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NASA NTRS2011

Literature Reviews on Modeling Internal Geometry of Textile Composites and Rate-Independent Continuum Damage

Textile composite materials have good potential for constructing composite structures where the effects of three-dimensional stresses are critical or geometric complexity is a manufacturing concern. There is a recent interest in advancing competence within Langley Research Center for modeling the degradation of mechanical properties of textile composites. In an initial effort, two critical areas are identified to pursue: (1) Construction of internal geometry of textile composites, and (2) Rate-independent continuum damage mechanics. This report documents reviews on the two subjects. Various reviewed approaches are categorized, their assumptions, methods, and progress are briefed, and then critiques are presented. Each review ends with recommended research.

Su-Yuen, Hsu↗

NASA NTRS1988

A cumulative damage model for continuous fiber composite laminates with matrix cracking and interply delaminations

The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.

Allen, David H.↗

NASA NTRS1984

Crack layer theory

A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.

Chudnovsky, A.↗

NASA NTRS1987

Crack layer theory

Chudnovsky, A.↗

NASA NTRS2008

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

Schuecker, Clara↗

NASA NTRS1991

Progressive failure methodologies for predicting residual strength and life of laminated composites

Two progressive failure methodologies currently under development by the Mechanics of Materials Branch at NASA Langley Research Center are discussed. The damage tolerance/fail safety methodology developed by O'Brien is an engineering approach to ensuring adequate durability and damage tolerance by treating only delamination onset and the subsequent delamination accumulation through the laminate thickness. The continuum damage model developed by Allen and Harris employs continuum damage laws to predict laminate strength and life. The philosophy, mechanics framework, and current implementation status of each methodology are presented.

Harris, Charles E.↗

NASA NTRS1988

Effect of microstructural damage on ply stresses in laminated composites

The mechanisms involved in damage and failure of laminated orthotropic composites are investigated theoretically. The continuum model developed accounts for both matrix cracks and interply delamination using second-order tensor-valued internal-state variables based on the locally averaged microcrack dynamics. The derivation of the model is given in detail, and numerical results for sample problems are presented in extensive graphs and tables. The model is shown to be effective in predicting stresses at the ply level, and significant damage-induced decreases in laminate stress states are found.

Allen, D. H.↗

NASA NTRS2013

Micromechanics Fatigue Damage Analysis Modeling for Fabric Reinforced Ceramic Matrix Composites

A micromechanics analysis modeling method was developed to analyze the damage progression and fatigue failure of fabric reinforced composite structures, especially for the brittle ceramic matrix material composites. A repeating unit cell concept of fabric reinforced composites was used to represent the global composite structure. The thermal and mechanical properties of the repeating unit cell were considered as the same as those of the global composite structure. The three-phase micromechanics, the shear-lag, and the continuum fracture mechanics models were integrated with a statistical model in the repeating unit cell to predict the progressive damages and fatigue life of the composite structures. The global structure failure was defined as the loss of loading capability of the repeating unit cell, which depends on the stiffness reduction due to material slice failures and nonlinear material properties in the repeating unit cell. The present methodology is demonstrated with the analysis results evaluated through the experimental test performed with carbon fiber reinforced silicon carbide matrix plain weave composite specimens.

Min, J. B.↗

NASA NTRS2002

Micro-Mechanical Modeling of Ductile Fracture in Welded Aluminum-Lithium Alloys

This study describes a 3-D computational framework to model stable extension of a macroscopic crack under mode I conditions in ductile metals. Material separation occurs through a local fracture mechanism based on the growth and coalescence of micro voids dispersed in the material. The Gurson-Tvergaard plasticity model for void materials describes the eventual loss of material stress capacity under sustained loading. Fixed-sized computational cell elements defined on a thin layer adjacent to the crack plane provide an implicit length scale for continuum damage model. Outside this layer, the material remains undamaged by void growth, consistent with metallurgical observations. The key micro-mechanics parameters are D, the thickness of cell layer, and f 0 , the initial cell porosity.

Ahmed Ibrahim↗

NASA NTRS2012

Computational Implementation of a Thermodynamically Based Work Potential Model For Progressive Microdamage and Transverse Cracking in Fiber-Reinforced Laminates

A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.

Pineda, Evan J.↗

NASA NTRSDate not supplied

TPSAS-NF1676L-13792-DND

Extreme structural requirements of future aerospace vehicles motivate the development of new, ultra-durable materials and game-changing methodologies for material certification and sustainment. Computational simulations spanning many orders of magnitude in length and time scales—from the nanoscale of underlying damage processes to the larger scales of continuum cracks—are being developed to support these requirements. Results of these simulations are used to deduce key aspects of material response to loads and environments, including: - The microstructural mechanics that govern metal fatigue crack initiation and growth - The variety and complexity of the dislocation-precipitate interac- tions that underpin plastic behavior and damage evolution - The energetic principles that govern the interaction of water with crack surfaces within a structural component - The mechanics of grain boundary separation Modeling the physics behind these metal fatigue behaviors is extremely complex, and requires intensive, high-fidelity simulations. The knowledge gained through these simulations, however, is forming the keystone for advanced material design and will enable development of more capable, reliable structures for aerospace vehicles.

Jacob Hochhalter↗

NASA NTRS2006

A Thermodynamically Consistent Damage Model for Advanced Composites

A continuum damage model for the prediction of damage onset and structural collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The principal damage mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a damage tensor that is fixed in space. Crack closure under load reversal effects are taken into account using damage variables established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different damage mechanisms occurring at the ply level. The constitutive damage model is implemented in a finite element code. The objectivity of the numerical model is assured by regularizing the dissipated energy at a material point using Bazant's Crack Band Model. To verify the accuracy of the approach, analyses of coupon specimens were performed, and the numerical predictions were compared with experimental data.

Maimi, Pere↗

NASA NTRS1983

Mechanics of composite materials: Recent advances; Proceedings of the Symposium, Virginia Polytechnic Institute and State University, Blacksburg, VA, August 16-19, 1982

The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.

Hashin, Z.↗

NASA NTRS1994

A methodology to predict damage initiation, damage growth and residual strength in titanium matrix composites

In this research, a methodology to predict damage initiation, damage growth, fatigue life, and residual strength in titanium matrix composites (TMC) is outlined. Emphasis was placed on micromechanics-based engineering approaches. Damage initiation was predicted using a local effective strain approach. A finite element analysis verified the prevailing assumptions made in the formulation of this model. Damage growth, namely, fiber-bridged matrix crack growth, was evaluated using a fiber bridging (FB) model which accounts for thermal residual stresses. This model combines continuum fracture mechanics and micromechanics analyses yielding stress-intensity factor solutions for fiber-bridged matrix cracks. It is assumed in the FB model that fibers in the wake of the matrix crack are idealized as a closure pressure, and an unknown constant frictional shear stress is assumed to act along the debond length of the bridging fibers. This frictional shear stress was used as a curve fitting parameter to the available experimental data. Fatigue life and post-fatigue residual strength were predicted based on the axial stress in the first intact 0 degree fiber calculated using the FB model and a three-dimensional finite element analysis.

Bakuckas, J. G., Jr.↗

NASA NTRS1992

Inelastic Deformation of Metal Matrix Composites: Plasticity and Damage Mechanisms - Part 1

The deformation mechanisms of a Ti 15-3/SCS6 (SiC fiber) metal matrix composite (MMC) were investigated using a combination of mechanical measurements and microstructural analysis. The objectives were to evaluate the contributions of plasticity and damage to the overall inelastic response, and to confirm the mechanisms by rigorous microstructural evaluations. The results of room temperature experiments performed on 0 degree and 90 degree systems primarily are reported in this report. Results of experiments performed on other laminate systems and at high temperatures will be provided in a forthcoming report. Inelastic deformation of the 0 degree MMC (fibers parallel to load direction) was dominated by the plasticity of the matrix. In contrast, inelastic deformations of the 90 degree composite (fibers perpendicular to loading direction) occurred by both damage and plasticity. The predictions of a continuum elastic plastic model were compared with experimental data. The model was adequate for predicting the 0 degree response; however, it was inadequate for predicting the 90 degree response largely because it neglected damage. The importance of validating constitutive models using a combination of mechanical measurements and microstructural analysis is pointed out. The deformation mechanisms, and the likely sequence of events associated with the inelastic deformation of MMCs, are indicated in this paper.

Majumdar, B. S.↗

NASA NTRS2015

Application of the Refined Zigzag Theory to the Modeling of Delaminations in Laminated Composites

The Refined Zigzag Theory is applied to the modeling of delaminations in laminated composites. The commonly used cohesive zone approach is adapted for use within a continuum mechanics model, and then used to predict the onset and propagation of delamination in five cross-ply composite beams. The resin-rich area between individual composite plies is modeled explicitly using thin, discrete layers with isotropic material properties. A damage model is applied to these resin-rich layers to enable tracking of delamination propagation. The displacement jump across the damaged interfacial resin layer is captured using the zigzag function of the Refined Zigzag Theory. The overall model predicts the initiation of delamination to within 8% compared to experimental results and the load drop after propagation is represented accurately.

Groh, Rainer M. J.↗

NASA NTRS1991

Determinants of the mechanical properties of bones

The mechanical properties of bones are governed by the same principles as those of man-made load-bearing structures, but the organism is able to adapt its bone structure to changes in skeletal loading. In this overview of the determinants of the strength and stiffness of bone, a continuum approach has been taken, in which the behavior of a macroscopic structure depends on its shape and size, and on the mechanical properties of the material within. The latter are assumed to depend on the composition (porosity and mineralization) and organization (trabecular or cortical bone architecture, collagen fiber orientation, fatigue damage) of the bone. The effects of each of these factors are reviewed. Also, the possible means of non-invasively estimating the strength or other mechanical properties of a bone are reviewed, including quantitative computed tomography, photon absorptiometry, and ultrasonic measurements. The best estimates of strength have been obtained with photon absorptiometry and computed tomography, which at best are capable of accounting for 90% of the strength variability in a simple in vitro test, but results from different laboratories have been highly variable.

Non-NASA Center↗

NASA NTRS2008

Multiscale Modeling of Damage Processes in fcc Aluminum: From Atoms to Grains

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, current analysis is limited to small domains and increasing the size of the MD domain quickly presents intractable computational demands. A preferred approach to surmount this computational limitation has been to combine continuum mechanics-based modeling procedures, such as the finite element method (FEM), with MD analyses thereby reducing the region of atomic scale refinement. Such multiscale modeling strategies can be divided into two broad classifications: concurrent multiscale methods that directly incorporate an atomistic domain within a continuum domain and sequential multiscale methods that extract an averaged response from the atomistic simulation for later use as a constitutive model in a continuum analysis.

Glaessgen, E. H.↗