Showing papers on "Micromechanics published in 2004"

The Effect of Nanotube Waviness and Agglomeration on the Elastic Property of Carbon Nanotube-Reinforced Composites

Abstract: Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the stiffening effect of carbon nanotubes is quantitatively investigated by micromechanics methods. Especially, the effects of the extensively observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight nanotubes. Then, a novel micromechanics model is developed to consider the waviness or curviness effect of nanotubes, which are assumed to have a helical shape. Finally, the influence of nanotube agglomeration on the effective stiffness is analyzed. Analytical expressions are derived for the effective elastic stiffness of carbon nanotube-reinforced composites with the effects of waviness and agglomeration. It is found that these two mechanisms may reduce the stiffening effect of nanotubes significantly. The present study not only provides the relationship between the effective properties and the morphology of carbon nanotubereinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites. @DOI: 10.1115/1.1751182#

Effective Elastic Properties of Carbon Nanotube Reinforced Composites

Abstract: We seek to obtain continuum level elastic properties for carbon nanotubes and carbon nanotube reinforced composites through a variety of micromechanics techniques. Using the in-plane elastic properties of graphene sheets the effective properties of carbon nanotubes are calculated using a modified composite cylinders micromechanics technique to treat the hollow nanotube as a transversely isotropic solid cylinder. Effective properties found for single-walled carbon nanotubes in this fashion are found to be in good agreement with both experimentally and theoretically obtained results available in the literature. Having a solid fiber then allows for the calculation of an Eshelby tensor and hence, the use of additional more advanced micromechanics techniques to calculate carbon nanotube reinforced composite effective elastic properties. In what are termed two-step approaches, the generalized self-consistent and Mori-Tanaka micromechanics techniques are employed to obtain effective elastic properties of composites consisting of aligned single or multi-walled effective carbon nanotubes embedded in a polymer matrix of EPON 862 at various effective carbon nanotube volume fractions. These results are compared to a single step composite cylinders approach wherein an additional phase consisting of the polymer matrix is placed around the carbon nanotube prior to obtaining the effective carbon nanotube properties, thereby obtaining the effective composite properties in a single calculation. It is found that the two-step Mori-Tanaka results yield nearly identical results as the single step composites cylinders approach. Finally, it has been observed in the literature that electrostatic clumping of nanotubes into nanotube bundles complicates the adequate dispersion of the nanotubes within the polymer matrix. The quantification and modeling of this clustering in aligned nanotube composites is accomplished herein using Dirichlet tessellation in conjunction with an n-phase generalized self-consistent technique. It is observed that the effect of clustering is to reduce in magnitude only the transverse to fiber alignment properties of the transversely isotropic effective composite as compared to the randomly distributed aligned carbon nanotube composite’s effective elastic properties, and that this reduction in transverse elastic properties increases with increasing global volume fraction of effective carbon nanotubes. Results indicate that, while the clustering effect does contribute to some reduction in composite properties, other factors such as cluster misalignment and poor fiber-matrix bonding may play a significantly larger role. Nomenclature 11 E = the one-direction Young’s modulus 12 ν = the one-direction Poisson’s ratio 23 κ = the 2-3-plane bulk modulus 12 μ = the 1-2-plane shear modulus 23 μ = the 2-3 plane shear modulus A E = the axial Young’s modulus of a fiber

Using nanoparticles to create self-healing composites

Abstract: The need for viable materials for optical communications, display technologies, and biomedical engineering is driving the creation of multilayer composites that combine brittle materials, such as glass, with moldable polymers. However, crack formation is a critical problem in composites where thin brittle films lie in contact with deformable polymer layers. Using computer simulations, we show that adding nanoparticles to the polymers yields materials in which the particles become localized at nanoscale cracks and effectively form “patches” to repair the damaged regions. Through micromechanics simulations, we evaluate the properties of these systems in the undamaged, damaged, and healed states and determine optimal conditions for harnessing nanoparticles to act as responsive, self-assembled “band aids” for composite materials. The results reveal situations where the mechanical properties of the repaired composites can potentially be restored to 75%–100% of the undamaged material.

Mechanics considerations for microporous titanium as an orthopedic implant material.

Abstract: This article investigates mechanics issues related to potential use of a recently developed porous titanium (Ti) material for load-bearing implants. This material may have advantages over solid Ti of enhancing the bone-implant interface strength by promoting bone and soft tissue ingrowth and of reducing the bone-implant modulus mismatch, which can lead to stress shielding. Experimental data from ultrasound experiments and uniaxial compression testing on microporous Ti are presented. Analytic models to predict its elastic modulus and Poisson's ratio are discussed, including "structural" approaches (Gibson and Ashby's cellular solids) and a "composite material" approach (Mori-Tanaka). Finally, two-dimensional finite element models based on optical micrographs of the material are presented. Simulations were performed for different conditions and levels of approximation. Results demonstrate that simple analytic models provide good estimates of the elastic properties of the porous Ti and that the moduli can be significantly reduced to decrease the mismatch between solid Ti and bone. The finite element simulations show that bone ingrowth will dramatically reduce stress concentrations around the pores.

Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? Arguments from a multiscale approach.

Abstract: As candidates for tissue-independent phases of cortical and trabecular bone we consider (i) hydroxyapatite, (ii) collagen, (iii) ultrastructural water and non-collagenous organic matter, and (iv) marrow (water) filling the Haversian canals and the intertrabecular space. From experiments reported in the literature, we assign stiffness properties to these phases (experimental set I). On the basis of these phase definitions, we develop, within the framework of continuum micromechanics, a two-step homogenization procedure: (i) at a length scale of 100–200 nm, hydroxyapatite (HA) crystals build up a crystal foam (“polycrystal”), and water and non-collagenous organic matter fill the intercrystalline space (homogenization step I); (ii) at the ultrastructural scale of mineralized tissues (5–10 microns), collagen assemblies composed of collagen molecules are embedded into the crystal foam, acting mechanically as cylindrical templates. At an enlarged material scale of 5–10 mm, the second homogenization step also accommodates the micropore space as cylindrical pore inclusions (Haversian and Volkmann canals, inter-trabecular space) that are suitable for both trabecular and cortical bone. The inputs for this micromechanical model are the tissue-specific volume fractions of HA, collagen, and of the micropore space. The outputs are the tissue-specific ultrastructural and microstructural (=macroscopic=apparent) elasticity tensors. A second independent experimental set (composition data and experimental stiffness values) is employed to validate the proposed model. We report a small mean prediction error for the macroscopic stiffness values. The validation suggests that hydroxyapatite, collagen, and water are tissue-independent phases, which define, through their mechanical interaction, the elasticity of all bones, whether cortical or trabecular.

Micromechanics-Based Durability Study of Polyvinyl Alcohol-Engineered Cementitious Composite

Abstract: Durability of engineered cementitious composites (ECC) reinforced with polyvinyl alcohol (PVA) fiber is investigated. ECCs have been realized as ductile strain-hardening cementitious composites with tensile strain capacity up to 5%. This material is being applied in new construction and for the repair and retrofit of structures. A micromechanics-based approach is adopted in this durability study. The micromechanics-based model relates fiber, matrix, and interface parameters to composite properties through knowledge of microdeformation mechanisms beyond the elastic stage. Composite property changes resulting from environmental loading are expected to be a manifestation of changes in properties at the fiber, matrix, and/or interface level. This concept is examined in this paper by experimentally determining the changes in the fiber and fiber-matrix interface properties with specimens exposed to accelerated testing and correlating such changes to changes in the ductility of composites exposed to the same accelerated testing conditions. The accelerated test used in this study is a hot water immersion test simulating a long-term hot and humid environment. It is found that the fiber-matrix interface chemical bond increases while the apparent fiber strength decreases when the exposure time reaches 26 weeks. Correspondingly the composite ductility also decreases. The micromechanical model provides a rational means of interpreting and correlating the data from these 2 levels of testing. Despite the deterioration, PVA-ECC is found to retain tensile ductility more than 200 times that of normal concrete or normal fiber-reinforced concrete after exposure to an equivalent of 70 years or more of hot and humid environmental conditions.

A Short Introduction to Continuum Micromechanics

Abstract: Basic issues in continuum mechanical modeling of microstructured materials are discussed and a number of physically based modeling approaches are presented, among them mean field and bounding methods as well as unit cell and embedding models. In addition, important aspects of multi-scale modeling strategies are addressed and a short introduction to the treatment of damage at the constituent level within micromechanical models is given.

Finite Element Micromechanics for Stiffness and Strength of Wavy Fiber Composites

Abstract: In this paper, a micromechanical model of a composite lamina material with fiber waviness is described. Results are presented and discussed with regard to stiffness and strength predictions for composite lamina. A micromechanical model of a unit cell from periodically distributed unidirectional waved cylindrical fibers embedded within matrix is proposed to withdraw the different material stiffness parameters. Finite element analysis of the periodic unit cell characterizing the structural stiffness of the composite material is carried out to determine the average stress and strain components. The composite stress-strain relations are then employed to determine the stiffness parameters. Numerical results for a typical composite constituted of polymer matrix and carbon fibers in the form of periodically hexagonal packing and initially sinusoidal waviness are presented for different amplitude to wavelength ratios and a range of fiber volume fractions. The results reveal the presence of local periodic-antisymm...

Compressive response and failure of braided textile composites: Part 2—computations

Abstract: In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.

Elastoplastic Modeling of Metal Matrix Composites Containing Randomly Located and Oriented Spheroidal Particles

Abstract: Micromechanics-based effective elastic and plastic formulations of metal matrix composites (MMCs) containing randomly located and randomly oriented particles are developed. The averaging process over all orientations upon three elastic governing equations for aligned particle-reinforced MMCs is performed to obtain the explicit formulation of effective elastic stiffness of MMCs with randomly oriented particles. The effects of volume fraction of particles and particle shape on the overall elastic constants are studied. Comparisons with the Hashin-Shtrikman bounds and Ponte Castaneda-Willis bounds show that the present effective elastic formulation does not violate the variational bounds. Good agreement with experimental elastic stiffness data is also illustrated. Furthermore, the orientational averaging procedure is employed to derive the overall elastoplastic yield function for the MMCs. Elastoplastic constitutive relations for the composites are constructed on the basis of the derived composite yield function. The stress-strain responses of MMCs under the axisymmetric loading are also investigated in detail. Finally, elastoplastic comparisons with the experimental data for SiCp/Al composites are performed to illustrate the capability of the proposed formulation.

Shear band evolution and accumulated microstructural development in Cosserat media

Abstract: This paper prepares the ground for the continuum analysis of shear band evolution using a Cosserat/micropolar constitutive equation derived from micromechanical considerations. The nature of the constitutive response offers two key advantages over other existing models. Firstly, its non-local character obviates the mathematical difficulties of traditional analyses, and facilitates an investigation of the shear band evolution (i.e. the regime beyond the onset of localization). Secondly, the constitutive model parameters are physical properties of particles and their interactions (e.g. particle stiffness coefficients, coefficients of inter-particle rolling friction and sliding friction), as opposed to poorly understood fitting parameters. In this regard, the model is based on the same material properties used as model inputs to a discrete element (DEM) analysis, therefore, the micromechanics approach provides the vehicle for incorporating results not only from physical experiments but also from DEM simulations. Although the capabilities of such constitutive models are still limited, much can be discerned from their general rate form. In this paper, an attempt is made to distinguish between those aspects of the continuum theory of localization that are independent of the constitutive model, and those that require significant advances in the understanding of micromechanics.

A micromechanical approach to the strength criterion of Drucker‐Prager materials reinforced by rigid inclusions

Abstract: At the microscopic scale, concrete can be considered as a frictional matrix (cement paste) surrounding rigid inclusions (aggregate or sand inclusions) The present paper proposes a theoretical approach to the strength criterion of such a composite material It is shown that the macroscopic stress states on the yield surface can be obtained from the solution to non-linear viscous problems defined on a representative volume element The practical determination of the yield surface implements a non-linear homogenization scheme based on the modified secant method The role of the interface between the matrix and the inclusions is also investigated Two extreme modellings are considered: perfect bonding and non-frictional interfaces In both cases, the method yields a macroscopic strength criterion of the Drucker-Prager type The macroscopic friction angle is a function of that of the matrix and of the volume fraction of the inclusions In the case of perfect bonding, the inclusions have a reinforcing effect In contrast, this may not be true for a non-frictional interface

Effective Elastic and Plastic Properties of Interpenetrating Multiphase Composites

Abstract: In interpenetrating phase composites, there are at least two phases that are each interconnected in three dimensions, constructing a topologically continuous network throughout the microstructure. The dependence relation between the macroscopically effective properties and the microstructures of interpenetrating phase composites is investigated in this paper. The effective elastic moduli of such kind of composites cannot be calculated from conventional micromechanics methods based on Eshelby's tensor because an interpenetrating phase cannot be extracted as dispersed inclusions. Using the concept of connectivity, a micromechanical cell model is first presented to characterize the complex microstructure and stress transfer features and to estimate the effective elastic moduli of composites reinforced with either dispersed inclusions or interpenetrating networks. The Mori–Tanaka method and the iso-stress and iso-strain assumptions are adopted in an appropriate manner of combination by decomposing the unit cell into parallel and series sub-cells, rendering the calculation of effective moduli quite easy and accurate. This model is also used to determine the elastoplastic constitutive relation of interpenetrating phase composites. Several typical examples are given to illustrate the application of this method. The obtained analytical solutions for both effective elastic moduli and elastoplastic constitutive relations agree well with the finite element results and experimental data.

Ferroelectric switching: a micromechanics model versus measured behaviour

Abstract: The behaviour of ferroelectric polycrystals is explored using a rate-independent crystal plasticity model with self-consistent homogenisation to capture grain–grain interactions. Dimensionless parameters are introduced that allow a simple connection to be made between material constants and the nonlinear ferroelectric behaviour. In particular, combinations of material parameters are identified that cause remanent straining to be strongly suppressed. The self-consistent scheme allows for the ferroelectric response of a composite of grains with distinct sets of switching systems to be modelled. This feature is used to explore the effect of pinned domain walls and of dielectric inclusions. The model is able to reproduce the electrical response of three materials (PZT-5H, PZT-4D and Barium Titanate) under proportional stress and electric field loading, as measured in a parallel study.

A theory for plastic-bonded materials with a bimodal size distribution of filler particles

Abstract: Plastic-bonded materials are composites consisting of grains of filler material embedded in a polymeric matrix. A micromechanics model is proposed for investigating the mechanical behaviour of plastic-bonded materials having two disparate grain sizes. A hybrid theory is proposed to handle some aspects of the bimodal grain size distribution. Our model uses the first-order method of cells with an eight-cell representative volume element where one of the eight cells contains a large grain and the seven remaining cells contain a mixture of small grains embedded in the polymeric binder material. A Mori–Tanaka-based analysis is used to describe the small grain-binder mechanical response. The small grains in this analysis are assumed to be spherical and uniformly distributed in the binder. In this work, we use the explosive PBX 9501, in its unreacted state, as our test system. The explosive grain particle size distribution of PBX 9501 consists of two broad peaks centred at approximately 1 and 200 µm. The constitutive behaviour of the large explosive grains are assumed to be elastic-plastic and damage by way of micro-crack brittle fracture. Only linear elasticity of the small grains is considered. The rate and temperature dependence of the mechanical response of the polymer binder is accounted for by a generalized Maxwell viscoelasticity model. The theoretical uniaxial stress–strain response for PBX 9501 is reported for quasi-static and split Hopkinson pressure bar loading rates and compared to experimental measurements.

Mechanics of thin films and microdevices

Abstract: This paper discusses the latest developments in nanomechanics of thin films with applications in microelectromechanical systems (MEMS) and microelectronics. A precise methodology that combines in situ atomic force microscopy (AFM) surface measurements of uniaxially tension-loaded MEMS specimens and strain analysis via digital image correlation (DIC) achieving 0.1 pixel spatial displacement resolution is presented. By this method, the mechanical deformation of thin films was obtained in areas as small as 4 /spl times/ 4 /spl mu/m and with 1-2 nm spatial displacement resolution supporting the derivation of interrelations between the material microstructure and the local mechanical properties. This methodology provided for the first time the values of Young's modulus and Poisson's ratio from specimens with cross-sections as small as 2 /spl times/ 6 /spl mu/m. The value of properties derived via AFM/DIC demonstrated very limited scatter compared to indirect mechanical property measurement methods. The application of this technique on nonuniform geometries resolved nanoscale displacement and strain fields in the vicinity of ultrasharp elliptical perforations achieving very good agreement with finite element models. Furthermore, the stochastic and deterministic material failure properties described via Weibull statistics and fracture toughness, respectively, are illustrated for brittle thin films. Failure initiated at notches was found to be influenced by the local radius of curvature and the stress concentration factor. Precise fracture toughness values for MEMS materials were obtained from MEMS specimens with atomically sharp cracks. These studies were supported by measurements of displacements/strains conducted for the first time in the vicinity of mathematically sharp cracks via the AFM/DIC method. The method can be applied to a variety of thermomechanical reliability problems in multilayered thin films and inhomogeneous/anisotropic materials.