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At least 145 records · Page 8

The buckling response of symmetrically laminated composite plates having a trapezoidal planform area

The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms Nx=P/W(x) and Ny=Nxy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of-plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5 percent, in general, and within 15 percent for the worst cases. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the analytical results regarding the buckling load and the prebuckling plate stiffness. However, the experimental results show that for some cases the analysis underpredicts the number of halfwaves in the buckled mode shape. In the context of the definitions of taper ratio and aspect ratio used in this study, it is concluded that the buckling load always increases as taper ratio increases for a given aspect ratio for plates having simply supported boundary conditions on the parallel ends. There are combinations of plate geometry and ply stackling sequences, however, that reverse this trend for plates having clamped boundary conditions on the parallel ends such that an increase in the taper ratio causes a decrease in the buckling load. The clamped boundary conditions on the parallel ends of the plate are shown to increase the buckling load compared to simply supported boundary conditions. Also, anisotropy (the D16 and D26 terms) is shown to decrease the buckling load and skew the buckled mode shape for both the simply supported and clamped boundary conditions.

Radloff, H. D., II↗

The stress distribution in pin-loaded orthotropic plates

The performance of mechanically fastened composite joints was studied. Specially, a single-bolt connector was modeled as a pin-loaded, infinite plate. The model that was developed used two dimensional, complex variable, elasticity techniques combined with a boundary collocation procedure to produce solutions for the problem. Through iteration, the boundary conditions were satisfied and the stresses in the plate were calculated. Several graphite epoxy laminates were studied. In addition, parameters such as the pin modulus, coefficient of friction, and pin-plate clearance were varied. Conclusions drawn from this study indicate: (1) the material properties (i.e., laminate configuration) of the plate alter the stress state and, for highly orthotropic materials, the contact stress deviates greatly from the cosinusoidal distribution often assumed; (2) friction plays a major role in the distribution of stresses in the plate; (3) reversing the load direction also greatly effects the stress distribution in the plate; (4) clearance (or interference) fits change the contact angle and thus the location of the peak hoop stress; and (5) a rigid pin appears to be a good assumption for typical material systems.

Klang, E. C.↗

Stress decay in an orthotropic half-plane under self-equilibrating sinusoidal loading

An elastic orthotropic half-plane subjected to sinusoidal normal loading along an entire straight edge is analyzed. Stresses are calculated for material property combinations which are representative of some unidirectional fiber reinforced composites and of (+ or - 45) (subs) laminates made from the same unidirectional materials. Plots of the stresses as functions of the distance from the loaded boundary show that they can differ greatly from their counterparts in the isotropic half-plane under the same loading. How the results impact the question of the applicability of St. Venant's principle to orthotropic materials is briefly discussed.

Fichter, W. B.↗

Generic buckling curves for specially orthotropic rectangular plates

Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

Brunnelle, E. J.↗

Determination of calibration constants for the hole-drilling residual stress measurement technique applied to orthotropic composites. I - Theoretical considerations

The hole-drilling technique for the measurement of residual stresses using electrical resistance strain gages has been widely used for isotropic materials and has been adopted by the ASTM as a standard method. For thin isotropic plates, with a hole drilled through the thickness, the idealized hole-drilling calibration constants are obtained by making use of the well-known Kirsch's solution. In this paper, an analogous attempt is made to theoretically determine the three idealized hole-drilling calibration constants for thin orthotropic materials by employing Savin's (1961) complex stress function approach.

Prasad, C. B.↗

Using Tabulated Experimental Data to Drive an Orthotropic Elasto-Plastic Three-Dimensional Model for Impact Analysis

An orthotropic elasto-plastic-damage three-dimensional model with tabulated input has been developed to analyze the impact response of composite materials. The theory has been implemented as MAT 213 into a tailored version of LS-DYNA being developed under a joint effort of the FAA and NASA and has the following features: (a) the theory addresses any composite architecture that can be experimentally characterized as an orthotropic material and includes rate and temperature sensitivities, (b) the formulation is applicable for solid as well as shell element implementations and utilizes input data in a tabulated form directly from processed experimental data, (c) deformation and damage mechanics are both accounted for within the material model, (d) failure criteria are established that are functions of strain and damage parameters, and mesh size dependence is included, and (e) the theory can be efficiently implemented into a commercial code for both sequential and parallel executions. The salient features of the theory as implemented in LS-DYNA are illustrated using a widely used composite - the T800S/3900-2B[P2352W-19] BMS8-276 Rev-H-Unitape fiber/resin unidirectional composite. First, the experimental tests to characterize the deformation, damage and failure parameters in the material behavior are discussed. Second, the MAT213 input model and implementation details are presented with particular attention given to procedures that have been incorporated to ensure that the yield surfaces in the rate and temperature dependent plasticity model are convex. Finally, the paper concludes with a validation test designed to test the stability, accuracy and efficiency of the implemented model.

Polymer Matrix Composites↗

BUCKLING OF LAYERED ORTHOTROPIC AND SANDWICH CYLINDRICAL SHELLS IN AXIAL COMPRESSION

Results of modifications of large-deflection theory for isotropic materials to shells constructed of orthotropic layers and sandwich are presented. Experimental evaluation of the buckling of a rather extensive series of plywood cylinders and of a few curved panels of sandwich construction shows reasonably good agreement with buckling predicted by theory.

BUCKLING↗

Effects of aeroconvective environments on 2D reinforced ceramic matrix composites

The effect of aeroconvective heating environment similar to that observed a spacecraft ascent or reentry from orbit, on the performance of a commercial carbon-reinforced ceramic matrix material specimens of two configurations (orthotropic and quasi-isotropic), fabricated by the Societe Europenne Propulsion (SEP) process was investigated using the NASA Ames Research Center 20 Megawatt Panel Test facility. The performance of the commercial material was compared with the SEP prepared materials. It was found that, whereas the quasi-isotropic SEP specimens exhibited a much higher mass loss rate and a significant dimensional change upon exposure to the thermal environment than did the orthotropic ones, the commercial SEP-like materials did not exhibit these characteristics. There was no greater mass loss rate for the quasi-isotropic specimens, and no dimension changes were observed. The Nicalon reinforced materials in both configurations, as fabricated by SEP or by the commercial source, showed no mass changes and no dimensional changes.

Riccitiello, Salvatore R.↗

An assessment of the accuracy of orthotropic photoelasticity

The accuracy of orthotropic photoelasticity was studied. The study consisted of both theoretical and experimental phases. In the theoretical phase a stress-optic law was developed. The stress-optic law included the effects of residual birefringence in the relation between applied stress and the material's optical response. The experimental phase had several portions. First, it was shown that four-point bending tests and the concept of an optical neutral axis could be conveniently used to calibrate the stress-optic behavior of the material. Second, the actual optical response of an orthotropic disk in diametral compression was compared with theoretical predictions. Third, the stresses in the disk were determined from the observed optical response, the stress-optic law, and a finite-difference form of the plane stress equilibrium equations. It was concluded that orthotropic photoelasticity is not as accurate as isotropic photoelasticity. This is believed to be due to the lack of good fringe resolution and the low sensitivity of most orthotropic photoelastic materials.

Hyer, M. W.↗

Stability optimization of laminated composite plates

The optimum design of plates with orthotropic layers under axial compression and shear is discussed. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of + alpha sub i and - alpha sub i with respect to the plate axis. The fiber directions which give the highest axial buckling stress and the highest shear buckling stress are found by utilizing a mathematical optimization technique for various aspect ratios of the plates. Inhomogeneity in the direction of the plate thickness (stacking sequence) is taken into account in this analysis.

Hirano, Y.↗

Optimum design of laminated plates under shear

This paper is concerned with the optimum design of plates with orthotropic layers under shear. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of + alpha sub i and - alpha sub i with respect to the plate axis. The fiber directions which give the highest shear buckling stress are found by utilizing a mathematical optimization technique.

Hirano, Y.↗

Effects of transverse shearing flexibility on the postbuckling of plates loaded by inplane shear

This paper presents buckling and postbuckling results for plates loaded by inplane shear. The buckling results have been plotted to show the effects of thickness on the stress coefficient for aluminum plates. Results are given for various length-to-width ratios. Postbuckling results for thin plates with transverse shearing flexibility are compared to results from classical theory. The problems considered are the postbuckling response of plates in shear made of aluminum and of a + or - 45 deg graphite-epoxy laminate. Thus the materials are isotropic and orthotropic, respectively. The plates are considered to be long with side edges simply supported, with various inplane edge conditions, and the plates are subject to a constant shearing displacement along the side edges. Characteristic curves presenting the average shear stress resultant as a function of the applied displacement are given. These curves indicate that change in inplane edge conditions influence plate postbuckling stiffness and that transverse shearing is important in some cases.

Stein, Manuel↗

Current status of the Iosipescu shear test method

During the past several years, considerable study of the Iosipescu shear test method has been conducted by a number of investigators, including the present authors. Several different test fixture designs have been developed, and variations of the specimen size and notch configuration have been considered. Materials with properties ranging from isotropic to highly orthotropic have been tested. The response of such materials has also been predicted using finite element techniques, and attempts have been made to correlate these predictions with available experimental data. This recent work is summarized here, with particular emphasis being given to the correlations and contradictions resulting from the published works of these various investigators.

Adams, Donald F.↗

Effects of fiber and interfacial layer architectures on the thermoplastic response of metal matrix composites

Examined here is the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs). A micromechanics model based on an arbitrarily layered concentric cylinder configuration is used to calculate thermal stress fields in MMCs subjected to spatially uniform temperature changes. The fiber is modelled as a layered material with isotropic or orthotropic elastic layers, whereas the surrounding matrix, including interfacial layers, is treated as a strain-hardening, elastoplastic, von Mises solid with temperature-dependent parameters. The solution to the boundary-value problem of an arbitrarily layered concentric cylinder under the prescribed thermal loading is obtained using the local/global stiffness matrix formulation originally developed for stress analysis of multilayered elastic media. Examples are provided that illustrate how the morphology of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface affect the evolution of residual stresses in SiC/Ti composites during fabrication cool-down.

Pindera, Marek-Jerzy↗

Verification of a three-dimensional resin transfer molding process simulation model

Experimental evidence was obtained to complete the verification of the parameters needed for input to a three-dimensional finite element model simulating the resin flow and cure through an orthotropic fabric preform. The material characterizations completed include resin kinetics and viscosity models, as well as preform permeability and compaction models. The steady-state and advancing front permeability measurement methods are compared. The results indicate that both methods yield similar permeabilities for a plain weave, bi-axial fiberglass fabric. Also, a method to determine principal directions and permeabilities is discussed and results are shown for a multi-axial warp knit preform. The flow of resin through a blade-stiffened preform was modeled and experiments were completed to verify the results. The predicted inlet pressure was approximately 65% of the measured value. A parametric study was performed to explain differences in measured and predicted flow front advancement and inlet pressures. Furthermore, PR-500 epoxy resin/IM7 8HS carbon fabric flat panels were fabricated by the Resin Transfer Molding process. Tests were completed utilizing both perimeter injection and center-port injection as resin inlet boundary conditions. The mold was instrumented with FDEMS sensors, pressure transducers, and thermocouples to monitor the process conditions. Results include a comparison of predicted and measured inlet pressures and flow front position. For the perimeter injection case, the measured inlet pressure and flow front results compared well to the predicted results. The results of the center-port injection case showed that the predicted inlet pressure was approximately 50% of the measured inlet pressure. Also, measured flow front position data did not agree well with the predicted results. Possible reasons for error include fiber deformation at the resin inlet and a lag in FDEMS sensor wet-out due to low mold pressures.

Fingerson, John C.↗

Mechanical property characterization and impact resistance of selected graphite/PEEK composite materials

To use graphite/PEEK material on highly curved surfaces requires that the material be drapable and easily conformable to the surface. The mechanical property characterization and impact resistance results are presented for laminates made from two types of graphite/PEEK materials that will conform to a curved surface. These laminates were made from two different material forms. These forms are: (1) a fabric where each yarn is a co-mingled Celion G30-500 3K graphite fiber and PEEK fiber; and (2) an interleaved material of Celion G30-500 3K graphite fiber interleaved with PEEK film. The experimental results from the fabric laminates are compared with results for laminates made from AS4/PEEK unidirectional tape. The results indicate that the tension and compression moduli for quasi-isotropic and orthotropic laminates made from fabric materials are at least 98 pct. of the modulus of equivalent laminates made from tape materials. The strength of fabric material laminates is at least 80 pct. of laminates made from tape material. The evaluation of the fabric material for shear stiffness indicates that a tape material laminate could be replaced by a fabric material laminate and still maintain 89 pct. of the shear stiffness of the tape material laminate.

Baker, Donald J.↗

Mechanical property characterization and impact resistance of selected graphite/PEEK composite materials

To use graphite polyetheretherketone (PEEK) material on highly curved surfaces requires that the material be drapable and easily conformable to the surface. This paper presents the mechanical property characterization and impact resistance results for laminates made from two types of graphite/PEEK materials that will conform to a curved surface. These laminates were made from two different material forms. These forms are: (1) a fabric where each yarn is a co-mingled Celion G30-500 3K graphite fiber and PEEK thermoplastic fiber; and (2) an interleaved material of Celion G30-500 3K graphite fabric interleaved with PEEK thermoplastic film. The experimental results from the fabric laminates are compared with results for laminates made from AS4/PEEK unidirectional tape. The results indicate that the tension and compression moduli for quasi-isotropic and orthotropic laminates made from fabric materials are at least 79 percent of the modulus of equivalent laminates made from tape material. The strength of fabric material laminates is at least 80 percent of laminates made from tape material. The evaluation of fabric material for shear stiffness indicates that a tape material laminate could be replaced by a fabric material laminate and still maintain 89 percent of the shear stiffness of the tape material laminate. The notched quasi-isotropic compression panel failure strength is 42 to 46 percent of the unnotched quasi-isotropic laminate strength. Damage area after impact with 20 ft-lbs of impact energy is larger for the co-mingled panels than for the interleaved panels. The inerleaved panels have less damage than panels made from tape material. Residual compression strength of quasi-isotropic panels after impact of 20 ft-lbs of energy varies between 33 percent of the undamaged quasi-isotropic material strength for the tape material and 38 percent of the undamaged quasi-isotropic material strength for the co-mingled fabric material.

Baker, Donald J.↗

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

We report numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

42 ENGINEERING↗