Tanaka Model Research Articles

A review on solid state fabrication methods and property characterization of functionally graded materials

FGMs are a specific class of composites in which materials are graded as per applications. The original idea of the compositional and structural gradient in material microstructure was first proposed for polymeric and composite materials in 1972. This paper focuses on the solid-state processing techniques of the functionally graded materials, gradation, and their application in various fields. Type of gradation, application, the combination of material, and their associated fabrication parameters are presented in tabular form which has been used by different authors which will help readers to identify the best combination of material, based on their requirements. Further, Voigt and MORI- Tanaka models used for theoretical analysis for measurement of effective properties of FGMs are also presented. Usually, the majority of the literature work has a place with the gradation of metal-ceramic material cocktail created utilizing PM procedure is accessible and their outcome uncovers improved mechanical properties contrasted with materials in pure form.

Nanotechnology efficacy on improvement of acute velocity in fluid-conveyed pipes under thermal load

Herein, nanotechnology efficacy on the acute velocity of fluid of fluid-conveyed-nanocomposite pipes is studied. The polymeric pipe is armed by carbon nanotubes utilising Mori and Tanaka model. The dynamic force induced by fluid is calculated utilising perturbation method. Based on method of energy and Lagrange model as well as Mindlin theory, the final equations are obtained. Utilising semi-exact solution, the relations are solved in order to calculate the acute velocity of fluid so that the efficacy of pipes geometrical constants and CNT percentage are investigated on the acute velocity of fluid. The outcomes are compared with other papers for showing the accuracy of this solution. With adding the CNT percentage, the acute velocity of fluid is improved. Indeed, the heat generation has a harmful efficacy on the acute velocity of fluid since it can reduce the acute value due to reduction in the stiffness of pipe.

Türkiye'de 17 Mart ile 12 Temmuz 2020 Arasında COVID-19 Vakaları Kullanılarak Büyüme Modellerinin Belirlenmesi Üzerine Bir Çalışma: Kesitsel Çalışma

Objective: We use the most frequently used growth functions in the literature for estimating Turkey's cumulative number of confirmed coronavirus disease-2019 (COVID-19) cases. We analyze Brody, Bertalanffy, Logistic, Generalized Logistic, Gompertz, Richards, Negative Exponential, Stevens, and Tanaka models for determining the appropriate model. Material and Methods: The number of cases of COVID-19 in Turkey between March 17, 2020 and July 12, 2020 were included in the study. The data used in the study were obtained from Johns Hopkins University. We used the most frequently used Non-linear growth models in the literature for estimating Turkey's cumulative number of confirmed COVID-19 cases. Matlab software was used to estimate the parameters in the models studied. non-linear least squares regression function is used in Matlab software. Results: According to the estimation results, the best fitting model is the Richards model in terms of both the mean squared error and R2 (coefficient of determination). Conclusion: We recommend to use the Richards model in modeling the cumulative COVID-19 cases. For estimating the future cases, it will be appropriate to use the Richards model. In addition, estimates of the number of daily cases obtained from the Richards model are not compatible with the actual number of daily cases. This may occur because estimations on these growth models can sometimes lead to erroneous results.

Effective elastic modulus of foamed long glass fiber reinforced polypropylene: Experiment and computation

The cross-section of an injection-molded plate of foamed long glass fiber reinforced polypropylene was analyzed using scanning electron microscopy. The distribution of the glass fiber orientations and the microcellular structure in the thickness direction were also studied. A multilayer representative volume element was constructed based on the fiber orientation tensors and the cell distribution. Nested and two-step homogenization methods based on the Mori–Tanaka and Voigt models were used to homogenize each layer of the representative volume element. Finally, classic laminate theory was used to obtain the effective elastic modulus of the material. The computed elastic moduli of the single-layer and multilayer representative volume element models with different loading directions predicted by the homogenization and finite element methods were compared with the experimental results. We found that the constructed multilayer representative volume element model can predict the elastic moduli of the foamed glass fiber reinforced polypropylene effectively and that the predicted results were accurate and stable.

Simple Homogenization-Based Approach to Predict Raveling in Porous Asphalt

In the Netherlands, more than 80% of the highways are surfaced by porous asphalt (PA) mixes. The benefits of using PA mixes include, among others, the reduction of noise and the improvement of skid resistance. However, pavements with PA mixes are known to have a shorter lifetime and higher maintenance costs as compared with traditional dense asphalt mixes. Raveling is one of the most prominent distresses that occur on PA mix pavements. To analyze the raveling distress of a PA mix pavement, the stress and strain fields at the component level are required. Computational models based on finite element methods (FEM), discrete element methods (DEM), or both, can be used to compute local stress and strain fields. However, they require the development of large FEM meshes and large-scale computational facilities. As an alternative, the homogenization technique provides a way to calculate the stress and strain fields at the component level without the need for much computation power. This study aims to propose a new approach to analyze the raveling distress of a PA mix pavement by using the homogenization technique. To demonstrate the application of the proposed approach, a real field-like example was presented. In the real field-like example, the Mori–Tanaka model was used as a homogenization technique. The commonly available pavement analysis tool 3D-MOVE was used to compute the response of the analyzed pavement. In general, it was concluded that the homogenization technique could be a reliable and effective way to analyze the raveling distress of a PA mix pavement.

Mechanical Properties of Cu-B/Diamond Composites Prepared by Gas Pressure Infiltration

Diamond particles reinforced boron-alloyed Cu matrix (Cu-xB/diamond, x = 0.1, 0.2, 0.3, 0.4, 0.5, and 1.0 wt.%) composites were prepared by gas pressure infiltration. The size of the diamond particles was ~ 230 μm and the diamond volume fraction in the composites was ~ 66%. The interfacial carbide evolution plays an important role in improving the interfacial bonding and enhancing the mechanical properties of the Cu-B/diamond composites. The tensile, compressive and bending strengths firstly increase and then decrease with increasing boron content, giving a maximum tensile strength of 204 MPa, a maximum compressive strength of 608 MPa, and a maximum bending strength of 513 MPa at 0.5 wt.% B addition. The monotonic uniaxial tensile stress–strain curves of the Cu-B/diamond composites were predicted by using the Mori–Tanaka, generalized self-consistent, and Torquato identical hard spheres approximation models. The results suggest that alloying B to Cu matrix is an effective route to strengthening Cu/diamond composites.

Mathematical modeling of pipes reinforced by agglomerated CNTs conveying turbulent nanofluid and application of semi-analytical method for studying the instable Nusselt number and fluid velocity

This paper deals with the instable Nusselt number and fluid velocity in nanocomposite pipes conveying nanofluid subjected to transient heat transfer. The CNTs due to its magnetic and elastic properties are selected for reinforcement of the pipes considering agglomeration of CNTs based on Mori–Tanaka model. The interactions of nanofluid on the pipe are divided to three sections of work of nanofluid viscosity by momentum equations of fluid, work of turbulent pressure by linear potential flow theory, kinetic, gyroscopic and potential energies of the nanofluid based on energy method. The convection of inner and outer fluids, conduction of pipe and heat generation induced by magnetic field are considered based on energy balance. The first order shear deformation theory (FSDT) and Lagrange method are applied for obtaining the coupled motion equations of the pipe-nanofluid. Applying semi-analytical and iterative methods, the instable fluid velocity, Reynolds and Nusselt numbers are determined. The influences of different parameters such as CNTs volume percent and agglomeration, volume percent, diameter and types of nanoparticles in the fluid as well as shell surface roughness are shown on the instable parameters. Numerical results indicate that SiO2-water nanofluid is the best choice among the assumed nanoparticles since the pipe will be instable at higher fluid velocity and Nusselt number.

Static stability analysis of agglomerated multi-scale hybrid nanocomposites via a refined theory

Present paper is proposed to capture the influences of carbon nanotubes’ agglomeration on the stability behaviors of multi-scale hybrid nanocomposite beams within the frameworks of refined higher order beam theories for the first time. In this research, a mixture of macroscale and nanoscale fillers will be utilized to be dispersed in an initial matrix to possess a multi-scale hybrid nanocomposite. The equivalent material properties are seemed to be calculated coupling the Eshelby–Mori–Tanaka model with the rule of the mixture to consider the effects of carbon nanotubes inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy-based approach is implemented to obtain the governing equations of the problem utilizing a refined higher order beam theorem. Next, the derived equations will be solved in the framework of Galerkin’s well-known analytical method to reach the critical buckling load. It is worth mentioning that influence of various boundary conditions is included, too. Once the validity of presented results is proven, a set of numerical examples are presented to explain how each variant can affect the structure’s stability endurance.

Three-phase modelling and characterization of elastic behavior of MWCNT reinforced GFRP composites: A combined numerical and experimental study

This paper presents modelling and characterization of the elastic behavior of multi-wall carbon nanotube (MWCNT) reinforced with glass fiber reinforced polymer (GFRP) composites. Firstly, atomistic based finite element modelling of MWCNT is developed using computational software ANSYS® by applying various loading and boundary conditions. The present developed atomistic based FE model of MWCNTs are validated with the available literature in terms of elastic properties. Secondly, a two-phase micromechanics model based on the Mori-Tanaka is used to evaluate the elastic properties of the MWCNT reinforced polymer nanocomposite by replacing MWCNTs with equivalent fibers as micro inclusions. Finally, Chamis model is used to evaluate the elastic properties of the three-phase MWCNT reinforced with GFRP composite. The equivalent elastic properties of the three-phase composite are compared and validated with the experimental results. Further, the detailed parametric study is performed to investigate the influence of tube chirality, weight percentage and agglomeration of MWCNT in terms of the elastic properties. It was concluded that the atomistic based FE modelling of MWCNT combined with Mori–Tanaka and Chamis model is efficient to evaluate the elastic properties of three-phase composites with the confidence on the extracted results compared with experimental results. Further, the presented combined model provides an efficient methodology and comprehensive understanding to analyze elastic behavior of MWCNTs and three-phase fiber/MWCNT/polymer composite. So, the presented combined numerical and experimental study could serve as guidelines in modelling and characterization of elastic behaviour of MWCNT reinforced with GFRP composites.

Proposed SMA Tension Sling Damper for Passive Seismic Control of Building

Passive Shape Memory Alloy (SMA) based Tension Sling Damper (TSD) is proposed to control seismic response of building represented as dynamic SDOF system. Non-linear hysteretic behavior of SMA is characterized by Tanaka model with seismic excitations as input. It is converted to equivalent piece-wise linear elastic viscous damping model described by stiffness constant ‘keff’ and damping constant ‘ceff’ to implement it with linear dynamic system. Damping constant ‘ceff’ is evaluated for TSD for given seismic excitation at each instance of time defined as instantaneous damping, unlike constant damping used in other studies, to derive accurate seismic response of the dynamic system. Seismic response control parameters – peak and rms perfor-mance indices (PI) for displacement and acceleration, peak damper force, maximum damping ratio are evalu-ated for flexible, moderately stiff and stiff dynamic systems fitted with TSD under pulse and strong ground motion type seismic excitations with varied PGA. Substantial reduction in PI is observed for controlled systems through varying design parameters of TSD – cross-sectional area and length of SMA sling. TSD yields better seismic response control for moderately stiff and flexible system due to super-elastic properties of SMA. Fur-ther, it works efficiently for seismic excitations with low to moderate PGA.

Mixed mode fatigue crack growth studies in AISI 316 stainless steel

Damage tolerance assessment requires the accurate prediction of fatigue crack growth lives. Numerical simulation techniques using mixed mode Paris' law and various equivalent stress intensity factor models (ΔKeq) are widely employed for fatigue life prediction. In the present work, mixed mode (I/II) fatigue crack growth experiments are performed using the compact tension shear specimens made of AISI 316 austenitic stainless steel for various loading angles. Finite element fatigue crack growth simulations are carried out, and the effect of ΔKeq model in fatigue life prediction is studied. To achieve this, a three parameter double exponential type best fit is proposed for fitting the experimental mixed mode crack length vs fatigue life. The performance and capability of various selected models are assessed by comparing the predicted life with the experimental results. Fractographic studies at different stages of crack propagation for different loading angles are also presented to aid the above assessments. Based on the overall consistent performance, Irwin's and Tanaka models are predicting life close to the experimental data and Richard's and Yan's models provide conservative solutions.

Thermodynamic insight into the thermoresponsive behavior of chitosan in aqueous solutions: A differential scanning calorimetry study

Thermoresponsivity of chitosan induced by β-glycerophosphate (GP) in diluted aqueous solutions has been first studied by high-sensitivity differential scanning calorimetry. It has been found that the GP solutions of chitosan undergo a first-order phase transition upon heating. The onset of this transition coincides with the cloud point of the system. This allows one to identify the thermoresponsivity of chitosan as a macroscopic demonstration of the phase separation transition. The transition temperature, enthalpy, heat capacity increment, and width were determined as functions of GP and chitosan concentrations, and the dielectric constant of the solvent. Based on this data, we suggested that GP binds cooperatively to the chitosan matrix at low temperatures. The standard free energy of GP binding (Δbgint= −6 ± 1 kJ mol−1) was estimated from the DSC data. It was shown that the Okada–Tanaka model of cooperative hydration of polymers adequately describes the thermogram of the GP induced phase transition of chitosan.

Micromechanics-based approach for the effective estimation of the elastic properties of fiber-reinforced polymer matrix composite

In this paper, we proposed a revised Mori–Tanaka model for the effective estimation of the elastic properties at lower fiber volume fraction. A review of some notable micromechanics-based models with the theories proposed by Voigt and Reuss, Hashin–Shtrikman model, Mori–Tanaka method and dilute dispersion scheme is carried out, and a critique is presented focusing on the limitations of these models. Finite Element (FE) simulations are performed using Representative Volume Element (RVE) technique to rationalize the analytical results. Our results revealed that revised Mori–Tanaka estimates and FE predictions are in agreement. Elastic properties of the test material are dependent on size of RVE suggesting the effective elastic modulus evaluated using RVE forms the lower bounds of true effective values. However, we still believe that there is room for the debate for evaluating the elastic properties of these composites at larger volume fractions with the inclusion of Eshelby’s tensor in Mori–Tanaka scheme. Thus the efficacy of micromechanics-based models for the effective estimation of elastic properties of polymer matrix composites is highlighted. Our findings may provide new significant insights of the effective estimation of elastic properties of PMC using micromechanics-based approach.

A Numerical Model to Predict the Anisotropy of Polymer Composites Reinforced with High-Aspect-Ratio Short Aramid Fibers

Some fiber types have a high aspect ratio and it is very difficult to predict their composites using traditional finite element (FE) modeling. In this study, an FE model was developed to predict the anisotropy of composites reinforced by short aramid fibers. Three fiber distribution types were studied as follows: perfectly aligned, normally distributed, and randomly distributed fibers. The elastic constants were obtained, and, for different alignment angles and parameters in the fiber orientation distribution function, their numerical results were compared to those of the Mori–Tanaka model. Good agreement was obtained; thus, the employed FE model is an excellent and simple method to predict the isotropy and anisotropy of a composite with high-aspect-ratio fibers. Therefore, the FE model was employed to predict the orientation distribution of a composite fiber with a nonlinear matrix. The predicted and experimental results agree well.

Validation of micromechanics models including imperfect interfaces for short fiber thermoplastic composites

Micromechanics models proposed by Nairn et al. and Hashin, which can treat imperfect bonded interfaces between fibers and polymer matrix, are evaluated for use in predicting the equivalent stiffness of a short fiber reinforced thermoplastic composite. Treatment of the imperfect interfaces is fundamentally important to address differences of interface connections that affect the mechanical properties of the composite. We first compare the Nairn–Hashin (NH) models with the Mori–Tanaka (MT) model under the condition of a perfect interface. Elastic moduli calculated from the NH models almost agree with that from the MT model. The NH models are then evaluated using elastic moduli measured for randomly fiber-oriented films of short glass fiber reinforced polypropylene. By considering the imperfect interface parameters estimated from pull-out tests of a single glass fiber embedded in a polypropylene matrix, the NH models predict the measured elastic moduli.

Effective behavior of composites with combined kinematic and isotropic hardening based on additive tangent Mori–Tanaka scheme

The goal of the present work is to propose a multi-scale approach for composite materials which accounts for kinematic hardening in the phases. For that purpose, the additive/sequential interaction rule and tangent linearization of viscoplastic response proposed for elastic–viscoplastic material can be extended in a straightforward manner. A two phase composite where each phase is elastic–viscoplastic is considered. The viscoplastic flow is governed by a J2 flow theory with an overstress. To find the overall behavior of the composite, a Mori–Tanaka model is applied. Numerical validation of the proposition is carried out by considering a representative volume element with 30 inclusions. Various configurations have been tested: hard or soft inclusion cases with or without isotropic hardening. It is shown that the quality of the model predictions is not affected by the introduction of the kinematic hardening component in the local constitutive behavior. Namely, in most cases considered in the paper the overall stress–strain response as well as the average stress–strain response per phase is accurately estimated. It has been also verified that the obtained backstress components are consistent with the ones predicted by Finite element calculations with ABAQUS Software.

Sensitivity and Uncertainty Analysis of One-Dimensional Tanaka and Liang-Rogers Shape Memory Alloy Constitutive Models.

A shape memory alloy (SMA) can remember its original shape and recover from strain due to loading once it is exposed to heat (shape memory effect). SMAs also exhibit elastic response to applied stress above the characteristic temperature at which transformation to austenite is completed (pseudoelasticity or superelasticity). Shape memory effect and pseudoelasticity of SMAs have been addressed by several microscopic thermodynamic and macroscopic phenomenological models using different modeling approaches. The Tanaka and Liang-Rogers models are two of the most widely used macroscopic phenomenological constitutive models for describing SMA behavior. In this paper, we performed sensitivity and uncertainty analysis using Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods for the Tanaka and Liang-Rogers models at different operating temperatures and loading conditions. The stress-dependent and average sensitivity indices have been analyzed and are presented for determining the most influential parameters for these models. The results show that variability is primarily caused by a change in operating temperature and loading conditions. Both models appear to be influenced by the uncertainty in elastic modulus of the material significantly. The analyses presented in this paper aim to provide a better insight for designing applications using SMAs by increasing the understanding of these models’ sensitivity to the input parameters and the cause of output variability due to uncertainty in the same input parameters.

Wave dispersion characteristics of agglomerated multi-scale hybrid nanocomposite beams

Herein, the agglomeration effect of nanoparticles on the wave dispersion of multi-scale hybrid nanocomposite beams is investigated. The constituent material consists of both macro- and nano-reinforcements which are dispersed in the polymer matrix. Homogenization is conducted according to the well-known micromechanical methods. Herein, the combination of the Eshelby–Mori–Tanaka model and the rule of the mixture is implemented in order to estimate the equivalent material properties of the nanocomposite beam. Also, a refined higher-order beam theory is used in order to calculate the kinetic relations free from utilizing an additional factor to account for the shear deformation. Furthermore, the governing equations are achieved by applying Hamilton’s principle. Then, the governing equations are solved analytically to enrich the wave frequency. The effects of various parameters on the variation in wave frequency and phase velocity of the multi-scale hybrid nanocomposite beam are studied. The results of this study reveal that the mechanical responses of the system decrease whenever the nanotubes are inside the clusters.

Prediction of dynamic modulus of asphalt mixture using micromechanical method with radial distribution functions

Inter-particle interaction is one of the major reinforcement mechanisms for aggregates in asphalt mixture, which is a classic example of high-volume fraction particulate composites. This paper introduced the modified Ju-Chen (J-C) micromechanical method based on two types of radial distribution assumptions for inclusions in the matrix, namely the uniform distribution and Percus–Yevick (P–Y) distribution. A two-step approach was proposed and the elastic–viscoelastic correspondence principle was used to predict the effective dynamic modulus of asphalt mixture at different frequencies. The prediction results show that the uniform distribution and P–Y distribution based J-C method could generate the upper and lower bounds of dynamic modulus for asphalt mixture, respectively. As compared to the measured dynamic modulus at different temperatures and loading frequencies, the modified J-C method showed better prediction accuracy as compared to two traditional micromechanical models based on single inclusion configuration, Mori–Tanaka (M–T) and differential scheme effective medium models. The J-C method assuming P–Y distribution provided better accuracy at the low frequencies; while the J-C method assuming the uniform distribution only had good accuracy at the high frequencies. The study findings indicate that dynamic modulus of asphalt mixture can be predicted based on laboratory tests conducted at the fine aggregate mix level and the void ratio and the gradation of coarse aggregate using appropriate micromechanics methods.

Resonant vibrations of FG viscoelastic imperfect Timoshenko beams

An investigation is performed on the viscoelastic nonlinear vibrations of functionally graded imperfect Timoshenko beams. The internal viscosity is incorporated using the Kelvin–Voigt scheme. Beam's centerline stretching is the cause of geometric nonlinearities. Material property distributions follow the Mori–Tanaka model. Shear deformation and rotary inertia are incorporated using the Timoshenko theory. A slight curvature is included to account for a geometric imperfection. The coupled axial/transverse/rotational motion model is developed using Hamilton's energy/work/energy loss. Galerkin's method is used, without neglecting the longitudinal inertia/displacement, and a large dimensional discretized/truncated model is obtained. Numerical integrations, using a continuation-based technique, are employed for force/frequency diagrams. Viscosity, material gradient index, and imperfection effects on the system vibrations are investigated.