Showing papers on "Micromechanics published in 1990"

Toughening of a Particulate-Reinforced Ceramic-Matrix Composite by Thermal Residual Stress

Abstract: The micromechanics involved in increased crack growth resistance, KR, due to the addition of TiB2 particulate in a SiC matrix was analyzed both experimentally and theoretically. The fractography evidence, in which, the advancing crack was attracted to adjacent particulates, was attributed to the tensile region surrounding a particulate. Countering this effect is the compressive thermal residual stress, which results in the toughening of the composite, in the matrix. This thermal residual stress field in a particulate-reinforced ceramic-matrix composite is induced by the mismatch in the coefficients of thermal expansion of the matrix and the particulate when the composite is cooled from the processing to room temperature. The increase in KR of the composite over the monolithic matrix, which was measured by using a hybrid experimental-numerical analysis, was 77%, and compared well with the analytically predicted increase of 52%. The increase in KR predicted by the crack deflection model was 14%. Dependence of KR on the volume fraction of particulates, fp, and of voids, fv, is also discussed.

Dislocation dynamics. I. A proposed methodology for deformation micromechanics.

Abstract: A new methodology in computational micromechanics, dislocation dynamics (DD), is introduced. Dislocation dynamics is developed for examining the dynamic behavior of dislocation distributions in solid materials. Under conditions of externally applied stress, dislocations exhibit glide with a velocity proportional to a power of the applied stress ${\mathrm{\ensuremath{\sigma}}}^{\mathit{m}}$ and climb motion with a velocity that is a function of the applied stress and temperature. These motions result from long-range force fields, comprising both externally applied stress and long-range interactions between individual dislocations. Short-range reactions are represented as discrete events. The DD methodology is to be differentiated from particle methods in statistical mechanics (e.g., molecular dynamics and the Monte Carlo method) in two respects. First, DD is developed to study the dynamical behavior of ``defects'' in the solid. Generally, the density of defects is less than that of the particles that make up the solid. Second, the small number of dislocations allows for a complete dynamical representation of the evolution of dislocations in the material medium without the requirement of statistical averaging. The purpose of the DD methodology is to bridge the gap between experimentally observed phenomena and theoretical descriptions of dislocation aggregates, particularly the evolution of self-organized dislocation structures under temperature, stress, and irradiation conditions.

Micromechanics and Inhomogeneity

Abstract: Micromechanics has emerged as a recognized discipline in the study of mechanics of materials. This book contains articles on micromechanics and inhomogeneity.

Composite materials in aircraft structures

Abstract: Origins of composite materials, J.E.Bailey the potential of composite materials, D.P.Bashford types of materials, D.R.Lovell matrices for advanced structural composites, E.Green the fibre-matrix interface and composite, strength, G.Dorey micromechanics and properties of fibre composites, F.R.Jones a design philosophy for composite materials, R.D.Pairdaudeau design rules and techniques for composite materials, S.W.Teal load-carrying joints, F.L.Matthews advanced composite tooling and manufacturing methods, M.W.Commander quality assurance, P.W.Groves et al non-destructive evaluation of composite aerospace components, P.R.Teagle repair techniques for composite structures, A.A.Baker case histories.

Interpretation of the fragmentation phenomenon in single‐filament composite experiments

Abstract: The fiber fragmentation phenomenon in the single‐filament composite test is currently among the most intensively researched aspects of composite micromechanics. By this method the interfacial shear strength, a physical parameter which reflects the quality of the fiber/matrix bonding, is calculated. In most studies various statistical models for the distribution of fragment lengths have been assumed without any justification other than a good fit to experimental data. Here we argue that if the flaws are assumed to be distributed along the fiber length according to a spatial Poisson process, then far from the saturation point the resulting fragment lengths must exactly follow a shifted exponential distribution. At the saturation limit, the distribution of fragment lengths is still approximately exponential. This is confirmed by single‐filament composite experiments with high strength carbon fibers embedded in epoxy. Cumulative distributions of interdefect spacings at various levels of stress (or strain) are...

Fiber-matrix interface effects in the presence of thermally induced residual stresses

Abstract: The mechanics of transversely loaded high-temperature composites with a thermally induced residual stress field and a vanishingly weak fiber-matrix interface strength was investigated using two analytical models. In particular, the effects of several physical properties defining the performance of the constituent fiber, matrix, and interface are examined relative to their effect on composite's behavior. Both models demonstrate that, if there is a thermally induced residual stress field in the composite, the initial transverse modulus for the composite will be the same regardless of whether there is a well-bonded or an unbonded interface. 10 refs.

Unified micromechanics of damping for unidirectional and off-axis fiber composites

Abstract: An integrated micromechanics methodology for the prediction of damping capacity in fiber-reinforced polymer matrix unidirectional composites has been developed. Explicit micromechanics equations based on hysteretic damping are presented relating the on-axis damping capacities to the fiber and matrix properties and fiber volume ratio. The damping capacities of unidirectional composites subjected to off-axis loading are synthesized from on-axis damping values. Predicted values correlate satisfactorily with experimental measurements. The hygro-thermal effect on the damping performance of unidirectional composites caused by temperature and moisture variations is also modeled. The damping contributions from interfacial friction between broken fibers and matrix are incorporated. Finally, the temperature rise in continuously vibrating composite plies is estimated. Application examples illustrate the significance of various parameters on the damping performance of unidirectional and off-axis fiber reinforced composites.

Stress distribution in an aluminum interconnect of very large scale integration

Abstract: Thermal stress‐induced void formation in aluminum interconnect has become a major reliability problem in the usage of very large scale integration circuits. The purpose of this work is to analytically evaluate stresses in the Al line. By applying Eshelby’s method in micromechanics, the stresses in the Al line were estimated analytically as a function of the aspect ratio of the Al line cross section. The yielding criteria in plasticity were applied to examine whether the calculated stresses can induce relaxation by plastic deformation. The analytically calculated results were compared with previous results of numerical calculation and experimental observation.

Factors Affecting the Transverse Tensile Strength of Unidirectional Continuous Silicon Carbide Fibre Reinforced 6061 Aluminum

Abstract: A study of the micromechanics of continuous silicon carbide fibre rein forced 6061 aluminum has been carried out using generalised plane strain non-linear finite element analysis. An interface element has been developed enabling separate shear and tensile strengths to be assigned, with a quadratic interaction equation. Residual stresses due to manufacturing were included in the analysis.The effect on transverse tensile strength of fibre packing geometry, fibre spacing, resid ual stresses, interface strengths and matrix material properties were investigated. It was found that the interface strength is the most important factor. Residual stresses are beneficial, these being largely controlled by the yield strength of the matrix material at the time the residual stresses are set up. Fibre packing and spacing and matrix strength do not significantly affect predicted strength.

Micromechanical Analysis of the Creep Response of Unidirectional Composites

Abstract: The paper outlines the use of the micromechanics model proposed by Aboudi in predicting the creep response of unidirectional composites consisting of linearly viscoelastic matrices and elastic fibers. The closed-form expressions for the effective elastic moduli given in terms of the phase moduli and volume fractions provided by the micromechanics model facilitate a straightforward application of the viscoelastic Correspondence Principle. The inversion of the effective moduli in the Laplace transform domain to the time domain is subsequently accomplished using the Bellman method. The predictions of the model are compared with the creep response of T300/934 graphite/epoxy unidirectional coupons at two different temperatures. Very good correlation between theory and experiment is illustrated for the linearly viscoelastic response characterized by relatively small creep strains.

A mechanical model for elastic fiber microbuckling

Abstract: A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (<0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.

The effective thermal conductivity of composites reinforced by coated cylindrically orthotropic fibers

Abstract: The present paper is concerned with coated‐fiber composites in which the fibers possess cylindrical orthotropy and may have an arbitrary orientation distribution. A micromechanics model is developed which predicts the effective thermal conductivity and estimates the local fields of such composites which may be subjected to uniform heat fluxes on its boundary. The micromechanics model is based on the Mori–Tanaka mean‐field concept [T. Mori and K. Tanaka, Acta Metall. 21, 571 (1973)] and provides explicit expressions for the effective conductivity of the considered composite aggregate which is highly complicated. The analysis shows that special care is needed in formulating an effective theory of composites with constituents possessing curvilinear anisotropy.

Micromechanics characterization of sublaminate damage

Abstract: A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.

Mechanics of damping for fiber composite laminates including hygrothermal effects

Abstract: An integrated mechanics theory was developed for the modeling of composite damping from the micromechanics to the laminate level. Simplified, design oriented equations based on hysteretic damping are presented for on-axis plies, off-axis plies, and laminates including the effect of temperature, moisture, and interply hysteretic damping. The temperature rise within vibrating composite laminates resulting from strain energy dissipation is also modeled, and their coupled hygro-thermo-mechanical response is predicted. The method correlates well with reported damping measurements. Application examples illustrate the effect of various ply, laminate, and hygro-thermal parameters on the overall damping performance of composite laminates.

Micro-mechanics of crack initiation

Abstract: Prior to the crack initiation, damage is most often localized at a scale below the size of the classical representative volume element of the continuum mechanics. This allows the stress and strain analyses in a component to neglect the strain-damage coupling at macro-scale. At the micro-scale, this coupling plays a very important role which can be emphasized by a two scale element of an elastoplastic damaged micro-element embedded in an elastic or elastoplastic macro-element. The Lin-Taylor hypothesis of strain compatibility allows the determination of the damage at micro-scale by solving the coupled constitutive equations for a given macro-strain history. It is shown how this model may be cast in the form of a post-processor of a finite element code and how a simple damage law coupled with strain constitutive equations replicates the main features of ductile or creep crack initiation, low cycle and high cycle fatigue for the case of a three-dimensional state of stress.

Micromechanics of failure of quasi-brittle materials

Abstract: Keynote speaker invited lecture experimental measurements failure localization and damage model micromechanics of geological materials ceramics, ice dynamic study I - response interface mechanics dynamic study II - energy release mechanisms micromechanics of concrete.

Influence of interfacial shear stress on first-matrix cracking stress in ceramic-matrix composites

Abstract: The first-matrix cracking stress and fiber-matrix interfacial shear stress were measured in zircon-matrix composites uniaxially reinforced with either uncoated or BN-coated silicon carbide filaments to study the role of intentional changes in interfacial shear stress on first-matrix cracking stress. The first-matrix cracking stress was measured by mechanical tests performed in either tension or flexure, and the filament-matrix interfacial shear stress was measured by a fiber pushout test. The first-matrix cracking stress was independent of the measured interfacial shear stress and did not conform to the predictions of a number of energy-based micromechanics models. In contrast, the first-matrix cracking stress showed a good correlation with the first-matrix cracking strain, which is hypothesized to be a more realistic criterion for first-matrix cracking in this class of filament-reinforced ceramic-matrix composites.

An integrated methodology for optimizing the passive damping of composite structures

Abstract: A method is presented for tailoring plate and shell composite structures for optimal forced damped dynamic response. The damping of specific vibration modes is optimized with respect to dynamic performance criteria including placement of natural frequencies and minimization of resonance amplitudes. The structural composite damping is synthesized from the properties of the constituent materials, laminate parameters, and structural geometry based on a specialty finite element. Application studies include the optimization of laminated composite beams and composite shells with fiber volume ratios and ply angles as design variables. The results illustrate the significance of damping tailoring to the dynamic performance of composite structures, and the effectiveness of the method in optimizing the structural dynamic response.

Nonlinear Response of Unidirectional Boron/Aluminum

Abstract: Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.

Computational simulation of high temperature metal matrix composites cyclic behavior

Abstract: A procedure was developed and is described which can be used to computationally simulate the cyclic behavior of high temperature metal matrix composites (HTMMC) and its degradation effects on the structural response. This procedure consists of HTMMC mechanics coupled with a multifactor interaction constituent material relationship and with an incremental iterative nonlinear analysis. The procedure is implemented in a computer code that can be used to computationally simulate the thermomechanical behavior of HTMMC starting from the fabrication process and proceeding through thermomechanical cycling, accounting for the interface/interphase region. Results show that combined thermal/mechanical cycling, the interphase, and in situ matrix properties have significant effects on the structural integrity of HTMMC.

The Nonlinear Behavior of Unidirectional and Laminated Composites-A Micromechanical Approach

Abstract: A micromechanics theory for the prediction of the nonlinear behavior of unidirectional fiber-reinforced materials and composite laminates is presented. The method relies on the properties of fibers and matrix, and involves two parameters which describe the nonlinear response of the unreinforced matrix. These two parameters can be backed-out from the nonlinear axial shear response of the unidirectional lamina. The predicted behavior of boron/epoxy, glass/epoxy, and graphite/polyimide composites is compared with available measured data, and good agreement is obtained in most cases. 22 refs.

Mechanical Properties of Cracked Solids: Validity of the Self-Consistent Method

Abstract: The evaluation of overall elastic moduli of materials containing inhomogeneities is one of the classical problems in micromechanics. Crack is one of the typical examples of inhomogeneities. The overall properties of solids containing cracks depend on the density, orientation, and distribution of cracks. To describe the overall response of such solids under applied stresses, some quantities are necessary that characterize the arrangement of cracks, and also the relationship between the quantities and the overall properties needs to be found.

Plastic behaviour under simple shear of thermosetting resins for fibre composite matrices

Abstract: Simple shear tests have been performed on four different types of resins (cyanate and epoxy-based) which are usually employed for carbon composites. Unexpectedly, all the resins exhibited an intensive plastic response, even at room temperature. Most of the specimens could undergo, at least in their central part, a local shear strain as large as about 0.5. Their constitutive behaviour is very similar to those of glassy thermoplastics — visco-elastic stage, strain softening, shear banding, strain hardening, ultimately homogeneous strain and rupture. It appeared thatτy decreases withTg. The results are discussed in terms of the molecular mechanisms of plasticity. Some consequences on the micromechanics of fibre-reinforced composites are also presented.

On the micromechanics of composites containing spherical inclusions

Abstract: Exact solutions for the stress distribution inside a spherical inclusion embedded in an other-wise homogeneous matrix are obtained. Such expressions provide a framework for discussing the load carrying capacity of rubber inclusions and the effect of interfacial bonding on the toughness of such filled systems. Parametric studies of the influence of constituent stiffness ratios on the resultant stress patterns in the inclusion and matrix have been conducted. Results indicate that chemical bonding between the particle and matrix is not necessary for soft inclusions, but is essential for rigid inclusions.

Local Stresses in Metal Matrix Composites Subjected to Thermal and Mechanical Loading

Abstract: An elasticity solution has been used to analyze matrix stresses near the fiber/matrix interface in continuous fiber-reinforced metal-matrix composites, modeling the micromechanics in question in terms of a cylindrical fiber and cylindrical matrix sheath which is embedded in an orthotropic medium representing the composite. The model's predictions for lamina thermal and mechanical properties are applied to a laminate analysis determining ply-level stresses due to thermomechanical loading. A comparison is made between these results, which assume cylindrical symmetry, and the predictions yielded by a FEM model in which the fibers are arranged in a square array.

Parametric studies to determine the effect of compliant layers on metal matrix composite systems

Abstract: Computational simulation studies are conducted to identify compliant layers to reduce matrix stresses which result from the coefficient of thermal expansion mismatch and the large temperature range over which the current metal matrix composites will be used. The present study includes variations of compliant layers and their properties to determine their influence on unidirectional composite and constituent response. Two simulation methods are used for these studies. The first approach is based on a three-dimensional linear finite element analysis of a 9 fiber unidirectional composite system. The second approach is a micromechanics based nonlinear computer code developed to determine the behavior of metal matrix composite system for thermal and mechanical loads. The results show that an effective compliant layer for the SCS 6 (SiC)/Ti-24Al-11Nb (Ti3Al + Nb) and SCS 6 (SiC)/Ti-15V-3Cr-3Sn-3Al (Ti-15-3) composite systems should have modulus 15 percent that of the matrix and a coefficient of thermal expansion of the compliant layer roughly equal to that of the composite system without the CL. The matrix stress in the longitudinal and the transverse tangent (loop) direction are tensile for the Ti3Al + Nb and Ti-15-3 composite systems upon cool down from fabrication. The fiber longitudinal stress is compressive from fabrication cool down. Addition of a recommended compliant layer will result in a reduction in the composite modulus.

Mechanics of Fatigue Fracture

Abstract: A survey of the theory of fatigue cracks initiation and propagation up to the final failure suggested by author is presented. The theory is based on the synthesis of macro- and micromechanics of fracture. The analytical mechanics of fracture is used treating a system “cracked body — loading” as a mechanical one with unilateral non-holonomic constraints. Comparison is performed between the generalized forces of the analytical mechanics of fracture and the conventional concepts of fracture mechanics such as stress intensity faotors, energy release rates, crack opening displacements, and path-independent integrals.