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At least 127 records · Page 7

Reliability analysis of ceramic matrix composite laminates

At a macroscopic level, a composite lamina may be considered as a homogeneous orthotropic solid whose directional strengths are random variables. Incorporation of these random variable strengths into failure models, either interactive or non-interactive, allows for the evaluation of the lamina reliability under a given stress state. Using a non-interactive criterion for demonstration purposes, laminate reliabilities are calculated assuming previously established load sharing rules for the redistribution of load as the failure of laminae occur. The matrix cracking predicted by ACK theory is modeled to allow a loss of stiffness in the fiber direction. The subsequent failure in the fiber direction is controlled by a modified bundle theory. Results using this modified bundle model are compared with previous models which did not permit separate consideration of matrix cracking, as well as to results obtained from experimental data.

Thomas, David J.↗

Symmetries in laminated composite plates

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Noor, A. K.↗

An Experimental and Analytical Evaluation of a Biaxial Test for Determining Shear Properties of Composite Materials

The results of an experimental and analytical investigation of a biaxial tension/compression test for determining shear properties of composite materials are reported. Using finite element models of isotropic and orthotropic laminates, a specimen geometry was optimized. A kinematic fixture was designed to introduce an equal and opposite pair of forces into a specimen with a one inch square test section. Aluminum and several composite laminates with the optimized geometry and a configuration with large stress gradients were tested in the fixture. The specimens were instrumented with strain gages in the center of the test section for shear stiffness measurements. Pure shear strain was measured. The results from the experiments correlated well with finite element results. Failure of the specimens occurred through the center of the test section and appeared to have initiated at the high stress points. The results lead to the conclusion that the optimized specimen is suitable for determining shear modulus for composite materials. Further revisions to the specimen geometry are necessary if the method is to give shear strength data.

Kennedy, John M.↗

A metal sheet stiffened by a partially debonded composite quarter-plate

An isotropic sheet stiffened by means of an orthotropic quarter-plate is considered. The quarter-plate is assumed to be perfectly bonded to the metal sheet everywhere except an area of debonding which may develop due to high stress concentrations. The adhesive which has a small constant thickness is treated as a shear spring. The loads are applied at infinity and supposed to be transmitted through the metal plate. Shear stress distribution between the two plates was obtained from the continuity of displacements along an area where they were bonded to each other.

Arin, K.↗

Stress concentration factors for cylindrically orthotropic plates

Stress concentration factors are presented for circular holes in circular composite plates of cylindrical orthotropy when the outer edge of the plate is subjected to uniform uniaxial traction. The values that can be calculated from the formulas presented and the values shown in the diagrams are valid rigorously only for the circular plate but they can be used as approximation for differently shaped (for instance, rectangular) finite plates also.

Hoff, N. J.↗

Characterization of elastic-plastic properties of AS4/APC-2 thermoplastic composite

Elastic and inelastic properties of AS4/APC-2 composites were characterized with respect to temperature variation by using a one-parameter orthotropic plasticity model and a one parameter failure criterion. Simple uniaxial off-axis tension tests were performed on coupon specimens of unidirectional AS4/APC-2 thermoplastic composite at various temperatures. To avoid the complication caused by the extension-shear coupling effect in off-axis testing, new tabs were designed and used on the test specimens. The experimental results showed that the nonlinear behavior of constitutive relations and the failure strengths can be characterized quite well using the one parameter plasticity model and the failure criterion, respectively.

Sun, C. T.↗

Analysis of cracked laminates with holes using the boundary force method

The boundary force method is an indirect boundary element technique for the analysis of composite laminates with holes and cracks which uses the orthotropic elasticity solution for a concentrated horizontal and vertical force applied at a given point in a cracked infinite sheet. The orthotropic formulation of the method is verified by comparison with accepted solutions for a counter-crack specimen that is subjected to uniaxial tension. Parametric studies are conducted for two configurations for which no orthotropic solutions are available: cracks emanating from a circular hole, and a four-hole cracked specimen; both are loaded in uniaxial tension.

Tan, P. W.↗

The effects of stress and physical aging on the creep compliance of a polymeric composite

An experimental study was performed to determine the effects of stress and physical aging on the matrix dominated viscoelastic properties of IM7/8320, a high temperature fiber reinforced thermoplastic composite. Established creep/aging test techniques developed for polymers were adapted for testing of the composite material. The transverse and shear compliance for an orthotropic plate were found from creep compliance measurements at constant, sub-Tg temperatures. These compliance terms were shown to be effected by physical aging. Aging time shift factors and shift rates were found to be a function of applied stress.

Gates, Thomas E.↗

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Mei, Chuh↗

Characterization of elastic-plastic behavior of AS4/PEEK thermoplastic composite for temperature variation

Inelastic and strength properties of AS4/PEEK composites were characterized with respect to temperature variation by using a one-parameter orthotropic plasticity model and a one-parameter failure criterion. Simple uniaxial off-axis tension tests were performed on coupon specimens of unidirectional AS4/PEEK thermoplastic composite at various temperatures. To avoid the complication caused by the extension-shear coupling effect in off-axis testing, new tabs were designed and used on the test specimens. Experimental results showed that the nonlinear behavior of constitutive relations and the strength can be characterized quite well using the one-parameter plasticity model and the failure criterion, respectively.

Sun, C. T.↗

Application of the MAT 213 Composite Impact Model to NASA Problems of Interest

A material model has been developed which incorporates several key capabilities which have been identified as lacking in currently available composite impact models. The material model utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength). The material model has been implemented into LS-DYNA® as MAT 213. The model can simulate the nonlinear deformation, damage and failure that takes place in a composite under dynamic loading conditions. The deformation model utilizes an orthotropic plasticity formulation. For the damage model, the nonlinear unloading response that is observed prior to the point where the peak stress is reached can be simulated, as well as the stress degradation response that occurs after the peak stress is reached. A variety of failure models, including a generalized tabulated failure model which facilitates the utilization of general failure surfaces, have been implemented into MAT 213. Recent studies at NASA have concentrated on using MAT 213 to analyze both the impact and crush response of a variety of laminated and textile architectures. Several of these studies will be discussed in the presented paper. For example, a woven carbon/Kevlar composite is currently being examined for use in an energy absorber system for rotorcraft structures. MAT 213 analyses have been conducted to examine the ability of the model to accurately simulate the dynamic crush response of this material. Studies are also being conducted to examine the ability of MAT 213 to simulate the ballistic impact response of representative laminated and woven thermoplastic and thermoset matrix composites. NASA efforts are also concentrated on developing methods and processes for improving characterization methods and developing “best practices” for using MAT 213, a summary of which will be discussed in the paper.

Polymer Matrix Composites↗

Multi-Scale Analysis of Effective Mechanical Properties of 3D Woven Composite Materials

This work aims to compute and analyze the mechanical properties of 3D woven composite materials that share the same yarn structure but differ in their matrix porosity and fiber volume fraction. Assuming linear elastic behavior, the software PuMA, developed at NASA, was used to characterize the different composites from their constituents' data averaging their elastic properties in three main directions to obtain their effective orthotropic mechanical properties. This was performed in three steps: firstly, the different phases (yarns/matrix) were analyzed as anisotropic materials separately at the micro-scale; then, the results from these analyses were homogenized and used to obtain the anisotropic elasticity tensor at the meso-scale for the different woven materials; and finally, assuming orthotropic mechanical behavior for the unit cell the mechanical properties were obtained at the macro-scale. The 3D woven composite materials selected for this study are made of phenolic resin with porosity values between 0 and 0.6, and resin infiltrated carbon fiber with volume fractions between 0.5 and 0.9 for the yarns. Results from PuMA were validated with external FEA simulations for the non-porous 3D woven material with a fiber volume fraction of 0.9 in the yarns. Results will be included in the final paper after completing the study detailed in Section II.

Sergio Fraile Izquierdo↗

Analysis of a finite composite plate with smooth rigid pin

An elastic continuum method of analysis developed for a smooth rigid pin in a finite composite plate by using complex potentials that satisfy the governing orthotropic differential equation is presented. The plate is subjected to uniaxial loading and the nonlinear problems of partial contact in the pin-plate are studied. Three types of pin fits are examined: interference, push, and clearance. The problems of stresses due to pure interference, load contact behavior, and stresses variations are addressed. The effects of the rectangular geometry and the orthotropic property of the plate are demonstrated through numerical results. It is found that the use of large hole diameter/plate width ratios have deleterious effects and the use of interference has beneficial effects. The solutions obtained will help in the development of special finite elements for fastener joints. Finally, the boundary conditions on the finite outer boundaries are found to be satisfied by a successive integration technique.

Naidu, A. C. B.↗

Predicted and measured strain response of rectangular panels due to acoustic loading

The objective of the research described in this paper is to assess the accuracy of classical linear acceleration/strain prediction theory for flat, rectangular panels excited by low level, acoustic plane waves. Predictions for both aluminum and laminated composite panels were based on the Ritz method using an orthotropic, multi-mode analysis with rotational springs on the boundaries. The measured natural frequencies and critical damping ratio of the panels were empirial inputs to the model. The comparison between measured and predicted acceleration was very good. Although a factor of three bias error was found between measured and predicted strains, the model was good for predicting the trends in the spatial variation in strain across the panel.

Roussos, L. A.↗

A three-node C deg element for analysis of laminated composite sandwich shells

A three-node flat shell element with C deg rotation fields has been developed for analysis of arbitrary composite shells. The element may consist of any number of orthotropic layers, each layer having different material properties and angular orientation. The formulation includes coupling between bending and extension, which is essential for analysis of unsymmetric laminates. Shearing deflections are included, since laminated and sandwich construction frequently results in shear stiffness much smaller than bending stiffness. Formulation of the element is straightforward, and calculation of its stiffness matrix is simple and fast. Convergence of solutions with mesh refinement is uniform for both thin and thick shells and is insensitive to element shape, although not as rapid as some other elements that lack one or more capabilities of the newly developed element. An experimental verification of the shall element is reported in the appendix.

Martin, C. Wayne↗

A stable numerical solution method in-plane loading of nonlinear viscoelastic laminated orthotropic materials

In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.

Gramoll, K. C.↗

Determination of Residual Stress in Composite Materials Using Ultrasonic Waves

The performance of high temperature composites can be significantly affected by the presence of residual stresses. These stresses arise during cooling processes from fabrication to room temperature due to mismatch of thermal expansion coefficients between matrix and fiber materials. This effect is especially pronounced in metal matrix and intermetallic composites. It can lead to plastic deformations, matrix cracking and fiber/matrix interface debonding. In this work the feasibility of ultrasonic techniques for residual stress assessment in composites is addressed. A novel technique for absolute stress determination in orthotropic materials from angular dependencies of ultrasonic velocities is described. The technique is applicable for determination of both applied and residual stresses and does not require calibration measurements on a reference sample. The important advantage of this method is that stress is determined simultaneously with stress-dependent elastic constants and is thus decoupled from the material texture. It is demonstrated that when the principal plane stress directions coincide with acoustical axes, the angular velocity data in the plane perpendicular to the stress plane may be used to determine both stress components. When the stress is off the acoustical axes, the shear and the difference of the normal stress components may be determined from the angular dependence of group velocities in the plane of stresses. Synthetic sets of experimental data corresponding to materials with different anisotropy and stress levels are used to check the applicability of the technique. The method is also verified experimentally. A high precision ultrasonic wave transmission technique is developed to measure angular dependence of ultrasonic velocities. Examples of stress determination from experimental velocity data are given. A method is presented for determination of velocities of ultrasonic waves propagating through the composite material with residual stresses. It is based on the generalized self-consistent multiple scattering model. Calculation results for longitudinal and shear ultrasonic wave velocities propagating perpendicular to the fibers direction in SCS-6/Ti composite with and without residual stresses are presented. They show that velocity changes due to presence of stresses are of order 1%.

Rokhlin, S. I.↗

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.↗