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NASA NTRSDate not supplied

Variational Asymptotic Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites

The objective of this paper is to develop a constitutive model for finitely deformed viscoelastic-viscoplastic materials and a micromechanics approach to homogenizing composites consisting of such materials. The development of the constitutive model involves establishing a thermodynamic framework based on finite strain theory, developing a viscoelasticity and a viscoplasticity model based on the thermodynamic framework, developing a radial return algorithm based on a classic framework, and deriving a closed-from incremental constitutive relation in the spatial configuration. The development of the micromechanics approach involves pulling-back the above constitutive relation to the material configuration, formulating a variational statement with the resulting constitutive relation, discretizing variational statement in a finite-dimensional space, and solving the discretized variational statement using an Euler–Newton predictor–corrector method. The constitutive model is calibrated via monotonic uniaxial compression tests on a polymer, and the calibrated model is validated by comparing its predictions with the cyclic test data. It is shown capable of characterizing viscoelasticity, viscoplasticity, and complex loading paths. The micromechanics approach’s capabilities are demonstrated through homogenizing a unidirectional fiber-reinforced composite, subjected to uniaxial, biaxial, and shear loading, at different strain rates. It is demonstrated to be capable of handling rate dependence and complex loading paths. The present framework can be further improved by implementing more sophisticated viscoelasticity and viscoplasticity models in future work.

Finite element analysis↗

NASA NTRSDate not supplied

Nonlinear Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites Using Mechanics of Structure Genome

The objective of this paper is to develop a micromechanics approach to homogenizing finitely deformed viscoelastic-viscoplastic composites using the mechanics of structure genome. The incremental constitutive relation for glassy polymers, formulated in the spatial configuration, is implemented in the present approach.This involves (1) pulling-back the constitutive model to the material configuration and (2)choosing the deformation gradient tensor and the first Piola–Kirchhoff stress tensor as the strain and the stress measures during homogenization, respectively. An Euler–Newton predictor–corrector method is developed for homogenization. Each step involves formulating a variational statement using the mechanics of structure genome, discretizing the statement in a finite-dimensional space, and solving the problem using an Euler/multilevel Newton method. The present approach is demonstrated by homogenizing fiber- and particle-reinforced composites undergoing uniaxial, biaxial, or shear deformation, at different stain rates.

Multi-scale modeling, High Strain Composites, Visc↗

NASA NTRS2012

Characterization and Analysis of Triaxially Braided Polymer Composites under Static and Impact Loads

In order to design impact resistant aerospace components made of triaxially-braided polymer matrix composite materials, a need exists to have reliable impact simulation methods and a detailed understanding of the material behavior. Traditional test methods and specimen designs have yielded unrealistic material property data due to material mechanisms such as edge damage. To overcome these deficiencies, various alternative testing geometries such as notched flat coupons have been examined to alleviate difficulties observed with standard test methods. The results from the coupon level tests have been used to characterize and validate a macro level finite element-based model which can be used to simulate the mechanical and impact response of the braided composites. In the analytical model, the triaxial braid unit cell is approximated by using four parallel laminated composites, each with a different fiber layup, which roughly simulates the braid architecture. In the analysis, each of these laminated composites is modeled as a shell element. Currently, each shell element is considered to be a smeared homogeneous material. Simplified micromechanics techniques and lamination theory are used to determine the equivalent stiffness properties of each shell element, and results from the coupon level tests on the braided composite are used to back out the strength properties of each shell element. Recent improvements to the model include the incorporation of strain rate effects into the model. Simulations of ballistic impact tests have been carried out to investigate and verify the analysis approach.

Goldberg, Robert K.↗

NASA NTRSDate not supplied

Mechanics of Structure Genome-Based Nonlinear Shell Analysis

In this paper, a mechanics of structure genome (MSG)-based nonlinear shell theory is introduced. The theory uses an implicit algorithm combining the Euler’s and Newton’s method that can be applied for shell modeling as well as 3D homogenization. This theory has been implemented into the general-purpose constitutive modeling code SwiftComp, which was originally developed for linear analyses. For the convenience of implementing different nonlinear material models, the SwiftComp user material (SCUMAT), which has a similar interface to the Abaqus user subroutine UMAT, is developed. The capability of the MSG-based nonlinear shell is validated with numerical examples with different material models. A 2-step nonlinear homogenization, with a micromechanics step and a shell analysis step, is demonstrated.

Yufei Long↗

NASA NTRS1993

Thermoelastic response of metal matrix composites with large-diameter fibers subjected to thermal gradients

A new micromechanical theory is presented for the response of heterogeneous metal matrix composites subjected to thermal gradients. In contrast to existing micromechanical theories that utilize classical homogenization schemes in the course of calculating microscopic and macroscopic field quantities, in the present approach the actual microstructural details are explicitly coupled with the macrostructure of the composite. Examples are offered that illustrate limitations of the classical homogenization approach in predicting the response of thin-walled metal matrix composites with large-diameter fibers when subjected to thermal gradients. These examples include composites with a finite number of fibers in the thickness direction that may be uniformly or nonuniformly spaced, thus admitting so-called functionally gradient composites. The results illustrate that the classical approach of decoupling micromechanical and macromechanical analyses in the presence of a finite number of large-diameter fibers, finite dimensions of the composite, and temperature gradient may produce excessively conservative estimates for macroscopic field quantities, while both underestimating and overestimating the local fluctuations of the microscopic quantities in different regions of the composite. Also demonstrated is the usefulness of the present approach in generating favorable stress distributions in the presence of thermal gradients by appropriately tailoring the internal microstructure details of the composite.

Aboudi, Jacob↗

NASA NTRS2001

Higher-Order Theory for Functionally Graded Materials

Functionally graded materials (FGM's) are a new generation of engineered materials wherein the microstructural details are spatially varied through nonuniform distribution of the reinforcement phase(s). Engineers accomplish this by using reinforcements with different properties, sizes, and shapes, as well as by interchanging the roles of the reinforcement and matrix phases in a continuous manner (ref. 1). The result is a microstructure that produces continuously or discretely changing thermal and mechanical properties at the macroscopic or continuum scale. This new concept of engineering the material's microstructure marks the beginning of a revolution both in the materials science and mechanics of materials areas since it allows one, for the first time, to fully integrate the material and structural considerations into the final design of structural components. Functionally graded materials are ideal candidates for applications involving severe thermal gradients, ranging from thermal structures in advanced aircraft and aerospace engines to computer circuit boards. Owing to the many variables that control the design of functionally graded microstructures, full exploitation of the FGM's potential requires the development of appropriate modeling strategies for their response to combined thermomechanical loads. Previously, most computational strategies for the response of FGM's did not explicitly couple the material's heterogeneous microstructure with the structural global analysis. Rather, local effective or macroscopic properties at a given point within the FGM were first obtained through homogenization based on a chosen micromechanics scheme and then subsequently used in a global thermomechanical analysis.

Aboudi, J.↗

NASA NTRS2014

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

nickel alloys↗

NASA NTRS2018

Multiscale Modeling of PEEK Using Reactive Molecular Dynamics Modeling and Micromechanics

Polyether ether ketone (PEEK) is a high-performance, semi-crystalline thermoplastic that is used in a wide range of engineering applications, including some structural components of aircraft. The design of new PEEK-based materials requires a precise understanding of the multiscale structure and behavior of semi-crystalline PEEK. Molecular Dynamics (MD) modeling can efficiently predict bulk-level properties of single phase polymers, and micromechanics can be used to homogenize those phases based on the overall polymer microstructure. In this study, MD modeling was used to predict the mechanical properties of the amorphous and crystalline phases of PEEK. The hierarchical microstructure of PEEK, which combines the aforementioned phases, was modeled using a multiscale modeling approach facilitated by NASA's MSGMC. The bulk mechanical properties of semi-crystalline PEEK predicted using MD modeling and MSGMC agree well with vendor data, thus validating the multiscale modeling approach.

Pisani, William A.↗

NASA NTRS1995

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

Pindera, Marek-Jerzy↗

NASA NTRS2010

Evolving Material Porosity on an Additive Manufacturing Simulation with the Generalized Method of Cells

The effect of material porosity on final part distortion and residual stresses in a selective laser sintering manufacturing simulation is presented here. A time-dependent thermomechanical model is used with the open-source FEA software CalculiX. Effective homogenized material properties for Inconel 625 are precomputed using NASA’s Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC). The evolving porosity of the material is estimated with each pass of the laser beam during simulation runtime. A comparison with a homogenous model and the evolving model shows that the evolving porous model predicts larger distortions with greater residual stresses.

Silva, Luis F.↗

NASA NTRS2020

Effect of Material Porosity on Residual Stress in an Additive Manufacturing Simulation using the Generalized Method of Cells

The effect of material porosity on final part distortion and residual stresses in a selective laser sintering manufacturing simulation is presented here. A time-dependent thermo-mechanical model is used with the open-source FEA software CalculiX. Effective homogenized material properties for Inconel 625 are precomputed using NASA’s Micromechanics Analysis Code with the Generalized Method of Cells. The evolving porosity of the material is estimated with each pass of the laser beam during simulation runtime. A comparison with a homogenous model and the evolving model shows that the model with evolving porosity predicts larger distortions with greater residual stresses.

Additive Manufactuirng↗

NASA NTRS2001

Micromechanics-Based Inelastic Finite Element Analysis Accomplished Via Seamless Integration of MAC/GMC

A critical issue in the micromechanics-based analysis of composite structures becomes the availability of a computationally efficient homogenization technique: one that is 1) Capable of handling the sophisticated, physically based, viscoelastoplastic constitutive and life models for each constituent; 2) Able to generate accurate displacement and stress fields at both the macro and the micro levels; 3) Compatible with the finite element method. The Generalized Method of Cells (GMC) developed by Paley and Aboudi is one such micromechanical model that has been shown to predict accurately the overall macro behavior of various types of composites given the required constituent properties. Specifically, the method provides "closed-form" expressions for the macroscopic composite response in terms of the properties, size, shape, distribution, and response of the individual constituents or phases that make up the material. Furthermore, expressions relating the internal stress and strain fields in the individual constituents in terms of the macroscopically applied stresses and strains are available through strain or stress concentration matrices. These expressions make possible the investigation of failure processes at the microscopic level at each step of an applied load history.

Arnold, Steven M.↗

NASA NTRSDate not supplied

A Nonlinear Viscoelastic-Viscoplastic Constitutive Model for Epoxy Polymers

The objective of this paper is to develop a nonlinear viscoelastic–viscoplastic constitutive model for epoxy polymers. The classic nonlinear viscoelasticity model is reformulated to yield a closed-form incremental constitutive relation, which relates the stress increments to the viscoelastic strain increments. A viscoplasticity model, which consists of the Drucker–Prager yield function, nonlinear isotropic and kinematic hardening laws, and the Perzyna viscosity function, is subsequently developed. The nonlinear viscoelasticity and the vis-coplasticity models are then implemented in a radial return algorithm. A closed-form algorithmic tangent operator is derived to facilitate model implementation. The nonlinear viscoelasticity model is validated by reproducing the test data for polymethyl methacrylate(PMMA). The present constitutive model’s capabilities are demonstrated through modeling viscoelastic–viscoplastic PMMA loaded at different strain rates. The mechanics of structure genome-based micromechanics approach, embedded with the present constitutive model, is used to homogenize a unidirectional fiber-reinforced composite with a PMMA matrix, subjected to uniaxial and shear loading at different strain rates. The viscoelastic characterization of PMT-F7 epoxy is evaluated by comparing the predicted creep–recovery responses by the present constitutive model with the experimental ones.

Liang Zhang↗

NASA NTRS2022

Multiscale Progressive Failure Analysis of 3D Woven Composites

Application of three-dimensional (3D) woven composites is growing as an alternative to the use of ply-based composite materials. However, the design, analysis, modeling, and optimization of these materials is more challenging due to their complex and inherently multiscale geometries. Herein, a multiscale modeling procedure, based on efficient, semi-analytical micromechanical theories rather than the traditional finite element approach, is presented and applied to a 3D woven carbon–epoxy composite. A crack-band progressive damage model was employed for the matrix constituent to capture the globally observed nonlinear response. Realistic microstructural dimensions and tow-fiber volume fractions were determined from detailed X-ray computed tomography (CT) and scanning electron microscopy data. Pre-existing binder-tow disbonds and weft-tow waviness, observed in X-ray CT scans of the composite, were also included in the model. The results were compared with experimental data for the in-plane tensile and shear behavior of the composite. The tensile predictions exhibited good correlations with the test data. While the model was able to capture the less brittle nature of the in-plane shear response, quantitative measures were underpredicted to some degree.

3D woven composites↗

NASA NTRS2019

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↗

NASA NTRS2013

The Effect of Fiber Strength Stochastics and Local Fiber Volume Fraction on Multiscale Progressive Failure of Composites

Continuous fiber unidirectional polymer matrix composites (PMCs) can exhibit significant local variations in fiber volume fraction as a result of processing conditions that can lead to further local differences in material properties and failure behavior. In this work, the coupled effects of both local variations in fiber volume fraction and the empirically-based statistical distribution of fiber strengths on the predicted longitudinal modulus and local tensile strength of a unidirectional AS4 carbon fiber/ Hercules 3502 epoxy composite were investigated using the special purpose NASA Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC); local effective composite properties were obtained by homogenizing the material behavior over repeating units cells (RUCs). The predicted effective longitudinal modulus was relatively insensitive to small (~8%) variations in local fiber volume fraction. The composite tensile strength, however, was highly dependent on the local distribution in fiber strengths. The RUC-averaged constitutive response can be used to characterize lower length scale material behavior within a multiscale analysis framework that couples the NASA code FEAMAC and the ABAQUS finite element solver. Such an approach can be effectively used to analyze the progressive failure of PMC structures whose failure initiates at the RUC level. Consideration of the effect of local variations in constituent properties and morphologies on progressive failure of PMCs is a central aspect of the application of Integrated Computational Materials Engineering (ICME) principles for composite materials.

multiscale analysis↗

NASA NTRS1989

Composite blade structural analyzer (COBSTRAN) user's manual

The installation and use of a computer code, COBSTRAN (COmposite Blade STRuctrual ANalyzer), developed for the design and analysis of composite turbofan and turboprop blades and also for composite wind turbine blades was described. This code combines composite mechanics and laminate theory with an internal data base of fiber and matrix properties. Inputs to the code are constituent fiber and matrix material properties, factors reflecting the fabrication process, composite geometry and blade geometry. COBSTRAN performs the micromechanics, macromechanics and laminate analyses of these fiber composites. COBSTRAN generates a NASTRAN model with equivalent anisotropic homogeneous material properties. Stress output from NASTRAN is used to calculate individual ply stresses, strains, interply stresses, thru-the-thickness stresses and failure margins. Curved panel structures may be modeled providing the curvature of a cross-section is defined by a single value function. COBSTRAN is written in FORTRAN 77.

Aiello, Robert A.↗

NASA NTRS1996

Micromechanics for particulate reinforced composites

A set of micromechanics equations for the analysis of particulate reinforced composites is developed using the mechanics of materials approach. Simplified equations are used to compute homogenized or equivalent thermal and mechanical properties of particulate reinforced composites in terms of the properties of the constituent materials. The microstress equations are also presented here to decompose the applied stresses on the overall composite to the microstresses in the constituent materials. The properties of a 'generic' particulate composite as well as those of a particle reinforced metal matrix composite are predicted and compared with other theories as well as some experimental data. The micromechanics predictions are in excellent agreement with the measured values.

Murthy, Pappu L. N.↗