Micromechanical Method Research Articles

Application of the Timoshenko–Mindlin Theory to the Calculation of Nonlinear Deformation and Stability of Anisotropic Shells

The nonlinear deformation and stability of composite shells are estimated by using the Timoshenko–Mindlin theory of anisotropic shells. The resolving system of equations is presented in a mixed form in displacements, forces, and moments. For its derivation, a modified version of the generalized Hu–Washizu variational principle formulated in rates for a quasi-static problem is used. However, instead of differentiation with respect to time, displacements, stresses, and loads are assumed to depend on a parameter, for which it is advisable to take the length of the arc of equilibrium states, as demonstrated in some studies. On variation of this parameter, the shell-load system can occur either at regular or singular points. A boundary value problem is formulated in the form of a normal system of differential equations in the derivatives of displacements, forces, and moments. In the separation of variables, the Fourier series are used in a complex form. The boundary value problem is solved by the Godunov discrete orthogonalization method in the field of complex numbers. Then, the Cauchy problem is solved by using known methods. Using the methodology developed, an analysis of the influence of composite properties and parameters of the layered structures on the form of the equilibrium curves of cylindrical shells is carried out. The mechanical characteristics of the initial elementary layers of the reinforced material are determined by the micromechanics methods developed by Eshelby, Mori–Tanaka, and Vanin.

Effect of fiber surface texture on the mechanical properties of glass fiber reinforced epoxy composite

The effect of fiber sizing and surface texture on the strength and energy absorbing capacity of fiber reinforced composites has been evaluated at two length scales using the macromechanical quasi-static punch shear test and the micromechanical microdroplet test methods. E-Glass/SC-79 epoxy composite laminates with four different fiber sizing formulations with various degrees of chemical bonding and surface texture have been investigated. The failure modes during perforation and different energy dissipating damage mechanisms were identified and quantified. The punch shear strength and the total energy absorption per unit volume of composite with hybrid sizing have increased by 48% and 100% over the incompatible sizing. These results showed linear correlations with the interphase properties reported earlier by the authors (Gao et al., 2011) and provided a methodology for developing new sizing by tailoring chemical bonding and the fiber surface texture at the fiber–matrix interphase for improving both strength and energy absorption of composites.

Initial and final failure strength analysis of composites based on a micromechanical method

In this paper, a micromechanical model for investigating initial and final failure surface of fiber-reinforced composites laminate is established. The Generalized Method of Cells, which effectively predicts the thermal stresses influence on stress–strain behaviors of fiber-reinforced composites, is combined with Von-Mises yield criterion to describe nonlinear stress–strain behaviors of composites laminate. The Tsai–Hill criterion is incorporated into the model for predicting failure strength of lamina and typical laminate in uniaxial tension and biaxial loading, respectively. The numerical simulations based on a micromechanical method are performed to study the effects of thermal residual stresses on initial and final failure strength. Results revealed that thermal residual stresses influence on failure strength of the UD lamina is closely dependent on fiber off-axis angles. The contribution of thermal residual stresses in the final failure surface of [0°/±30°/90°]2 laminate and [90°/±45°/0°]2 laminate can be ignored. The results in longitudinal for lamina and biaxial tensile loadings for [90°/±45°/0°]2 laminate show good agreement with the experimental data.

Small-scale characterisation of irradiated nuclear materials: Part II nanoindentation and micro-cantilever testing of ion irradiated nuclear materials

This paper demonstrates the ability of advanced micro-mechanical testing methods, based on FIB machined micro-cantilevers, to measure the mechanical properties of ion implanted layers without the influence of underlying unimplanted material. The first section describes a study of iron–12wt% chromium alloy implanted with iron ions. It is shown that by careful cantilever design and finite element modelling that changes in yield stress after implantation can be measured even with the influence of a strong size effect. The second section describes a study of tungsten implanted with both tungsten ions and tungsten and helium ions using spherical and sharp nanoindentation, and micro-cantilevers. The spherical indentation allows yield properties and work hardening behaviour of the implanted layers to be measured. However the brittle nature of the implanted tungsten is only revealed when using micro-cantilevers. This demonstrates that when applying micro-mechanical methods to ion implanted layers care is needed to understand the nature of size effects, careful modelling of experimental procedure is required and multiple experimental techniques are needed to allow the maximum amount of mechanical behaviour information to be collected.

On the study of elastic properties of CNT-reinforced composites based on element-free MLS method with nanoscale cylindrical representative volume element

This paper presents a micromechanical element-free method to study elastic properties of carbon nanotubes (CNTs) reinforced composites. A three-dimensional nanoscale cylindrical representative volume element (RVE) has been considered in the analysis, in which CNT and matrix are both modeled as elastic materials based on continuum mechanics. The proposed model is used to investigate the behaviors of CNT-reinforced composites with respect to their effective mechanical properties. The relevant formulas to extract the effective material constants for three loading cases are derived in detail, based on the elasticity theory. Besides, the meshless method based on the moving least-squares (MLS) approximation and element-free Galerkin (EFG) method is implemented to evaluate the established model. The computed results are compared with the available solutions obtained from other analytical and numerical methods. Moreover, these results show that the presence of CNTs can significantly improve the longitudinal and transverse characteristics of the composite materials.

Tight-binding parameters of graphite determined with angle-resolved photoemission spectra

An exfoliated Kish graphite sample on a heavily n-doped Si substrate covered with native oxide was prepared with a conventional micromechanical cleavage method. From angle-resolved photoemission spectra (ARPES), we measured the band structure of graphite over photon energies from 28eV to 116eV. The inner potential V0=17.25eV is determined with a period from the band dispersion in the KH direction. A set of parameters in the tight-binding method and the SWMcC model for graphite is extracted from the fitted results. A comparison of constant-energy mapping results at large binding energy indicates the reliability of the tight-binding parameters extracted from the ARPES results.

Prediction of the overall Young’s moduli of clay-based polymer nanocomposites

In our previous work, molecular dynamics simulation was used to calculate Young’s modulus of both fully and partially exfoliated effective clay (montmorillonite, MMT) clusters. In this work, we expand that work to predict the overall Young’s moduli of nylon 6/MMT nanocomposites. First, a micromechanics method (i.e. the rule-of-mixtures) is shown to be effective in calculating the overall Young’s moduli of clay-based polymer nanocomposites. Then, the overall Young’s moduli of clay-based polymer nanocomposites with either well-aligned or randomly dispersed effective clay clusters of various clay volume fractions are calculated based on the individual Young’s moduli of effective clay clusters and polymer matrix by the rule-of-mixtures method. By comparing the simulated results with measured data in the literature, it is shown that the present approach provides an effective way to predict the overall Young’s moduli of nylon 6/MMT nanocomposites.

Uniaxial Compression Creep Prediction of Asphalt Mixture Using the Eshelby Equivalent Inclusion Method

Asphalt mixture was simply treated as a two-phase composite, in which coarse aggregates are embedded into asphalt mastic matrix. According to the elastic-viscoelastic correspondence principle, an elastic micromechanical method is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded into viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different stress conditions in order to determine the matrix constitutive parameters, the presented framework is validated by comparison with the experiment, and then some predictions to uniaxial compression creep behavior of asphalt mixture in different stress conditions are given.

A strain-rate dependent micromechanical constitutive model for glass/epoxy composites

The mechanical behavior of polymeric fibrous composites under dynamic loading is not completely investigated. Therefore, in the preset research, a strain-rate dependent micromechanical constitutive model is developed to predict the dynamic mechanical behavior and elastic properties of fibrous composites under arbitrary loading rates. First, strain rate dependent mechanical behavior of matrix and fibers are experimentally characterized and for each constituent a dynamic empirical material equation is presented. Then, the bridging matrix micromechanical model in combination with a constitutive equation for polymers is utilized to predict the elastic properties and mechanical behavior of fiber-reinforced polymeric composites under arbitrary applied strain rates. Moreover, the strain rate sharing of each constituent of composites (matrix and fiber) is calculated. In order to validate the present method, results predicted by the model are compared with the experimental data. It is shown that the present micromechanical method is able to simulate the rate dependent elastic behavior of fiber-reinforced composites with a good accuracy.

A combined micromechanical–numerical model to simulate shear behavior of carbon nanofiber/epoxy nanocomposites

In the present research a method was developed that by having the stress–strain behavior of the neat epoxy, the stress strain behavior of carbon nano fibers/epoxy nanocomposites under tensile and torsional loadings were simulated. First, a micromechanical method was used to simulate the tensile stress–strain curve of nano phased polymer composites. Then, using the tensile stress–strain curve of the nano phased polymer and using a finite element method, the shear properties of nanocomposites are predicted. Three weight fractions 0.15, 0.25 and 0.40wt.% of carbon nano fibers (CNFs) were considered and an experimental program was conducted to validate the present approach. The experimental results indicated that employing carbon nano fibers improves tensile and shear mechanical properties of the neat epoxy. The maximum improvements in tensile and shear mechanical properties of the neat epoxy are achieved by adding 0.40% and 0.25wt.% of the CNF, respectively. Moreover, a comparison between predicted and experimental results shows a good agreement.

Three-dimensional nonlinear strength criterion for rock-like materials based on the micromechanical method

In this paper, it is assumed the rock-like materials contain penny-shaped microcracks. The modes II and III stress intensity factors at tips of the three-dimensional penny-shaped microcracks are determined. The micro-failure orientation angle α is given out to describe the failure of rock-like materials. The formulation between the micro-failure orientation angle α and stress components is obtained from the mixed-mode fracture criterion. Failure characteristic parameters under true triaxial compression condition are defined, which are an invariant and are relative to the intermediate and minimum principal stresses. A three-dimensional nonlinear strength criterion of rock-like materials, in which the effects of the intermediate principal stress on the failure of rock-like materials is taken into account, is developed based on micromechanical methods. The theoretical nonlinear strength criterion is novel, which is not found in the previous references. By comparison with experimental data, it is shown that the present theoretical strength criterion is in good agreement with the experimental results.

Numerical Simulation for Mechanical Behavior of Carbon Black Filled Rubber Composites Based on Cubic Representative Volume Element

Based on the connection between macroscopic and microscopic characteristics of carbon black filled rubber composites, Representative Volume Element (RVE) containing one single particle has been proposed, and three dimensional cubic RVE has been established to study and analyze the macroscopic mechanical properties of the carbon black filled rubber composites by the micromechanical finite element method. The research shows that the stiffness of the composite is increased with the increase of the volume fraction of carbon black filler particles. By comparison, it is shown that the results of the predictions on the stress-strain behavior of the rubber composite made with the cubic RVE numerical models containing one spherical particle are in good agreement with the experimental results for seven and fifteen percent carbon black filler content, but there is some discrepancy between them for twenty-five percent carbon black filler content. The results of the predictions on the stress-strain behavior of the rubber composite made with the cubic RVE numerical models containing one cubical particle are higher than the experimental results, and the higher the carbon black filler content, the greater is the discrepancy between them.

Effect of interface on the thermal conductivity of thermal barrier coatings: A numerical simulation study

Interface is an important structure in the materials, some rather peculiar physical phenomena can occur at the interface under the application of the exterior physical field. Especially, the grain boundary, phase interface and layer interface are significant factors for improving the thermal insulation behavior of thermal barrier coatings (TBCs). In this paper, finite element method was employed to simulate the heat transfer behavior of TBCs with different interfacial characteristic based on several different interfacial thermal resistance (ITR) models. The simulation results indicate that the heat flux around the interface has exhibited fantastic changing characteristic, the thermal insulation effect of TBCs would be enhanced with the area of the interface increasing. The interface roughness (amplitude) also has a very important effect on the effective thermal conductivity of the as-sprayed TBCs. A novel method, Computational Micromechanics Method (CMM), was utilized to depict the heat transfer behavior of actual coatings with irregular inner interface. The “thermal rectification” mechanism of heat diffusion around the interface make that the heat flux which passes through the interface has exhibited different flow characteristic compared with the positions without interface. In addition, some simple experiments have further verified the existence of the ITR between the bond-coat and top-coat. The investigation results will also provide us a powerful guide to design coating with high thermal insulation property using the physical theory and mechanism of the ITR.

Thickness dependence of the charge-density-wave transition temperature in VSe2

A set of three-dimensional charge-density-wave (3D CDW) VSe2 nano-flakes with different thicknesses were obtained by the scotch tape-based micro-mechanical exfoliation method. Resistivity measurements showed that the 3D CDW transition temperature Tp decreases systematically from 105 K in bulk to 81.8 K in the 11.6 nm thick flake. The Hall resistivity ρxy of all the flakes showed a linear dependent behavior against the magnetic field with a residual electron concentration of the order of ∼1021 cm−3 at 5 K. The electron concentration n increases slightly as the thickness d decreases, possibly due to the CDW gap is reduced with the decrease of the thickness.

Investigation on microstructures of cementitious composites incorporating slag

Cementitious composites incorporating slag were investigated by multiple techniques, including scanning electron microscopy with backscattered electron and energy-dispersive X-ray spectroscopy detectors, thermogravimetric analysis, instrumented nanoindentation and ultrasonic measurements. The physical and mechanical properties of individual phases in cementitious composites with and without slag at different water to binder ratios were studied and are reported here. Subsequently, based on the identified phase properties, the macroscopic elastic moduli were calculated through a micromechanical method and verified with the experimental data. The results of this study show that the physical and mechanical properties of hydration products in cementitious composites incorporating slag are quite different from those of pure cement pastes. To explain the differences and improve scientific understanding of the influence of slag on the properties of hydration products, the composition, microstructures and mechanical properties were linked together for cementitious composites incorporating slag through this study.

Characterization and simulation of impact behavior of graphene/polypropylene nanocomposites using a novel strain rate–dependent micromechanics model

The current paper examines a newly developed model to simulate the strain rate–dependent constitutive equation of graphene/polypropylene nanocomposites. The model is a combination of the Halpin-Tsai micromechanics method and the Goldberg model which is called the strain rate–dependent micromechanics model. First, tensile properties of pure polypropylene are measured experimentally. Then by utilizing the Halpin-Tsai micromechanics method, tensile properties of graphene/polypropylene nanocomposites under static loading conditions are achieved. The obtained properties from the micromechanics method are used by the Goldberg model in order to simulate the strain rate–dependent mechanical behavior of nanocomposites under dynamic loading conditions. The material constants of the Johnson-Cook material model are calculated by the strain rate–dependent micromechanics model. The material constants are used in a material model which is implemented in the explicit finite element code LS-DYNA, to simulate the strain rate strain rate–dependent micromechanics-dependent mechanical behavior of the standard Charpy impact test specimen. Polypropylene reinforced with 0.5, 1.0 and 2.0 wt% graphene sheets were prepared via coating polypropylene with graphene particles. Then, by melt blending in a twin-screw extruder followed by an injection molding process, the nanocomposites samples are manufactured. The results revealed that the incorporation of a low amount of graphene caused a good improvement in impact strength of polypropylene. To evaluate the current model, the results are compared with the experimental results of the standard Charpy test specimens. A good agreement between the experimental data and the strain rate–dependent micromechanics model is achieved.

A novel combined molecular dynamics–micromechanics method for modeling of stiffness of graphene/epoxy nanocomposites with randomly distributed graphene

In this paper, by combining molecular dynamics and micromechanics methods, a new approach for prediction of the stiffness of the nanocomposites with randomly distributed nanoparticles in the macro level is presented. The molecular dynamics method is used to model the stiffness of the graphene/epoxy nanocomposites containing one layer of an aligned nano graphene embedded in epoxy resin. By considering the large sizes of the length and width of the nano graphene in comparison with its thickness and the shortcomings of the available hardware and software for simulation purposes, a new approach for modeling is also developed. This new approach, by using the moduli of different graphene sheets with different sizes embedded in a representative volume element, can predict the moduli of a real size graphene embedded in the matrix along the longitudinal, transverse and normal directions in the nano-scale. In order to consider the effect of the random distribution of graphene sheets in epoxy resin, a micromechanical approach is used. The results obtained by the molecular dynamics method are used by the micromechanics approach and the stiffness of graphene/epoxy nanocomposites with randomly distributed graphene in the macro-scale is predicted. An experimental program is conducted to evaluate the capability of the model. The result of the modeling is in a very good agreement with the experimental data.

Determination of electrical conductivity of double-porosity formations by using generalized differential effective medium approximation

Abstract In this paper, we propose an approach for simulating the effective electrical conductivity of porous rocks. This approach is based on the Generalized Differential Effective Medium (GDEM) method that allows us to calculate the effective conductivity of a rock up to the percolation threshold. We consider a porous medium composed of a porous matrix with small scale pores (primary pores) and large-scale pores placed in the matrix (secondary pores). For double porosity formations we applied two-step homogenization scheme starting from the smallest scale of inclusions. At the first step, we apply a model composed by a conductive host and two types of inclusions placed in it: nonconductive grains and pores with a conductive fluid. The electrical conductivities of the host and saturating fluid are equal. At the second homogenization step we consider the conductive host with effective electrical conductivity determined at the first step and large-scale inclusions with conductivity corresponded to the pore saturating fluid. To take into account the percolation for the secondary pore system we introduce two types of inclusions. For porosities less than the critical porosity (secondary pores are disconnected), we consider spheroids that describe secondary pores of different shapes (vugs and cracks). For porosities more than the critical value, we additionally introduce infinite ellipsoidal cylinders that ensure the pore connectivity. Application of the proposed model allows us to take into account the void percolation for a porous matrix and the percolation threshold for a secondary pore system that we consider as an advantage of the proposed method with comparison of Archie law or classical micromechanical methods.

Stiffness prediction of graphene nanoplatelet/epoxy nanocomposites by a combined molecular dynamics–micromechanics method

In this research, by a combined molecular dynamics–micromechanics method the stiffness of graphene nanoplatelet/epoxy nanocomposites is predicted. It is assumed that graphene sheets are randomly oriented in the polymer matrix. First, the stiffness of a multilayered graphene nanoplatelet was achieved using the molecular dynamics (MD). Then, results obtained by the molecular dynamics were used by the Mori–Tanaka (MT) and the Halpin-Tsai (HT) micromechanics models to predict nanocomposite stiffness. These combined models are called the MD–MT and MD–HT models, respectively. The results obtained show that the MD–MT model is more compatible with the result of experiments at low filler contents (<0.25wt.%) in comparison with the MD–HT model. While, the MD–HT model is more reliable at high filler contents (>0.25wt.%). Mechanical properties of graphene nanoplatelet/epoxy nanocomposites with several contents of graphene nanoplatelet, i.e. 0.05, 0.1, 0.25, 0.5 and 1wt.% were considered and the optimum graphene content was obtained.

Solution of general integral equations of micromechanics of heterogeneous materials

One considers a linear composite materials (CM), which consists of a homogeneous matrix containing a random set of heterogeneities. An operator form of solution of the general integral equation (GIE) for the general cases of local and nonlocal problems, static and wave motion phenomena for composite materials with random (statistically homogeneous and inhomogeneous, so-called graded) structures containing coated or uncoated inclusions of any shape and orientation with perfect and imperfect interfaces and subjected to any number of coupled or uncoupled, homogeneous or inhomogeneous external fields of different physical nature. The GIE, connecting the driving fields and fluxes in a point being considered and the fields in the surrounding points, are obtained for the random fields of heterogeneities in the infinite media. Estimations of the effective properties and both the first and second statistical moments of fields in the constituents of CMs are presented in a general form of perturbations introduced by the heterogeneities and taking into account a possible imperfection of interface conditions. The solution methods of GIEs are obtained without any auxiliary assumptions such as the effective field hypothesis (EFH), which is implicitly exploited in the known methods of micromechanics. Some particular cases, asymptotic representations, and simplifications of proposed methods are presented for the particular constitutive equations such as linear thermoelastic cases with the perfect and imperfect interfaces, conductivity problem, problems for piezoelectric and other coupled phenomena, composites with nonlocal elastic properties of constituents, and the wave propagation in composites with electromagnetic, optic and mechanical responses.