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NASA NTRS1992

A micromechanics-based strength prediction methodology for notched metal matrix composites

An analytical micromechanics based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and post fatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.

Bigelow, C. A.↗

NASA NTRS1991

Micromechanics for ceramic matrix composites

The fiber substructuring concepts and the micromechanics equations that are embedded in the Ceramic Matrix Composite Analyzer (CEMCAN) computer code are described as well as the code itself, its current features and capabilities, and some examples to demonstrate the code's versatility. The methodology is equally applicable to metal matrix and polymer matrix composites. The prediction of ply mechanical and thermal properties agree very well with the existing models in the Integrated Composite Analyzer and the Ceramic Matrix Composite Analyzer, lending credence to the fiber substructuring approach. Fiber substructuring can capture greater local detail than conventional unit-cell-based micromechanical theories. It offers promise in simulating complex aspects of micromechanics in ceramic matrix composites.

Murthy, P. L. N.↗

NASA NTRS1993

A micromechanics-based strength prediction methodology for notched metal-matrix composites

An analytical micromechanics-based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three-dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and postfatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics-based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.

Bigelow, C. A.↗

NASA NTRS1995

Micromechanical Machining Processes and their Application to Aerospace Structures, Devices and Systems

Micromechanical machining processes are those micro fabrication techniques which directly remove work piece material by either a physical cutting tool or an energy process. These processes are direct and therefore they can help reduce the cost and time for prototype development of micro mechanical components and systems. This is especially true for aerospace applications where size and weight are critical, and reliability and the operating environment are an integral part of the design and development process. The micromechanical machining processes are rapidly being recognized as a complementary set of tools to traditional lithographic processes (such as LIGA) for the fabrication of micromechanical components. Worldwide efforts in the U.S., Germany, and Japan are leading to results which sometimes rival lithography at a fraction of the time and cost. Efforts to develop processes and systems specific to aerospace applications are well underway.

Friedrich, Craig R.↗

NASA NTRS1997

Mechanical Characterization and Micromechanical Modeling of Woven Carbon/Copper Composites

The present investigation examines the in-plane mechanical behavior of a particular woven metal matrix composite (MMC); 8-harness (8H) satin carbon/copper (C/Cu). This is accomplished via mechanical testing as well as micromechanical modeling. While the literature is replete with experimental and modeling efforts for woven and braided polymer matrix composites, little work has been done on woven and braided MMC's. Thus, the development and understanding of woven MMC's is at an early stage. 8H satin C/Cu owes its existence to the high thermal conductivity of copper and low density and thermal expansion of carbon fibers. It is a candidate material for high heat flux applications, such as space power radiator panels. The experimental portion of this investigation consists of monotonic and cyclic tension, compression, and Iosipescu shear tests, as well as combined tension-compression tests. Tests were performed on composite specimens with three copper matrix alloy types: pure Cu, Cu-0.5 weight percent Ti (Cu-Ti), and Cu-0.7 weight percent Cr (Cu-Cr). The small alloying additions are present to promote fiber/matrix interfacial bonding. The analytical modeling effort utilizes an approach in which a local micromechanical model is embedded in a global micromechanical model. This approach differs from previously developed analytical models for woven composites in that a true repeating unit cell is analyzed. However, unlike finite element modeling of woven composites, the geometry is sufficiently idealized to allow efficient geometric discretization and efficient execution.

Bednarcyk, Brett A.↗

NASA NTRS1998

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

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

Goldberg, Robert K.↗

NASA NTRS1999

Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach

Potential gas turbine applications will expose polymer matrix composites to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under extreme conditions. Specifically, analytical methods designed for these applications must have the capability of properly capturing the strain rate sensitivities and nonlinearities that are present in the material response. The Ramaswamy-Stouffer constitutive equations, originally developed to analyze the viscoplastic deformation of metals, have been modified to simulate the nonlinear deformation response of ductile, crystalline polymers. The constitutive model is characterized and correlated for two representative ductile polymers. Fiberite 977-2 and PEEK, and the computed results correlate well with experimental values. The polymer constitutive equations are implemented in a mechanics of materials based composite micromechanics model to predict the nonlinear, rate dependent deformation response of a composite ply. Uniform stress and uniform strain assumptions are applied to compute the effective stresses of a composite unit cell from the applied strains. The micromechanics equations are successfully verified for two polymer matrix composites. IM7/977-2 and AS4/PEEK. The ultimate strength of a composite ply is predicted with the Hashin failure criteria that were implemented in the composite micromechanics model. The failure stresses of the two composite material systems are accurately predicted for a variety of fiber orientations and strain rates. The composite deformation model is implemented in LS-DYNA, a commercially available transient dynamic explicit finite element code. The matrix constitutive equations are converted into an incremental form, and the model is implemented into LS-DYNA through the use of a user defined material subroutine. The deformation response of a bulk polymer and a polymer matrix composite are predicted by finite element analyses. The results compare reasonably well to experimental values, with some discrepancies. The discrepancies are at least partially caused by the method used to integrate the rate equations in the polymer constitutive model.

Goldberg, Robert K.↗

NASA NTRS2000

Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were implemented into a mechanics of materials based micromechanics method. In the current work, the computation of the effective inelastic strain in the micromechanics model was modified to fully incorporate the Poisson effect. The micromechanics equations were also combined with classical laminate theory to enable the analysis of symmetric multilayered laminates subject to in-plane loading. A quasi-incremental trapezoidal integration method was implemented to integrate the constitutive equations within the laminate theory. Verification studies were conducted using an AS4/PEEK composite using a variety of laminate configurations and strain rates. The predicted results compared well with experimentally obtained values.

Goldberg, Robert K.↗

NASA NTRS1994

The Relationship Between Constraint and Ductile Fracture Initiation as Defined by Micromechanical Analyses

The use of small laboratory specimens to predict the integrity of large, complex structures relies on the validity of single parameter fracture mechanics. Unfortunately, the constraint loss associated with large scale yielding, whether in a laboratory specimen because of its small size or in a structure because it contains shallow flaws loaded in tension, can cause the breakdown of classical fracture mechanics and the loss of transferability of critical, global fracture parameters. Although the issue of constraint loss can be eliminated by testing actual structural configurations, such an approach can be prohibitively costly. Hence, a methodology that can correct global fracture parameters for constraint effects is desirable. This research uses micromechanical analyses to define the relationship between global, ductile fracture initiation parameters and constraint in two specimen geometries (SECT and SECB with varying a/w ratios) and one structural geometry (circumferentially cracked pipe). Two local fracture criteria corresponding to ductile fracture micromechanisms are evaluated: a constraint-modified, critical strain criterion for void coalescence proposed by Hancock and Cowling and a critical void ratio criterion for void growth based on the Rice and Tracey model. Crack initiation is assumed to occur when the critical value in each case is reached over some critical length. The primary material of interest is A516-70, a high-hardening pressure vessel steel sensitive to constraint; however, a low-hardening structural steel that is less sensitive to constraint is also being studied. Critical values of local fracture parameters are obtained by numerical analysis and experimental testing of circumferentially notched tensile specimens of varying constraint (e.g., notch radius). These parameters are then used in conjunction with large strain, large deformation, two- and three-dimensional finite element analyses of the geometries listed above to predict crack initiation loads and to calculate the associated (critical) global fracture parameters. The loads are verified experimentally, and microscopy is used to measure pre-crack length, crack tip opening displacement (CTOD), and the amount of stable crack growth. Results for A516-70 steel indicate that the constraint-modified, critical strain criterion with a critical length approximately equal to the grain size (0.0025 inch) provides accurate predictions of crack initiation. The critical void growth criterion is shown to considerably underpredict crack initiation loads with the same critical length. The relationship between the critical value of the J-integral for ductile crack initiation and crack depth for SECT and SECB specimens has been determined using the constraint-modified, critical strain criterion, demonstrating that this micromechanical model can be used to correct in-plane constraint effects due to crack depth and bending vs. tension loading. Finally, the relationship developed for the SECT specimens is used to predict the behavior of circumferentially cracked pipe specimens.

Panontin, Tina L.↗

NASA NTRS2001

Implementation of Fiber Substructuring Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were incorporated into a mechanics of materials based micromechanics method. In the current work, the micromechanics method is revised such that the composite unit cell is divided into a number of slices. Micromechanics equations are then developed for each slice, with laminate theory applied to determine the elastic properties, effective stresses and effective inelastic strains for the unit cell. Verification studies are conducted using two representative polymer matrix composites with a nonlinear, strain rate dependent deformation response. The computed results compare well to experimentally obtained values.

Goldberg, Robert K.↗

NASA NTRS2002

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

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

Goldberg, Robert K.↗

NASA NTRS2004

Implementation of Higher Order Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A procedure has been developed to investigate the nonlinear response of composite plates under large strain and high strain rate loading. A recently developed strain dependent micromechanics model is extended to account for the shear effects during impact. Four different assumptions of shear deformation effects are investigated to improve the development strain rate dependent micromechanics model. A method to determine through the thickness strain and transverse Poisson's ratio is developed. The revised micromechanics model is implemented into higher order laminate theory. Parametric studies are conducted to investigate transverse shear effects during impact.

Kim, Heung Soo↗

NASA NTRS2005

Development, Implementation and Application of Micromechanical Analysis Tools for Advanced High Temperature Composites

This document contains the final report to the NASA Glenn Research Center (GRC) for the research project entitled Development, Implementation, and Application of Micromechanical Analysis Tools for Advanced High-Temperature Composites. The research supporting this initiative has been conducted by Dr. Brett A. Bednarcyk, a Senior Scientist at OM in Brookpark, Ohio from the period of August 1998 to March 2005. Most of the work summarized herein involved development, implementation, and application of enhancements and new capabilities for NASA GRC's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) software package. When the project began, this software was at a low TRL (3-4) and at release version 2.0. Due to this project, the TRL of MAC/GMC has been raised to 7 and two new versions (3.0 and 4.0) have been released. The most important accomplishments with respect to MAC/GMC are: (1) A multi-scale framework has been built around the software, enabling coupled design and analysis from the global structure scale down to the micro fiber-matrix scale; (2) The software has been expanded to analyze smart materials; (3) State-of-the-art micromechanics theories have been implemented and validated within the code; (4) The damage, failure, and lifing capabilities of the code have been expanded from a very limited state to a vast degree of functionality and utility; and (5) The user flexibility of the code has been significantly enhanced. MAC/GMC is now the premier code for design and analysis of advanced composite and smart materials. It is a candidate for the 2005 NASA Software of the Year Award. The work completed over the course of the project is summarized below on a year by year basis. All publications resulting from the project are listed at the end of this report.

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NASA NTRS2006

Micromechanics Modeling of Functionally Graded Interphase Regions in Carbon Nanotube-Polymer Composites

The effective elastic properties of a unidirectional carbon fiber/epoxy lamina in which the carbon fibers are coated with single-walled carbon nanotubes are modeled herein through the use of a multi-scale method involving the molecular dynamics/equivalent continuum and micromechanics methods. The specific lamina representative volume element studied consists of a carbon fiber surrounded by a region of epoxy containing a radially varying concentration of carbon nanotubes which is then embedded in the pure epoxy matrix. The variable concentration of carbon nanotubes surrounding the carbon fiber results in a functionally graded interphase region as the properties of the interphase region vary according to the carbon nanotube volume fraction. Molecular dynamics and equivalent continuum methods are used to assess the local effective properties of the carbon nanotube/epoxy comprising the interphase region. Micromechanics in the form of the Mori-Tanaka method are then applied to obtain the global effective properties of the graded interphase region wherein the carbon nanotubes are randomly oriented. Finally, the multi-layer composite cylinders micromechanics approach is used to obtain the effective lamina properties from the lamina representative volume element. It was found that even very small quantities of carbon nanotubes (0.36% of lamina by volume) coating the surface of the carbon fibers in the lamina can have a significant effect (8% increase) on the transverse properties of the lamina (E22, k23, G23 and G12) with almost no affect on the lamina properties in the fiber direction (E11 and v12).

Seidel, Gary D.↗

NASA NTRS2010

Micromechanics-Based Structural Analysis (FEAMAC) and Multiscale Visualization within Abaqus/CAE Environment

A unified framework is presented that enables coupled multiscale analysis of composite structures and associated graphical pre- and postprocessing within the Abaqus/CAE environment. The recently developed, free, Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software couples NASA's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with Abaqus/Standard and Abaqus/Explicit to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. The Graphical User Interfaces (FEAMAC-Pre and FEAMAC-Post), developed through collaboration between SIMULIA Erie and the NASA Glenn Research Center, enable users to employ a new FEAMAC module within Abaqus/CAE that provides access to the composite microscale. FEA IAC-Pre is used to define and store constituent material properties, set-up and store composite repeating unit cells, and assign composite materials as sections with all data being stored within the CAE database. Likewise FEAMAC-Post enables multiscale field quantity visualization (contour plots, X-Y plots), with point and click access to the microscale i.e., fiber and matrix fields).

Arnold, Steven M.↗

NASA NTRS2006

Micromechanics and Piezo Enhancements of HyperSizer

The commercial HyperSizer aerospace-composite-material-structure-sizing software has been enhanced by incorporating capabilities for representing coupled thermal, piezoelectric, and piezomagnetic effects on the levels of plies, laminates, and stiffened panels. This enhancement is based on a formulation similar to that of the pre-existing HyperSizer capability for representing thermal effects. As a result of this enhancement, the electric and/or magnetic response of a material or structure to a mechanical or thermal load, or its mechanical response to an applied electric or magnetic field can be predicted. In another major enhancement, a capability for representing micromechanical effects has been added by establishment of a linkage between HyperSizer and Glenn Research Center s Micromechanics Analysis Code With Generalized Method of Cells (MAC/GMC) computer program, which was described in several prior NASA Tech Briefs articles. The linkage enables Hyper- Sizer to localize to the fiber and matrix level rather than only to the ply level, making it possible to predict local failures and to predict properties of plies from those of the component fiber and matrix materials. Advanced graphical user interfaces and database structures have been developed to support the new HyperSizer micromechanics capabilities.

Arnold, Steven M.↗

NASA NTRS2005

Comprehensive Micromechanics-Analysis Code - Version 4.0

Version 4.0 of the Micromechanics Analysis Code With Generalized Method of Cells (MAC/GMC) has been developed as an improved means of computational simulation of advanced composite materials. The previous version of MAC/GMC was described in "Comprehensive Micromechanics-Analysis Code" (LEW-16870), NASA Tech Briefs, Vol. 24, No. 6 (June 2000), page 38. To recapitulate: MAC/GMC is a computer program that predicts the elastic and inelastic thermomechanical responses of continuous and discontinuous composite materials with arbitrary internal microstructures and reinforcement shapes. The predictive capability of MAC/GMC rests on a model known as the generalized method of cells (GMC) - a continuum-based model of micromechanics that provides closed-form expressions for the macroscopic response of a composite material in terms of the properties, sizes, shapes, and responses of the individual constituents or phases that make up the material. Enhancements in version 4.0 include a capability for modeling thermomechanically and electromagnetically coupled ("smart") materials; a more-accurate (high-fidelity) version of the GMC; a capability to simulate discontinuous plies within a laminate; additional constitutive models of materials; expanded yield-surface-analysis capabilities; and expanded failure-analysis and life-prediction capabilities on both the microscopic and macroscopic scales.

Arnold, S. M.↗

NASA NTRS2018

Coupled Thermomechanical Micromechanics Modeling of the Influence of Thermally Grown Oxide Layer in an Environmental Barrier Coating System

Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting critical components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) from extreme thermal/chemical environments. However, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination. Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting silicon based ceramic matrix composite (CMC) components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) such as silicon carbide from extreme thermal/chemical environments. In a typical CMC/EBC system, an EBC may or may not be adhered to an underlying substrate with a bond coat (e.g., silicon). Irrespective, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination, recession, chemical attack and dissolution, thermo-mechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites and will be used herein to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer in EBC/CMC systems without a silicon bond coat. To accomplish this a sensitivity study is conducted to examine the influence of uniformly and non-uniformly grown oxide layer on the associated driving forces leading to mechanical failure (spallation) of EBC layer when subjected to isothermal loading, recession, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites (Aboudi et al., 1999, Composites B). For example, HOTFGM was previously used (Arnold et al, 1995, NASA CP 10178, paper 34), to assess interlaminar stresses (including free edge effects) in a substrate with a thermal barrier coating (TBC). In this study, HOTFGM micromechanics analyses will be used to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer between a silicon carbide substrate and a ytterbium disilicate EBC. In order to realistically simulate TGO growth, an evolution law will be incorporated into HOTFGM. In addition, the effect of TGO roughness will be explored consistent with previous TBC work (Pindera et al., 2000. Material Science and Engineering, A284, pp. 158-175). This model represents a first step in developing a robust analysis tool that can ultimately be used to design durable EBC systems. Additional failure modes will be considered as part of a future work.

environmental barrier coating↗