Micromechanical Method Research Articles

Vibration analysis of the embedded piezoelectric polymeric nano-composite panels in the elastic substrate

Abstract In the present study the vibrations of a smart thin micro panel of polymeric nano-composite reinforced by the Single-Walled Boron-Nitride Nano-Tubes (SWBNNTs) and the matrix Poly-VinyliDene Fluoride (PVDF) on an elastic substrate is studied. Using the micromechanics method, the nano-composite structural equations are obtained for a sample volume element and by considering a unidirectional electric field and stress in the field. The stress-strain relationships that include mechanical and electric terms are obtained for the micro-tubes. The micro-panel is considered as the thin wall shell and Donnell’s non-linear theory is used for the strain-displacement relations. To obtain the equations of motion, the minimum energy method or Hamilton’s principle is used. The external work is caused by the elastic environment as well as the magnetic field energies. Given that the work has been in small micro scale the strain gradient, modified coupled stress and classic theories are used to consider the small-scale effect in the equations. The results showed Stiffness of the panel is reduced by increasing length and reducing volume fraction of BNNT and lower frequencies are obtained. Angling nanotubes is reduced panel frequency and the severity of this reduction is increased at higher volume percentages. The maximum frequency is happened in the full cylinder sector.

Optical contrast spectra studies for determining thickness of stage-1 graphene-FeCl3 intercalation compounds

Because of novel features in their structural, electronic, magnetic and optical properties, especially potential applications in nanoelectronics, the few-layer graphene intercalation compounds (FLGICs) have been intensively studied recently. In this work, the dielectric constant of the doped graphene of stage-1 FeCl3-GIC is obtained by fitting the optical contrast spectra. And fully intercalated stage-1 FeCl3-FLGICs were prepared by micromechanical cleavage method from graphite intercalation compounds (GICs) for the first time. Finally, we demonstrated that the thickness of stage-1 FeCl3-GICs by micromechanical cleavage can be determined by optical contrast spectra. This method also can be used to other FLGICs, such as SbCl5-FLGICs and AuCl5-FLGICs, etc.

Graphene‐Based Nanocomposites for Energy Storage

Since the first report of using micromechanical cleavage method to produce graphene sheets in 2004, graphene/graphene‐based nanocomposites have attracted wide attention both for fundamental aspects as well as applications in advanced energy storage and conversion systems. In comparison to other materials, graphene‐based nanostructured materials have unique 2D structure, high electronic mobility, exceptional electronic and thermal conductivities, excellent optical transmittance, good mechanical strength, and ultrahigh surface area. Therefore, they are considered as attractive materials for hydrogen (H2) storage and high‐performance electrochemical energy storage devices, such as supercapacitors, rechargeable lithium (Li)‐ion batteries, Li–sulfur batteries, Li–air batteries, sodium (Na)‐ion batteries, Na–air batteries, zinc (Zn)–air batteries, and vanadium redox flow batteries (VRFB), etc., as they can improve the efficiency, capacity, gravimetric energy/power densities, and cycle life of these energy storage devices. In this article, recent progress reported on the synthesis and fabrication of graphene nanocomposite materials for applications in these aforementioned various energy storage systems is reviewed. Importantly, the prospects and future challenges in both scalable manufacturing and more energy storage‐related applications are discussed.

Computationally efficient High-Fidelity Generalized Method of Cells micromechanics via order-reduction techniques

The High-Fidelity Generalized Method of Cells (HFGMC) is a powerful technique for simulating composite materials. The HFGMC uses a higher-order approximation for the subcell displacement field that allows for accurate determination of the subcell stress/strain fields. In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic RUCs was reduced in size through the use of Proper Orthogonal Decomposition. Accurate order-reduced HFGMC models were then implemented within a special-purpose finite element user material subroutine and used to perform multiscale composite analyses. A number of cases were presented that demonstrate the computational feasibility of using order-reduction techniques to solve solid mechanics problems with complex microstructures. By simulating composite materials in a more computationally efficient manner, a pathway forward is presented for performing high-fidelity multiscale analyses of composite structures.

Copper–graphite composites: thermal expansion, thermal and electrical conductivities, and cross-property connections

The paper focuses on thermal and electrical properties of copper–graphite composites. Copper–graphite composites in the range of 0–50 vol% of graphite were prepared from the mixture of copper and graphite powder by the powder metallurgy method. Such composites combine high thermal and electrical conductivities provided by copper matrix and low thermal expansion coefficient and lubricating properties due to the graphite phase. We model thermal and electrical conductivities and thermal expansion coefficient using methods of micromechanics in connection with the material microstructure and measure these quantities experimentally to compare with the results of modeling. Cross-property connections between thermal and electrical properties of the composites are established and experimentally verified.

Perforation forces of the intact porcine anterior lens capsule

During the first step of cataract surgery, the lens capsule is perforated and a circular hole is created with a sharp instrument, a procedure called capsulorhexis. To develop automated systems that can assist ophthalmologists during capsulorhexis, the forces required must be quantified. This study investigates perforation forces of the central anterior lens capsule in porcine eyes, which are used as a conservative model for the human eye. A micro-mechanical characterisation method is presented that measures capsular bag perforation forces with a high precision positioning and high-resolution force sensing system. The force during perforation of the anterior lens capsule was measured with various sized needles and indentation speeds and is found to be 15–35mN. A bio-mechanical model is identified that describes an exponential correlation between indentation force and depth, indicating strain hardening behaviour of the porcine anterior lens capsule.

An extended micromechanics method for probing interphase properties in polymer nanocomposites

Inclusions comprised on filler particles and interphase regions commonly form complex morphologies in polymer nanocomposites. Addressing these morphologies as systems of overlapping simple shapes allows for the study of dilute particles, clustered particles, and interacting interphases all in one general modeling framework. To account for the material properties in these overlapping geometries, weighted-mean and additive overlapping conditions are introduced and the corresponding inclusion-wise integral equations are formulated. An extended micromechanics method based on these overlapping conditions for linear elastic and viscoelastic heterogeneous material is then developed. An important feature of the proposed approach is that the effect of both the geometric overlapping (clustered particles) and physical overlapping (interacting interphases) on the effective properties can be distinguished. We apply the extended micromechanics method to a viscoelastic polymer nanocomposite with interphase regions, and estimate the properties and thickness of the interphase region based on experimental data for carbon-black filled styrene butadiene rubbers.

Size effect on the magnetic phase in Sr4Ru3O10

High quality Sr4Ru3O10 nanoflakes are obtained by the scotch tape-based micro-mechanical exfoliation method. The metamagnetic transition temperature is found to decrease in line with the decrease of thickness, while the ferromagnetic (FM) phase, the ordinary, and anomalous Hall effects (OHE and AHE) are independent on the thickness of the flake. Analysis of the data demonstrates that the AHE reflects the FM nature of Sr4Ru3O10, and the decrease of thickness favors the Ru moments aligned in the ab-plane, which induces a decrease of the metamagnetic transition temperature compared with the bulk.

Parametric Studies of Shape Memory Alloy Hybrid Composite Laminates Under Low-Velocity Impact

AbstractIn the paper, the influence of shape memory alloy (SMA) by varying the parameters such as volume fraction, orientation, and temperature on the hybrid-SMA composite laminate subjected to low-velocity impact is studied. A theoretical model for the composite laminated plate bonded with SMA reinforced layers is presented. The constitutive relation of the SMA layer is obtained by using the method of micromechanics. The governing relations obtained can be used for theoretical predications of thermomechanical properties of SMA plies in this paper. The analytical expressions for the hybrid SMA composite plate are derived based on Tanaka's constitutive equation and linear phase transformation kinetics presented by Liang and Rogers.The laminated plate theory, first-order shear deformation theory and minimal potential energy principle is utilized to solve the governing equations of the hybrid composite plate and calculate the absorbed energies including tensile, shear and bending.An orthogonal array and analysis of variance is employed to investigate the influence of the mentioned parameters on the energy absorption of the hybrid laminated plate. The results showed that the effects of the phase transformation temperature are more significant than the effects of the volume fraction and orientation of SMA on structural energy absorption.

New micromechanics model for saturated porous media with connected pores

A new micromechanics method is proposed to investigate the effective properties of saturated porous media with connected pores. This topic is seldom discussed in the literature because it is difficult to describe the connected pores and skeleton using conventional micromechanics methods. A new micromechanics model (i.e., Model I) is suggested to characterize such saturated porous media in which the pores saturated by fluid are taken as the matrix, and the interconnected randomly oriented long fiber (ROLF)-like solid skeleton is taken as the inclusions. The proposed model is verified by numerical simulations; the simulation results indicate that the difference of the elastic constants calculated for media with interconnected pores and for those with dispersed ROLF solid inclusions is small. Thus, the elastic moduli of Model I can be treated as approximate values for porous media with connected pores. Further, a modified Eshelby tensor for spherical inclusions is derived based on the equivalency of the elastic moduli of Model I and a conventional micromechanics model in which spherical fluid inclusions are distributed randomly in a solid matrix. By means of the modified Eshelby tenor, conventional micromechanics methods can be utilized directly to calculate the effective mechanical and thermal properties of saturated porous media with interconnected pores. Some examples are presented to show that the macroscopic elastic moduli predicted by the proposed method are in good agreement with test data found in the literature.

A simple damage model for concrete considering irreversible mode‐II microcracks

AbstractA simple damage model with the concept of mode‐II microcracks on crack wall contributing to the irreversible strains for concrete is developed. By applying the micromechanics method, a microcell‐based damage model is introduced to understand the damage behaviour. Further, by introducing the physical interpretation of the damage variable using thermodynamic method, a novel damage variable (irreversible‐damage variable) is proposed to describe the irrecoverable strains generated by both mode‐II microcracks and irreversible‐frictional sliding. With this methodology, a simple continuum damage mechanics model is developed in which both elastic and irreversible damages are considered. As demonstrated by the comparison with experimental results, the proposed model is characterized by accuracy of solutions, sufficiency of physical sense and convenience of implementation.

Characterization of pervious concrete through image based micromechanical modeling

Pervious concrete has been widely used in parking lots and airport fields. However, past experience has shown durability and strength of the pervious concrete remains a challenge for adopting them in wider applications, as the binding material proportion is low and the use of fine aggregates is nearly zero. When loading in compression, the failure appears first in the weak concrete zone induced by the random distribution of voids. The process continues until the failure of the whole specimen occurs. Thus, the position, size and shape distribution of voids in the pervious concrete microstructure control the overall behavior of the material. In this work, the influence of the distribution of voids on the strength, stiffness, and permeability of pervious concrete microstructure is studied by 2D image analysis and finite element modeling. The position and size distribution of the microstructure voids are first summarized through Fast Fourier Transformation (FFT) analysis. A finite element analysis is then conducted on the microstructure models regenerated through the derived microstructure characteristics using ANSYS Parametric Design Language (APDL). The effect of the sample size of 2D microstructures is studied by varying the section size and a possible representative volume element (RVE) is therefore found. Predicted stress-strain plots are generated for the 2D specimen under compressive load and the obtained results, including stiffness, strength and permeability are compared with the results from the experiments conducted following ASTM standards. The comparison between models and physical experiments showed around or above 90% accuracy, which validates the suggested micromechanical analysis method of the previous concrete composite.

Iterative approaches to extend dilute homogenization predictions of Willis materials to higher volume fractions

Dynamic homogenization of generally heterogeneous elastic materials leads to three different effective material properties: stiffness, density, and parameters that couple momentum to strain and stress to velocity. This formulation was first proposed by Willis [Wave Mot. 3, 1–11, (1981)] and is thus commonly referred to as Willis coupling. While there are some homogenization methods which account for Willis coupling, those models rely on either the assumption of periodic media or on dilute concentrations of coupled inhomogeneities in an otherwise homogeneous matrix. This work presents the use of dilute models with iterative micromechanical methods to predict general material properties in materials with no long-range order and elevated volume fractions of inhomogeneity. Two such methods, self-consistent and differential effective medium models, will be presented for the homogenization of composites of arbitrary anisotropy and Willis coupling resulting from the presence of Willis coupled inclusions in an el...

Statistical nanoindentation technique in application to hardened cement pastes: Influences of material microstructure and analysis method

Statistical nanoindentation technique has been widely used to study the microstructural mechanical properties of various types of hardened cement pastes, which has significantly improved the fundamental understanding on the mechanical performances of concrete and other cementitious composites. However, it was noted that the contradictory results from statistical nanoindentation technique appeared in the literatures and the critical aspects in the application of this technique to hardened cement pastes were recognized. This work is designed to provide an insight into the critical aspects, including the influences of material microstructure and statistical analysis method. Firstly, the microstructure of hardened cement pastes was investigated by SEM-BSE/EDX analysis. Then, the influence of heterogeneous material microstructure on the nanoindentation results was investigated through a micromechanical method. After that, two general methods of parameter estimation were applied to analyze the nanoindentation data and global optimal results were sought by multiple runs with the random starting values. This work revealed that the indented ‘Calcium-Silicate-Hydrate’ microstructure is a fact of the composites and the analysis result largely depends on the selected statistical analysis method. The influences of material microstructure and statistical analysis method may cause unreliable result. In this paper, a method for the verification of the result from statistical nanoindentation technique in hardened cement pastes was proposed.

Direct evaluation of grain boundary hydrogen embrittlement: A micro-mechanical approach

In order to directly investigate the grain boundary (GB) hydrogen embrittlement in polycrystalline materials, a novel micro-mechanical testing method was developed. By combining a site-specific sampling technique and a high-voltage environmental transmission electron microscope (HV ETEM), the fracture property of micro-cantilever specimens fabricated from the same GB in a nickel-aluminide (Ni3Al) polycrystal was critically compared in environments with/without hydrogen (H2) gas. For randomly oriented GBs, brittle fracture nucleation accompanied by plastic deformation was observed in a H2-containing environment except for ones with small orientation difference. No GB fracture was observed for coherent Σ3 boundaries. It also appeared that the similitude of the hydrogen-enhanced decohesion (HEDE) mechanism was still valid even for the submicron-scale specimens.

The Eshelby, Hill, Moment and Concentration Tensors for Ellipsoidal Inhomogeneities in the Newtonian Potential Problem and Linear Elastostatics

One of the most cited papers in Applied Mechanics is the work of Eshelby from 1957 who showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in an unbounded (in all directions) homogeneous isotropic host would feel uniform strains and stresses when uniform strains or tractions are applied in the far-field. Of specific importance is the uniformity of Eshelby’s tensor $\mathbf{S}$ . Following Eshelby’s seminal work, a vast literature has been generated using and developing Eshelby’s result and ideas, leading to some beautiful mathematics and extremely useful results in a wide range of application areas. In 1961 Eshelby conjectured that for anisotropic materials only ellipsoidal inhomogeneities would lead to such uniform interior fields. Although much progress has been made since then, the quest to prove this conjecture is still not complete; numerous important problems remain open. Following a different approach to that considered by Eshelby, a closely related tensor $\mathbf{P}=\mathbf{S}\mathbf{D}^{0}$ arises, where $\mathbf{D}^{0}$ is the host medium compliance tensor. The tensor $\mathbf{P}$ is associated with Hill and is of course also uniform when ellipsoidal inhomogeneities are embedded in a homogeneous host phase. Two of the most fundamental and useful areas of applications of these tensors are in Newtonian potential problems such as heat conduction, electrostatics, etc. and in the vector problems of elastostatics. Knowledge of the Hill and Eshelby tensors permit a number of interesting aspects to be studied associated with inhomogeneity problems and more generally for inhomogeneous media. Micromechanical methods established mainly over the last half-century have enabled bounds on and predictions of the effective properties of composite media. In many cases such predictions can be explicitly written down in terms of the Hill tensor, or equivalently the Eshelby tensor and can be shown to provide excellent predictions in many cases. Of specific interest is that a number of important limits of the ellipsoidal inhomogeneity can be taken in order to be employed in predictions of the effective properties of, for example, layered media and fibre reinforced composites and also to the cases when voids and cracks are present. In the main, results for the Hill and Eshelby tensors are distributed over a wide range of articles and books, using different notation and terminology and so it is often difficult to extract the necessary information for the tensor that one requires. The case of an anisotropic host phase is also frequently non-trivial due to the requirement of the associated Green’s tensor. Here this classical problem is revisited and a large number of results for problems that are felt to be of great utility in a wide range of disciplines are derived or recalled. A scaling argument leads to the derivation of the Eshelby tensor for potential problems where the host phase is at most orthotropic, without the requirement of using the anisotropic Green’s function. The Concentration tensor $\boldsymbol{\mathcal{A}}$ linking interior fields to those imposed in the far-field is derived for a wide variety of problems. These results can therefore be used in the various micromechanical schemes. Directly related to the tensors of Eshelby and Hill is the so-called Moment tensor $\mathbf{M}$ . As well as arising in the literature on micromechanics, this tensor is important in the vast area of research associated with inverse problems and specifically with the problem of identifying an object inside some domain given the application of a specific set of boundary conditions. Due to its fundamental importance and direct link to the Eshelby and Hill tensors, here we state the connection between $\mathbf{M}, \mathbf{P}$ and $\mathbf{S}$ in an effort to ensure that the work is of use to as wide a community as possible. Both tensor and matrix formulations are considered and contrasted throughout. Appendices give various details that illustrate the implementation of both approaches.

Pulsed laser deposition of single layer, hexagonal boron nitride (white graphene, h-BN) on fiber-oriented Ag(111)/SrTiO3(001)

We report on the growth of 1–10 ML films of hexagonal boron nitride (h-BN), also known as white graphene, on fiber-oriented Ag buffer films on SrTiO3(001) by pulsed laser deposition. The Ag buffer films of 40 nm thickness were used as substitutes for expensive single crystal metallic substrates. In-situ, reflection high-energy electron diffraction was used to monitor the surface structure of the Ag films and to observe the formation of the characteristic h-BN diffraction pattern. Further evidence of the growth of h-BN was provided by attenuated total reflectance spectroscopy, which showed the characteristic h-BN peaks at ∼780 cm−1 and 1367.4 cm−1. Ex-situ photoelectron spectroscopy showed that the surface of the h-BN films is stoichiometric. The physical structure of the films was confirmed by scanning electron microscopy. The h-BN films grew as large, sub-millimeter sheets with nano- and micro-sheets scattered on the surface. The h-BN sheets can be exfoliated by the micromechanical adhesive tape method. Spectral analysis was performed by energy dispersive spectroscopy in order to identify the h-BN sheets after exfoliation. The use of thin film Ag allows for reduced use of Ag and makes it possible to adjust the surface morphology of the thin film prior to h-BN growth.

Micropolar effect on the cataclastic flow and brittle‐ductile transition in high‐porosity rocks

AbstractA micromechanical distinct element method (DEM) model is adopted to analyze the grain‐scale mechanism that leads to the brittle‐ductile transition in cohesive‐frictional materials. The cohesive‐frictional materials are idealized as particulate assemblies of circular disks. While the frictional sliding of disks is sensitive to the normal compressive stress exerted on contacts, normal force can be both caused by interpenetration and long‐range cohesive bonding between two particles. Our numerical simulations indicate that the proposed DEM model is able to replicate the gradual shift of porosity change from dilation to compaction and failure pattern from localized failures to cataclastic flow upon rising confining pressure in 2‐D biaxial tests. More importantly, the micropolar effect is examined by tracking couple stress and microcrack initiation to interpret the transition mechanism. Numerical results indicate that the first invariant of the couple stress remains small for specimen sheared under low confining pressure but increases rapidly when subjected to higher confining pressure. The micropolar responses inferred from DEM simulations reveal that microcracking may occur in a more diffuse and stable manner when the first invariant of the macroscopic couple stress are of higher magnitudes.

On the thermal buckling of simply supported rectangular plates made of a sigmoid functionally graded Al/Al2O3 based material

We study the thermal buckling of a simply supported sigmoid functionally graded (SFGM) rectangular plate using first-order shear deformation theory. The S-FGM system consists of ceramic (Al2O3) and metal (Al) phases varying across the plate thickness according to a law described by two power-law functions. The effective properties of the composite are determined by the rule of mixtures, whose implementation is simpler than that of methods of micromechanics. The thermal heating is characterized by a uniform, linear, or sinusoidal temperature distribution across the plate thickness. The effects of the plate aspect ratio, the relative thickness, the gradient index, and the transverse shear on the buckling temperature difference are studied.

Elastic Behavior of 2D Grain Packing Modeled as Micromorphic Media Based on Granular Micromechanics

AbstractDiscrete simulation and continuum modeling are two competing methods for analyzing the behavior of complex material systems and granular assemblies. In this paper, a two-dimensional (2D) granular micromechanics model for micromorphic media is presented. The granular micromechanics method is enhanced by incorporating nonclassical terms in the kinematics. These include, in addition to the usual macroscale displacement gradient, the fluctuations in displacement gradient and also the second gradient of displacement. Microscopic intergranular force vectors and macroscopic stress tensors conjugate to the kinematic measures are defined, and the macroscopic strain energy density function is set equal to the volume average of grain-pair energies. As a result, continuum stiffness tensors are formulated on the basis of intergranular stiffness coefficients and fabric parameters defining the geometry of grains and their contacts. To demonstrate the applicability of the continuum method, a random granular assem...