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NASA NTRS1993

Modelling of thick composites using a layerwise laminate theory

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

Robbins, D. H., Jr.↗

NASA NTRS1993

Three-dimensional finite element progressive failure analysis of composite laminates under axial extension

A three-dimensional (3D) progressive failure algorithm is developed, where the layerwise laminate theory (LWLT) of Reddy is used for kinematic description. The finite element model based on the layerwise theory predicts both inplane and interlaminar stresses with the same accuracy as that of a conventional 3D finite element model and provides a convenient format for modeling the 3D stress fields in composite laminates. A parametric study is conducted to investigate the effect of out-of-plane material properties, 3D stiffness reduction methods, and boundary conditions on the failure loads and strains of a composite laminate under axial extension. The results indicate that different parameters have a different degree of influence on the failure loads and strains. The predictive ability of various phenomenological failure criteria is evaluated in the light of experimental results available in the literature, and the predictions of the LWLT are compared with those of the first-order shear deformation theory. It is concluded that a 3D stress analysis is necessary to predict accurately the failure behavior of composite laminates.

Reddy, Yeruva S.↗

NASA NTRS1993

Analysis of delamination in cross-ply laminates initiating from impact induced matrix cracking

Two-dimensional finite element analyses of (02/90(8)/02) glass/epoxy and graphite/epoxy composite laminates were performed to investigate some of the characteristics of damage development due to an impact load. A cross section through the thickness of the laminate with fixed ends, and carrying a transverse load in the center, was analyzed. Inclined matrix cracks, such as those produced by a low-velocity impact, were modeled in the 90 deg ply group. The introduction of the matrix cracks caused large interlaminar tensile and shear stresses in the vicinity of both crack tips in the 0/90 and 90/0 interfaces, indicating that matrix cracking may give rise to delamination. The ratio of Mode I to total strain energy release rate, G(I)/G(total), at the beginning of delamination, calculated at the two (top and bottom) matrix crack tips was 60 and 28 percent, respectively, in the glass/epoxy laminate. The corresponding ratio was 97 and 77 percent in the graphite/epoxy laminate. Thus, a significant Mode I component of strain energy release rate may be present at the delamination initiation due to an impact load. The value of strain energy release rate at either crack tip increased due to an increase in the delamination length at the other crack tip and may give rise to an unstable delamination growth under constant load.

Salpekar, S. A.↗

NASA NTRS1989

A mechanics framework for a progressive failure methodology for laminated composites

A laminate strength and life prediction methodology has been postulated for laminated composites which accounts for the progressive development of microstructural damage to structural failure. A damage dependent constitutive model predicts the stress redistribution in an average sense that accompanies damage development in laminates. Each mode of microstructural damage is represented by a second-order tensor valued internal state variable which is a strain like quantity. The mechanics framework together with the global-local strategy for predicting laminate strength and life is presented in the paper. The kinematic effects of damage are represented by effective engineering moduli in the global analysis and the results of the global analysis provide the boundary conditions for the local ply level stress analysis. Damage evolution laws are based on experimental results.

Harris, Charles E.↗

NASA NTRS1923

Internal Stresses in Laminated Construction

This report reviews the procedure employed in an investigation of the sources and influence of internal stresses in laminated construction, and discusses the influence of shrinkage and swelling stresses caused by atmospheric conditions upon the tensile strength across grain in laminated construction with special reference to airplane propellers. The investigation covered three sources of internal stress, namely, the combination of plain-sawed and quarter-sawed material in the same construction, the gluing together of laminations of different moisture contents, and the gluing together of laminations of different densities. Glued specimens and free specimens, made up under various manufacturing conditions, were subjected to various climatic changes inducing internal stresses and then were tested.

Heim, A L↗

NASA NTRS1993

Optimal Synthesis of Hot Composite Laminates with Interphase Layers

A method for the optimal grading of a single interphase layer in metal matrix composite laminates for the minimization of residual stresses is described. The capability to simultaneously tailor some fabrication parameters is also incorporated. Applications for unidirectional, cross-ply and quasi-isotropic Graphite/Copper laminates are investigated to assess the potential of interphase layer in reducing matrix residual stresses in various laminate configurations. Simultaneous optimization of interphase and fabrication characteristics appears to be more effective in decreasing residual stresses. The results also indicate that the interphase layer is more effective in lowering residual stresses in unidirectional composites and selectively within individual plies of a laminate. Embedded interphase layers in all the plies did not produce a significant global reduction in residual stresses.

Rabzak, Christopher↗

NASA NTRS1994

A comparison of graphite/epoxy tape laminates and 2-D braided composites mechanical properties

A comparison of the in-plane mechanical properties of unidirectional composite tape laminates and of two dimensional triaxially braided composite was conducted. The tape laminate layups were designed to match the percentage of axial fibers and the angle of the bias tows in the braided composite. The material system used for the laminates is AS4/3501-6 which was chosen as the closest available match to AS4/1895 used for the braids. This report documents the results of the testing of the laminates and compares these results with data previously obtained for the braided composite. The strength and stiffness properties measured here include tension, open-hole tension, filled-hole tension, compression, and open-hole compression, all of these in both the longitudinal and transverse direction, as well as in-plane shear and bearing.

Minguet, Pierre J.↗

NASA NTRS1995

Effects of Delaminations on the Damped Dynamic Characteristics of Composite Laminates: Mechanics and Experiments

Analytical and experimental work is presented on the damped free-vibration of delaminated laminates and beams. A laminate theory is developed where the unknown kinematic perturbations induced by a delamination crack are treated as additional degrees of freedom. The generalized stiffness, inertia and damping matrices of the laminate are formulated. An analytical solution is developed for the prediction of natural frequencies, modes and modal damping in composite beams with delamination cracks. Evaluations of the mechanics on various cantilever beams with a central delamination are performed. Experimental results for the modal frequencies and damping of composite beams with a single delamination are also presented and correlations between analytical predictions and measured data are shown. The effects of delamination vary based on crack size, laminate configuration, and mode order. The implications of the mechanics in developing delamination detection techniques are also discussed.

Saravanos, D. A.↗

NASA NTRS1994

Integrated damping mechanics for thick composite laminates and plates

A method for predicting the damped dynamic characteristics of thick composite laminates and plates is presented. Unified damping mechanics relate the damping of composite plates to constituent properties, fiber volume ratio, fiber orientation, laminate configuration, plate geometry, temperature, and moisture. Discrete layer damping mechanics for thick laminates, entailing piecewise continuous displacement fields and including the effects of interlaminar shear damping, are described. A semi-analytical method for predicting the modal damping and natural frequencies of thick simply-supported specialty composite plates is included. Applications demonstrate the validity, merit, and ranges of applicability of the new theory. The applications further illustrate the significance of interlaminar shear damping, and investigate the effects of lamination, thickness aspect ratio, fiber content, and temperature.

Saravanos, D. A.↗

NASA NTRS1995

Microcracking in composite laminates under thermal and mechanical loading

Composites used in space structures are exposed to both extremes in temperature and applied mechanical loads. Cracks in the matrix form, changing the laminate thermoelastic properties. The goal of the present investigation is to develop a predictive methodology to quantify microcracking in general composite laminates under both thermal and mechanical loading. This objective is successfully met through a combination of analytical modeling and experimental investigation. In the analysis, the stress and displacement distributions in the vicinity of a crack are determined using a shear lag model. These are incorporated into an energy based cracking criterion to determine the favorability of crack formation. A progressive damage algorithm allows the inclusion of material softening effects and temperature-dependent material properties. The analysis is implemented by a computer code which gives predicted crack density and degraded laminate properties as functions of any thermomechanical load history. Extensive experimentation provides verification of the analysis. AS4/3501-6 graphite/epoxy laminates are manufactured with three different layups to investigate ply thickness and orientation effects. Thermal specimens are cooled to progressively lower temperatures down to -184 C. After conditioning the specimens to each temperature, cracks are counted on their edges using optical microscopy and in their interiors by sanding to incremental depths. Tensile coupons are loaded monotonically to progressively higher loads until failure. Cracks are counted on the coupon edges after each loading. A data fit to all available results provides input parameters for the analysis and shows them to be material properties, independent of geometry and loading. Correlation between experiment and analysis is generally very good under both thermal and mechanical loading, showing the methodology to be a powerful, unified tool. Delayed crack initiation observed in a few cases is attributed to a lack of preexisting flaws assumed by the analysis. Some interactions between adjacent ply groups are attributed to local stress concentrations. These two effects are not captured by the analysis due to its global nature. The analysis is conservative in these cases and agrees well with data after the observed onset of cracking.

Maddocks, Jason R.↗

NASA NTRS1995

Effects of stitching on fracture toughness of uniweave textile graphite/epoxy laminates

The effects of through-the-thickness stitching on impact damage resistance, impact damage tolerance, and Mode 1 and Mode 2 fracture toughness of textile graphite/epoxy laminates were studied experimentally. Graphite/epoxy laminates were fabricated from AS4 graphite uniweave textiles and 3501-6 epoxy using Resin Transfer Molding. The cloths were stitched with Kevlar(tm) and glass yarns before resin infusion. Delamination was implanted during processing to simulate impact damage. Sublaminate buckling tests were performed in a novel fixture to measure Compression After Impact (CAI) strength of stitched laminates. The results show that CAI strength can be improved up to 400% by through-the-thickness stitching. Double Cantilever Beam tests were performed to study the effect of stitching on Mode 1 fracture toughness G(sub 1c). It was found that G(sub 1c) increased 30 times for a low stitching density of 16 stitches/sq in. Mode 2 fracture toughness was measured by testing the stitched beams in End Notch Flexure tests. Unlike in the unstitiched beams, crack propagation in the stitched beams was steady. The current formulas for ENF tests were not found suitable for determining G(sub 2C) for stitched beams. Hence two new methods were developed - one based on crack area measured from ultrasonic C-scanning and the other based on equivalent crack area measured from the residual stiffness of the specimen. The G(sub 2c) was found to be at least 5-15 times higher for the stitched laminates. The mechanisms by which stitching increases the CAI strength and fracture toughness are discussed.

Sankar, Bhavani V.↗

NASA NTRS1995

The initial buckling behavior of flat and curved fiber metal laminate panels

Local buckling is expected to become an important design issue when metallic materials in conventional stiffened panels are replaced by fiber metal laminates. An experimental study to validate the use of existing design methods for the initial buckling and postbuckling of flat and curved unstiffened fiber metal laminate panels is reported on. All existing design methods can be used for fiber metal laminate panels with the same efficiency and accuracy as for metals. The influence of the collapse behavior and imperfections on the material's mechanical behavior are equal for metallic materials and fiber metal laminate materials. The collapse is found to be important for plates with a curvature parameter of greater than approximately seven, while imperfections are found to play an role for plates with curvature parameters exceeding 20.

Verolme, Koos↗

NASA NTRS1996

The Influences of Lamination Angles on the Interior Noise Levels of an Aircraft

The feasibility of reducing the interior noise levels of an aircraft passenger cabin through optimization of the composite lay up of the fuselage is investigated. MSC/NASTRAN, a commercially available finite element code, is used to perform the dynamic analysis and subsequent optimization of the fuselage. The numerical calculation of sensitivity of acoustic pressure to lamination angle is verified using a simple thin, cylindrical shell with point force excitations as noise sources. The thin shell used represents a geometry similar to the fuselage and analytic solutions are available for the cylindrical thin shell equations of motion. Optimization of lamination angle for the reduction of interior noise is performed using a finite element model of an actual aircraft fuselage. The aircraft modeled for this study is the Beech Starship. Point forces simulate the structure borne noise produced by the engines and are applied to the fuselage at the wing mounting locations. These forces are the noise source for the optimization problem. The acoustic pressure response is reduced at a number of points in the fuselage and over a number of frequencies. The objective function is minimized with the constraint that it be larger than the maximum sound pressure level at the response points in the passenger cabin for all excitation frequencies in the range of interest. Results from the study of the fuselage model indicate that a reduction in interior noise levels is possible over a finite frequency range through optimal configuration of the lamination angles in the fuselage. Noise reductions of roughly 4 dB were attained. For frequencies outside the optimization range, the acoustic pressure response may increase after optimization. The effects of changing lamination angle on the overall structural integrity of the airframe are not considered in this study.

Fernholz, Christian M.↗

NASA NTRS1997

A Higher-Order Bending Theory for Laminated Composite and Sandwich Beams

A higher-order bending theory is derived for laminated composite and sandwich beams. This is accomplished by assuming a special form for the axial and transverse displacement expansions. An independent expansion is also assumed for the transverse normal stress. Appropriate shear correction factors based on energy considerations are used to adjust the shear stiffness. A set of transverse normal correction factors is introduced, leading to significant improvements in the transverse normal strain and stress for laminated composite and sandwich beams. A closed-form solution to the cylindrical elasticity solutions for a wide range of beam aspect ratios and commonly used material systems. Accurate shear stresses for a wide range of laminates, including the challenging unsymmetric composite and sandwich laminates, are obtained using an original corrected integration scheme. For application of the theory to a wider range of problems, guidelines for finite element approximations are presented.

Cook, Geoffrey M.↗

NASA NTRS1998

Prediction of Composite Laminate Fracture: Micromechanics and Progressive Fracture

An investigation is described on the prediction of first-ply failure and fracture in selected composite laminates. The laminates are made from glass fibers and graphite fibers in epoxy matrices. Failure envelopes are generated for combined loading of these laminates on the basis of first-ply failure and laminate fracture. The evaluation is performed by a micromechanics-based theory and progressive fracture.

Gotsis, P. K.↗

NASA NTRS1999

Progressive Failure Analysis Methodology for Laminated Composite Structures

A progressive failure analysis method has been developed for predicting the failure of laminated composite structures under geometrically nonlinear deformations. The progressive failure analysis uses C(exp 1) shell elements based on classical lamination theory to calculate the in-plane stresses. Several failure criteria, including the maximum strain criterion, Hashin's criterion, and Christensen's criterion, are used to predict the failure mechanisms and several options are available to degrade the material properties after failures. The progressive failure analysis method is implemented in the COMET finite element analysis code and can predict the damage and response of laminated composite structures from initial loading to final failure. The different failure criteria and material degradation methods are compared and assessed by performing analyses of several laminated composite structures. Results from the progressive failure method indicate good correlation with the existing test data except in structural applications where interlaminar stresses are important which may cause failure mechanisms such as debonding or delaminations.

Sleight, David W.↗

NASA NTRS1998

Prediction of Composite Laminate Fracture: Micromechanics and Progressive Fracture

Gotsis, P. K.↗

NASA NTRS2000

Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.

Goldberg, Robert K.↗