Graded Material Layer Research Articles

Stability analysis of axially loaded sandwich beams with a five-layered composite core made of viscoelastic and functionally graded material layers

Stability analysis of axially loaded sandwich beams with a five-layered composite core made of viscoelastic and functionally graded material layers

Structural Study of Four-Layered Cylindrical Shell Comprising Ring Support

In this work, the vibration analysis of a layered, cylinder-shaped shell is undertaken. The structure of the shell layers is composed of functionally graded and isotropic materials. The vibrations of four-layered cylindrical shells with a ring support along the axial direction are investigated in this research. The two internal layers are composed of isotropic materials, and the external two layers are composed of functionally graded materials. The outer functionally graded material layers considered are stainless steel, zirconia, and nickel. The inner two isotropic layers considered are aluminum and stainless steel. The shell frequency equation is acquired by employing the Rayleigh–Ritz method under the shell theory of Sanders. The trigonometric volume fraction law is used to sort the functionally graded material composition of the FGM layers. The natural frequencies are attained under two boundary conditions, namely simply supported–simply supported and clamped–clamped.

Vibration of hybrid eccentrically stiffened sandwich auxetic double curved shallow shells in thermal environment

Adding stiffeners or forming a sandwich structure are two ways to reduce unnecessary risks or costs for structures made of advanced materials. Through the proposal of a hybrid sandwich shell model consisting of three layers: Functionally graded graphene platelets reinforced composite layer (FG-GPL), Auxetic core layer, and Functionally graded material layer (FGM) with reinforcement stiffeners, this study presents an analytical solution to illustrate the significant effects of geometrical and material parameters as well as stiffeners on the vibration of sandwich double-curved shallow shells (SDCS shells) subjected to blast loading in a temperature environment and visco-Pasternak medium. The results demonstrate that the shell with stiffener has a higher load-carrying capacity compared to a non-stiffener case and the combination of material layers in a hybrid shell has significant advantages over a homogeneous shell, even under blast load. These findings have practical implications for expanding the application fields of sandwich structures by synthesizing the benefits of each material layer.

Effect of Kaolin powder on the static and dynamic behavior of heterogeneous laminate constituted of functionally graded material layers

This work investigated the mechanical properties of glass/epoxy laminates reinforced by kaolin powder with graded properties by performing tensile, 3-point bending, impact tests, and compression after impact (CAI) tests. Firstly, we evaluated the effects of mixing parameters on particle dispersion and the effect of kaolin powder rate on the epoxy properties. It was found that the optimal parameters for a good distribution are a temperature of 60°C with 10 min of stirring time and the optimum kaolin powder rate is 5 wt %. Secondly, four graded heterogeneous laminates were elaborated with increased powder rate at each 1, 2, 3, and 4 layers named models 1/1, 2/2, 3/3, and 4/4, respectively. The test results showed that the powder gradient distribution considerably influences the behavior of the composite, with a significant improvement in mechanical properties compared to unreinforced glass/epoxy laminates. The model 1/1 on the top side exhibits the most significant increase in flexural modulus and maximum flexural strength, respectively, compared to the unfilled specimen. The impact tests showed that the powder distribution gradient is essential in absorbing the leading force and energy. The model 1/1 on the top side showed the best impact strength. According to this previous finding, adding ceramic particles in a polymer matrix; with a particular gradient distribution; significantly enhances the composite laminates' properties, especially under bending load. This heterogeneous composite type finds its application in closed structures where the load side is known, such as tanks and aircraft wings, and will allow a considerable weight gain.

Effect of an edge crack on stress concentration around hole surrounded by functionally graded material layer

The present work aims to investigate the effect of an edge crack on the stress concentration around the circular hole surrounded by Functionally Graded Material (FGM) in an infinite plate subjected to uniaxial tensile load. The numerical investigation has been carried out using Extended Finite Element Method (XFEM). Two cases have been analysed in this work, i.e. the whole plate made up of radial FGM and homogeneous material plate having radial FGM layer around the hole. Young’s modulus of FGM varies according to exponential and power law function. The relations of stress intensity factor (SIF) and stress concentration factor (SCF) with normalised crack length, Young’s modulus ratio, FGM layer thickness and power law index have been presented. It has been observed that the FGM layer case has low SCF around hole than FGM plate case in presence of an edge crack.

On the group velocity of Love-type waves in composite structure loaded with viscous fluid

The present problem has been formulated to understand the working of surface acoustic wave devices under the viscous liquid loading. An analytical study has been employed to compute the group velocity of Love-type waves in composite structure consists of functionally graded material layer embedded over magnetoelastic self-reinforced substrate immersed in viscous fluid. Profound effects of the material gradient, magneto-elasticity, initial stress, viscosity and liquid mass density on the group velocities are observed and depicted by means of graphs. It is revealed from the study that the group velocity of Love-type waves diminishes with increasing values of both density and viscosity of the viscous liquid.

Exact bending solutions of circular sandwich plates with functionally graded material-undercoated layer subjected to axisymmetric distributed loads

In this study, the closed-form bending solutions of simply supported circular sandwich plates subjected to linearly or power-law, or partial uniform distributed loads are derived. The circular sandwich plate contains two homogeneous substrates and a functionally graded material-undercoated layer added between two homogeneous substrates. The Poisson’s ratio of the circular sandwich plates is assumed to be uniform. The Young’s moduli in the undercoated functionally graded material layer vary continuously throughout the thickness according to the volume fraction of constituents based on power-law, sigmoid, or exponential function. To solve the problem, first, the in-plane and bending problems of circular sandwich plate are uncoupled by properly choosing the origin of the z-axis such that the parameter [Formula: see text]. Then the fundamental bending solution of a simply supported circular sandwich plate under axisymmetric ring load is found based on the classical plate theory. Finally, by superposing the fundamental solutions, the closed-form bending solutions of circular sandwich plates under arbitrarily axisymmetric transverse loads are determined. Results reveal that the closed-form solutions agree very well with the finite element calculation and, when degenerated, coincide with the available solutions for isotropic homogenous plates in the literature. Moreover, the exact solutions of the circular sandwich plates subjected to axisymmetric transverse loads exhibit the relation of [Formula: see text] for the stresses [Formula: see text] and bending moments [Formula: see text]. The effects of the material gradient, the material distribution, and the thickness of the undercoated-functionally graded material layer on the mechanical behaviors of the circular sandwich plates are under investigation in detail.

Electro-magnetic potential effects on free vibration of rotating circular cylindrical shells of functionally graded materials with laminated composite core and piezo electro-magnetic two face sheets

In this study, the effect of electric and magnetic potential on the free vibration of rotating circular cylindrical shell of functionally graded piezo electromagnetic composed with fiber reinforced polymers has been investigated. The laminated fiber reinforced polymer is in the core and is supported with the functionally graded material layer on the both sides, and two piezoelectric layers are mounted on the outside and inside of the cylindrical shells. Relationships between strain and displacement are expressed based on Love’s first approximation shell theory. Then according to Hamilton’s principle, the governing equations for the cylindrical shell are extracted. Also, the Navier’s solution is used to solve the equations of the cylindrical shell for the simply–simply supported boundary conditions. The numerical results of the analytical solution for the rotating functionally graded piezoelectric–fiber reinforced polymer cylindrical shells based on the effect of magnetic and electric potential, axial and circumferential wave number and speed rotation are obtained. These results are compared with other research and demonstrated a good agreement.

Nonlinear buckling behavior of functionally graded material sandwich cylindrical shells with tangentially restrained edges subjected to external pressure and thermal loadings

An analytical investigation on buckling and postbuckling behavior of sandwich cylindrical shells comprising functionally graded material layers and subjected to uniform temperature rise and external pressure in thermal environments is presented in this paper. Two sandwich models corresponding to functionally graded material face sheets and core layer are considered. The properties of constitutive materials are assumed to be temperature dependent and effective properties of functionally graded material are determined according to linear rule of mixture. Formulations are based on the classical shell theory taking Von Karman–Donnell nonlinearity and elastic constraint at edges into consideration. Multi-term solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive nonlinear load–deflection relations from which buckling loads and postbuckling paths are determined. The effects of sandwich configurations, material gradation, tangential constraints of edges, and temperature dependence of material properties on buckling loads and postbuckling curves are analyzed through numerical examples.

Thermal fatigue behavior of functionally graded W/EUROFER-layer systems using a new test apparatus

Abstract In future fusion reactors tungsten coatings shall protect First Wall components, made of reduced activation ferritic martensitic steel, against the plasma, because of tungsten’s favourable thermo-mechanical properties and low sputtering yield. Functionally graded material layers implemented between the coating and the steel substrate, compensate the difference in the coefficient of thermal expansion. By using the vacuum plasma spraying technique several layer systems were successfully produced and tested, among other aspects, in regard to their thermal fatigue behaviour up to 500 thermal cycles in a vacuum furnace. However, higher numbers of thermal cycles are anticipated for future fusion reactors and, therefore, a less time consuming approach for thermal fatigue testing is required. Hence, a new testing apparatus with induction heating and inert gas cooling was built and first thermal fatigue experiments with up to 5000 cycles were carried out on different functionally graded tungsten/steel layers systems. The subsequent investigations of these samples show that the layer systems are stable for the applied number of thermal cycles and their properties are solely determined during their respective coating processes.

Stress concentration reduction using different functionally graded materials layer around the hole in an infinite panel

Stress concentration reduction using different functionally graded materials layer around the hole in an infinite panel

Modeling the behavior of bilayer shape memory alloy/functionally graded material beams considering asymmetric shape memory alloy response

A new model is proposed to describe the response of laminated composite beams consisting of one shape memory alloy layer and one functionally graded material layer. The model accounts for asymmetry in tension and compression of the shape memory alloy behavior and successfully describes the dependence of the position of the neutral surface on phase transformation within the shape memory alloy and on the load direction. Moreover, the model is capable of describing the response of the composite beam to both loading and unloading cases. In particular, the derivation of the equations governing the behavior of the beam during unloading is presented for the first time. The effect of the functionally graded material gradient index and of temperature on the neutral axis deviation and on the overall behavior of the beam is also discussed. The results obtained using the model are shown to fit three-dimensional finite element simulations of the same beam.

Hygro-thermo-mechanical modelling and analysis of multilayered plates with embedded functionally graded material layers

This work addresses the modelling and analysis of multilayered plates with embedded functionally graded material (FGM) layer(s) under hygro-thermo-mechanical loadings. The hygroscopic, thermal and mechanical problems are all solved simultaneously using a new layerwise mixed model based on least-squares formulation with multi-field independent variables, namely, displacements, temperature, moisture, transverse stresses, transverse heat flux, transverse moisture flux, in-plane strains and in-plane components of both thermal and moisture gradients. This mixed formulation ensures that interlaminar C0 continuity requirements, where the material properties may actually change, are fully fulfilled a priori. An added feature is included to fully describe the FGM layer z-continuous effective properties through-thickness, using any homogenization method, by applying a high-order z-expansion to its effective properties, similarly to finite element approximations. The numerical results demonstrate the effects of hygrothermal environments in the analysis of distinct multilayered plates with embedded FGM layers, considering different side-to-thickness ratios, under a series of hygro-thermo-mechanical loadings. The rule of mixtures is used to estimate the FGM layer effective properties, including different material gradation profiles. Three-dimensional (3D) approximate solutions corroborate this model’s capability to predict accurately a quasi-3D hygro-thermo-mechanical description of the through-thickness distributions of displacements and stresses, temperature and heat flux, moisture and moisture flux.

Generalized Fractional Heat Conduction in a One-Dimensional Functionally Graded Material Layer

Functionally graded materials (FGMs) have been widely used. This work studies a heat conduction problem in an FGM layer with different exponential gradients. Based on a generalized fractional heat conduction theory with phase lag of heat flux, a mixed initial-boundary value problem is solved. Analytical expression for temperature change in the Laplace transform domain is derived. Numerical results of the transient temperature response in the time domain are evaluated by applying a numerical inversion of the Laplace transform. Two representative boundary conditions related to given temperature or heat convective transfer are discussed. For different Biot numbers, the effects of phase lag of heat flux, fractional order, and material properties on temperature field are illustrated graphically. A comparison of the temperature fields based on the non-Fourier model and classic Fourier model is made. The obtained results show that wave-like behaviors may occur for the generalized fractional heat transfer, which does not occur for the classical Fourier heat conduction. The material properties play an important role in the heat transfer process. The derived results are of benefit to the design of materials for thermoresistance and abstraction of heat.

The Effect of Power Law - Functionally Graded Material Layers on the Natural Frequency of Al/ZrO2 Cantilever Beam

The Effect of Power Law - Functionally Graded Material Layers on the Natural Frequency of Al/ZrO2 Cantilever Beam

Deformations and stresses of multilayered plates with embedded functionally graded material layers using a layerwise mixed model

This work presents a new layerwise mixed model for the static analysis of multilayered plates with embedded functionally graded material (FGM) layers subjected to transverse mechanical loads. This model is capable to fully describe a two-constituent metal-ceramic FGM layer continuous variation of material properties in the thickness direction, using any given homogenization method to estimate its effective properties. The present model is based on a mixed least-squares formulation with a layerwise variable description for displacements, transverse stresses and in-plane strains, chosen as independent variables. This mixed formulation ensures that the interlaminar C0 continuity requirements at the layers interfaces, where the material properties actually change, are fully fulfilled a priori for all independent variables. The order of the in-plane two-dimensional finite element approximations and the order of the z-expansion through each layer thickness, as well as the number of layers, whether FGM layers or not, are considered free parameters. The full description of the FGM effective properties is achieved by applying to the z-continuous elastic coefficients a z-expansion through the layer thickness of a given order, set as an added free parameter, in a similar approach to finite element approximations. The numerical results consider both single-layer and multilayered functionally graded plates with different side-to-thickness ratios, using either Mori-Tanaka or the rule of mixtures estimates for the FGM effective properties with different material gradation profiles. The present model results are assessed by comparison with three-dimensional (3D) exact solutions and closed form solutions, which demonstrate its capability to predict a highly accurate quasi-3D description of the displacements and stresses distributions altogether.

Residual stress and fracture strength of brazed joint of ceramic and titanium alloy with the aid of laser deposited functionally graded material layers

To improve the strength of a ceramic (ZrC-SiC) and a titanium alloy (TC4) brazed joint, laser deposited functionally graded material layers (FGM layers) between ZrC-SiC and TC4 were designed to reduce the residual stress in the brazed joint. A simulation model of the brazed joint was created to investigate the mechanism of residual stress reduction due to FGM layers. The results show that the residual stress component in the normal direction of the brazing interface (normal stress) is tensile at the ZrC-SiC edges and the in-plane residual stress component on the brazing interface is compressive in the ZrC-SiC adjacent to the brazing seam. The adoption of the FGM layers significantly reduces both the normal residual stress and in-plane residual stress. During the shear test, the normal stress concentrates at the ZrC-SiC edges near the brazing seam. By applying fracture forces 645 N and 1365 N measured in shear experiments to the ZrC-SiC/TC4 joint model and ZrC-SiC/TC4-FGM joint model respectively, the local fracture stress in the normal direction is identified to be 648 MPa and 671 MPa from both models, respectively. Although the fracture force for both models are quite different due to the difference of residual stress produced by brazing, the identified local fracture stress is close each other. The predicted cracking initial position is around the corner of the ZrC-SiC close to the brazed zone which is the same as observed in experiments.

Study of the surface wave vibrations in a functionally graded material layered structure: a WKB method

In this paper, a theoretical investigation is described of the propagation behaviour of Love-type waves in a functionally graded material layered structure. The Wentzel–Kramers–Brillouin (WKB) method was applied to obtain the analytical solution for the functionally graded material layer. The study was carried out to investigate the transference of Love-type waves in a functionally graded material layer bounded by a viscous fluid layer and a highly anisotropic half-space. Two cases were studied, one in which the material property variation of the functionally graded material layer was arbitrary and one in which the material property variation was taken as exponential. A variable separation method was employed to obtain the displacement components in both the viscous liquid and the highly anisotropic medium. Profound effects of material gradient coefficient, viscous coefficient, liquid mass density, initial stress parameter and wavelength on real and imaginary components of phase velocities were established. Some numerical calculations were also made. The considered model facilitates a theoretical foundation and practical application for the development of surface acoustic wave devices.

Strengthening the ZrC-SiC ceramic and TC4 alloy brazed joint using laser additive manufactured functionally graded material layers

In order to improve the ZrC-SiC and TC4 brazed joint property, functionally graded material (FGM) layers (two SiC particles reinforced TC4-based composite layers) were designed to relieve the residual stress in the ZrC-SiC and TC4 brazed joint. The FGM layers were fabricated on the TC4 surface using laser additive manufacturing technology before the brazing. Then the TC4 coated with the FGM layers and ZrC-SiC ceramic were brazed using Ti-15Cu-15Ni (wt%) filler. According to the SEM and TEM results, the volume fractions of SiC particles in the FGM layers could reach 20% and 39% respectively. Ti from the braze filler and TC4 reacted with the ZrC-SiC ceramic to form TiC and Ti5Si3 adjacent to the ZrC-SiC ceramic. The shear test results indicate that the adoption of the FGM layers and the brazing temperature both affected the joint property significantly. The FGM layers could benefit the mitigation of coefficient of thermal expansion (CTE) mismatch between the ZrC-SiC and TC4, so that the residual stress caused by the CTE mismatch in the joint was relieved and the joint strength increased. The brazing temperature would affect the microstructure of the brazing seam and then control the joint strength. When the ZrC-SiC ceramic and TC4 coated with the FGM layers were brazed at 970 °C for 10 min, the maximum shear strength could reach 91 MPa, and cracks propagated in the ZrC-SiC ceramic substrate during the shear test.

Development of W-coating with functionally graded W/EUROFER-layers for protection of First-Wall materials

To protect First-Wall components, made of reduced activation ferritic martensitic steel, against the plasma of future fusion reactors, tungsten coatings are a feasible option. The difference in coefficient of thermal expansion between the coating and the steel substrate can be compensated using functionally graded material layers. Such layers were successfully produced by vacuum plasma spraying. This technique reduces, however, the hardness of the substrate surface near zone. Modified spraying parameters moderate the hardness loss. The parameters may, though, affect also the layer bonding toughness which is evaluated in this work by four point bending tests. Furthermore, the layers behavior on First-Wall Mock‐ups and under different thermal loads is investigated by finite element simulations.The measurement of the layer adhesion indicates that the layer adhesion decreases only for modified spraying parameters that do not reduce the substrate hardness. It follows also from the toughness calculation that without layer residual stresses the toughness values depend on coating thickness. In regard to the Mock‐up behavior the simulations show that intermediate steps are necessary during heating and cooling to prevent artificial stresses and inelastic deformation. It is, however, not possible to avoid stresses and inelastic deformation completely as they originate from the residual stresses.