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NASA NTRS1987

Study of matrix cracking and delamination in glass/epoxy laminates

This study focused on characterizing matrix cracking and delamination behavior in multidirectional laminates. Static tension and tension-tension fatigue tests were conducted on two different layups. Damage onset, accumulation, and residual properties were measured. Matrix cracking was shown to have a considerable influence on residual stiffness of glass epoxy laminates, and could be predicted reasonably well for cracks in 90 deg piles using a simple shear lag analysis. A fracture mechanics analysis for the strain energy release rate associated with 90 deg ply-matrix crack formation was developed and was shown to correlate the onset of 90 deg ply cracks in different laminates. The linear degradation of laminate modulus with delamination area, previously observed for graphite epoxy laminates, was predicted for glass epoxy laminates using a simple rule of mixtures analysis. The strain energy release rate associated with edge delamination formation under static and cyclic loading was difficult to analyze because of the presence of several contemporary damage phenomena.

Caslini, Massimo↗

NASA NTRS1989

Effect of adhesive interleaving and discontinuous plies on failure of composite laminates subject to transverse normal loads

Results of a series of tests to determine the effects of adhesive interleaving and discontinuous plies (plies with end-to-end gaps) on the displacements, failure loads and failure modes of graphite-epoxy laminates subjected to transverse normal loads are presented. Adhesive interleaving can be used to contain local damage within a group of plies, i.e., to arrest crack propagation on the interlaminate level, and it can increase the amount of normal displacement the laminate can withstand before failure. However, the addition of adhesive interleaving to a laminate does not significantly increase its load carrying capability. A few discontinuous plies in a laminate can reduce the normal displacement and load at failure by 10 to 40 percent compared to a laminate with no discontinuous plies, but the presence of the ply discontinuities does not generally change the failure location or the failure mode of the laminate.

Jegley, Dawn C.↗

NASA NTRS1988

Analysis of delamination growth from matrix cracks in laminates subjected to bending loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, Gretchen Bostaph↗

NASA NTRS1989

Composite laminate free-edge reinforcement with U-shaped caps. I - Stress analysis. II - Theoretical-experimental correlation

The present generalized plane-strain FEM analysis for the prediction of interlaminar normal stress reduction when a U-shaped cap is bonded to the edge of a composite laminate gives attention to the highly variable transverse stresses near the free edge, cap length and thickness, and a gap under the cap due to the manufacturing process. The load-transfer mechanism between cap and laminate is found to be strain-compatibility, rather than shear lag. In the second part of this work, the three-dimensional composite material failure criteria are used in a progressive laminate failure analysis to predict failure loads of laminates with different edge-cap designs; symmetric 11-layer graphite-epoxy laminates with a one-layer cap of kevlar-epoxy are shown to carry 130-140 percent greater loading than uncapped laminates, under static tensile and tension-tension fatigue loading.

Howard, W. E.↗

NASA NTRS1989

Predictions of Poisson's ratio in cross-ply laminates containing matrix cracks and delaminations

A damage-dependent constitutive model for laminated composites has been developed for the combined damage modes of matrix cracks and delaminations. The model is based on the concept of continuum damage mechanics and uses second-order tensor valued internal state variables to represent each mode of damage. The internal state variables are defined as the local volume average of the relative crack face displacements. Since the local volume for delaminations is specified at the laminate level, the constitutive model takes the form of laminate analysis equations modified by the internal state variables. Model implementation is demonstrated for the laminate engineering modulus E(x) and Poisson's ratio nu(xy) of quasi-isotropic and cross-ply laminates. The model predictions are in close agreement to experimental results obtained for graphite/epoxy laminates.

Harris, Charles E.↗

NASA NTRS1991

A continuum model for damage evolution in laminated composites

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

Lo, D. C.↗

NASA NTRS1992

A micromechanics-based progressive failure model for laminated composite structures

A micromechanics-based mechanistic model for progressive failure analysis of laminated composite shell structures is developed. A finite-element program for laminated shell analysis is coupled with a micromechanical elasticity solution for predicting failure and effective composite properties. The laminate model is based on a third-order shell theory which allows for both transverse normal and shearing deformations. Results are presented for the progressive failure of a (0/90(4)s graphite/epoxy laminate under uniaxial tension. The effect of fiber volume fraction in the 90-deg plies on laminate behavior was studied, and it was found that decreasing the fiber-volume fraction in the off-axis plies did not affect the laminate stiffness or the ultimate failure load, but significantly increased the load at which initial failure occurred.

Averill, R. C.↗

NASA NTRS1992

Tailored metal matrix laminates for high-temperature performance

A multi-objective tailoring methodology is presented to maximize stiffness and load carrying capacity of a metal matrix cross-ply laminated at elevated temperatures. The fabrication process and fiber volume ratio are used as the design variables. A unique feature is the concurrent effects from fabrication, residual stresses, material nonlinearity, and thermo-mechanical loading on the laminate properties at the post-fabrication phase. For a (0.90) (sub s) graphite/copper laminate, strong coupling was observed between the fabrication process, laminate characteristics, and thermo-mechanical loading. The multi-objective tailoring was found to be more effective than single objective tailoring. Results indicate the potential to increase laminate stiffness and load carrying capacity by controlling the critical parameters of the fabrication process and the laminate.

Morei, Michael R.↗

NASA NTRS1991

A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading

An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.

Norwood, D. S.↗

NASA NTRS1991

Thermo-mechanical response predictions for metal matrix composite laminates

An analytical micromechanical model is employed for prediction of the stress-strain response of metal matrix composite laminates subjected to thermomechanical loading. The predicted behavior of laminates is based upon knowledge of the thermomechanical response of the transversely isotropic, elastic fibers and the elastic-viscoplastic, work-hardening matrix. The method is applied to study the behavior of silicon carbide/titanium metal matrix composite laminates. The response of laminates is compared with that of unidirectional lamina. The results demonstrate the effect of cooling from a stress-free temperature and the mismatch of thermal and mechanical properties of the constituent phases on the laminate's subsequent mechanical response. Typical results are presented for a variety of laminates subjected to monotonic tension, monotonic shear and cyclic tensile/compressive loadings.

Aboudi, J.↗

NASA NTRS1992

Tension fracture of laminates for transport fuselage. Part 1: Material screening

Transport fuselage structures are designed to contain pressure following a large penetrating damage event. Application of composites to fuselage structures requires a data base and supporting analysis on tension damage tolerance. Tests with 430 fracture specimens were used to accomplish the following: (1) identify critical material and laminate variables affecting notch sensitivity, (2) evaluate composite failure criteria, and (3) recommend a screening test method. Variables studied included fiber type, matrix toughness, lamination manufacturing process, and intraply hybridization. The laminates found to have the lowest notch sensitivity were manufactured using automated tow placement. This suggests a possible relationship between the stress distribution and repeatable levels of material inhomogeneity that are larger than found in traditional tape laminates. Laminates with the highest notch sensitivity consisted of toughened matrix materials that were resistant to a splitting phenomena that reduces stress concentrations in load bearing plies. Parameters for conventional fracture criteria were found to increase with the crack length of the smallest notch sizes studied. Most materials and laminate combinations followed less than a square root singularity for the largest crack sizes studied. Specimen geometry, notch type, and notch size were evaluated in developing a screening test procedure. Results indicate that a range of notch sizes must be tested to determine notch sensitivity.

Walker, T. H.↗

NASA NTRS1992

Higher order finite element analysis of thick composite laminates

A higher order, sub-parametric, laminated, 3D solid finite element was used for the analysis of very thick laminated composite plates. The geometry of this element is defined by four nodes in the X-Y plane which define a prism of material through the thickness of the laminate. There are twenty-four degrees of freedom at each node; translations at the upper and lower surfaces of the laminate in each of the three coordinate directions, and the derivatives of these translations with respect to each coordinate. This choice of degrees of freedom leads to displacement and strain compatibility at the corners. Stacking sequence effects are accounted for by explicitly integrating the strain energy density through the thickness of the element. The laminated solid element was combined with a gap-contact element to analyze thick laminated composite lugs loaded through flexible pins. The resulting model accounts for pin bending effects that produce non-uniform bearing stresses through the thickness of the lug. A thick composite lug experimental test program was performed, and provided data that was used to validate the analytical model. Two lug geometries and three stacking sequences were tested.

Goering, J.↗

NASA NTRS1993

Response of automated tow placed laminates to stress concentrations

In this study, the response of laminates with stress concentrations is explored. Automated Tow Placed (ATP, also known as Fiber Placement) laminates are compared to conventional tape layup manufacturing. Previous tensile fracture tests on fiber placed laminates show an improvement in tensile fracture of large notches over 20 percent compared to tape layup laminates. A hierarchial modeling scheme is presented. In this scheme, a global model is developed for laminates with notches. A local model is developed to study the influence of inhomogeneities at the notch tip, which are a consequence of the fiber placement manufacturing technique. In addition, a stacked membrane model was developed to study delaminations and splitting on a ply-by-ply basis. The results indicate that some benefit with respect to tensile fracture (up to 11 percent) can be gained from inhomogeneity alone, but that the most improvement may be obtained with splitting and delaminations which are more severe in the case of fiber placement compared to tape layup. Improvements up to 36 percent were found from the model for fiber placed laminates with damage at the notch tip compared to conventional tape layup.

Cairns, Douglas S.↗

NASA NTRS1995

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

A comparison of the 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 materials system used for the laminates is AS4/3501-6 which was chosen as the closest available match to As4/1895 used for the braids. 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. Results show that the longitudinal modulus of both material forms is quite similar, but that the transverse modulus of the braids is lower. In terms of strength, the longitudinal unnotched strength of the braids is lower than that of the laminates, while the transverse strength is significantly lower. For both strength and stiffness, the crimp in the bias tows of the braid is probably the main cause for reduced properties. On the other hand, a very significant increase in open-hole and filled-hole tension strength was observed for the braids compared to the tape laminates. However, this was not observed in compression where all the braid properties are lower than for the laminates.

Minguet, Pierre J.↗

NASA NTRS1996

Coupled mixed-field laminate theory and finite element for smart piezoelectric composite shell structures

Mechanics for the analysis of laminated composite shells with piezoelectric actuators and sensors are presented. A new mixed-field laminate theory for piezoelectric shells is formulated in curvilinear coordinates which combines single-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an 8-node finite-element is formulated for the static and dynamic analysis of adaptive composite structures of general laminations containing piezoelectric layers. Evaluations of the method and comparisons with reported results are presented for laminated piezoelectric-composite plates, a closed cylindrical shell with a continuous piezoceramic layer and a laminated composite semi-circular cantilever shell with discrete cylindrical piezoelectric actuators and/or sensors.

Saravanos, Dimitris A.↗

NASA NTRS1997

Tracer Lamination in the Stratosphere: A Global Climatology

Vertical soundings of stratospheric ozone often exhibit laminated tracer structures characterized by strong vertical tracer gradients. The change in time of these gradients is used to define a tracer lamination rate. It is shown that this quantity can be calculated by the cross product of the horizontal temperature and horizontal tracer gradients. A climatology based on UARS satellite-borne ozone data and on ozone-like pseudotracer data is presented. Three stratospheric regions with high lamination rates were found: the part of the stratospheric overworld which is influenced by the polar vortex, the part of the lowermost stratosphere which is influenced by the tropopause and a third region in the subtropical lower stratosphere mainly characterized with strong vertical shear. High lamination rates in the stratospheric overworld were absent during summer, whereas in the lowermost stratosphere high lamination rates were found year-round. This is consistent with the occurrence and seasonal variation of the horizontal tracer gradient and vertical shear necessary for tilting the tracer surfaces. During winter, high lamination rates associated with the stratospheric polar vortex are present down to approximately 100 hPa. Several features of the derived climatology are roughly consistent with earlier balloon-borne studies. The patterns in the southern and northern hemisphere are comparable, but details differ as anticipated from a less disturbed and more symmetric southern polar vortex.

Appenzeller, Christof↗

NASA NTRS2000

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.

Nemeth, Michael P.↗

NASA NTRS2006

Nonlinear Spring Finite Elements for Predicting Mode I-Dominated Delamination Growth in Laminated Structure with Through-Thickness reinforcement

One particular concern of polymer matrix composite laminates is the relatively low resistance to delamination cracking, in particular when the dominant type of failure is mode I opening. One method proposed for alleviating this problem involves the insertion pultruded carbon pins through the laminate thickness. The pins, known as z-pins, are inserted into the prepreg laminate using an ultrasonic hammer prior to the curing process, resulting in a field of pins embedded normal to the laminate plane as illustrated in Figure. 1. Pin diameters range between 0.28-mm to 0.5-mm and standard areal densities range from 0.5% to 4%. The z-pins are provided by the manufacturer, Aztex(Registered TradeMark) , in a low-density foam preform, which acts to stabilize orientation of the pins during the insertion process [1-3]. Typical pin materials include boron and carbon fibers embedded in a polymer matrix. A number of methods have been developed for predicting delamination growth in laminates reinforced with z-pins. During a study on the effect of z-pin reinforcement on mode I delamination resistance, finite element analyses of z-pin reinforced double cantilever beam (DCB) specimens were performed by Cartie and Partridge [4]. The z-pin bridging stresses were modeled by applying equivalent forces at the pin locations. Single z-pin pull-out tests were performed to characterize the traction law of the pins under mode I loading conditions. Analytical solutions for delamination growth in z-pin reinforced DCB specimens were independently derived by Robinson and Das [5] and Ratcliffe and O'Brien [6]. In the former case, pin bridging stresses were modeled using a distributed load and in the latter example the bridging stresses were discretely modeled by way of grounded springs. Additionally, Robinson and Das developed a data reduction strategy for calculating mode I fracture toughness, G(sub Ic), from a z-pin reinforced DCB specimen test [5]. In both cases a traction law similar to that adopted by Cartie and Partridge was used to represent z-pin failure under mode I loading conditions. In the current work spring elements available in most commercial finite element codes were used to model z-pins. The traction law used in previous analyses [4-6] was employed to represent z-pin damage. This method is intended for and is limited to simulating z-pins in composite laminate structure containing mode I-dominated delamination cracking. The current technique differs from previous analyses in that spring finite elements (available in commercial codes) are employed for simulating zpins, reducing the complexity of the analysis construction process. Furthermore, the analysis method can be applied to general structure that experiences mode I-dominated delamination cracking, in contrast to existing analytical solutions that are only applicable to coupon DCB specimens.

Ratcliffe, James G.↗