damage. In general, ply cracks did not propagate into adjacent plies of differing fiber orientation. To help understand the varied fatigue observations, the interlaminar stress distribution was calculated with finite element analysis for the regions around the hole and along the straight free edge. Comparison of observed delamination locations with the calculated stresses indicated that both interlaminar shear and peel stresses must be considered when predicting delamination. The effects of the fatigue cycling on residual strength and stiffness were measured for some specimens of each laminate type. Fatigue loading generally caused only small stiffness losses. In all cases, residual strengths were greater than or equal to the virgin strengths

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included

Superposition method for analysis of free-edge stresses

Superposition techniques were used to transform the edge stress problem for composite laminates into a more lucid form. By eliminating loads and stresses not contributing to interlaminar stresses, the essential aspects of the edge stress problem are easily recognized. Transformed problem statements were developed for both mechanical and thermal loads. Also, a technique for approximate analysis using a two dimensional plane strain analysis was developed. Conventional quasi-three dimensional analysis was used to evaluate the accuracy of the transformed problems and the approximate two dimensional analysis. The transformed problems were shown to be exactly equivalent to the original problems. The approximate two dimensional analysis was found to predict the interlaminar normal and shear stresses reasonably well

Buckling of a sublaminate in a quasi-isotropic composite laminate

The buckling of an elliptic delamination embedded near the surface of a thick quasi-isotropic laminate was predicted. The thickness of the delaminated ply group (the sublaminate) was assumed to be small compared to the total laminate thickness. Finite-element and Rayleigh-Ritz methods were used for the analyses. The Rayleigh-Ritz method was found to be simple, inexpensive, and accurate, except for highly anisotropic delaminated regions. Effects of delamination shape and orientation, material anisotropy, and layup on buckling strains were examined. Results show that: (1) the stress state around the delaminated region is biaxial, which may lead to buckling when the laminate is loaded in tension; (2) buckling strains for multi-directional fiber sublaminates generally are bounded by those for the 0 deg and 90 deg unidirectional sublaminates; and (3) the direction of elongation of the sublaminate that has the lowest buckling strain correlates with the delamination growth direction

Fatigue damage of notched boron/epoxy laminates under constant amplitude loading

Fatigue damage in (0, + or - 45) and (0, + or - 45,90) boron/epoxy laminates was studied with X-ray radiography and scanning electron microscopy. In addition, limited tests for residual strength and stiffness were performed. The results of this study suggest that in boron/epoxy laminates the 45-degree plies play a key role in the fatigue process of boron/epoxy laminates that contain them. The fatigue process in the + or - 45-degree plies starts as intralaminar matrix cracks

A new look at numerical analyses of free-edge stresses in composite laminates

The edge stress problem for a + or - 45 deg graphite/epoxy laminate was examined. The reliability of the displacement formulated finite element method in analyzing the edge stress problem was investigated. 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 of singularity. Stress distributions for a + or - 45 deg laminate showed the same behavior near the singularity found in the well known problems with exact solutions. The displacement formulated finite element method appears to be a highly accurate technique for calculating interlaminar stress in composite laminates. The disagreement among the numerical methods was attributed to the unsymmetric stress tensor at the singularity

A simple rectangular element for 2-dimensional analysis of laminated composites

A simple rectangular finite element was developed for two dimensional analysis of laminated composite materials. The rectangular laminated composite element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffness and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed

Finite element analysis of instability-related delamination growth

A parametric study of postbuckled through-width delaminations in laminated coupons was performed. A finite element analysis was developed to analyze the coupons as a combination of linear and geometrically nonlinear components. Because most of the coupon configuration studied behaves linearly, the mixed linear and nonlinear analysis greatly reduced computational costs. The analysis was verified by comparing numerical with exact solutions for simple hypothetical problems. In addition, measured lateral deflections of postbuckled through-width delaminations in laminated coupons were compared with predicted deflections. In the parametric study, stress distributions and strain-energy release rates were calculated for various delamination lengths, delamination depths, applied loads, and lateral deflections. Also, a small number of coupons with through-width delaminations were fatigue tested to obtain delamination growth data. Calculated strain-energy release rates were compared with the observed growth rates to determine the relative importance of the Mode 1 and Mode 2 components of energy release. Growth process was dominated by G sub I

Strain energy release rate analysis of cyclic delamination growth in compressively loaded laminates

Delamination growth in compressively loaded composite laminates was studied analytically and experimentally. The configuration used was a laminate with an across-the-width delamination. An approximate super-position stress analysis was developed to quantify the effects of various geometric, material, and load parameters on mode 2 and mode 2 strain energy release rates G sub/1 and G sub 2, respectively. Calculated values of G sub 1 and G sub 2 were then compared with measured cyclic delamination growth rates to determine the relative importance of G sub 1 and G sub 2. High growth rates were observed only when G sub 1 was large. However, slow growth was observed even when G sub 1 was negligibly small. This growth apparently was due to a large value of G sub 2

Approximate analysis of postbuckled through-width delaminations

An approximate analysis was developed to analyze the postbuckling behavior of through-width delaminations in a laminated coupon. The analysis contains two parameters which are determined using a finite element analysis. After calculating the parameters for a few configurations, the approximate analysis was used to analyze many other configurations. Lateral deflections and mode I strain-energy release rates obtained with the approximate analysis were compared with results from the finite element analysis. For the configurations analyzed, the approximate analysis agreed very well with the finite element results