Showing papers on "Micromechanics published in 1993"

Micromechanics: Overall Properties of Heterogeneous Materials

Abstract: Part 1 Overall properties of heterogeneous solids: aggregate properties and averaging methods aggregate properties, averaging methods elastic solids with microcavities and microcracks linearly elastic solids, elastic solids with traction-free defects, elastic solids with micrcavities, elastic solids with microcracks elastic solids with micro-inclusions overall elastic modulus and compliance tensors, examples o elastic solids with elastic micro-inclusions, upper and lower bounds for overall elastic moduli, self-consistent differential and related averaging methods, Eshelby's tensor and related topics solids with periodic microstructure general properties and field equations, overall properties of solids with periodic microstructure, mirror-image decomposition of periodic fields. Part 2 Introduction to basic elements of elasticity theory: foundations geometric foundations, kinematic foundations, dynamic foundations, constitutive relations elastostatic problems of linear elasticity boundary-value problems and extremum principles three-dimensional problems solution of singular problems. Appendix: references.

From micromechanics to structural engineering - the design of cementitious composites for civil engineering applications

Abstract: This paper reviews the development of pseudo strain-hardening cement based short fiber composites employing the Performance Driven Design Approach. The micromechanics theory behind the design concept is reviewed, and the unique mechanical properties of the resulting composite are summarized. The translation of material properties to structural properties is demonstrated with the structural response of the Ohno shear beam.

Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys. I: Derivation of general relations

Abstract: A MICROMECHANICS constitutive model has been proposed in this paper to describe the pseudoelastic and shape memory behavior of polycrystalline shape memory alloys under various temperatures The derivation of the model is based on the thermodynamics, micromechanics and microstructural physical mechanism analysis of the material during deformation and it is shown that the inelastic deformation of the material in the mechanical and/or thermal loading processes is associated with some temperature, stress state and loading history dependent yielding surfaces which microscopically correspond to the forward and reverse transformation (or reorientation) processes, respectively

Micromechanics of crack bridging in fibre-reinforced concrete

Abstract: The stress-crack width relationship has been determined experimentally for concretes reinforced with two types of fibres, steel and polypropylene, of various fibre volume fractions. A micromechanics-based theoretical model is proposed which captures the essential features of the stress-crack width relationships at small crack widths (less than 0.3 mm). Micromechanisms accounted for include the bridging actions due to aggregates and fibres, Cook-Gordon interface debonding and fibre pre-stress. The fibre bridging action involves interface slip-dependent friction as well as snubbing friction for fibres bridging at inclined angles. Theoretical predictions based on independent parametric inputs compare favourably with experimental measurements of the stress-crack width relationship. Findings in this research provide confidence in the use of the proposed model for materials engineering targeted at prescribed structural performance.

An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities

Abstract: A set of four tensors corresponding to Eshelby’s tensor in elasticity are obtained for an ellipsoidal inclusion embedded in an infinite piezoelectric medium. These tensors, which describe the elastic, piezoelectric, and dielectric constraint of the matrix, are obtained from W. F. Deeg’s solution to inclusion and inhomogeneity problems in piezoelectric solids. These tensors are then used as the backbone in the development of a micromechanics theory to predict the effective elastic, dielectric, and piezoelectric moduli of particle and fibre reinforced composite materials. The effects of interaction among inhomogeneities at finite concentrations are approximated through the Mori-Tanaka mean field approach. This approach, although widely utilized in the study of uncoupled elastic and dielectric behaviour, has not before been applied to the study of coupled behaviour. To help ensure confidence in the theory, the analytical predictions are proven to be self-consistent, diagonally symmetric, and to exhibit the correct behaviour in the low and high concentration limits. Finally, numerical results are presented to illustrate the effects of the concentration, shape, and material properties of the reinforcement on the effective properties of piezoelectric composites and analytical predictions are shown to result in good agreement with existing experimental data.

Damage in composite materials

Abstract: Part 1 Analysis: constitutive behaviour of multiphase metal matrix composites with interfacial damage by the generalized cells model, J. Aboudi an energy-based failure criterion for anisotrophic solids subject to damage, M.W. Biegler and M.M. Mehrabadi damage in solids due to periodically distributed cracks of arbitrary geometry, S. Nemat-Nasser et al the behaviour of of cracked cross-ply composite laminates under general in-plane loading, C.-L. Tsai and I.M. Daniel micromechanical characterization of damage-plasticity in metal matrix composites, G.Z. Voyiadjis and P.I. Katan on the micromechanics of defects in fibre-matrix composites, H.M. Zbib and I. Demir. Part 2 Analysis/applications: heterogeneity and its implications - micromechanical, statistical, fractal approach and their similarity, G. Frantziskonis fatigue crack growth characteristics of Ti-beta21S monolithic laminate, H. Ghonem et al progressive brittle damage modelling of fibrous composities by micromechanics based failure surfaces, C.-M. Huang and D.C. Lagoudas damage modelling at the macro- and meso-scales for 3D composites, P. Ladeveze et al. Part 3 Experiments: fracture toughness of discontinuous metal matrix composites, R.J. Arsenault analysis of residual stresses induced by cool down in viscoplastic metal matrix composites, G.S. Jeong et al eddy current characterization of silicon carbide reinforced aluminium metal-matrix composites, P.K. Liaw et al.

Modeling Damage in a Plain Weave Fabric-Reinforced Composite Material

Abstract: A method for describing damage propagation in a woven fabric-reinforced composite material subjected to tension or shear loading is presented. A three-dimensional unit cell description of a plain weave graphite/epoxy fabric-reinforced composite was constructed. From this description, finite element models were generated. An incremental iterating finite element algorithm was developed to analyze loading response. This finite element program included capabilities to model nonlinear constitutive material behavior (anisotropic plasticity), and a scheme to estimate the effects of damage propagation by stiffness reduction. Tension and shear loadings were modeled. Results from the finite element analysis compared favorably with experimental data. Nonlinear shear stress-strain behavior of the fabric composite was shown to be principally caused by damage propagation rather than by plastic deformation of the matrix.

Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys. II: Study of the individual phenomena

Abstract: T he constitutive relation for various phenomena of SMA ( superelasticity, rubber-like elasticity, ferroelasticity, elastic anomaly, shape memory effect ) is studied in detail and compared with the available experimental data. It is shown that the micromechanical model developed in Part I can satisfactorily describe the main peculiarities of the macroscopic thermomechanical constitutive behavior in the course of uniaxial mchanical and/or thermal loadings and that the existing phenomenological models are special cases of the proposed theory under proportional loading conditions. Some theoretical predictions and discussions for complex loading paths are also given which are yet subject to experimental verification.

Continuum and micromechanics treatment of constraint in fracture

Abstract: Two complementary methodologies are described to quantify the effects of crack-tip stress triaxiality (constraint) on the macroscopic measures of elastic-plastic fracture toughness J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodology, two parameters J and Q suffice to characterize the full range of near-tip environments at the onset of fracture. J sets the size scale of the zone of high stresses and large deformations while Q scales the near-tip stress level relative to a high triaxiality reference stress state. The material's fracture resistance is characterized by a toughness locus Jc(Q) which defines the sequence of J-Q values at fracture determined by experiment from high constraint conditions (Q∼0) to low constraint conditions (Q<0). A micromechanics methodology is described which predicts the toughness locus using crack-tip stress fields and critical J-values from a few fracture toughness tests. A robust micromechanics model for cleavage fracture has evolved from the observations of a strong, spatial self-similarity of crack-tip principal stresses under increased loading and across different fracture specimens. We explore the fundamental concepts of the J-Q description of crack-tip fields, the fracture toughness locus and micromechanics approaches to predict the variability of macroscopic fracture toughness with constraint under elastic-plastic conditions. Computational results are presented for a surface cracked plate containing a 6:1 semielliptical, a=t/4 flaw subjected to remote uniaxial and biaxial tension. Crack-tip stress fields consistent with the J-Q theory are demonstrated to exist at each location along the crack front. The micromechanics model employs the J-Q description of crack-front stresses to interpret fracture toughness values measured on laboratory specimens for fracture assessment of the surface cracked plate.

Micromechanics of coupled electroelastic composites: Effective thermal expansion and pyroelectric coefficients

Abstract: The effective thermal‐expansion and pyroelectric coefficients of two‐phase coupled electroelastic composite materials are obtained by coupling various micromechanics theories with exact relations connecting their effective thermal and electroelastic moduli. Results are obtained for composites reinforced by ellipsoidal piezoelectric inhomogeneities and thus are applicable to a wide range of microstructural geometry including lamina, spherical particle, and continuous fiber reinforcement. The analytical framework is developed in a matrix formulation in which the electroelastic moduli are conveniently represented by a 9×9 matrix and the thermal‐expansion and pyroelectric coefficients by a 9×1 column vector. Numerical results are presented for some typical composite microstructures which show the interesting behavior of these materials.

Thermomechanical response of shape memory composites

Abstract: The Mori-Tanaka micromechanics method is used to predict the effective properties of composite materials consisting of a polymer matrix reinforced by a fiber made of a transformation shape memory effect (SME) material. The composite response is plotted for combinations of the following scenarios: (1) isothermal longitudinal and transverse stress input, (2) stress-free thermal loading, (3) constant fiber thermoelastic properties, and (4) thermoelastic fiber properties that vary with the martensite volume fraction. For the case of an isothermal stress input, the composite transformation stress, the maximum transformation strain, and the hysteresis are all reduced vis-a-vis the monolithic SME material. In contrast to a monolithic SME material, stress-free thermal loading of a SME composite can produce a transformation strain. It is shown that closed form solutions for the effective martensite and austenite start temperatures can be derived, that they are sensitive to the stress-free reference temperature of the fiber, and that the stress-free austenite and martensite start temperatures are higher than those of the monolithic SME material.

Micromechanical Modeling of Composite Compressive Strength

Abstract: Composite compressive failure is studied using a micromechanical (beam-on-elastic foundation) model, and the stiffness of the foundation is determined through an elasticity solution of the foundation model problem. An explicit expression has been derived for evaluation of composite longitudinal compressive strengths (CLCS). It is found that this expression predicts relatively lower CLCS compared to classical models, and closely matches some experimental data for carbon fiber/epoxy composites. It is found that a complete matrix slippage will reduce the CLCS by over 50%.

Computational modeling of metal matrix composite materials. I: Isothermal deformation patterns in ideal microstructures

Abstract: The mechanical behavior of particulate reinforced metal composites, in particular an SiC reinforced Al-3 wt% Cu model system, was analyzed numerically. The Computational micromechanics approach was taken, i.e. a detailed representation of microstructure in which the material was characterized by a finite deformation, thermo-elastic-viscoplastic crystallographic theory. Individual matrix grains and reinforcing particles were represented, in the context of two dimenssional repeating unit cell models. The performance of the microstructure under variation in microstructural parameters such as (1) reinforcement volume fraction, (2) morphology and (3) matrix strain hardening properties was investigated, as was the effect of change in loading state. In this, the first in a series of four articles, the isothermal microstructural deformation behavior is examined in detail. Localization of plastic deformation is seen to be a natural part of the deformation process and evolves according to patterns, which develop from the onset of yield and are determined for the most part by the positions of the reinforcing particles. This is in contrast to the microscale behavior of single phase polycrystals where deformation patterns only emerge at larger overall strains. Localization intensity depends strongly on reinforcement volume fraction and morphology and less significantly on matrix hardening properties. Results for tensile and compressive loading histories are compared showing differences that depend on particle position and finite geometry changes during deformation.

Exact Results in the Micromechanics of Fibrous Piezoelectric Composites Exhibiting Pyroelectricity

Abstract: Piezoelectric fibrous composites of two, three and four phases are considered. The phase boundaries are cylindrical but otherwise the microgeometry is totally arbitrary. The constituents are transversely isotropic, and exhibit pyroelectricity. Exact relations are derived between the local fields arising under a uniform electromechanical loading and a uniform temperature change in the piezoelectric composite. For given overall material symmetry, exact connections are obtained among the effective elastic, piezoelectric and dielectric constants of two- and three- phase systems. It is also shown that the effective thermal stress and pyroelectric coefficients can be expressed in terms of the effective elastic, piezoelectric, dielectric constants and constituent properties in two-, three- and four-phase composites.

A Study of the Opening Displacement of Transverse Cracks in Cross-Ply Laminates

Abstract: Transverse cracks in cross-ply laminates are investigated experimentally to reveal the essential characteristics of their opening displacement under tensile loads. The average crack opening displacement is studied as a function of the longitudinal overall strain and the effects of matrix toughness and transverse ply thickness on this parameter are examined. The interactive effects between closely spaced transverse cracks are also ex- amined and found to be significant. Implications of the experimentally observed features on the micromechanics and continuum damage type models are discussed.

Effects of interface degradation on fiber bridging of composite fatigue cracks

Abstract: This paper presents a theoretical analysis that examines the effects of cyclic degradation of interface on fiber bridging of fatigue cracks in metal-matrix or intermetallic-matrix composites. Using fiber bridging models and crack-tip micromechanics results available in the literature, the frictional stresses on individual fiber/matrix interfaces located within the bridging zone in the wake of a fatigue crack in a SCS-6/Ti-6Al-4V composite are calculated. The results are used to demonstrate that a reduction of the interface friction stress by fatigue can lead to a decrease of the fiber bridging stress, and an increase in the near-tip stress intensity range. The consequence is that the near-tip stress intensity range and, thus, the crack growth of a bridged fatigue crack are sensitive to cyclic interface degradation and the distribution of the frictional stress within the bridged zone.

Analysis of the deformation of aramid fibres and composites using Raman spectroscopy

Abstract: It is demonstrated that Raman spectroscopy can be used to study both the deformation micromechanics of high-performance aramid polymer fibres and of these fibres in model, single-fibre epoxy resin matrix composites. It is shown that the peak position of the 1610 cm−1 aramid Raman band shifts to lower frequency under the action of tensile stress or strain due to the macroscopic deformation leading to direct stretching of the polymer molecules. These strain-induced band shifts can be used to map the distribution of stress or strain along a discontinuous, aramid fibre inside an epoxy resin matrix from which the interfacial shear stress can be calculated. It is shown that the behaviour is consistent with that predicted by the classical shear-lag analysis. The technique was also used to study the fragmentation process for an aramid fibre in an epoxy resin matrix in which the matrix strain exceeds the failure strain of the fibre. It is further demonstrated that the technique can be used to compare the interfacial properties of aramid fibres where the interfacial shear stress is found to be higher for sized fibres than for those which have been de-sized.

Interfacial micromechanics in model composites using laser Raman spectroscopy

Abstract: The mechanisms of load transfer in single carbon-fibre/epoxy-resin model composites, are investigated. The composites are subjected to incremental tensile loading and the fibre fragmentation process is continuously monitored. The fibre strain distribution along the fibre fragments is derived through the Raman spectrum of the carbon fibre and its strain dependence. In turn, the interfacial shear stress distribution is evaluated by means of a balance of forces analysis. The effect of fibre surface treatment and fibre modulus upon the stress transfer profiles and the distribution of the interfacial shear stress along the fibre, are also examined. Finally, the importance of parameters, such as, fibre/matrix debonding and interphasial yielding at the vicinity of fibre breaks, is discussed.

Strengthening of Metal Matrix Composite by Shape Memory Effect

Abstract: The strengthening of a metal matrix composite (MMC) by the shape memory effect of dispersed TiNi particles was theoretically studied. An analytical model was constructed for the prediction of the Young's modulus (E), yield stress σ y ) and work-hardening rate E TC ), on the bases of the Eshelby's equivalent inclusion method. The analysis was performed on the TiNi particle/Al metal matrix composites with varying volume fractions and prestrains of the particle. The present analysis has shown that E, σ y and E TC increase with increasing the volume fraction of the particles, and σ y increases with increasing prestrain while E and E TC are independent of prestrain