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Carbon fiber composites that utilize flattened, large tow yarns in woven or braided forms are being used in many aerospace applications. The complex fiber architecture and large unit cell size in these materials present challenges for both understanding the deformation process and measuring reliable material properties. In this paper composites made using flattened 12k and 24k (referring to the number of fibers in the fiber tow) standard modulus carbon fiber yarns in a 0[degrees] /+ 60[degrees]/-60[degrees] triaxial braided architecture are examined. Standard straight-sided tensile coupons were tested with the 0[degrees] axial braid fibers either parallel to (axial tensile test) or perpendicular to (transverse tensile test) the applied tensile load. The nonuniform surface strain resulting from the triaxial braided architecture was examined using photogrammetry. Local regions of high strain concentration were examined to identify where failure initiates and to determine the local strain at the time of failure initiation. Splitting within fiber bundles was the first failure mode observed at low to intermediate strains. For axial tensile tests the splitting was primarily in the [+ or -]60[degrees] bias fibers, which were oriented 60[degrees] to the applied load. At higher strains in the axial tensile test, out-of-plane deformation associated with localized delamination between fiber bundles or damage within fiber bundles was observed. For transverse tensile tests, the splitting was primarily in the 0[degrees] axial fibers, which were oriented transverse to the applied load. The initiation and accumulation of local damage caused the global transverse stress-strain curves to become nonlinear and caused failure to occur at a reduced ultimate strain for both the axial and transverse tensile tests. Extensive delamination at the specimen edges was also observed. Modifications to the standard straight-sided coupon geometry are needed to minimize these edge effects when testing the large unit cell type of material examined in this work. DOI: 10.1061/(ASCE)0893-1321(2009)22:3(270) CE Database subject headings: Composite materials; Polymers: Epoxy resins: Imaging techniques; Material tests; Static tests; Tensile loads; Damage.

The next generation aircraft engines are designed to be lighter and stronger than engines currently in use by using carbon fiber composites. In order to certify these engines, ballistic impact tests and computational analyses must be completed, which will simulate a 'blade out' event in a catastrophic engine failure In order to computationally simulate the engine failure, properties of the carbon fiber and resin matrix must be known. When conducting computer simulations using a micromechanics approach, experimental tensile, compressive, and shear data are needed for constitutive modeling of the resin matrix material. The material properties of an Epon E862 epoxy resin will be investigated because it is a commercial 176[degrees]C (350[degrees]F) cure resin currently being used in these aircraft engines. These properties will be measured using optical measurement techniques. The epoxy specimens will be tested in tension, compression and torsional loadings under various strain rates ranging from [10.sup.-5] to [10.sup.-1] [s.sup.-1] and temperatures ranging from room temperature to 80[degrees]C. To test the specimens at high temperatures, a specialized clear temperature chamber was used. The results show that the test procedure developed can accurately and quickly categorize the material response characteristics of an epoxy resin. In addition, the results display clear strain rate and temperature dependencies in the material response. CE Database subject headings: Polymers; Material properties; Material tests; Constitutive models; Strain rate; Temperature effects; Measurement; Epoxy resins.

A modified Hashin failure model is developed to characterize different failure modes related to high-velocity impact of composite laminates. Hashin's compressive fiber failure mode has been extended to consider the shear stress effect. Several micromechanics-based degradation rules are developed and applied to the stress and material property calculations according to different failure modes after the corresponding failure criterion is satisfied. This model has been implemented into a recently developed micromechanics model. Computational results show that this model is able to address shear failure, delamination, and tearing failure observed in the high-velocity impact of composite laminates. CE Database subject headings: Failure modes; Polymers; Laminates; Composite materials; Velocity.

An experimental and analytical program is carried out to explore key behaviors in the loading and unloading behavior of polymers. Specifically, the effects of strain rate and hydrostatic stresses on the nonlinear portions of the deformation response are examined. Tension, compression, and shear load only and load/unload tests are conducted on a representative polymer across a range of strain rates, and key features of the experimental results are identified. To conduct a preliminary exploration of how the key features of the deformation response could be simulated analytically, a previously developed set of constitutive equations, which were developed to analyze the strain rate dependent, nonlinear deformation of polymers including the effects of hydrostatic stresses, were modified in order to approximate key features of the nonlinear unloading behavior observed in the polymer. The constitutive relations are based on state variable constitutive equations originally developed for metals. The nonlinear unloading observed in the experiments is approximated by reducing the unloading modulus of the material as the effective inelastic strain is increased. The effects of the hydrostatic stress state on the unloading modulus are also simulated analytically. To examine the revised formulation, the loading and load/unload responses of the representative polymer in tension, compression, and shear are examined at several strain rates. Results computed using the developed constitutive equations were found to correlate reasonably well with the experimental data. CE Database subject headings: Constitutive equations; Polymers; Strain rate; Viscoplasticity; Deformation.

The mechanical response of E-862 and PR-520 resins is investigated in tensile and shear loadings. At both types of loading the resins are tested at strain rates of about 5 X [10.sup.-5], 2, and 450-700 [s.sup.-1]. In addition, dynamic shear modulus tests are carried out at variousfrequencies and temperatures, and tensile stress relaxation tests are conducted at room temperature. The results show that the toughened PR-520 resin can carry higher stresses than the untoughened E-862 resin. Strain rate has a significant effect on the response of both resins. In shear, both resins show a ductile response with maximum stress that is increasing with strain rate. In tension, a ductile response is observed at low strain rate (~5 X [10.sup.-5] [s.sup.-1]), and brittle response is observed at the medium and high strain rates (2 and 700 [s.sup.-1]). The hydrostatic component of the stress in the tensile tests causes premature failure in the E-862 resin. Localized deformation develops in the PR-520 resin when loaded in shear. An internal state variable constitutive model is proposed for modeling the response of the resins. The model includes a state variable that accounts for the effect of the hydrostatic component of the stress on the deformation. DOI: 10.1061/(ASCE)0893-1321(2007)20:2(75) CE Database subject headings: Strain rate; Epoxy resins; Deformation; Laminates.

A numerical procedure has been developed to investigate the nonlinear and strain-rate-dependent deformation response of polymer matrix composite laminated plates under high strain-rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain-rate-dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated to improve the developed strain-rate-dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher-order laminated plate theory that is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain-rate loadings. Results show that the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain-rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical [J.sub.2] plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of a representative polymer are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. 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. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results. DOI: 10.1061/(ASCE)0893-1321(2005)18:1(18) CE Database subject headings: Composite materials; Constitutive equations; Polymers; Strain rate; Hydrostatic pressure; Deformation analysis.

Theoretical and implementation details of an orthotropic plasticity model are presented. The model is comprised of three sub-models dealing with elastic and inelastic deformations, damage, and failure. The input to the three sub-models involves tabulated data that can be obtained from laboratory and/or virtual testing. In this article, the focus is on the development of the failure sub-model and its links to the other components. Details of how the user-selected failure criterion is used, and what steps are implemented post-failure are presented. The well-known Puck failure criterion is used in the numerical examples. Three validation tests are used to illustrate the strengths and weaknesses of the failure sub-model—10°, 15°, and 30° off-axis tests, a stacked-ply test carried out at room temperature under quasi-static loading, and finally, a high-speed impact test. Results indicate that while the deformation and damage sub-models give reasonably accurate results, the failure predictions are a huge challenge especially for high-speed impact tests. [ABSTRACT FROM AUTHOR]

The focus of this paper is the development of test procedures to characterize the damage-related behavior of a unidirectional composite at room temperature and quasi-static loading conditions and use the resulting data in the damage sub-model of a newly developed material model for orthotropic composites. This material model has three distinct sub-models to handle elastic and inelastic deformations, damage, and failure. A unidirectional composite—T800/F3900 that was the focus of our previous work, is used to illustrate how the deformation and damage-related experimental procedures are developed and used. The implementation of the damage sub-model into LS-DYNA is verified using single-element tests and validated using impact tests. Results show that the implementation yields reasonably accurate predictions of impact behavior involving deformation and damage in structural composites. [ABSTRACT FROM AUTHOR]

The need for accurate material models to simulate the deformation, damage, and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage, and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. For the failure model, a tabulated approach is utilized in which a stress- or strain-based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed. [ABSTRACT FROM AUTHOR]

Test procedures for characterizing the orthotropic behavior of a unidirectional composite at room temperature and quasi-static loading conditions are developed and discussed. The resulting data consisting of 12 stress–strain curves and associated material parameters are used in a newly developed material model—an orthotropic elasto-plastic constitutive model that is driven by tabulated stress–strain curves and other material properties that allow for the elastic and inelastic deformation model to be combined with damage and failure models. A unidirectional composite—T800/F3900, commonly used in the aerospace industry, is used to illustrate how the experimental procedures are developed and used. The generated data are then used to model a dynamic impact test. Results show that the developed framework implemented into a special version of LS-DYNA yields reasonably accurate predictions of the structural behavior. [ABSTRACT FROM AUTHOR]

The need for accurate material models to simulate the deformation, damage, and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. There are a variety of material models currently available within commercial transient dynamic finite-element codes to analyze the response of composite materials under impact conditions. However, there are several features that are lacking in the currently available models that could improve the predictive capability of the impact simulations. To address these needs, a combined elasto-plastic model with damage suitable for implementation within transient dynamic finite-element codes has been developed. A key feature of the improved material model is the use of tabulated stress-strain data in a variety of coordinate directions to fully define the stress-strain response of the material. Currently, the model development efforts have focused on creating the plasticity portion of the model. A commonly used composite failure model has been generalized and extended to a strain-hardening-based orthotropic yield function with a non-associative flow rule. The coefficients of the yield function are computed based on the input stress-strain curves using the effective plastic strain as the tracking variable. The coefficients of the flow rule are determined in a systematic manner based on the available stress-strain data for the material. The evolution of the yield surface is examined, in detail, for a sample composite. A numerical algorithm based on the classic radial return method is employed to compute the evolution of the effective plastic strain. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model. The developed material model is suitable for use within commercial transient dynamic finite-element codes for use in analyzing the nonlinear response of polymer composites. [ABSTRACT FROM AUTHOR]

In this work, the modeling of triaxially braided composites was explored through a subcell approach using an improved semianalytical discretization scheme. The unit cell of the braided composite was divided into four unique subcells, each approximated by a mosaic stacking of unidirectional composite plies and modeled through the use of layered-shell elements within the finite-element model. Two subcell discretization schemes were investigated: a model explicitly capturing pure matrix regions, and a model which absorbed pure matrix pockets into neighboring tow plies. Differences in the mesostructure between single-ply and multi-ply braid coupons were addressed through modifications to the subcell discretization. The absorbed matrix model simulated the unique out-of-plane deformations observed experimentally in single-ply tensile tests with acceptable moduli predictions. An investigation of single-shell versus multi-shell coupons for the analysis of multi-ply braids revealed the through-thickness modeling approach was found to have a significant effect on the apparent transverse modulus. Improved moduli predictions in both the axial and transverse directions were obtained by explicitly modeling braided plies with individual layers of shell elements. [ABSTRACT FROM AUTHOR]

The objectives of this paper include identifying important architectural parameters that describe the SiC/SiC five-harness satin weave composite and characterizing the statistical distributions and correlations of those parameters from photomicrographs of various cross sections. In addition, realistic artificial cross sections of a 2D representative volume element (RVE) are generated reflecting the variability found in the photomicrographs and include explicitly modeled voids (something not routinely done for woven CMCs). These models are used to make preliminary observation of the effects of architectural variability on the thermo-mechanical properties (material constants). Lastly, information is obtained on the sensitivity of linear thermo-mechanical properties to architectural variations. Two-dimensional finite element analysis is used in combination with a response surface and it is shown that the present method is effective in determining the effects of architectural variability on thermo-mechanical properties and their variability. [ABSTRACT FROM AUTHOR]

An introduction to articles published within the issue is presented, including inspace propulsion, cryogenic fluids management and communications technology and development.

An analytical method has been developed to analyze the impact response of triaxially braided carbon fiber composites, including the penetration velocity and impact damage patterns. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. Currently, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. To determine the stiffness and strength properties required for the constitutive model, a top-down approach for determining the strength properties is merged with a bottom-up approach for determining the stiffness properties. The top-down portion uses global strengths obtained from macroscale coupon-level testing to characterize the material strengths for each subcell. The bottom-up portion uses microscale fiber and matrix stiffness properties to characterize the material stiffness for each subceii. Simulations of quasi-static coupon-level tests for several representative composites are conducted along with impact simulations. [ABSTRACT FROM AUTHOR]

A new three-dimensional finite-element model of two-dimensional, triaxially braided composites is presented in this paper. This mesoscale modeling technique is used to examine and predict the deformation and damage observed in tests of straight-sided specimens. A unit cell-based approach is used to consider the braiding architecture and the mechanical properties of the fiber tows, the matrix, and the fiber tow-matrix interface. A 0°/±60° braiding configuration has been investigated by conducting static finite-element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by using the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results with those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated. [ABSTRACT FROM AUTHOR]

A macro-level finite element-based model has been developed to simulate the mechanical and impact response of triaxially-braided polymer matrix composites. In the analytical model, the triaxial-braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. The material stiffness and strength values required for the constitutive model are determined based on coupon-level tests on the braided composite. Simulations of quasi-static coupon tests of a representative braided composite are conducted. Varying the strength values that are input to the material model is found to have a significant influence on the effective material response predicted by the finite element analysis, ,sometimes in ways that at first glance appear nonintuitive. A parametric study involving the input strength parameters provides guidance on how the analysis model can be improved. [ABSTRACT FROM AUTHOR]

A modified Hashin failure model is developed to characterize different failure modes related to high-velocity impact of composite laminates. Hashin’s compressive fiber failure mode has been extended to consider the shear stress effect. Several micromechanics-based degradation rules are developed and applied to the stress and material property calculations according to different failure modes after the corresponding failure criterion is satisfied. This model has been implemented into a recently developed micromechanics model. Computational results show that this model is able to address shear failure, delamination, and tearing failure observed in the high-velocity impact of composite laminates. [ABSTRACT FROM AUTHOR]

A multiscale micro-macro numerical procedure has been developed to model the transient responses of polymeric composite shell structures. A micromechanics model which accounts for the transverse shear stress effect, the effect of strain rate dependency, and the effect of inelasticity is used for analyzing the mechanical responses of the fiber and matrix constituents. The accuracy of the micromechanics model under transverse shear loading is verified by comparison with an existing procedure. A higher-order laminated shell theory is extended to capture the inelastic deformations of the composite shell and is implemented using the finite element technique. A detailed parametric study is conducted to investigate the influence of geometry, ply stacking sequence, material models, and loading conditions on the transient response of laminated shell structures under impact loadings. [ABSTRACT FROM AUTHOR]

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. The Ramaswamy--Stouffer viscoplastic constitutive equations for metals have been modified to model the strain rate dependent inelastic deformation of ductile polymers, including hydrostatic stress effects. These equations have been incorporated into a mechanics of materials based micromechanics model that was developed to analyze uniaxial composites at various fiber orientation angles. The Hashin failure criteria have been implemented into the micromechanics to predict ply failure strengths. The deformation response and ply failure strengths for the representative composite AS4/PEEK have been successfully predicted for a variety of fiber orientations and strain rates. [ABSTRACT FROM AUTHOR]

The article discusses various reports published within the issue including "Multiterrain Earth Landing Systems Applicable for Manned Space Capsules," "Orion Crew Member Injury Predictions During Land and Water Landings," and "Shuttle Debris Impact Analysis: Post Return to Flight Real-Time Mission Support."

Woven and braided polymer composite structures are used in many primary aerospace applications because of their superior behavior under dynamic loading conditions and light weight. Characterization of all anisotropic properties under various strain rate and temperature conditions becomes essential for analysis, design, and numerical simulations. This paper aims to present a review of critical testing methods of polymer and composite materials. In the second part, a review of numerical and analytical models for the dynamic analysis of woven and braided composites is presented. This review article cites 138 references. [ABSTRACT FROM AUTHOR]

A numerical procedure has been developed to investigate the nonlinear and strain-rate-dependent deformation response of polymer matrix composite laminated plates under high strain-rate impact loadings. A recently developed strength of materials based micromechanics mode!, incorporating a set of nonlinear, strain-rate-dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated to improve the developed strain-rate-dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher-order laminated plate theory that is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain-rate loadings. Results show that the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain-rate dependency and material nonlinearity is found in the deformation response of representative composite specimens. [ABSTRACT FROM AUTHOR]