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NASA NTRS2003

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.↗

NASA NTRS2004

Material Modeling of Space Shuttle Leading Edge and External Tank Materials For Use in the Columbia Accident Investigation

Upon the commencement of the analytical effort to characterize the impact dynamics and damage of the Space Shuttle Columbia leading edge due to External Tank insulating foam, the necessity of creating analytical descriptions of these materials became evident. To that end, material models were developed of the leading edge thermal protection system, Reinforced Carbon Carbon (RCC), and a low density polyurethane foam, BX-250. Challenges in modeling the RCC include its extreme brittleness, the differing behavior in compression and tension, and the anisotropic fabric layup. These effects were successfully included in LS-DYNA Material Model 58, *MAT_LAMINATED_ COMPOSITE_ FABRIC. The differing compression and tension behavior was modeled using the available damage parameters. Each fabric layer was given an integration point in the shell element, and was allowed to fail independently. Comparisons were made to static test data and coupon ballistic impact tests before being utilized in the full scale analysis. The foam's properties were typical of elastic automotive foams; and LS-DYNA Material Model 83, *MAT_FU_CHANG_FOAM, was successfully used to model its behavior. Material parameters defined included strain rate dependent stress-strain curves for both loading and un-loading, and for both compression and tension. This model was formulated with static test data and strain rate dependent test data, and was compared to ballistic impact tests on load-cell instrumented aluminum plates. These models were subsequently utilized in analysis of the Shuttle leading edge full scale ballistic impact tests, and are currently being used in the Return to Flight Space Shuttle re-certification effort.

Carney, Kelly↗

NASA NTRS1995

A study of the relationship between mineral content and mechanical properties of turkey gastrocnemius tendon

The vertebrate skeletal system undergoes adaptation in response to external forces, but the relation between the skeletal changes and such forces is not understood. In this context, the variation in the amount and location of calcification has been compared with changes in mechanical properties of the normally mineralizing turkey gastrocnemius tendon using ash weight measurements, X-ray radiography, and mechanical testing. Radiographic evidence from 12- to 17-week-old birds showed calcification in only portions of gastrocnemius tendons proximal to the tarsometatarsal joint. Mechanical testing of these dissected proximal regions demonstrated an increased ultimate stress and modulus and a decreased maximum strain that appeared to parallel calcification. Further, stress-strain curves of portions of uncalcified turkey gastrocnemius tendon were shaped similar to those of other typical unmineralized tendon curves while highly calcified tendons yielded curves resembling those of bone. The proximal portions of the gastrocnemius where mineralization begins were observed to have a decreased tendon cross-sectional area compared with distal portions which do not mineralize. Based on the resultant measures of mineral content and location and mechanical properties, it is hypothesized that increased calcification is a result of increased stresses at certain locations of the tendon, perhaps the consequence of the natural forces exerted by the large leg muscles of the bird into which the gastrocnemius inserts. More specifically, tendon calcification may be the result of stress-induced exposure of charged sites on the surfaces of collagen molecules, fibrils, or fibers so that deposition of mineral and subsequent mechanical reinforcement occur in the tissue.(ABSTRACT TRUNCATED AT 250 WORDS).

Non-NASA Center↗

NASA NTRS2011

Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

Detailed two-dimensional finite element analyses of the cross-sections of a model CVI (chemical vapor infiltrated) SiC/SiC (silicon carbide fiber in a silicon carbide matrix) ceramic matrix composites are performed. High resolution images of the cross-section of this composite material are generated using serial sectioning of the test specimens. These images are then used to develop very detailed finite element models of the cross-sections using the public domain software OOF2 (Object Oriented Analysis of Material Microstructures). Examination of these images shows that these microstructures have significant variability and irregularity. How these variabilities manifest themselves in the variability in effective properties as well as the stress distribution, damage initiation and damage progression is the overall objective of this work. Results indicate that even though the macroscopic stress-strain behavior of various sections analyzed is very similar, each section has a very distinct damage pattern when subjected to in-plane tensile loads and this damage pattern seems to follow the unique architectural and microstructural details of the analyzed sections.

Mital, Subodh K.↗

NASA NTRS2012

Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures

A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.

Mital, Subodh K.↗

NASA NTRS2013

Enhanced Schapery Theory Software Development for Modeling Failure of Fiber-Reinforced Laminates

Progressive damage and failure analysis (PDFA) tools are needed to predict the nonlinear response of advanced fiber-reinforced composite structures. Predictive tools should incorporate the underlying physics of the damage and failure mechanisms observed in the composite, and should utilize as few input parameters as possible. The purpose of the Enhanced Schapery Theory (EST) was to create a PDFA tool that operates in conjunction with a commercially available finite element (FE) code (Abaqus). The tool captures the physics of the damage and failure mechanisms that result in the nonlinear behavior of the material, and the failure methodology employed yields numerical results that are relatively insensitive to changes in the FE mesh. The EST code is written in Fortran and compiled into a static library that is linked to Abaqus. A Fortran Abaqus UMAT material subroutine is used to facilitate the communication between Abaqus and EST. A clear distinction between damage and failure is imposed. Damage mechanisms result in pre-peak nonlinearity in the stress strain curve. Four internal state variables (ISVs) are utilized to control the damage and failure degradation. All damage is said to result from matrix microdamage, and a single ISV marks the micro-damage evolution as it is used to degrade the transverse and shear moduli of the lamina using a set of experimentally obtainable matrix microdamage functions. Three separate failure ISVs are used to incorporate failure due to fiber breakage, mode I matrix cracking, and mode II matrix cracking. Failure initiation is determined using a failure criterion, and the evolution of these ISVs is controlled by a set of traction-separation laws. The traction separation laws are postulated such that the area under the curves is equal to the fracture toughness of the material associated with the corresponding failure mechanism. A characteristic finite element length is used to transform the traction-separation laws into stress-strain laws. The ISV evolution equations are derived in a thermodynamically consistent manner by invoking the stationary principle on the total work of the system with respect to each ISV. A novel feature is the inclusion of both pre-peak damage and appropriately scaled, post-peak strain softening failure. Also, the characteristic elements used in the failure degradation scheme are calculated using the element nodal coordinates, rather than simply the square root of the area of the element.

Pineda, Evan J.↗

NASA NTRS2016

Analysis and Characterization of Damage Utilizing an Orthotropic Generalized Composite Material Model Suitable for Use in Impact Problems

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 communities. In order to address a series of issues identified by the aerospace community as being desirable to include in a next generation composite impact model, an orthotropic, macroscopic constitutive model incorporating both plasticity and damage suitable for implementation within the commercial LS-DYNA computer code is being developed. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain hardening-based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used in which a load in one direction results in a stiffness reduction in multiple material coordinate directions. A detailed analysis is carried out to ensure that the strain equivalence assumption is appropriate for the derived plasticity and damage formulations that are employed in the current model. Procedures to develop the appropriate input curves for the damage model are presented and the process required to develop an appropriate characterization test matrix is discussed.

Impact↗

NASA NTRS2016

Analysis and Characterization of Damage Utilizing an Orthotropic Generalized Composite Material Model Suitable for Use in Impact Problems

Impact↗

NASA NTRS2016

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

GMC↗

NASA NTRS2016

Analysis and Characterization of Damage and Failure Utilizing a Generalized Composite Material Model Suitable for Use in Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in state-of-the art composite impact models is under development. In particular, a next generation composite impact material model, jointly developed by the FAA and NASA, is being implemented into 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 orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a semi-coupled approach is employed where the overall damage in a particular coordinate direction is assumed to be a multiplicative combination of the damage in that direction resulting from the applied loads in the various coordinate directions. Due to the fact that the plasticity and damage models are uncoupled, test procedures and methods to both characterize the damage model and to covert the material stress-strain curves from the true (damaged) stress space to the effective (undamaged) stress space have been developed. A methodology has been developed to input the experimentally determined composite failure surface in a tabulated manner. An analytical approach is then utilized to track how close the current stress state is to the failure surface.

Finite Element Method↗

NASA NTRS2017

A Compilation of MATLAB Scripts and Functions for MACGMC Analyses

The primary aim of the current effort is to provide scripts that automate many of the repetitive pre- and post-processing tasks associated with composite materials analyses using the Micromechanics Analysis Code with the Generalized Method of Cells. This document consists of a compilation of hundreds of scripts that were developed in MATLAB (The Mathworks, Inc., Natick, MA) programming language and consolidated into 16 MATLAB functions. (MACGMC). MACGMC is a composite material and laminate analysis software code developed at NASA Glenn Research Center. The software package has been built around the generalized method of cells (GMC) family of micromechanics theories. The computer code is developed with a user-friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermo-mechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated to increase the user friendliness, as well as to make it more robust in terms of input preparation and code execution. Finally, classical lamination theory has been implemented within the software, wherein GMC is used to model the composite material response of each ply. Thus, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. The pre-processing tasks include generation of a multitude of different repeating unit cells (RUCs) for CMCs and PMCs, visualization of RUCs from MACGMC input and output files and generation of the RUC section of a MACGMC input file. The post-processing tasks include visualization of the predicted composite response, such as local stress and strain contours, damage initiation and progression, stress-strain behavior, and fatigue response. In addition to the above, several miscellaneous scripts have been developed that can be used to perform repeated Monte-Carlo simulations to enable probabilistic simulations with minimal manual intervention. This document is formatted to provide MATLAB source files and descriptions of how to utilize them. It is assumed that the user has a basic understanding of how MATLAB scripts work and some MATLAB programming experience.

Materials Engineering↗

NASA NTRS2018

Implementation of J-A Methodology Elastic-Plastic Crack Instability Analysis Capability into the WARP-3D Code

Characterization of the near crack-tip stress/strain fields is the foundation of fracture mechanics. The description of the near tip stress field and the prediction of when fracture occurs is well established for brittle materials that exhibit linear elastic behavior. However, in ductile materials or conditions that violate linear elastic assumptions (Aluminum alloys, Al 2024-T3, Al 2024- T351 etc.), the elastic-plastic crack-tip stress fields are characterized by the Hutchison-Rice-Rosengren (HRR) field. The J-integral is commonly used to characterize amplitude of the HRR field under elastic-plastic conditions. The J-integral has been demonstrated for crack-tip fields that are under high constraint conditions (i.e., small-scale plasticity where the J-dominance is maintained). However, as the external load increases, yielding changes from small- to largescale plasticity and usually a loss of constraint (i.e., reduction in the triaxial stress field along the crack front). The loss of constraint leads to the deviation of the crack-tip stress fields from that given by the HRR field. Hence, the J-dominance will be gradually lost and additional parameter(s) are required to quantify the crack-tip stress fields and predict fracture behavior. The assessment objectives were to: 1) implement a two-parameter (i.e., J-A) fracture criterion into an elastic-plastic three-dimensional (3D) finite element analysis (FEA), 2) validate the implementation by comparison with the A parameter from literature data, 3) conduct material characterization tests to quantify the material behavior and provide fracture data for validation of the J-A fracture criteria, and (4) perform evaluations to establish if the J-A criteria can be used to predict fracture in a ductile metallic material (e.g., aluminum alloys). The A parameter in these criteria is the second parameter in a three-term elastic-plastic asymptotic expansion of the neartip stress behavior. A series of extensive FEAs were performed using WARP3D software package to obtain solutions for the A parameter for different specimen configurations. The methodology needed for the estimation of the A parameter in the asymptotic expansion was developed and implemented using Matlab®. A user material (UMAT) routine was used to model the material stress-strain response using a Ramberg-Osgood power law with a hardening exponent (n) and a material coefficient (alpha). This UMAT routine was successfully implemented in WARP3D software and validated through comparison with the experimental data. Three configurations were extracted from published results: 1) center cracked plate (CCP), 2) single edge-cracked plate (SECP), and 3) double edge-cracked plate (DECP). These configurations and four other configurations (three-hole tension (THT)), three-point bend (3PTB), three-hole compact tension (3PCT), and compact tension (CT)) were analyzed to verify the methodology that was developed and implemented into WARP3D. Solutions of the A parameter were obtained for remote tension loading conditions that started with small-scale yielding and continued into the large-scale plasticity regime. The results indicate that the methodology developed can be used to calculate the elastic-plastic J-A parameters for test specimens with a range of crack geometries, material strain hardening behaviors, and loading conditions. The J-A parameters were implemented as fracture criteria and used to predict the test results. For comparison, other fracture criteria were used to predict the same test results. Major findings include: The A constraint parameter A varies with specimen type and applied load thus accurate determination is crucial in predicting the failure load, and the A parameter is asymptotic as the failure load is approached, making an accurate determination difficult (i.e., small differences in the A parameter can cause large variations in failure load) for materials exhibiting elastic-plastic behavior. The failure predictions from J-A methodology were more accurate than the traditionally used KC and J methods, and have comparable scatter to that observed when using the crack-tip opening angle (CTOA) method. However, the J-A methodology requires considerable effort (expertise level and labor) to implement and to evaluate the A parameter for different specimen types and materials, or to apply this methodology to part-through crack (e.g., 3D problems) structural applications.

Hamm, Kenneth R., Jr.↗

NASA NTRSDate not supplied

Enabling Nuclear and Solar Thermal Propulsion with the Computational Laboratory: Faster and Cheaper Materials Characterization

Nuclear and solar thermal propulsion offer enhanced efficiencies for in-space travel which may open up the outer Solar System to both crewed and automated craft. However, these advanced propulsion systems require cutting-edge materials which are often not easily tested in the laboratory. Ab initio thermodynamics and other computational methods offer a way to test materials at high pressures and temperatures more quickly, and with reduced cost. Here, several case studies are presented which highlight the utility of modern simulation techniques. First, an extensive thermodynamic study was performed at the ab initio level to elucidate the role of hot hydrogen flow on the erosion of four refractory carbides to examine their appropriateness for use as channel coatings. A detailed analysis of reaction products informs estimates of erosion which are validated in comparison with heritage NERVA data. Specific material suggestions are made for both nuclear and solar designs. Secondly, we examined the mechanical behavior and chemical stability of various components of an idealized nuclear cermet core design using techniques spanning from the atomic to microscale. Next, the mechanical and chemical behavior of tungsten (a potential matrix material) and the stability of uranium mononitride (a potential ceramic fuel element), are characterized in the presence of hydrogen and at elevated temperatures with ab initio thermodynamics. Finally, the mechanical response and failure of tungsten under tensile strain is simulated at the micron scale with a combined finite element and dislocation dynamics approach. The resultant stress-strain data agrees well with experiments and leads to a workflow which can incorporate ab initio thermodynamic data into micron-scale simulations and thus provide real-world relevant estimates of erosion and stress-strain behavior. The power of this framework and our plans to use it in the future will be discussed.

William C Tucker↗

NASA NTRSDate not supplied

Multiscale Prediction of Yarn Pullout Failure Mode in Unreinforced Textile Fabrics

Unreinforced woven fabrics have been implemented in a variety of high performance applications, including body armor, deployable structures, and as the reinforcement material in composites. Multiscale modeling techniques have significantly improved the capabilities of simulation-based tools to capture fabric mechanics efficiently and accurately, but often lack in their prediction of failure and require pairing with finite element analysis (FEA) software, limiting their application to the design of ‘fit-for-purpose’ materials. NASA’s Multiscale Analysis Tool (NASMAT) is a standalone multiscale program that has been traditionally used in the analysis of reinforced composites materials. More recently, it has been amended to simulate unreinforced fabric behavior by allowing the geometric state of the tows to change with applied loading due to the lack of a reinforcement material, such as the matrix seen in composites. Previous work has shown the ability of NASMAT to capture nonlinear macroscale behavior by predicting geometric changes in the state of each subcell as a function of the applied loading and allowing each subcell in the analysis to rotate according to these predicted changes, as well as predict nonlinear behavior due to the fiber breakage failure mode. In this work, the capability of predicting the onset and propagation of failure in plain woven fabrics in NASMAT is presented for the yarn pullout failure mode, which occurs when a fabric is loaded at an off-axis angle relative to the warp of weft tow direction. Yarn pullout behavior is initiated by determining the applied load in which the shear resistance of the contact area between yarn families is overcome. When failure is initiated, yarn pullout is determined to have occurred when the applied displacement, calculated from global strain, exceeds the deformed position of a given contact points between yarn families, determined from pin-joint kinematics. Contact points where pullout has occurred contribute to a global damage parameter used to modify the homogenized stiffness of the fabric, resulting in nonlinear behavior observed at the macroscale. The off-axis loading behavior and yarn pullout failure theory have been developed and implemented into NASMAT such that users can simulate off-axis tensile behavior of fabrics in a single, standalone multiscale tool. Simulations are compared to uniaxial tensile tests at various off-axis angles to demonstrate the capability of the tool in its prediction of both the onset of failure at each off-axis angles and the stress-strain behavior as failure progresses.

Materials↗