John D. Whitcomb

Buckling of a Sublaminate in a Quasi-Isotropic Composite Laminate

Buckling of a delaminated region can cause high interlaminar stresses which, in turn, lead to delamination growth. Hence, buckling strain is an important parameter in assessing the potential for strength loss due to the delamination. The objective of this study was to predict the buckling of an elliptic delamination embedded near the surface of a thick quasi-isotropic laminate. 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 showed 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.

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 deflec tions. 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 deter mine the relative importance of the Mode I and Mode II components of energy release. GI was shown to dominate the growth process.

Three-dimensional analysis of a postbuckled embedded delamination

Delamination growth caused by local buckling of a delaminated group of plies was investigated. Delamination growth was assumed to be governed by the strain- energy release rates GI, GII, and GIII. The strain-energy release rates were calculated using a geometrically nonlinear, three-dimensional, finite element analysis. The program is described and several checks of the analysis are discussed. Based on a limited para metric study, the following conclusions were reached: 1. The problem is definitely mixed-mode. In some cases GI is larger than GII ; for other cases the opposite is true. 2. In general, there is a large gradient in the strain-energy release rates along the delamination front. 3. The locations of maximum GI, and GII depend on the delamination shape and the ap plied strain. 4. The mode III component was negligible for all cases considered. 5. The analysis predicted that parts of the delamination would overlap. The results pre sented herein did not impose contact constraints to prevent overlapping. Further work is needed to determine the effects of allowing the overlapping.

Three-dimensional stress analysis of plain weave composites

Techniques were developed and described for performing three-dimensional finite element analysis of plain weave composites. Emphasized here are aspects of the analysis which are different from analysis of traditional laminated composites, such as the mesh generation and representative unit cells. The analysis was used to study several different variations of plain weaves which illustrate the effects of tow waviness on composite moduli, Poissons ratios, and internal strain distributions. In-plane moduli decreased almost linearly with increasing tow waviness. The tow waviness was shown to cause large normal and shear strain concentrations in composites subjected to uniaxial load. These strain concentrations may lead to earlier damage initiation than occurs in traditional cross-ply laminates.

Parametric analytical study of instability-related delamination growth

Abstract When a laminated composite is subjected to compressive loads a delaminated region may buckle. This causes high interlaminar stresses at the delamination front and the delamination may grow. The effect of various parameters on instability-related delamination growth was studied analytically. The configuration studied consisted of a thick composite laminate with a single through-width delamination located near one surface. Both mechanical and thermal loads were considered. All conclusions were based on the assumption that GI and GII govern delamination growth. An approximate superposition stress analysis was developed which gives closed form expressions for GI and GII. The simplicity of the analysis permitted examination of numerous configurations. Both GI and GII were found to be very sensitive to delamination length and location through the thickness. The magnitude of GI was also very sensitive to initial imperfections, which might be the result of an inclusion of finite thickness in the delamination. Critical oads for delamination growth were calculated based on three growth criteria. Large differences in the predictions highlight the need for a verified mixed-mode delamination growth criterion.

Analysis of a Laminate with a Postbuckled Embedded Delamination, Including Contact Effects

The behavior of a postbuckled embedded delamination was studied using geometrically-nonlinear 3-D finite element analysis. Nonlinearities due to both significant rotations and delamination face contact were considered. The analysis showed that the postbuckling deformation can lead to matrix cracking and fiber breakage in addition to delamination growth. These calculations agree qualitatively with experimental results. Also, for the configuration analyzed and moderate strain levels, the strain-energy release rates can be calculated with reasonable accuracy without including contact effects in the analysis

Derivation of Boundary Conditions for Micromechanics Analyses of Plain and Satin Weave Composites

Efficient 3D analysis of periodic structures depends on identifying the smallest region to be modeled and the appropriate boundary conditions. This paper describes systematic procedures for deriving the boundary conditions for general periodic structures. These procedures are then used to derive the boundary conditions for plain and satin weave composites.

Geometrically Nonlinear Analysis of Adhesively Bonded Joints

A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-release rates (G1/G2) was found to be strongly affected by the adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements. Previously announced in STAR as N83-13497

Iterative global/local finite element analysis

In spite of the advances in computer technology, there is still a need for more computationally efficient methods for performing stress analysis. One approach which is receiving increasing attention is global/local analysis. Such analyses can take a variety of forms. The form described herein uses two distinct meshes (one global and one local), but retains the same level of accuracy as one would obtain if one was to use a single refined global mesh. The accuracy is retained by using an iterative procedure to enforce equilibrium between the global and local regions. The procedure was tested for two configurations. The good performance observed indicates that the iterative global/local procedure warrants further examination.

Effect of various approximations on predicted progressive failure in plain weave composites

Three-dimensional finite element analysis was used to simulate progressive failure of a plain weave composite subjected to in-plane extension. The loading was parallel to one of the tow directions. The effects of various characteristics of the finite element model on predicted behavior were examined. The predicted behavior was found to be sensitive to quadrature order, mesh refinement and the material degradation model. Also the sensitivity of the predictions to the tow waviness was studied. The predicted strength decreased considerably with increased waviness. More numerical studies and comparisons with experimental data are needed to establish reliable guidelines for accurate progressive failure prediction.