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NASA NTRS1990

Damage states in laminated composite three-point bend specimens: An experimental-analytical correlation study

Damage states in laminated composites were studied by considering the model problem of a laminated beam subjected to three-point bending. A combination of experimental and theoretical research techniques was used to correlate the experimental results with the analytical stress distributions. The analytical solution procedure was based on the stress formulation approach of the mathematical theory of elasticity. The solution procedure is capable of calculating the ply-level stresses and beam displacements for any laminated beam of finite length using the generalized plane deformation or plane stress state assumption. Prior to conducting the experimental phase, the results from preliminary analyses were examined. Significant effects in the ply-level stress distributions were seen depending on the fiber orientation, aspect ratio, and whether or not a grouped or interspersed stacking sequence was used. The experimental investigation was conducted to determine the different damage modes in laminated three-point bend specimens. The test matrix consisted of three-point bend specimens of 0 deg unidirectional, cross-ply, and quasi-isotropic stacking sequences. The dependence of the damage initiation loads and ultimate failure loads were studied, and their relation to damage susceptibility and damage tolerance of the mean configuration was discussed. Damage modes were identified by visual inspection of the damaged specimens using an optical microscope. The four fundamental damage mechanisms identified were delaminations, matrix cracking, fiber breakage, and crushing. The correlation study between the experimental results and the analytical results were performed for the midspan deflection, indentation, damage modes, and damage susceptibility.

Starbuck, J. Michael↗

NASA NTRS1982

Prediction of residual tensile strength of transversely impacted composite laminates

The response to low velocity impact of graphite-epoxy T300/5208 composite laminates is discussed. Steel balls of 3/8 inch, 5/8 inch, and 1 inch diameter were the projectiles. Impact energy was limited to 1.2 joules. Impacted specimens were ultrasonically C scanned to determine the impact damaged region. The threshold value of impact energy for impact damage was found to be approximately 0.3 joules. A model was developed to predict the tensile residual strength of impact damaged specimens from fracture mechanics concepts. Impacted specimens were tested in tension to provide a fracture data base. The experimental results agreed well with the predictions from fracture mechanics. In this study, the maximum impact velocity used to simulate the low velocity transverse impact from common objects like tool drops was 10 m/s.

Lal, K. M.↗

NASA NTRS1985

Importance of anisotropic bending stiffnesses on buckling of symmetrically laminated composite plates loaded in compression

The differential equation governing buckling of symmetrically laminated composite plates loaded in compression is presented in nondimensional form. From this equation, nondimensional material coefficients are obtained and a nondimensional parameter is presented that is used to assess when anisotropic bending stiffnesses can be neglected in a buckling analysis. Results obtained using finite element analyses are presented that show how boundary conditions, aspect ratio, fiber orientation, stacking sequence, and thickness affect the importance of the anisotropic bending stiffnesses.

Nemeth, M. P.↗

NASA NTRS1986

Prediction of the long-term creep compliance of general composite laminates

An accelerated viscoelastic characterization procedure for use with polymer-based composite materials is presented which employs short term test data obtained using unidirectional specimens to predict the long term viscoelastic behavior of general composite laminates. This procedure is here illustrated using the Schapery (1966, 1969) nonlinear theory as the required viscoelastic constitutive model, as well as classical lamination theory for the lamination scheme. The technique is applied to T300/5208 graphite/epoxy.

Tuttle, M. E.↗

NASA NTRS1991

Analytical modelling of laminated composites

This paper presents a unique approach to the analysis of thick laminated composites by presenting two simple finite element methods. The first uses the predictor corrector technique to extend the simple Mindlin-type element to achieve greater accuracy, and the second develops a new least squares element which can approximate a C(1) continuous element. The least squares element has the capability to incorporate a simplified higher-order basis into a piecewise continuous displacement field creating an accurate, yet computationally simple, element. These two methods have the potential to significantly upgrade analysis methods with little additional computational cost.

Kouri, Jeffrey V.↗

NASA NTRS1998

Failure of Laminated Composites at Thickness Discontinuities: An Experimental and Analytical Study

Failure initiation of laminated composites at a thickness discontinuity is studied experimentally with the aid of an optical microscope under combined loading of tension, transverse shear and bending, making use of three- and four-point bending arrangements. Because transverse shear produced relatively small effects in failure initiation results are presented as tension-bending interactions. Two loading frames for three- and four-point bending were designed to apply moment and tension simultaneously to produce failure by generating a ply crack; this initiation was evaluated by finite element analysis using ABAQUS. For cross-plies bounding the interface at the base of the step it is found that a maximum strain criterion applied to the continuing (long) ply describes the failure initiation. Ultimate failure resulted at loads on the order of 25 to 35% higher than those at failure initiation.

Lee, Sangwook↗

NASA NTRS2009

Refined Zigzag Theory for Laminated Composite and Sandwich Plates

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.

Tessler, Alexander↗

NASA NTRS1990

A model for predicting damage induced fatigue life of laminated composite structural components

This paper presents a model for predicting the life of laminated composite structural components subjected to fatigue induced microstructural damage. The model uses the concept of continuum damage mechanics, wherein the effects of microcracks are incorporated into a damage dependent lamination theory instead of treating each crack as an internal boundary. Internal variables are formulated to account for the effects of both matrix cracks and internal delaminations. Evolution laws for determining the damage variables as functions of ply stresses are proposed, and comparisons of predicted damage evolution are made to experiment. In addition, predicted stiffness losses, as well as ply stresses are shown as functions of damage state for a variety of stacking sequences.

Allen, David H.↗

DOE OSTI2022

In-situ imaging of flexure-induced fracture in tape-laminate composites using high-resolution X-ray computed tomography

Here, this study presents development of an in-situ flexure test for imaging progressive inter- and intralaminar fracture in tape-laminate composites using X-ray computed tomography (CT). The intent of this test is to provide detailed experimental observations of ply-level damage that can be used to validate existing, and develop new, progressive damage analysis (PDA) tools. The test consists of a vertically mounted specimen which is flexed using two eccentric compressive loads using an in-situ uniaxial load stage. The flexure specimen contains a starter notch mid-span which promotes initiation of composite failure within the X-ray field of view. Specimens with two different laminate stacking sequences were tested, imaged, analyzed. For a quasi-isotropic laminate with large angle changes between adjacent plies, there was near simultaneous growth of transverse cracks and delaminations below the midplane of the laminate. For a laminate with small angles between adjacent plies, there was extensive formation of transverse crack networks which penetrated the laminate thickness without delamination growth. In addition to imaging fracture, the X-ray CT data from both specimen types were used to quantify the variability in thickness and analyze the local orientation of individual plies. Overall, the proposed test and the image-data analysis methodology provided an important insight into the fracture processes in tape laminates and highlights the inherent ply-level geometrical variabilities that should be accounted for in PDA simulations.

42 ENGINEERING↗

NASA NTRS1976

Residual stresses in polymer matrix composite laminates

Residual stresses in composites are induced during fabrication and by environmental exposure. The theory formulated can describe the shrinkage commonly observed after a thermal expansion test. Comparison between the analysis and experimental data for laminates of various material systems indicates that the residual stress-free temperature can be lower than the curing temperature, depending on the curing process. Effects of residual stresses on ply failure including the acoustic emission characteristics are discussed.

Hahn, H. T.↗

NASA NTRS1992

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗

NASA NTRS1988

The strength of laminated composite materials under repeated impact loading

When low velocity and energy impact is exerted on a laminated composite material, in a perpendicular direction to the plane of the laminate, invisible damage may develop. It is shown analytically and experimentally that the invisible damage occurs during the first stage of contact between the impactor and the laminate and is a result of the contact stresses. However, the residual flexural strength changes only slightly, because it depends mainly on the outer layers, and these remain undamaged. Repeated impact intensifies the damage inside the laminate and causes larger bending under equivalent impact load. Finally, when the damage is most severe, even though it is still invisible, the laminate fails because of bending on the tension side. If the repeated impact is halted before final fracture occurs the residual strength and modulus would decrease by a certain amount.

Rotem, Assa↗

NASA NTRS1990

A New Approach to Fibrous Composite Laminate Strength Prediction

A method of predicting the strength of cross-plied fibrous composite laminates is based on expressing the classical maximum-shear-stress failure criterion for ductile metals in terms of strains. Starting with such a formulation for classical isotropic materials, the derivation is extended to orthotropic materials having a longitudinal axis of symmetry, to represent the fibers in a unidirectional composite lamina. The only modification needed to represent those same fibers with properties normalized to the lamina rather than fiber is a change in axial modulus. A mirror image is added to the strain-based lamina failure criterion for fiber-dominated failures to reflect the cutoffs due to the presence of orthogonal fibers. It is found that the combined failure envelope is now identical with the well-known maximum-strain failure model in the tension-tension and compression-compression quadrants but is truncated in the shear quadrants. The successive application of this simple failure model for fibers in the 0/90 degree and +/- 45 degree orientations, in turn, is shown to be the necessary and sufficient characterization of the fiber-dominated failures of laminates made from fibers having the same tensile and compressive strengths. When one such strength is greater than the other, the failure envelope is appropriately truncated for the lesser direct strain. The shear-failure cutoffs are now based on the higher axial strain to failure since they occur at lower strains than and are usually not affected by such mechanisms as microbuckling. Premature matrix failures can also be covered by appropriately truncating the fiber failure envelope. Matrix failures are excluded from consideration for conventional fiber/polymer composites but the additional features needed for a more rigorous analysis of exotic materials are covered. The new failure envelope is compared with published biaxial test data. The theory is developed for unnotched laminates but is easily shrunk to incorporate reductions to allow for bolt holes, cutouts, reduced compressive strength after impact, and the like.

Hart-Smith, L. J.↗

NASA NTRS2020

Progressive Failure Analysis Correlation with Notched Composite Laminate Test Data

Testing of small and intermediate laminate panels with notches was performed and Progressive Failure Analyses (PFA) models were developed for aid in test planning and for correlation with the test data. Two progressive damage failure models were included in the study: the commercially available Abaqus built-in damage model and COmplete STress Reduction (COSTR) damage model developed at NASA Langley Research Center (LaRC). The finite elements models used for the analysis were developed using shell elements. The pre-test PFA results obtained from the two damage models were compared to test data. Then a post-test PFA with updated material properties based on additional available material property data was executed with the COSTR damage model and compared to the test data. The panels tested in compression all exhibited less scatter in the failure load with self-similar failure behavior. The panels tested in tension exhibited more scatter in the failure load with a failure mode that included delamination of plies. However, a self-similar crack path was also observed as the overall failure mode for all panels tested. When comparing test data to the pre-test analysis results, both damage models with shell element models were considered adequate for predicting the behavior and failure load of both the small and intermediate panels when tested in compression. However, for the tension load cases, larger differences were observed between the test and analysis results. When comparing test data to the post-test analysis performed using the COSTR damage model, better correlation was observed. However, large discrepancies were still observed for the tension load cases. Consequently, a higher fidelity finite element model including solid elements for sub-laminates and the modeling of cohesive layers between sub-laminate layers is recommended for tension loading of notched composite laminates.

Damage Model,Progressive Failure Analysis,Open Hol↗

NASA NTRS1996

Evaluation of the Edge Crack Torsion (ECT) Test for Mode 3 Interlaminar Fracture Toughness of Laminated Composites

An analytical and experimental investigation was carried out on G40-800/R6376 graphite epoxy laminates to evaluate the Edge Crack Torsion (ECT) test as a candidate for a standard Mode 3 interlaminar fracture toughness test for laminated composites. The ECT test consists of a (90/(+/- 45)(sub 3)/(+/- 45)(sub 3)/90))(sub s) laminate with a delamination introduced by a non-adhesive film at the mid-plane along one edge and loaded in a special fixture to create torsion along the length of the laminate. Dye penetrate enhanced X-radiograph of failed specimens revealed that the delamination initiated at the middle of the specimen length and propagated in a self similar manner along the laminate mid-plane. A three-dimensional finite element analysis was performed that indicated that a pure Mode 3 delamination exists at the middle of specimen length away from both ends. At the ends near the loading point a small Mode 2 component exists. However, the magnitude of this Mode 2 strain energy release rate at the loading point is small compared to the magnitude of Mode 3 component in the mid-section of the specimen. Hence, the ECT test yielded the desired Mode 3 delamination. The Mode 3 fracture toughness was obtained from a compliance calibration method and was in good agreement with the finite element results. Mode 2 End-Notched Flexure (ENF) tests and Mode 1 Double Cantilever Beam (DCB) tests were also performed for the same composite material. The Mode 1 fracture toughness was much smaller than both the Mode 2 and Mode 3 fracture toughness. The Mode 2 fracture toughness was found to be 75% of the Mode 3 fracture toughness.

Li, Jian↗

NASA NTRS1990

Impact damage in composite laminates

A low-velocity impact-damage model for quasi-symmetric graphite-fiber composite plates is presented. The distribution of damage in each layer of the plate was calculated by employing Di Sciuva's composite laminate theory together with Hashin's failure criterion for fiber-reinforced composites. The dynamic deformation of the target plate was represented by the lower vibrational modes of the plate. The principle of virtual work was applied in the formulation of the problem. In the analysis, the material was regarded as 'damaged' when its designed strength was reduced by the failure of its constituents. The constituent failures consisted of matrix crackings, fiber breakages, and delamination between layers. According to damage modes, the moduli of material in the damaged zone were reduced according to the failure criteria. The interaction between layers and its role in damage propagation were also studied.

Wang, Chung-Yue↗

NASA NTRS1992

Coupled elastic response of open section laminated composite beams subject to generalized beam loading

A generalized beam theory for arbitrary open section laminated composite beams subjected to generalized beam loading is developed using a strength of materials approach. At present, the theory is limited to statistically determinate beams. Solution of the general system of equations yields strain and curvature distributions as functions of the axial coordinate x and the contour coordinate s. Average stresses on a given cross section or ply stresses in a local coordinate system are determined using these distributions. Data obtained for thin-walled open section composite beams reveal that elastic coupling occurs among curvatures, shearing strains, and axial strain, depending on the laminate stiffness parameters. Laminate ply layup does not affect the location of the shear center in the thin-wall approximation, but may have a significant impact for thicker walled open sections. The average axial stress distribution is found to be distinctly different from the isotropic distribution, but the average shear stress distribution is the same as that in the isotropic case.

Zvarick, Albert G.↗

NASA NTRS1978

On Poisson's ratio for metal matrix composite laminates

The definition of Poisson's ratio for nonlinear behavior of metal matrix composite laminates is discussed and experimental results for tensile and compressive loading of five different boron-aluminum laminates are presented. It is shown that there may be considerable difference in the value of Poisson's ratio as defined by a total strain or an incremental strain definition. It is argued that the incremental definition is more appropriate for nonlinear material behavior. Results from a (0) laminate indicate that the incremental definition provides a precursor to failure which is not evident if the total strain definition is used.

Herakovich, C. T.↗