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Micromechanical Modeling of High-Strain Thin-Ply Composites

This paper presents a micromechanical analysis for the elastic and viscoelastic behavior of high-strain thin-ply composites. The modeling approach is based on unit cell homogenization. The geometry of the internal weave architecture and ply configuration is characterized via micrographic analysis and explicitly modeled in the unit cell. The composites are modeled as Kirchhoff plates and the homogenization analysis computes the effective relaxation ABD matrix represented by Prony series using the elastic and viscoelastic properties of the constituent fiber and matrix. The formulation of the micromechanical model and numerical implementation d. Composite laminates with 3-ply and 4-ply configurations are studied.

Hamillage, Milinda Yapa↗

Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites

The results presented here are part of an ongoing research program to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric matrix materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical 5 plasticity theory definitions of effective stress and effective plastic strain are modified by applying variations of the Drucker-Prager yield criterion. To verify the revised formulation, the shear and tensile deformation of a representative toughened epoxy is analyzed across a wide range of strain rates (from quasi-static to high strain rates) and the results are compared to experimentally obtained values. For the analyzed polymers, both the tensile and shear stress-strain curves computed using the analytical model correlate well with values obtained through experimental tests. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. In the micromechanics, the unit cell is divided up into a number of independently analyzed slices, and laminate theory is then applied to obtain the effective deformation of the unit cell. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite (composed using the representative polymer analyzed for the correlation of the polymer constitutive equations) for several fiber orientation angles across a variety of strain rates. The computed values compare favorably to experimentally obtained results.

Goldberg, Robert K.↗

Hydrostatic Stress Effects Incorporated Into the Analysis of the High-Strain-Rate Deformation of Polymer Matrix Composites

Procedures for modeling the effect of high strain rate on composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and strain rate dependence of the composite response is primarily due to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. An experimental program has been carried out through a university grant with the Ohio State University to obtain tensile and shear deformation data for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used at the NASA Glenn Research Center to develop, characterize, and correlate a material model in which the strain rate dependence and nonlinearity (including hydrostatic stress effects) of the polymer are correctly analyzed. To obtain the material data, Glenn s researchers designed and fabricated test specimens of a representative toughened epoxy resin. Quasi-static tests at low strain rates and split Hopkinson bar tests at high strain rates were then conducted at the Ohio State University. The experimental data confirmed the strong effects of strain rate on both the tensile and shear deformation of the polymer. For the analytical model, Glenn researchers modified state variable constitutive equations previously used for the viscoplastic analysis of metals to allow for the analysis of the nonlinear, strain-rate-dependent polymer deformation. Specifically, we accounted for the effects of hydrostatic stresses. An important discovery in the course of this work was that the hydrostatic stress effects varied during the loading process, which needed to be accounted for within the constitutive equations. The model is characterized primarily by shear data, with tensile data used to characterize the hydrostatic stress effects.

Goldberg, Robert K.↗

Incorporation of Mean Stress Effects into the Micromechanical Analysis of the High Strain Rate Response of Polymer Matrix Composites

The results presented here are part of an ongoing research program, to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. A micromechanics approach is employed in this work, in which state variable constitutive equations originally developed for metals have been modified to model the deformation of the polymer matrix, and a strength of materials based micromechanics method is used to predict the effective response of the composite. In the analysis of the inelastic deformation of the polymer matrix, the definitions of the effective stress and effective inelastic strain have been modified in order to account for the effect of hydrostatic stresses, which are significant in polymers. Two representative polymers, a toughened epoxy and a brittle epoxy, are characterized through the use of data from tensile and shear tests across a variety of strain rates. Results computed by using the developed constitutive equations correlate well with data generated via experiments. The procedure used to incorporate the constitutive equations within a micromechanics method is presented, and sample calculations of the deformation response of a composite for various fiber orientations and strain rates are discussed.

Goldberg, Robert K.↗

Practical approaches for application of resistance type strain gages on high temperature composites

Four major areas of interest with respect to utilizing strain gages on carbon/carbon (with SiC surfaces) and titanium matrix composites are addressed. Strain gage and adhesive combinations on carbon/carbon (C/C) at temperatures from minus 190 C to to 540 C, half-bridge gaging for reducing apparent strain on C/C using Poisson's ratio and bending configurations, a review of the 'field installation' techniques developed for gaging a C/C hypersonic generic elevon, and results of initial strain gaging efforts on titanium matrix composites are discussed. Current research in developing techniques for increasing the maximum temperature for strain gages on carbon/carbon are reviewed.

Moore, Thomas C., Sr.↗

Practical approaches for application of hi-temperature strain gages on high temperature composites

Four major areas of interest with respect to utilizing strain gages on carbon/carbon (with SiC surfaces) and titanium matrix composites are addressed. Strain gage and adhesive combinations on carbon/carbon (C/C) at temperatures from minus 190 C to 540 C, half-bridge gaging for reducing apparent strain on C/C using Poisson's ratio and bending configurations, review of the 'field installation' techniques developed for gaging a C/C hypersonic generic elevon, and results of initial strain gaging efforts on titanium matrix composites are discussed. Current research in developing techniques for increasing the maximum temperature for strain gages on carbon/carbon are reviewed.

Moore, Thomas C., Sr.↗

Environmental effects on high strain rate properties of graphite/epoxy composite

The effects of hygrothermal conditions on the high-strain-rate properties of a unidirectional graphite/epoxy material, AS4/3501-6, were evaluated using standard physical and mechanical tests to determine the properties of the lamina. A time-temperature-moisture equivalence principle was applied to obtain master curves for the longitudinal, transverse, and in-plane shear moduli and corresponding strengths and ultimate strains of the specimens. It was found that the longitudinal properties of the material remained unchanged at all conditions, except for the longitudinal modulus, which showed a slight increase with temperature, moisture, and strain rate. On the other hand, all transverse and intralaminar shear properties were found to decrease with increasing temperature and moisture contents at a fixed strain rate.

Yaniv, Gershon↗

Computational Simulation of the High Strain Rate Tensile Response of Polymer Matrix Composites

A research program is underway to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Under these types of loading conditions, the material response can be highly strain rate dependent and nonlinear. State variable constitutive equations based on a viscoplasticity approach have been developed to model the deformation of the polymer matrix. The constitutive equations are then combined with a mechanics of materials based micromechanics model which utilizes fiber substructuring to predict the effective mechanical and thermal response of the composite. To verify the analytical model, tensile stress-strain curves are predicted for a representative composite over strain rates ranging from around 1 x 10(exp -5)/sec to approximately 400/sec. The analytical predictions compare favorably to experimentally obtained values both qualitatively and quantitatively. Effective elastic and thermal constants are predicted for another composite, and compared to finite element results.

Goldberg, Robert K.↗

Environmental and high strain rate effects on composites for engine applications

The complex environmental and loading conditions experienced by many turbine engine components impose severe durability and damage tolerance requirements for component materials. Programs are being conducted to establish the structural performance of composite materials under anticipated engine operating environments. A description is presented of the results obtained in connection with several of these programs. A comparison of predicted and measured hygrothermal effects is considered along with hygrothermal effects on defect growth, high strain rate effects on composite mechanical properties, dynamic stress intensity factors for composites, and the indentation laws for composite impact analysis.

Chamis, C. C.↗

Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites

Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.

polymer matrix composites↗

Strain rate characterization of unidirectional graphite/epoxy composite

For an investigation of problems of composites at high strain rates with dominant wave propagation effects, such as dynamically loaded composite jet engine blades, the longitudinal, transverse, and in-plane shear properties of unidirectional SP 288/AS graphite/epoxy were measured at various strain rates ranging from quasi-static to over 500/s. The test specimens were rings 10.16 cm in diameter, 2.54 cm long, 6 to 8 plies thick, and with fibers at 0, 90, and 10 deg off-axis. Quasi-static testing was conducted in a fixture which applies hydraulic pressure to the ring specimens, and dynamic testing was conducted by applying an internal pressure pulse through a liquid in a special fixture. Dynamic stress-strain curves are presented. For the 0-deg specimens, the modulus increases with strain up to 20 percent of the static value. The modulus and strength increase sharply in the 90-deg rings with strain rate reaching values two to three times the corresponding static rate.

Daniel, I. M.↗

High Strain Rate Behavior of Polymer Matrix Composites Analyzed

Procedures for modeling the high-speed impact of composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. To characterize and validate material models that could be used in the design of impactresistant engine cases, researchers must obtain material data over a wide variety of strain rates. An experimental program has been carried out through a university grant with the Ohio State University to obtain deformation data for a representative polymer matrix composite for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used to characterize and validate a constitutive model that was developed at the NASA Glenn Research Center.

Goldberg, Robert K.↗

Experimental Techniques for Evaluating the Effects of Aging on Impact and High Strain Rate Properties of Triaxial Braided Composite Materials

An experimental program is underway to measure the impact and high strain rate properties of triaxial braided composite materials and to quantify any degradation in properties as a result of thermal and hygroscopic aging typically encountered during service. Impact tests are being conducted on flat panels using a projectile designed to induce high rate deformation similar to that experienced in a jet engine fan case during a fan blade-out event. The tests are being conducted on as-fabricated panels and panels subjected to various numbers of aging cycles. High strain rate properties are being measured using a unique Hopkinson bar apparatus that has a larger diameter than conventional Hopkinson bars. This larger diameter is needed to measure representative material properties because of the large unit cell size of the materials examined in this work. In this paper the experimental techniques used for impact and high strain rate testing are described and some preliminary results are presented for both as-fabricated and aged composites.

Pereira, J. Michael↗

Study of High Strain Rate Response of Composites

The objective of the research was to continue the experimental study of the effect of strain rate on mechanical response (deformation and failure) of epoxy resins and carbon fibers/epoxy matrix composites, and to initiate a study of the effects of temperature by developing an elevated temperature test. The experimental data provide the information needed for NASA scientists for the development of a nonlinear, rate dependent deformation and strength models for composites that can subsequently be used in design. This year effort was directed into testing the epoxy resin. Three types of epoxy resins were tested in tension and shear at various strain rates that ranges from 5 x 10(exp -5), to 1000 per second. Pilot shear experiments were done at high strain rate and an elevated temperature of 80 C. The results show that all, the strain rate, the mode of loading, and temperature significantly affect the response of epoxy.

Gilat, Amos↗

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Composite Micromechanical Model - Part 2

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this second paper of a two part report, a three-dimensional composite micromechanical model is described which allows for the analysis of the rate dependent, nonlinear deformation response of a polymer matrix composite. Strain rate dependent inelastic constitutive equations utilized to model the deformation response of a polymer are implemented within the micromechanics method. The deformation response of two representative laminated carbon fiber reinforced composite materials with varying fiber orientation has been predicted using the described technique. The predicted results compare favorably to both experimental values and the response predicted by the Generalized Method of Cells, a well-established micromechanics analysis method.

Goldberg, Robert K.↗

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Goldberg, Robert K.↗

Environmental and High-Strain Rate effects on composites for engine applications

The Lewis Research Center is conducting a series of programs intended to investigate and develop the application of composite materials to structural components for turbojet engines. A significant part of that effort is directed to establishing resistance, defect growth, and strain rate characteristics of composite materials over the wide range of environmental and load conditions found in commercial turbojet engine operations. Both analytical and experimental efforts are involved.

Chamis, C. C.↗