Showing papers on "Micromechanics published in 2008"

Introduction to micromechanics and nanomechanics

Abstract: Introduction Preliminary Microstructures and Homogenization Green's Function and Fourier Transform Eigenstrain Theory Finite Eshelby Tensors Comparison Variational Principles Homogenization I Homogenization II Introduction of Dislocation Theory.

Strain hardening behaviour and the Taylor factor of pure magnesium

Abstract: Taylor orientation factors for strain hardening in textured and random polycrystals of magnesium were derived from the ratio of the strain hardening rates of polycrystals to that of single crystals deforming by equivalent polyslip. For polycrystals with textures that inhibit basal and prismatic slip while favouring pyramidal polyslip, the Taylor factor is estimated to be between 2.1 and 2.5, increasing to about 4.5 for randomly textured polycrystals. The micromechanics of strain hardening in polycrystals are discussed.

Measurement of Epoxy Resin Tension, Compression, and Shear Stress–Strain Curves over a Wide Range of Strain Rates Using Small Test Specimens

Abstract: The next generation aircraft engines are designed to be lighter and stronger than engines currently in use by using carbon fiber composites. In order to certify these engines, ballistic impact tests and computational analyses must be completed, which will simulate a “blade out” event in a catastrophic engine failure In order to computationally simulate the engine failure, properties of the carbon fiber and resin matrix must be known. When conducting computer simulations using a micromechanics approach, experimental tensile, compressive, and shear data are needed for constitutive modeling of the resin matrix material. The material properties of an Epon E862 epoxy resin will be investigated because it is a commercial 176°C (350°F) cure resin currently being used in these aircraft engines. These properties will be measured using optical measurement techniques. The epoxy specimens will be tested in tension, compression and torsional loadings under various strain rates ranging from 10−5 to 10−1 s−1 and tempera...

Micro-Mechanics of Failure (MMF) for Continuous Fiber Reinforced Composites:

Abstract: The micromechanics of failure was developed to predict the failure of continuous fiber reinforced composites. A micromechanical approach using unit cells of square and hexagonal arrays was employed to compute the micro stresses of constituents and at the fiber—matrix interface, which were used to determine the failure initiation of a unidirectional ply. The constituent properties include two tensile and compressive strengths of fiber and matrix, plus normal and shear strengths at the interface. The matrix and interfacial dominated strength properties are determined by matching the micro stresses at the constituent levels with the observed transverse tensile and compressive strengths on the macro ply level. The longitudinal shear failure is then expected to be a result of damage progression after initial failure. Based on the current MMF, in the graphite/epoxy considered in this study both transverse tensile and compressive failure are expected to occur via matrix failure. However, in the glass/epoxy the t...

Micromechanics-based conversion of CT data into anisotropic elasticity tensors, applied to FE simulations of a mandible.

Abstract: Computer Tomographic (CT) image data have become a standard basis for structural analyses of bony organs. In this context, regression functions between stiffness components and Hounsfields units (HU) from CT, related to X-ray attenuation coefficients, are widely used for the definition of the (actually inhomogeneous and anisotropic) material behavior inside the organ. Herein, we suggest to derive the functional dependence of the fully orthotropic stiffness tensors on the Hounsfield units from the physical information contained in the X-ray attenuation coefficients: (i) Based on voxel average rules for the X-ray attenuation coefficients, we assign to each voxel the volume fraction occupied by water (marrow) and that occupied by solid bone matrix. (ii) By means of a continuum micromechanics representation for bone, which is based on voxel-invariant (species and whole bone-specific) stiffness properties of solid bone matrix and of water, we convert the aforementioned volume fractions into voxel-specific orthotropic stiffness tensor components. The micromechanics model, in combination with the average rule for X-ray attenuation coefficients, predicts a quasi-linear relationship between axial Young’s modulus and HU, and highly nonlinear relationships for both circumferential and radial Young’s moduli as well as for the shear moduli in all principal material directions. Corresponding whole-organ Finite Element (FE) analyses of a partially edentulous human mandible characterized by atrophy of the alveolar ridge show that volumetric strain concentrations/peaks within the organ are decreased when considering material anisotropy, and increased when considering material inhomogeneity.

Exploring the applicability of gradient elasticity to certain micro/nano reliability problems

Abstract: It has long been assessed that continuum mechanics can be used successfully to address a variety of mechanical problems at both macroscopic and microscopic scales. The term “micromechanics”, in particular, has been used in considering elasticity, plasticity, damage, and fracture mechanics problems at the micron scale involving metallic, ceramic and polymeric materials, as well as their composites. Applications to automobile, aerospace, and concrete industries, as well as to chemical and microelectronic technologies have already been documented. The recent developments in the field of nanotechnology have prompted a substantial literature in nanomechanics. While this term was first introduced by the author in the early 90’s to advance a generalized continuum mechanics framework for applications at the nanoscale, it is mainly used today in considering “hybrid” ab-initio/molecular dynamics/finite element simulations, usually based on elasticity theory, to interpret the mechanical response of nano-objects (nanotubes, nanowires, nanoaggregates) and extract information on nano-configurations (dislocation cores, crack tips, interfaces). The modest goal of this article is to show that continuum elasticity can indeed be extended to describe a variety of problems at the micro/nano regime. The resultant micro/nanoelasticity theory includes long-range or nonlocal material point interactions and surface effects in the form of (phenomenological) higher-order stress/strain gradients. Coupled thermo-diffuso-chemo-mechanical processes can also be considered within such a higher-order theory. Size effects on micro/nano holes and micro/nano cracks can conveniently be modeled, and some standard strength of materials formulas routinely used for micro/nano beams can be improved, with potential applications to MEMS/NEMS devices and micro/nano reliability components.

Effects of Fiber Arrangement on Mechanical Behavior of Unidirectional Composites

Abstract: Micromechanical approaches are employed to investigate the influence of different fiber arrangement on the mechanical behavior of unidirectional composites (UD) under various loading conditions. A micromechanical model with a random fiber array is generated and used in a finite element analysis together with two frequently used representative volume elements (RVE), or unit cell models of square and hexagonal arrays. The algorithm for generating the random fiber array is verified by comparing the comprehensive performance of a unit cell based on our random array and that of a unit cell based on a real fiber distribution in the UD cross-section. Performance of the random and regular fiber arrays is also evaluated through frequency distributions of stress invariants in matrix and tractions at the fiber—matrix interface due to various loading types. The effects of different loading angles on the overall response of regular arrays to various loading conditions are investigated thoroughly. Finally, the Weibull ...

Distribution of Micro Stresses and Interfacial Tractions in Unidirectional Composites

Abstract: A micromechanical approach is developed to determine the micro stress within a unidirectional composite under various mechanical and thermal loading conditions. Based on linear stress—strain relations, the concept of a stress amplification factor is introduced, and the correlations between macro stress and micro stress are explicitly expressed in mathematical equations. Three unit cell models, square, hexagonal, and diamond fiber arrays, are analyzed and compared using three-dimensional finite element methods. Subsequently, effective material properties, the distribution of micro stress in the fiber/matrix, as well as traction distribution at the fiber—matrix interface, and the effect of different interfacial stiffness, are obtained.

A discrete element model for the development of compaction localization in granular rock

Abstract: [1] A discrete element model was developed to simulate the micromechanics of compaction localization in a granular rock. The rock was modeled as a bonded assembly of circular disks, and seven different distributions of radius were considered. To simulate grain crushing and pore collapse, an intragranular damage mechanism was introduced that allows for the shrinkage of a disk if one of its normal contact stresses attains a critical value. The model captures key attributes of failure mode and damage evolution associated with the brittle-ductile transition in porous sandstones. Our simulations indicate that the development of discrete compaction bands is promoted in a relatively homogeneous granular aggregate, while diffuse band growth and distributed cataclastic flow are preferred modes of compaction in a more heterogeneous system. To interpret the former result an Eshelby inclusion model was proposed to estimate analytically the local stress perturbations due to pore collapse in a homogeneous aggregate.

Temperature and loading rate effects on tensile properties of kenaf bast fiber bundles and composites

Abstract: This paper presents extensive experiments and micromechanics-based modeling to evaluate systematically the tensile properties of kenaf bast fibers bundle (KBFB) and kenaf bast fiber-reinforced epoxy strands. Uniaxial tension behaviors of KBFBs and KBFB-reinforced epoxy strands were evaluated statistically using large sample sets. The elastic modulus, tensile strength, as well as failure strains of KBFBs, displayed large scatter statistically ranging from 10% to 30%. The loading rate-dependency was evaluated at three strain rates ranging from approximately 10−4 ∼ 10−2/s. The tensile strength increases gradually as the loading rate increases, while the tensile modulus almost remains the same as the loading rate increases until the loading rate reaches 10−2/s, at which a much higher modulus was presented. The high temperatures (170–180 °C), possibly subjected during fiber processing and composite fabrication, do not impose significant effects on the tensile properties of KBFBs if the duration is less than 1-h. The tensile properties of KBFB were not affected by the conditioning at 130 °C for 24-h, which mimics the severe service temperature of automotive front-end components. KBFB-epoxy composite strands were further evaluated at various loading rates. A micromechanics-based Mori–Tanaka model was implemented to predict the anisotropic elastic moduli of KBFB and KBFB-epoxy composite strands based on the microstructural compositions.

Scale bridging method to characterize mechanical properties of nanoparticle/polymer nanocomposites

Abstract: Multiscale analysis to characterize the size effect of silica nanoparticles on the mechanical properties of nanoparticle/polymer nanocomposites is developed and verified through a molecular dynamics simulation and continuum micromechanics model. In the micromechanics model, the particle-matrix interface mechanical property is incorporated, and the thickness and elastic properties of the interface are extracted from the atomistic structures. The proposed multiscale micromechanics model accurately reflects the size effect of the nanoparticle. The prediction by the current multiscale model at various volume fractions is compared to the results of the molecular dynamics simulations in order to validate the present multiscale analysis model.

From micron-sized needle-shaped hydrates to meter-sized shotcrete tunnel shells: micromechanical upscaling of stiffness and strength of hydrating shotcrete

Abstract: Knowledge on the stresses in shotcrete tunnel shells is of great importance, as to assess their safety against severe cracking or failure. Estimation of these stresses from 3D optical displacement measurements requires shotcrete material models, which may preferentially consider variations in the water–cement and aggregate–cement ratios. Therefore, we employ two representative volume elements within a continuum micromechanics framework: the first one relates to cement paste (with a spherical material phase representing cement clinker grains, needle-shaped hydrate phases with isotropically distributed spatial orientations, a spherical water phase, and a spherical air phase; all being in mutual contact), and the second one relates to shotcrete (with phases representing cement paste and aggregates, whereby aggregate inclusions are embedded into a matrix made up by cement paste). Elasticity homogenization follows self-consistent schemes (at the cement paste level) and Mori–Tanaka estimates (at the shotcrete level), and stress peaks in the hydrates related to quasi-brittle material failure are estimated by second-order phase averages derived from the RVE-related elastic energy. The latter permits upscaling from the hydrate strength to the shotcrete strength. Experimental data from resonant frequency tests, ultrasonics tests, adiabatic tests, uniaxial compression tests, and nanoindentation tests suggest that shotcrete elasticity and strength can be reasonably predicted from mixture- and hydration-independent elastic properties of aggregates, clinker, hydrates, water, and air, and from strength properties of hydrates. At the structural level, the micromechanics model, when combined with 3D displacement measurements, predicts that a decrease of the water–cement ratio increases the safety of the shotcrete tunnel shell.

Multiwalled carbon nanotube reinforced polymer composites

Abstract: Due to their high stiffness and strength, as well as their electrical conductivity, carbon nanotubes are under intense investigation as fillers in polymer matrix composites. The nature of the carbon nanotube/polymer bonding and the curvature of the carbon nanotubes within the polymer have arisen as particular factors in the efficacy of the carbon nanotubes to actually provide any enhanced stiffness or strength to the composite. Here the effects of carbon nanotube curvature and interface interaction with the matrix on the composite stiffness are investigated using micromechanical analysis. In particular, the effects of poor bonding and thus poor shear lag load transfer to the carbon nanotubes are studied. In the case of poor bonding, carbon nanotubes waviness is shown to enhance the composite stiffness.

Determination of interface properties from experiments on the fragmentation process in single-fiber composites

Abstract: This paper attempts to quantify the fracture properties (strength and toughness) of the fiber–matrix interface in composites, using the fragmentation process and debonding growth for HI-Nicalon™ SiC single-fiber and T300 carbon single-fiber epoxy (Bisphenol-A type epoxy resin with triethylenetetramine (TETA) as curing agent) composite systems. This method is based on the numerical modeling for the microscopic damage and fragmentation process in single-fiber composite (SFC) tests, with a cohesive zone model (CZM). For the HI-Nicalon™ SiC single-fiber epoxy composite in which the major damage near a fiber break is interfacial debonding, interface properties were reasonably determined as ( T II,max , G IIc ) = (75 MPa, 200 J/m 2 ). In contrast, for T300 carbon single-fiber epoxy composite, we could not determine unique interfacial properties, since the variation of the cohesive parameters hardly affects the microscopic damage process due to the transition to the damage pattern dominated by matrix cracking.

Transverse properties of carbon fibres by nano-indentation and micro-mechanics

Abstract: In this study the transverse modulus of three high modulus (M40, M46 and K63712) carbon fibres has first been measured directly by nano-indentation measurements. Transverse tensile tests on unidirectional epoxy composites were then performed, and the comparison was made between transverse fibre properties from indentation and those needed to obtain the measured transverse composite modulus using micromechanics expressions. The latter tended to underestimate values from indentation, by up to 36%, and reasons for this are discussed. Values of transverse fibre modulus determined by both methods decrease as longitudinal fibre modulus increases.