Showing papers on "Micromechanics published in 1994"

Principles of Composite Material Mechanics

Abstract: Introduction Basic Concepts Constituent Materials for Composites Structural Applications of Composites Multifunctional Applications of Composites Fabrication Processes Elements of Mechanical Behavior of Composites Review of Basic Mechanics of Materials Equations Lamina Stress-Strain Relationships Introduction Effective Moduli in Stress-Strain Relationships Symmetry in Stress-Strain Relationships Orthotropic and Isotropic Engineering Constants The Specially Orthotropic Lamina The Generally Orthotropic Lamina Effective Moduli of a Continuous Fiber-Reinforced Lamina Introduction Elementary Mechanics of Materials Models Improved Mechanics of Materials Models Elasticity Models Semiempirical Models Strength of a Continuous Fiber-Reinforced Lamina Introduction Multiaxial Strength Criteria Micromechanics Models for Lamina Strength Analysis of Lamina Hygrothermal Behavior Introduction Hygrothermal Degradation of Properties Lamina Stress-Strain Relationships Including Hygrothermal Effects Micromechanics Models for Hygrothermal Properties Analysis of a Discontinuously Reinforced Lamina Introduction Aligned Discontinuous Fibers Off-Axis-Aligned Discontinuous Fibers Randomly Oriented Discontinuous Fibers Nanofibers and Nanotubes Particulates Hybrid Multiscale Reinforcements Analysis of Laminates Introduction Theory of Laminated Beams Theory of Laminated Plates with Coupling Stiffness Characteristics of Selected Laminate Configurations Derivation and Use of Laminate Compliances Hygrothermal Effects in Laminates Interlaminar Stresses Laminate Strength Analysis Deflection and Buckling of Laminates Selection of Laminate Designs Application of Laminate Analysis to Composite Structures Analysis of Viscoelastic and Dynamic Behavior Introduction Linear Viscoelastic Behavior of Composites Dynamic Behavior of Composites Nanoenhancement of Viscoelastic and Dynamic Properties Analysis of Fracture Introduction Fracture Mechanics Analysis of Through-Thickness Cracks Stress Fracture Criteria for Through-Thickness Notches Interlaminar Fracture Nanoenhancement of Fracture Toughness Mechanical Testing of Composites and Their Constituents Introduction Measurement of Constituent Material Properties Measurement of Basic Composite Properties Measurement of Viscoelastic and Dynamic Properties Measurement of Hygrothermal Properties Appendix A: Matrix Concepts and Operations Appendix B: Stress Equilibrium Equations Appendix C: Strain-Displacement Equations Index Problems and References appear at the end of each chapter.

Composite materials : engineering and science

Abstract: Reinforcements and the reinforcement-matrix interface Composites with metallic matrices Ceramic matrix composites Polymer matrix composites Stiffness, strength and related topics Stiffness of unidirectional composites and laminates Micromechanics of unidirectional composites Strength of unidirectional composites and laminates Short fibre composites Fracture mechanics and toughening mechanisms Impact resistance Fatigue and environmental effects Joining Non-destructive testing.

Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities

Abstract: A micromechanical framework is proposed to investigate effective mechanical properties of elastic multiphase composites containing many randomly dispersed ellipsoidal inhomogeneities. Within the context of the representative volume element (RVE), four governing micromechanical ensemble-volume averaged field equations are presented to relate ensemble-volume averaged stresses, strains, volume fractions, eigenstrains, particle shapes and orientations, and elastic properties of constituent phases of a linear elastic particulate composite. A renormalization procedure is employed to render absolutely convergent integrals. Therefore, the micromechanical equations and effective elastic properties of a statistically homogeneous composite are independent of the shape of the RVE. Various micromechanical models can be developed based on the proposed ensemble-volume averaged constitutive equations. As a special class of models, inter-particle interactions are completely ignored. It is shown that the classical Hashin-Shtrikman bounds, Walpole's bounds, and Willi's bounds for isotropic or anisotropic elastic multiphase composites are related to the “noninteracting” solutions. Further, it is demonstrated that the Mori-Tanaka methodcoincides with the Hashin-Shtrikman bounds and the “noninteracting” micromechanical model in some cases. Specialization to unidirectionally aligned penny-shaped microcracks is also presented. An accurate, higher order (in particle concentration), probabilistic pairwise particle interaction formulation coupled with the proposed ensemble-volume averaged equations will be presented in a companion paper.

Thermomechanical Response of Shape Memory Composites

Abstract: A micromechanics method based on the Mori-Tanaka averaging scheme is used to predict the effective thermomechanical properties of composite materials reinforced by Shape Memory Alloy (SMA) fibers. ...

Nonlocal Damage Theory Based on Micromechanics of Crack Interactions

Abstract: A nonlocal continuum model for strain‐softening damage is derived by micromechanics analysis of a macroscopically nonhomogeneous (nonuniform) system of interacting and growing microcracks, using Kachanov's simplified version of the superposition method. The homogenization is obtained by seeking a continuum field equation whose possible discrete approximation coincides with the matrix equation governing a system of interacting microcracks. The result is a Fredholm integral equation for the unknown nonlocal inelastic stress increments, which involves two spatial integrals. One integral, which ensues from the fact that crack interactions are governed by the average stress over the crack length rather than the crack center stress, represents short‐range averaging of inelastic macro‐stresses. The kernel of the second integral is the long‐range crack influence function which is a second‐rank tensor and varies with directional angle (i.e., is anisotropic), exhibiting sectors of shielding and amplification. For l...

Analysis of woven and braided fabric reinforced composites

Abstract: A general purpose micromechanics analysis that discretely models the yarn architecture within the textile repeating unit cell, was developed to predict overall, three dimensional, thermal and mechanical properties. This analytical technique was implemented in a user-friendly, personal computer-based, windows compatible code called Textile Composite Analysis for Design (TEXCAD). TEXCAD was used to analyze plain, 5-harness satin, and 8-harness satin weave composites along with 2-D braided and 2x2, 2-D triaxial braided composites. The calculated overall stiffnesses correlated well with available 3-D finite element results and test data for both the woven and the braided composites. Parametric studies were performed to investigate the effects of yarn size on the yarn crimp and the overall thermal and mechanical constants for plain weave composites. The effects of braid angle were investigated for the 2-D braided composites. Finally, the effects of fiber volume fraction on the yarn undulations and the thermal and mechanical properties of 2x2, 2-D triaxial braided composites were also investigated.

A Micromechanics Model for Thermoelastic Properties of Plain Weave Fabric Composites

Abstract: A micromechanics model is presented to predict thermoelastic properties of composites reinforced with plain weave fabrics. A representative volume element is chosen for analysis and the fiber architecture is described by a few simple functions. Equations are developed to calculate various phase fractions from geometric parameters that can be measured on a cross section. Effective elastic moduli and effective thermal expansion coefficients are determined under the assumption of uniform strain inside the representative volume element. The resulting model is similar to the classical laminated theory, and hence is easier to use than other models available in the literature. An experimental correlation is provided for a number of Nicalon SiC/CVI SiC and Graphite/CVI SiC composite laminates.

Mechanical behavior of damage tolerant TiB whisker-reinforced in situ titanium matrix composites

Abstract: The results of a systematic study of the effects of alloying and microstructure on the mechanical behavior of in situ titanium matrix composites are reported in this paper. In situ composites are produced by alloying with B which promotes the formation of TiB whiskers during rapid solidification processing. The composite powders are subsequently compacted and extruded to align the whiskers prior to systematic heat treatment in the β and/or α + β phase fields. The processing conditions for the development of in situ composites with attractive combinations of strength, ductility, damage tolerance and creep resistance are thus established. The improvements in the composite properties are rationalized using simple micromechanics principles. The paper highlights the potential for the microstructural design of composites using micromechanics and conventional physical metallurgy principles.

A Self-Consistent Fabric Geometry Model: Modification and Application of a Fabric Geometry Model to Predict the Elastic Properties of Textile Composites

Abstract: A method for predicting the elastic properties of textile-reinforced composites is presented with applications. The method is a modification of a Fabric Geometry Model (FGM) [1–3] that relates fiber architecture and material properties of textile-reinforced composites to its global stiffness matrix through micromechanics and stiffness averaging technique. The FGM, although proven to be a quick and successful method [4], suffers two major drawbacks: 1. incompatibility of the basic transverse isotropy assumption with the theoretical mathematical derivation, (i.e., the mathematical derivation produces elastic constants that do not exhibit transverse isotropy) and 2. inconsistency of the transformation matrices associated with the stiffness calculations (i.e., the technique is not sufficiently robust to handle all cases). In this paper, these problems are discussed and solutions are presented. Comparison between stiffness and compliance averaging approaches is investigated. Moreover, predictions using the Self-Consistent FGM are compared with experimental data available in literature.

Macroscopic fracture characteristics of random particle systems

Abstract: This paper deals with determination of macroscopic fracture characteristics of random particle systems, which represents a fundamental but little explored problem of micromechanics of quasibrittle materials. The particle locations are randomly generated and the mechanical properties are characterized by a triangular softening force-displacement diagram for the interparticle links. An efficient algorithm, which is used to repetitively solve large systems, is developed. This algorithm is based on the replacement of stiffness changes by inelastic forces applied as external loads. It makes it possible to calculate the exact displacement increments in each step without iterations and using only the elastic stiffness matrix. The size effect method is used to determine the dependence of the mean macroscopic fracture energy and the mean effective process zone size of two-dimensional particle systems on the basic microscopic characteristics such as the microscopic fracture energy, the dominant inhomogeneity spacing (particle size) and the coefficients of variation of the microstrength and the microductility. Some general trends are revealed and discussed.

Micromechanics of Active Composites With SMA Fibers

Abstract: The study of the effective thermomechanical response of active fibrous composites with shape memory alloy (SMA) fibers is the subject of this work. A 3-D constitutive response for the SMA fibers is formulated first. To model thermomechanical loading path dependence, an incremental approach is used assuming that within each stress and temperature increment the volume fraction of the martensitic phase remains constant in the SMA fibers. The Mori-Tanaka averaging scheme is then used to give an estimate of the instantaneous effective thermomechanical properties in terms of the thermomechanical properties of the two phases and martensitic volume fraction. A unit cell model for a periodic active composite with cubic and hexagonal arrangement of fibers is also developed to study the effective properties using finite element analysis. It is found that since the fibers and not the matrix undergo the martensitic phase transformation that induces eigenstrains, the Mori-Tanaka averaging scheme accurately models the thermomechanical response of the composite, relative to the finite element analysis, for different loading paths. Specific results are reported for the composite pseudoelastic and shape memory effect for an elastomeric matrix continuous SMA fiber composite.

Micromechanics and effective elastoplastic behavior of two-phase metal matrix composites

Abstract: A micromechanical framework is presented to predict effective (overall) elasto-(visco-)plastic behavior of two-phase particle-reinforced metal matrix composites (PRMMC). In particular, the inclusion phase (particle) is assumed to be elastic and the matrix material is elasto-(visco-)plastic. Emanating from Ju and Chen's (1994a,b) work on effective elastic properties of composites containing many randomly dispersed inhomogeneities, effective elastoplastic deformations and responses of PRMMC are estimated by means of the effective yield criterion'' derived micromechanically by considering effects due to elastic particles embedded in the elastoplastic matrix. The matrix material is elastic or plastic, depending on local stress and deformation, and obeys general plastic flow rule and hardening law. Arbitrary (general) loadings and unloadings are permitted in the framework through the elastic predictor-plastic corrector two-step operator splitting methodology. The proposed combined micromechanical and computational approach allows one to estimate overall elastoplastic responses of PRMMCs by accounting for the microstructural information (such as the spatial distribution and micro-geometry of particles), elastic properties of constituent phases, and the plastic behavior of the matrix-only materials.

The micromechanics of friction in a granular layer

Abstract: A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model differs from the simpler asperity model in that it recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The model provides an explanation for the observed differences in the friction of granular layers deformed between rough surfaces and those deformed between smooth surfaces and for the evolution of the friction parameters with displacement. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure.

Micromechanics as a Basis of Continuum Random Fields

Abstract: Department of Materials Science and Mechanics, Michigan State University, East Lansing MI 48824-1226 Many problems in solid and geomechanics require the concept of a meso-continuum, which allows a resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale. Passage from the microstructure to such a meso-continuum is based on a scale depen­dent window playing the role of a Representative Volume Element (RVE). It turns out that the material properties at the mesoscale cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields, corresponding to essential and natural boundary conditions on RVE, need to be introduced to bound the material response from above and from below. In this paper Monte Carlo simulations are used to obtain the first- and second-order one- and two-point characteristics of these two random fields for random chessboards and matrix-inclusion composites. Special focus is on the correlation functions describing the auto-covariances and crosscovariances of effective random meso-scale conductivity tensor Q; and its dual Sjj. Following issues are investigated: i) scale-dependence of noise-to-signal ratios of various components of Cy and Sjj, ii) spatial structure of the correlation function, iii) uniform strain versus exact calculations in determination of the correlation function, iv) correlation structure of compos­ites with inclusions without and with overlap. 1. INTRODUCTION One of the classical goals of micromechanics is the derivation of macroscopic properties on scales practically infinitely larger than the lengthscales at the microlevel. There are, how­ever, situations where description of material response at intermediate levels - so-called meso-level (or meso-scale) -is necessary. These are, for example, i) necessity to resolve local fields (of stress, say), ii) materials with spatially-depen­dent statistics, iii) solution of boundary value problems at macro-scales. Case i) is exemplified by almost any one of many problems in soil mechanics where a meso-scale has to be introduced to define a continuum over a granular mass in the first place (Ostoja-Starzewski, 1992). Case ii) is a situation where a pas­sage to an infinite scale would be beyond interest, such as for instance in a heterogenous interface problem (Ostoja-Starze­wski and Jasiuk, 1992; Jasiuk and Ostoja-Starzewski, 1994). A paradigm of case iii) is provided by so-called Stochastic Finite Elements (SFE) - a field of research developing over the past fifteen years, in which a micromechanical basis in set­ting up of a stochastic stiffness matrix is sorely needed (Ostoja-Starzewski, 1993a and 1993b). Most of the past research in SFE concerned linear elastic structural responses and relied on a straightforward generali­zation of Hooke's law (see e.g. Contreras, 1980; Liu, et al, 1986; Benaroya and Rehak, 1988; Shinozuka, 1988; Ghanem andSpanos, 1991), that is

Handbook of polymer-fibre composites

Abstract: Sommaire : 1.Fibrous reinforcements for composite materials. 2.Matrices. 3.Fabrication of polymer composites. 4.Mechanical properties of composites - micromechanics. 5.Mechanical properties - macromechanics. 6.Environmental aspects

Composite Structures for Civil and Architectural Engineering

Abstract: Introduction. Historical necessity. Basic concept of composites. Matrix. Reinforcements. Filamentary type composites. Composite manufacture. Application, present and future. Further reading. Properties of composites. Introduction. Reinforcements. Matrices. Particulate composites. Other matrix based composites. Mechanical properties of fibrous composite. 'Comingle' and 'FIT' - new concepts for thermoplastic composites. References. Further reading. Classical theory of elasticity and mechanics. Assumptions for classical theory of elasticity. Stress and strain. Hooke's Law. Two-dimensional problems (plane) problems. Stress at a point. Mohr's circle. Strain at a point. Pure shear. Equilibrium equations and boundary conditions for two-dimensional problem. Compatibility equations. Stress function. Application of stress function in rectangular coordinate system. Displacements in two-dimensional problem. Application of stress function using Fourier Series. Equilibrium equations in terms of displacements. Two-dimensional problems in polar coordinates. Solution of two-dimensional problems in polar coordinates. Problems of concentrated loads. Strain energy and principle of virtual work. Examples of use of the energy method. Castigliano's theorem. Equilibrium equations in three dimensions. Boundary conditions in three-dimensional problems. Compatibility equations in three-dimensional problems. Saint Venant', solution of the problem of torsion of a prismatic bar. Membrane analogy for torsional problems. Asymmetric bending of prismatic beams. Asymmetrical bending of a beam with longitudinal stringers. Torsion of thin-walled structures with longitudinal stringers. Determination of rate of twist of a cell. Shear centre of beams with longerons. Shear flow distribution in multicell beams with longerons. Out-of-plane bending of curved girders. Alternative formulation for out-of-plane bending of curved beams with constant radius. Bending in the plane of the ring. Elementary theory of thin shell. Space frame. Space trusses. Cable. Guyed tower. Review of beam theory. Plates with irregular shapes and arbitrary boundary conditions. References. Further reading. Eigenvalue problems of beams and frames of isotropic materials. Stability of beams and frames. Structural vibration of beams and frames. References. Further reading. Anisotropic elasticity. Introduction. Stress-strain relations of anitotropic materials. Engineering constants for orthotropic materials. Stress-strain relations of plane stress and plane strain problems for unidirectionally reinforced lamina. Transformation equations. Invariants. Laminates. Micromechanics - mechanical properties of composites. Numerical examples. References. Further reading. One-dimensional structural elements of composite materials. Equations for beams and rods. Beams with hollow cross-sections. Eigenvalue problems of beams and frames of anisotropic materials. References

Micromechanical modelling of stress-assisted martensitic transformation

Abstract: A computational micromechanics study of stress-assisted martensitic transformation using finite elements is carried out within a thermomechanical framework including the aspect of plastic deformation. The phase transformation is treated by a stress-free transformation tensor corresponding to a certain habit plane variant involving a shape change resulting from shear and dilatational deformations which are eigenstrains within the emerging martensitic phase. General plane strain and axisymmetric analyses are carried out introducing different micromechanical models with appropriate boundary conditions required for the microfield approach. The introduced models are compared with a micromechanical model developed by Tvergaard in the viewpoint of thermodynamic aspects concerning the formation of martensite. The representative volume elements are specified with respect to the Schmid factor for the transformation shear corresponding to an average crystallographic orientation of a grain. We examine elastic-plastic deformations and distribution of transformation-induced microstress fields in both the parent and the emerging product phase due to accommodation of the transformation shape change. Analytical results for the linear elastic case based upon the Eshelby approach will be compared with numerical results. The plastic behavior of austenitic and martensitic microconstituents is described in the context of J2-flow theory with isotropic hardening. The thermomechanical framework is based on an explicit form of a potential suggesting the form of Gibbs free energy, from which transformation conditions on the mesodomain-, interface- and nucleation-site level are derived. The arrangement of martensitic microregions transforming in a stress field is studied considering the thermomechanical coupling of orientation and accommodation effects.

Subcritical Crack Growth in CVI Silicon Carbide Reinforced with Nicalon Fibers: Experiment and Model

Abstract: Subcritical crack growth measurements of ceramic-matrix composites have been conducted on materials consisting of CVI SiC matrix reinforced with Nicalon fibers (SiC/SiCf) having C and BN fiber–matrix interfaces. Velocities of effective elastic cracks were determined as a function of applied stress intensity in pure Ar and in Ar plus 2000 ppm O2 at 1100°C. A stage-II regime, where the crack velocity depends only weakly on the applied stress intensity, was observed in the V–K diagrams over a range of applied stress intensities that correspond to the R-curve of the materials. This stage-II behavior was followed by a stage-III, or power-law, regime at higher stress intensity values. Oxygen was observed to increase the crack velocity in the stage-II regime and to shift the stage-II-to-stage-III transition to lower stress intensity values. A 2D micromechanics approach was developed to model the time dependence of observed crack-bridging events and is able to rationalize the measured effective crack velocities, the time dependence of the crack velocity, and the stage-II-to-stage-III transition in terms of the stress relaxation of crack-bridging fibers.

An Analysis of Thermal Residual Stresses in Ti-6-4 Alloy reinforced with SiC and Al2O3 Fibres

Abstract: Thermal residual stresses in Ti6Al4V alloy reinforced with silicon carbide (SiC) and sapphire alumina (Al2O3) fibres are estimated based on an elastic-viscoplastic micromechanics analysis. Effects of fibre volume fraction and different manufacturing procedures are considered and comparisons made with published experimental results for the SiC fibre composite. Stress components in the Ti-6-4/Al2O3 are generally less than half the corresponding values in the Ti-6-4/SiC composite.

Matrix cracking of cross-ply ceramic composites

Abstract: A micromechanics study is presented of the matrix cracking behavior of laminated, fiber-reinforced ceramic cross-ply composites when subject to tensile stressing parallel to fibers in the 0° plies. Cracks extending across the 90° plies are assumed to exist, having developed at relatively low tensile stresses by the tunnel cracking mechanism. The problem addressed in this study is the subsequent extension of these initial cracks into and across the 0° plies. Of special interest is the relation between the stress level at which matrix cracks are able to extend all the way through the 0° plies and the well known matrix cracking stress for steady-state crack extension through a uni-directional fiber-reinforced composite. Depending on the initial crack distribution in the 90° plies, this stress level can be as large as the uni-directional matrix cracking stress or it can be as low as about one half that value. The cracking process involves a competition between crack bridging by the fibers in the 0° plies and interaction among multiple cracks. Crack bridging is modeled by a line-spring formulation where the nonlinear springs characterize the sliding resistance between fibers and matrix. Crack interaction is modeled by two representative doubly periodic crack patterns, one with collinear arrays and the other with staggered arrays. Material heterogeneity and anisotropy are addressed, and it is shown that a homogeneous, isotropic average approximation can be employed. In addition to conditions for matrix cracking, the study provides results which enable the tensile stress-strain behavior of the cross-ply to be predicted, and it provides estimates of the maximum stress concentration in the bridging fibers. Residual stress effects are included.