Showing papers on "Micromechanics published in 2001"

Tensile strain-hardening behavior of polyvinyl alcohol engineered cementitious composite (pva-ecc)

Abstract: A high-performance polyvinyl alcohol fiber-reinforced engineered cementitious composite (PVA-ECC) was developed for structural applications under the performance-driven design approach. Fiber, matrix, and fiber/matrix interfacial properties were tailored to micromechanics models to satisfy the pseudo strain-hardening condition. This research experimentally investigated the effects of fiber surface treatment and sand content on the composite performance. Results from uniaxial tensile tests show an ultimate strain exceeding 4%, as well as an ultimate strength of 4.5 MPa for the composites, with a moderate fiber volume fraction of 2%. The specimens reveal saturated multiple cracking with crack width at ultimate strain limited to below 100 nanometers. The underlying reason of the distinctly different tensile behavior between normal fiber-reinforced concrete and PVA-ECC is highlighted by the comparison of complementary energy from their fiber bridging stress and crack opening curves.

Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems

Abstract: In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromecchanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.

Plastic potentials for anisotropic porous solids

Abstract: The aim of this paper is to incorporate plastic anisotropy into constitutive equations of porous ductile metals. It is shown that plastic anisotropy of the matrix surrounding the voids in a ductile material could have an influence on both effective stress–strain relation and damage evolution. Two theoretical frameworks are envisageable to study the influence of plastic flow anisotropy: continuum thermodynamics and micromechanics. By going through the Rousselier thermodynamical formulation, one can account for the overall plastic anisotropy, in a very simple manner. However, since this model is based on a weak coupling between plasticity and damage dissipative processes, it does not predict any influence of plastic anisotropy on cavity growth, unless a more suitable choice of the thermodynamical force associated with the damage parameter is made. Micromechanically-based models are then proposed. They consist of extending the famous Gurson model for spherical and cylindrical voids to the case of an orthotropic material. We derive an upper bound of the yield surface of a hollow sphere, or a hollow cylinder, made of a perfectly plastic matrix obeying the Hill criterion. The main findings are related to the so-called ‘scalar effect’ and ‘directional effect’. First, the effect of plastic flow anisotropy on the spherical term of the plastic potential is quantified. This allows a classification of sheet materials with regard to the anisotropy factor h ; this is the scalar effect. A second feature of the model is the plasticity-induced damage anisotropy. This results in directionality of fracture properties (‘directional effect’). The latter is mainly due to the principal Hill coefficients whilst the scalar effect is enhanced by ‘shear’ Hill coefficients. Results are compared to some micromechanical calculations using the finite element method.

Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model

Abstract: The overall thermal–mechanical properties of a fibrous composite out of an elastic deformation range can be simply simulated using a recently developed micromechanics model, the Bridging Model. Only the in situ constituent fiber and matrix properties of the composite and the fiber volume fraction are required in the simulation. This general yet easy-to-implement micromechanics model is reviewed and summarized in the present paper. Application of the model to predict various properties of unidirectional laminae and multidirectional laminates, including thermoelastic behavior, elasto-plastic response, ultimate failure strength, strength at elevated temperature, and fatigue strength and S–N curve, is demonstrated. It is suggested that use of the bridging model, appropriately calibrated with experimental data, can therefore inform composite design by identifying suitable constituent materials, their contents, and their geometrical arrangements. Some technical issues regarding applications of the bridging model are also addressed.

Deformation mechanisms in cellulose fibres, paper and wood

Abstract: The use of Raman spectroscopy in probing the deformation mechanisms of cellulose fibres (regenerated and natural), and two natural cellulose composite systems (wood and paper) is described. It is shown that during tensile deformation the 1095 cm−1 Raman band, corresponding to the stretching of the cellulose ring structure, shifts towards a lower wavenumber due to molecular deformation. By analysing a number of fibres with different microstructures this shift is shown to be invaluable in understanding the micromechanisms of deformation in these materials. Moreover, the rate of Raman band shift is shown to be invariant with stress for all fibre types, consistent with a fibre microstructure based on a modified series aggregate model. In the composite systems, such as wood and paper, it is shown that the stress-induced Raman band shift in the cellulose gives an important insight into their local deformation micromechanics.

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

Abstract: A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model's predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.

Averaging and finite-element discretization approaches in the numerical analysis of functionally graded materials

Abstract: Thermomechanical properties and responses of dual-phase functionally graded materials have been estimated by conventional averaging approaches, such as rules of mixtures, mean-field micromechanics and so on. However, the appropriateness of such models has been recently reported to be questionable. In this paper, we numerically investigated three representative averaging estimation methods, the linear and modified rules of mixtures and the Wakashima–Tsukamoto estimate, by comparing with the finite-element discretization approach utilizing rectangular cells. Through numerical experiments for the elastic and thermoelastic response of Ni–Al 2 O 3 functionally graded materials (FGMs), we presented comparative results together with introduction of a suggestive approach.

Scale-dependent bounds on effective elastoplastic response of random composites

Abstract: We consider the mechanical response of random, heterogeneous materials, where each phase is elastic–plastic with an associated flow rule, and the microstructure's statistics is homogeneous and ergodic. Under proportional monotonic loading, the effective (in the macroscopic sense, or overall) elastoplastic response is shown to be bounded from above and below by those obtained, respectively, from displacement and traction boundary conditions applied to finite size domains (square shaped windows). A scale dependent hierarchy of these bounds is obtained by extending the methods used earlier for the elastic moduli estimation: the larger the scale relative to the heterogeneity, the closer are the bounds. A fiber reinforced metal matrix composite is employed to illustrate the theoretical results. Its constitutive response and plastic strain field are investigated by computational micromechanics for different window sizes under both types of boundary conditions; it is found here that the displacement conditions result in denser and more uniformly distributed slip band patterns, while the traction conditions lead to more localized fields. We also investigate a mixed boundary condition, under which the mechanical response of composite is found to fall between those under displacement and traction controlled boundary conditions.

Generalised Mori-Tanaka Scheme to Model Anisotropic Damage Using Numerical Eshelby Tensor:

Abstract: This work presents a new micromechanical model to describe the 3-D elastic and damaged behaviour of randomly oriented fibre composite. The damage mechanisms are described by the progressive introduction of oriented microcracks in a random discontinu- ous fibre composite. In this work, the homogenisation is performed using a Mori-Tanaka scheme. Whereas, symmetry is not obtained in estimates of the overall stiffness for multiphase systems with heterogeneity of different shapes or orientations. For this reason, in this work two levels of homogenisation are considered. The Mori-Tanaka method is applied on the matrix with microcracks to give an equivalent damaged matrix, which can be anisotropic. The Mori-Tanaka scheme is used for the second time to homogenise fibres em- bedded in the new equivalent damage matrix. Generally, this new matrix is anisotropic and for this case no explicit formula for the Eshelby tensor (S) has been obtained. Thus, it is nec- essary to compute numerically the components of this fourth order tensor. Moreover damage mechanisms can be modelled using statistical considerations. The damage onset and growth can appear in the matrix, fibres or interface. Hence, overall damaged behaviour can be mod- elled and predicted as well as the microscopic damage accumulation process.

A micromechanics study on strain-localization-induced fracture initiation in bending using crystal plasticity models

Abstract: A crystal-plasticity-based computational micromechanics model is presented to study the localization and fracture initiation modes in bending of sheet materials. The model accounts for the orientation-dependent non-uniform deformation within each grain. Parameters evaluated include strain hardening, second-phase particle position and distribution, and crystallographic texture. Surface roughening and localized deformation are found to result naturally from orientation and slip geometry diŒerences across neighbouring grains. Shear bands initiate on or near the outer surface and from the low points of surface roughness. The maximum plastic strain may occur below the free surface, which is diŒerent from the predictions based on continuum elastic± plastic theories. Computational results also suggest that constituent particles, especially near the free surface, can signi®cantly increase the localization intensity and the surface roughening. Crystallographic textures that contain high volume fractions of rolling texture components can increase the surface roughening signi®cantly compared with a random texture. Bifurcation analysis results in further understanding of the diŒerent localization modes between the tension and the compression sides of the bending specimen. These ®ndings from the theoretical±computational study agree well with experimental observations. They give insights into improving the bendability of aluminium sheet alloys.

Micro- and mesomechanics of 8-harness satin woven fabric composites: I — evaluation of elastic behavior

Abstract: In part I of this two-part paper, simplified two-dimensional micromechanics and mesomechanics models have been introduced to predict the elastic behavior of 8-harness satin (8HS) woven fabric composites. The woven warp and fill tows were independently treated as unidirectional composites and composite cylinder assemblage (CCA) theory was adopted to predict tow elastic properties from constituent fiber and matrix properties. Since evaluation of woven lamina stiffness requires an accurate description of tow geometry, a method was also developed to describe arbitrary tow geometries by mathematically fitting cubic splines and/or polynomials to micrographs of composite cross-sections. Finally, classical lamination theory was introduced to determine the overall elastic behavior of an n-layered composite laminate, assuming the woven lamina was a modified, two-layer laminate. The simplified mechanics model was evaluated using results from numerical strain energy and equivalent force approaches and results from a series of experimental Iosipescu shear tests and off-axis tensile tests on T650-35(3k), 8HS woven graphite-PMR 15 composites. Issues regarding exclusion of a matrix layer in the simplified, 2-layer laminate analysis were addressed in the strain energy analysis of an idealized 3-D, representative volume element (RVE). The mechanics model was found adequate in estimating the lower bounds of 8HS woven fabric, composite elastic properties. The model also provided a reasonable estimation of symmetric cross-ply composite properties.

The energetics of heterogeneous deformation in open-cell solid foams

Abstract: Compressed open–cell solid foams frequently exhibit spatially heterogeneous distributions of local stretch. The theoretical aspects of this deformation habit have not been clearly elucidated. Here we propose a simple nonlinear model aimed at illustrating the most salient features of the micromechanics of uniaxially stretched solid foams. Then we study the energetics of the model to show that the stretch heterogeneity observed in experiments stems from the lack of convexity of the governing energy functional, which favours two characteristic values of local stretch. These characteristic values are independent of the applied overall stretch and define two configurational phases of the foam. The predicted stretch distributions correspond to stratified mixtures of the phases; stretching occurs in the form of a phase transformation, by growth of one of the phases at the expense of the other. We also compare the predicted mechanical response with experimental data for a series of foams of different densities and discuss the analogy between the stretching of foams and the liquefaction of van der Waals gases. Lastly, we perform displacement field measurements using the digital image correlation technique and find the results to be in agreement with our predictions.