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NASA NTRS2014

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

Generalized Method of Cells↗

NASA NTRS1995

Influence of fiber architecture on the elastic an d inelastic response of metal matrix composites

This three part paper focuses on the effect of fiber architecture (i.e., shape and distribution) on the elastic and inelastic response of metal matrix composites. The first part provides an annotative survey of the literature, presented as a historical perspective, dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix and metal matrix composites. Previous investigations dealing with both continuously and discontinuously reinforced composites are included. A summary of the state-of-the-art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of metal matrix composites. This micromechanics model, referred to as the generalized method of cells (GMC), is capable of predicting the overall, inelastic behavior of unidirectional, multi-phased composites given the properties of the constituents. In particular, the model is sufficiently general to predict the response of unidirectional composites reinforced by either continuous or discontinuous fibers with different inclusion shapes and spatial arrangements in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments regarding this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third pan provides qualitative results generated using GMC for a representative titanium matix composite system, SCS-6/TlMETAL 21S. Results are presented that correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep response, with both strong and weak fiber/matrix interfacial bonds. The fiber arrangements include square, square diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes include circular, square and cross-shaped cross sections. The effect of fiber volume fraction on the observed stress-strain response is also discussed, as the thus-far poorly documented strain rate sensitivity effect. In addition to the well documented features of architecture dependent response of continuously reinforced two-phase MMC's, new results involving continuous multi-phase internal architectures are presented. Specifically, stress strain and creep response of composites with different size fibers having different internal arrangements and bond strengths are investigated with the aim of determining the feasibility of using this approach to enhance the transverse toughness and creep resistance of TMC's.

Arnold, Steven M.↗

NASA NTRS1994

Micromechanical analysis of thermo-inelastic multiphase short-fiber composites

A micromechanical formulation is presented for the prediction of the overall thermo-inelastic behavior of multiphase composites which consist of short fibers. The analysis is an extension of the generalized method of cells that was previously derived for inelastic composites with continuous fibers, and the reliability of which was critically examined in several situations. The resulting three dimensional formulation is extremely general, wherein the analysis of thermo-inelastic composites with continuous fibers as well as particulate and porous inelastic materials are merely special cases.

Aboudi, Jacob↗

NASA NTRSDate not supplied

Progressive Failure Analysis of 3D Woven Composites via Multiscale Recursive Micromechanics

Multiscale progressive failure simulations have been performed for a 3D woven composite considering six length scales, spanning from the woven composite repeating unit cell to the matrix material containing voids. The Multiscale Recursive Micromechanics approach, which enables micromechanics models to call other micromechanics models (or themselves recursively) to consider finer and finer length scales, has been employed. The multiscale model uses both the generalized method of cells and Mori-Tanaka micromechanics theories and considers failure and damage at the lowest length scale. A simple subvolume elimination damage model, as well as the crack band model, are employed for the matrix and their predicted composite responses compared with and without a preexisting binder tow disbond. Results are also compared with experimental data for an AS4 carbon fiber/RTM6 epoxy matrix 3D orthogonal woven PMC, with good agreement in terms of global stiffness and global failure stress.

3D woven↗

NASA NTRSDate not supplied

Multiscale Failure Analysis of a 3D Woven Unit Cell Containing Defects

Multiscale failure simulations have been performed for a Three-dimensional woven composite unit cell considering five, or more, length scales spanning the woven composite mesoscale to the sub-microscale voids. The multiscale recursive micromechanics approach, which enables recursive integration of general micromechanics theories over an arbitrary number of length scales, has been employed within the NASA Multiscale Analysis Tool. The multiscale model uses both the generalized method of cells and Mori-Tanaka micromechanics theories, and considers failure in the constituent materials using a simple damage model. Baseline results, containing distributed voids, are compared to uniaxial experimental data for an AS4 carbon fiber/ RTM6 epoxy matrix 3D orthogonal woven composite with good agreement in terms of global stiffness and global failure stress. The simulations demonstrate that the 3D woven composite exhibits damage tolerance through sustaining increasing axial load far beyond the first initiation of damage. The multiscale model is used to examine the nonlinear response of the material to other loading conditions. Case studies, motivated by X-ray computed tomography data, are presented on the effects of manufacturing induced voids and cracks.

3D woven↗

NASA NTRS2007

Micromechanics of Spray-On Foam Insulation

Understanding the thermo-mechanical response of the Space Shuttle External Tank spray-on foam insulation (SOFI) material is critical, to NASA's Return to Flight effort. This closed-cell rigid polymeric foam is used to insulate the metallic Space Shuttle External Tank, which is at cryogenic temperatures immediately prior to and during lift off. The shedding of the SOFI during ascent led to the loss of the Columbia, and eliminating/minimizing foam lass from the tank has become a priority for NASA as it seeks to resume scheduled space shuttle missions. Determining the nature of the SOFI material behavior in response to both thermal and mechanical loading plays an important role as any structural modeling of the shedding phenomenon k predicated on knowledge of the constitutive behavior of the foam. In this paper, the SOFI material has been analyzed using the High-Fidelity Generalized Method of Cells (HFGMC) micromechanics model, which has recently been extended to admit a triply-periodic 3-D repeating unit cell (RUC). Additional theoretical extensions that mere made in order to enable modeling of the closed-cell-foam material include the ability to represent internal boundaries within the RUC (to simulated internal pores) and the ability to impose an internal pressure within the simulated pores. This latter extension is crucial as two sources contribute to significant internal pressure changes within the SOFI pores. First, gas trapped in the pores during the spray process will expand or contract due to temperature changes. Second, the pore pressure will increase due to outgassing of water and other species present in the foam skeleton polymer material. With HFGMC's new pore pressure modeling capabilities, a nonlinear pressure change within the simulated pore can be imposed that accounts for both of these sources, in addition to stmdar&-thermal and mechanical loading; The triply-periodic HFGMC micromechanics model described above was implemented within NASA GRC's MAC/GMC software package, giving the model access to a range of nonlinear constitutive models for the polymeric foam skeleton material. A repeating unit cell architecture was constructed that, while relatively simple, still accounts for the geometric anisotropy of the porous foam microstructure and its thin walls and thicker edges. With the lack of reliable polymeric foam skeleton materia1 properties, many simulations were executed aimed at backing out these material properties. Then, using these properties, predictions of the thermo-mechanical behavior of the foam, including calculated internal applied pressure profiles, were performed and compared with appropriate experimental data.

Bednarcyk, Brett A.↗

NASA NTRS2003

High-Fidelity Micromechanics Model Enhanced for Multiphase Particulate Materials

This 3-year effort involves the development of a comprehensive micromechanics model and a related computer code, capable of accurately estimating both the average response and the local stress and strain fields in the individual phases, assuming both elastic and inelastic behavior. During the first year (fiscal year 2001) of the investigation, a version of the model called the High-Fidelity Generalized Method of Cells (HFGMC) was successfully completed for the thermo-inelastic response of continuously reinforced multiphased materials with arbitrary periodic microstructures (refs. 1 and 2). The model s excellent predictive capability for both the macroscopic response and the microlevel stress and strain fields was demonstrated through comparison with exact analytical and finite element solutions. This year, HFGMC was further extended in two technologically significant ways. The first enhancement entailed the incorporation of fiber/matrix debonding capability into the two-dimensional version of HFGMC for modeling the response of unidirectionally reinforced composites such as titanium matrix composites, which exhibit poor fiber/matrix bond. Comparison with experimental data validated the model s predictive capability. The second enhancement entailed further generalization of HFGMC to three dimensions to enable modeling the response of particulate-reinforced (discontinuous) composites in the elastic material behavior domain. Next year, the three-dimensional version will be generalized to encompass inelastic effects due to plasticity, viscoplasticity, and damage, as well as coupled electromagnetothermomechanical (including piezoelectric) effects.

Pindera, Marek-Jerzy↗

NASA NTRS2014

A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis

It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).

softening↗

DOE OSTI2022

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. Further, the trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Modeling creep behavior in ceramic matrix composites

Here, in this work, a three-dimensional viscoplasticity formulation with progressive damage is developed and used to investigate the complex time-dependent constituent load transfer and progressive damage behavior in ceramic matrix composites (CMCs) subjected to creep. The viscoplasticity formulation is based on Hill's orthotropic plastic potential, an associative flow rule, and the Norton-Bailey creep power law with Arrhenius temperature dependence. A fracture mechanics-informed isotropic matrix damage model is used to account for CMC brittle matrix damage initiation and propagation, in which two scalar damage variables capture the effects of matrix porosity as well as matrix property degradation due to matrix crack initiation and propagation. The Curtin progressive fiber damage model is utilized to simulate progressive fiber failure. The creep-damage formulation is subsequently implemented as a constitutive model in the generalized method of cells (GMC) micromechanics formulation to simulate time-dependent deformation and material damage under creep loading conditions. The developed framework is used to simulate creep of single fiber SiC/SiC microcomposites. Simulation results are in excellent agreement with experimental and numerical data available in the literature.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Multi deep learning-based stochastic microstructure reconstruction and high-fidelity micromechanics simulation of time-dependent ceramic matrix composite response

A multi deep learning-based framework is developed for efficient, automated microstructure reconstruction and generation of stochastic representative volume elements (SRVEs) with periodic boundary conditions (PBCs) for accurate modeling of ceramic matrix composite (CMC) response. The methodology comprises a convolutional neural network coupled with regression layers to act as a vanilla regression network for semantic segmentation of the microstructure, allowing accurate characterization of the phases and their distributions at the microscale. Scanning electron microscope and confocal microscope are used to obtain C/SiNC and SiC/SiNC CMCs micrographs for vanilla regression testing. Microstructure variability in terms of fiber volume fraction and porosity are quantified through the output regression layer, ensuring accurate representation of material variability in SRVE construction. Generative adversarial network (GAN) and its variants are designed to produce high-fidelity SRVE, spanning CMCs microstructure variability space. A circular padding algorithm is developed to generate SRVEs with PBCs during training of GANs. The accuracy of the generated SRVEs is established through micromechanics simulations, where an efficient formulation of the high-fidelity generalized methods of cells (HFGMC) approach is used to compute the effective mechanical properties. Furthermore, an iterative algorithm is implemented in the HFGMC solver to simulate time-dependent deformation of SiC/SiNC subjected to creep loading conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Stochastic microstructural analysis of ceramic matrix composites using a high-fidelity multiscale framework

This paper presents a high-fidelity multiscale framework to simulate the mechanical behavior of ceramic matrix composites (CMCs), accounting for the complex micromorphology captured using detailed material characterization. First, high-resolution micrographs are obtained for the specific carbon fiber silicon-carbide-nitride matrix (C/SiNC) CMC to characterize the variability of the architectural features and manufacturing-induced defects at the microscale. An image processing algorithm is then used to precisely estimate the size and distribution of all subscale features and defects from the micrographs. The information is then used to generate a three-dimensional stochastic representative volume element (SRVE) to reconstruct microscale constituents accounting for the variability. As a result, the generated SRVEs are simulated using the high-fidelity generalized method of cells (HFGMC) micromechanics theory to investigate the effects of defects on the elastic properties of C/SiNC CMCs.

Ceramic Matrix Composites↗

DOE OSTI2025

Physics-Informed Machine Learning Model for Ceramic Matrix Composite Creep

A physics-informed recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear, time-dependent constitutive behavior of ceramic matrix composites (CMCs) driven by matrix damage and constituent creep at the microscale. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the high-fidelity generalized method of cells (HFGMC) approach which calls appropriate creep and damage models for each of the constituents. This coupling permits simulating the nonlinear behavior of CMCs based on constituent response at the microscale along with microstructural features such as fiber and porosity volume fraction and fiber radius. The microscale repeating unit cell is loaded under creep fatigue conditions to replicate the material loading experienced in a turbine engine. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input stress sequence, temperature, and microstructural features, the resulting strain history response while satisfying physical constraints related to creep rate, isochoric inelastic deformation, and strain energy density. The trained surrogate model is shown to effectively match the strain history over quantified distributions of microstructural features and relevant loading regimes and temperatures. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore, the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex microstructures, nonlinear time-dependent material response, and under non-monotonic loading conditions.

ceramic matrix composites↗

NASA NTRS1994

Micromechanics Analysis Code (MAC) User Guide: Version 1.0

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions it must be based on a micromechanics approach which utilizes physically based deformation and life constitutive models and allows one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Here the user guide for the recently developed, computationally efficient and comprehensive micromechanics analysis code, MAC, who's predictive capability rests entirely upon the fully analytical generalized method of cells, GMC, micromechanics model is described. MAC is a versatile form of research software that 'drives' the double or triple ply periodic micromechanics constitutive models based upon GMC. MAC enhances the basic capabilities of GMC by providing a modular framework wherein (1) various thermal, mechanical (stress or strain control), and thermomechanical load histories can be imposed; (2) different integration algorithms may be selected; (3) a variety of constituent constitutive models may be utilized and/or implemented; and (4) a variety of fiber architectures may be easily accessed through their corresponding representative volume elements.

Wilt, T. E.↗

NASA NTRS1995

Micro-mechanics of micro-composites

The Structural Dynamics branch at NASA LaRC is working on developing an active passive mount system for vibration control. Toward this end a system utilizing piezoelectric actuators is currently being utilized. There are limitations to the current system related to space applications under which it is desired to eliminate deformations in the actuators associated with thermal effects. In addition, a material that is readily formable into complex shapes and whose mechanical properties can be optimized with regards to vibration control would be highly desirable. Microcomposite material are currently under study to service these needs. Microcomposite materials are essentially materials in which particles on the scale of microns are bound together with a polyimide (LaRC Si) that has been developed at LaRC. In particular a micro-composite consisting of LaRC Si binder and piezoelectric ceramic particles shows promise in satisfying the needs of the active passive mount project. The LaRC/ Si microcomposite has a unique combination of piezoelectric properties combined with a near zero coefficient of thermal expansion and easy machinability. The goal of this ASEE project is to develop techniques to analytically determine important material properties necessary to characterize the dynamic properties of actuators and mounts made from the LaRC Si / ceramic microcomposite. In particular, a generalized method of cells micromechanics originally developed at NASA Lewis is employed to analyze the microstructural geometry of the microcomposites and predict the overall mechanical properties of the material. A testing program has been established to evaluate and refine the GMC approach to these materials. In addition, a theory of mixtures analysis is being developed that utilizes the GMC micromechanics information to analyze complex behavior of the microcomposite material which has a near zero CTE.

Donovan, Richard P.↗

NASA NTRS1996

Micromechanics Analysis Code (MAC). User Guide: Version 2.0

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions it must be based on a micromechanics approach which utilizes physically based deformation and life constitutive models and allows one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Here the user guide for the recently developed, computationally efficient and comprehensive micromechanics analysis code's (MAC) who's predictive capability rests entirely upon the fully analytical generalized method of cells (GMC), micromechanics model is described. MAC is a versatile form of research software that 'drives' the double or triply periodic micromechanics constitutive models based upon GMC. MAC enhances the basic capabilities of GMC by providing a modular framework wherein (1) various thermal, mechanical (stress or strain control) and thermomechanical load histories can be imposed, (2) different integration algorithms may be selected, (3) a variety of constituent constitutive models may be utilized and/or implemented, and (4) a variety of fiber and laminate architectures may be easily accessed through their corresponding representative volume elements.

Wilt, T. E.↗

NASA NTRS1996

The Development of Computational Techniques for the Nonlinear Analysis of Composite Structures at High Temperature

The objective of this research project was to develop robust and efficient computational tools for deformation and life analysis techniques. This included: development of viscoplastic continuum models, associated numerical integration techniques, suitable micromechanics models/methods, and coupled deformation and damage algorithms. The work was involved with models/methods applicable to composite structures on both microscale and macroscale levels. The microscale analysis utilized Aboudi's generalized method of cells (GMS) micromechanical model as well as finite element models of similar composite architectures, i.e., square and hexagonal fiber pack models.

Keith, Theo G., Jr.↗

NASA NTRS1997

Experimental Characterization and Micromechanical Modeling of Woven Carbon/Copper Composites

The results of an extensive experimental characterization and a preliminary analytical modeling effort for the elastoplastic mechanical behavior of 8-harness satin weave carbon/copper (C/Cu) composites are presented. Previous experimental and modeling investigations of woven composites are discussed, as is the evolution of, and motivation for, the continuing research on C/Cu composites. Experimental results of monotonic and cyclic tension, compression, and Iosipescu shear tests, and combined tension-compression tests, are presented. With regard to the test results, emphasis is placed on the effect of strain gauge size and placement, the effect of alloying the copper matrix to improve fiber-matrix bonding, yield surface characterization, and failure mechanisms. The analytical methodology used in this investigation consists of an extension of the three-dimensional generalized method of cells (GMC-3D) micromechanics model, developed by Aboudi (1994), to include inhomogeneity and plasticity effects on the subcell level. The extension of the model allows prediction of the elastoplastic mechanical response of woven composites, as represented by a true repeating unit cell for the woven composite. The model is used to examine the effects of refining the representative geometry of the composite, altering the composite overall fiber volume fraction, changing the size and placement of the strain gauge with respect to the composite's reinforcement weave, and including porosity within the infiltrated fiber yarns on the in-plane elastoplastic tensile, compressive, and shear response of 8-harness satin C/Cu. The model predictions are also compared with the appropriate monotonic experimental results.

Bednarcyk, Brett A.↗