Effect of anisotropy on steady state creep in functionally graded cylinder

The steady state creep in transversely isotropic functionally graded cylinder, operating under internal and external pressures, has been investigated. The cylinder is composed of functionally graded material (FGM) containing silicon carbide whiskers in a matrix of 6061Al. The creep behavior of the FGM has been described by a threshold stress based creep law. The effect of anisotropy on creep stresses and creep rates in the FGM cylinder has been analysed and compared with an isotropic FGM cylinder. The anisotropy is represented by a parameter α, defined as the ratio of radial (or axial) and tangential yield strength. The study reveals that in an anisotropic FGM cylinder i.e. when α deviates from unity, radial and tangential stresses are marginally affected whereas axial and effective stresses are significantly affected as compared to those in an isotropic FGM cylinder. The strain rates as well as inhomogeneity in strain rates in the FGM cylinder decrease significantly when α reduces from 1.3 to 0.7. The magnitude of stresses, strain rates and inhomogenity in strain rates in the FGM cylinder, subjected to internal pressure alone, could be significantly reduced by subjecting it to both internal and external pressures though the stress inhomogenity in the FGM cylinder increases.     

Thermal stress in rotating functionally graded hollow circular disks

The analysis of thermoelastic problem of a rotating functionally graded hollow circular disk is made. The hollow disk is assumed to have varying material properties along the radial direction. An analytical method is presented to investigate steady thermal stresses in a functionally graded circular annulus rotating with constant angular velocity about its central axis. The associated boundary value problem is reduced to a Fredholm integral equation. The thermal stresses and radial displacement are obtained by numerically solving the resulting equation. A comparison of the numerical results with the exact ones for material properties of special power-law profile confirms the effectiveness of the method. For generally varying material parameters, numerical results are presented graphically to show the effects of gradient parameter, temperature change, angular velocity and thickness of the disk on the distribution of thermal stresses and radial displacement.     

Mechanical properties of functionally graded 2-D cellular structures: A finite element simulation

Functionally graded cellular structures such as bio-inspired functionally graded materials for manufacturing implants or bone replacement, are a class of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties. A gradual increase in cell size distribution, can impart many improved properties which may not be achieved by having a uniform cellular structure.The material properties of functionally graded cellular structures as a function of density gradient have not been previously addressed within the literature. In this study, the finite element method is used to investigate the compressive uniaxial and biaxial behavior of functionally graded Voronoi structures. Furthermore, the effect of missing cell walls on its overall mechanical (elastic, plastic, and creep) properties is investigated.The finite element analysis showed that the overall effective elastic modulus and yield strength of structures increased by increasing the density gradient. However, the overall elastic modulus of functionally graded structures was more sensitive to density gradient than the overall yield strength. The study also showed that the functionally graded structures with different density gradient had similar sensitivity to random missing cell walls. Creep analysis suggested that the structures with higher density gradient had lower steady-state creep rate compared to that of structures with lower density gradient.     

Three-dimensional Green’s functions for a steady point heat source in a functionally graded half-space and some related problems

Three-dimensional Green’s functions are derived for a steady point heat source in a functionally graded half-space where the thermal conductivity varies exponentially along an arbitrary direction. We first introduce an auxiliary function which satisfies an inhomogeneous Helmholtz equation. Then by virtue of the image method which was first proposed by Sommerfeld for the homogeneous half-space Green’s function of a steady point heat source, we arrive at an explicit expression for this function. Finally with this auxiliary function, we derive the three-dimensional Green’s functions due to a steady point heat source in a functionally graded half-space. Also investigated in this paper are the temperature field induced by a point heat source moving at a constant speed in a functionally graded full-space; the electric potential due to a static point electric charge in a dielectric full-space with electric field gradient effects; and the two-dimensional time-harmonic dynamic Green’s function for homogeneous and functionally graded materials with strain gradient effects.     

Thermo-elastic analysis of a functionally graded piezoelectric rotating hollow cylindrical shell subjected to dynamic loads

In this study, dynamo-thermo-elastic analysis of a rotating piezoelectric hollow cylinder made of functionally material is presented. Coupled differential quadrature and finite difference methods are used to solve boundary/initial value equations of the problem. Material properties are assumed to be graded in radial direction and temperature independent. Numerical results obtained and convergence are studied, and then verified with reported results in literature. Effect of variations of the grading parameter, angular velocity, thermal gradient and ratio of the outer to inner radii on the stresses, radial displacement and electrical potential are presented.     

Piezoelectric Behavior of an Inhomogeneous Hollow Cylinder with Thermal Gradient

An analytical solution to the axisymmetric problem of a radially polarized, radially orthotropic piezoelectric hollow cylinder with a thermal gradient and subjected to various boundary conditions is developed. The elastic coefficients, piezoelectric coefficients, stress-temperature moduli, dielectric coefficient, pyroelectric coefficients, thermal conductivity coefficient, and thermal expansion coefficients of the hollow cylinder are assumed to be graded in the radial direction according to a simple power-law distribution. The governing second-order differential equations are derived from the equilibrium equation, the charge equation of electrostatics, and steady state heat transfer equation through the radial direction of the inhomogeneous hollow cylinder. The displacement, stresses, and potential field distributions in the cylinder are examined. The influence of the inhomogeneity parameter on the numerical results is investigated.     

Semi-analytical solution of time-dependent thermomechanical creep behavior of FGM hollow spheres

By using a method of successive elastic solution, the time-dependent creep behavior of a functionally graded hollow sphere under thermomechanical loads has been investigated. Based on volume percentage, the mechanical and thermal properties of material, except for the Poisson’s ratio, are assumed to be radially dependent. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are temperature-, stress- and time-dependent. Using the Prandtl–Reuss relations and Sherby’s law, histories of stresses and strains are presented from their initial elastic values at zero time up to 30 years after loading. The results show that the creep stresses and strains change with time and material inhomogeneity has influence on thermomechanical creep behavior. The aim of this work was to understand the effect of creep behavior on a functionally graded hollow sphere subjected to thermomechanical load.     

Computer Simulation of the Indentation Creep Tests on Particle-Reinforced Composites

A systematical simulation has been carried out on the indentation creep test on particle-reinforced composites.The deformation ,failure mechanisms and life are analyzed by three reasonable models.The following five factors have been considered simultaneously:creep property of the particle,creep property of the matrix,the shape of the particle, the volume faction of the particle and the size(relative size to the particle )of the indentation indenter.For all the cases,the power law respecting to the applied stress can be used to model the steady indentation creep depth rate of the indenter,and the detail expressions have been presented.The computer simulation is analyzed by the two-phase model and the three-phase model.Two places of the stress concentration are found in the composites.One is ahead of the indentation indenter, where the high stress state is deduced by the edge of theindenter and will decrease rapidly near to a steady value with the creep time The other one is at the interface,where the high stress state is deduced by the misfit of material properties between the particles and matrix.It has been found that the creep dissipation energy density other than a stress parameter can be used to be the criterion to model the debonding of the interfaces.With the criterion of the critical creep dissipation energy density, a power law to the applied stress with negative exponent can be used to model the failure life deduced by the debonding of interfaces.The influences of the shape of the particles and the matching of creep properties of particle and matrix can be discussed for the failure.With a crack model,the further growthe of interface crack is analyzed, and some important experimental phenomena can be predicted.The failure mechanism which the particle will be punched into matrix has been also discussed.The critical differences between the creep properties of the particles and matrix have been calculated, after a parameter has been defined.In the view of competition of failure mechanisms, the best matching of the creep properties of the two phases and the best shape of the particles are discussed for the composite design.     

Vibration of turbomachinery rotating blades made-up of functionally graded materials and operating in a high temperature field

Summary. The vibration of turbomachinery rotating blades made-up of functionally graded materials and operating in a temperature field is considered. In this context, the blade is modeled as a thin-walled beam mounted on a rigid hub at a presetting angle, rotating with a constant angular velocity, and exposed to a steady temperature field of a prescribed gradient through the blade wall thickness. The effect of the initial twist of the blade is also taken into consideration. Results are presented for two constituents, metal-ceramic based materials that are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. Numerical results highlighting the effects of the volume fraction in conjunction with those of the presetting and pretwist angles, temperature gradient, rotating speed and hub radius are presented, and pertinent conclusions are outlined.     

Transient solution of temperature field in functionally graded hollow cylinder with finite length using multi layered approach

In this paper by using a multi-layered approach based on the theory of laminated composites, the solution of temperature in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions are presented. The material properties are assumed to be temperature-independent and radially dependent. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Employing Laplace transform techniques and series solving method for two-dimensional heat conduction equation in the cylinder, solutions for the variation of temperature with time as well as temperature distribution through the cylinder are obtained.     

Multiphysical time-dependent creep response of FGMEE hollow cylinder in thermal and humid environment

In this paper, we investigate the history of radial displacement, stresses, electric potential, and magnetic potential of a functionally graded magneto-electro-elastic (FGMEE) hollow cylinder subjected to an axisymmetric hygro-thermo-magneto-electro-mechanical loading for the plane strain condition. The material properties are taken as a power-law function of radius. Using stress-displacement relations, equations of equilibrium, electrostatic and magnetostatic equations, we find a differential equation including creep strains. Initially, eliminating creep strains, we obtain an analytical solution for the primitive stresses and electric and magnetic potential. In the next step, considering creep strains, we find the creep stress rates by applying the Norton law and Prandtl–Reuss equations for steady-state hygrothermal boundary condition. Finally, using an iterative method, we find the time-dependent creep stresses, radial displacement, and magnetic and potential field redistributions at any time. In numerical section, are comprehensively investigate the effects of grading index, hygrothermal environmental conditions, rotating speed, and temperature- and moisture-dependency of elastic constant of FGMEE.

     

A functionally graded syntactic foam material for high energy absorption under compression

A functionally graded structure for hollow particle (microballoon) filled syntactic foams is fabricated that is capable of withstanding compression for 60–75% strain without any significant loss in strength. The new functionally graded structure is based on creating a gradient in microballoon wall thickness. This material has the same volume fraction of microballoons throughout the structure, eliminating the undesirable effects of the present functionally graded composites containing a gradient of particle volume fraction. Three compositions of such material are fabricated and tested in the present study. Results show that the compressive modulus, strength, and total energy absorption of the new syntactic foams can be controlled by using appropriate type and volume fraction of microballoons.     

Analysis of two-dimensional functionally graded rotating thick disks with variable thickness

Elasticity solutions of two-dimensional functionally graded rotating annular and solid disks with variable thickness are presented. Material properties vary through both the radial and axial directions continuously. Axisymmetric conditions are assumed for the two-dimensional functionally graded disk. The graded finite element method (GFEM) has been applied to solve the equations. The distributions of displacements and stresses in radial and axial directions for four different thickness profiles (constant, linear, concave and convex) and various power law exponents have been investigated. The achieved results show that by the use of functionally graded materials and variable thicknesses, the stresses are reduced, so a higher capability of angular velocity can be obtained. Also, using two-dimensional functionally graded materials leads to a more flexible design in comparison with conventional one-dimensional functionally graded materials. The GFEM solution of a functionally graded thin rotating annular disk has been compared with the published literature and it shows good agreement.     

Elastic behavior of glass-like functionally graded infinite hollow cylinder under hydrostatic loads using finite element method

A glass-like (viscoelastic) functionally graded cylinder is studied by using finite element method to investigate the mechanical responses. A subroutine is developed by using ANSYS parametric design language (APDL) to simulate two nonlinearities, which are the variation of material properties with respect to time and position. The cylinder is made of two different viscoelastic materials, namely, pure material one at inner and pure material two at outer surfaces. The material properties are assumed to be presented by simple power law distribution and moreover, bulk and shear moduli are varying with respect to time using the kernel functions depicted regarding Prony series. It is shown that the hoop stresses take the same values at the mean radius (middle of the thickness) for different values of time and grading index. It is found that the radial stress decreases to certain values for specific grading index and then by increasing the grading index it increases to maximum value that related to pure material cylinder. It is shown that unlike the zero axial stress in pure material cylinders, it varies along the thickness from minimum to maximum at inner and outer surfaces, respectively. It is concluded that the viscoelastic functionally graded (VFG) materials play an important role in steady and transient response of hollow cylinder under hydrostatic load.     

Experimental and theoretical studies on thermo‐mechanical fatigue test for aluminium cast alloy

Evaluation of the thermo‐mechanical behaviour and prediction of the service life of cast aluminium alloys are important for the design of automobile engine cylinder heads. In this study, cast Al alloy specimens are extracted from cylinder heads and subjected to in‐phase thermo‐mechanical cyclic loading. The hysteresis curves related to stress and strain were recorded under the individual thermo‐mechanical loading conditions. The number cycles to failure corresponding to multiple mechanical strain and temperature ranges were obtained. It is found that the cyclic stress amplitude decreases and the cyclic softening rate increases with increasing maximum temperature rise. A modified fatigue‐creep model based on energy conservation has been developed for prediction of the fatigue life of cylinder heads. The proposed method shows good agreement with the well‐established Ostergren model and low standard deviations. In summary, the proposed method described in this study provides an option for prediction of the thermo‐mechanical behaviour of metals.     

Coupled thermoelasticity and second sound in finite length functionally graded thick hollow cylinders (without energy dissipation)

In this article, the coupled thermoelasticity behavior of functionally graded thick hollow cylinders is studied. The governing coupled thermoelasticity and the energy equations are solved for a finite length functionally graded cylinder subjected to thermal shock load. The coupled thermoelastic equations are considered based on Green–Naghdi theory. The mechanical properties of cylinder are graded across the thickness as a power law function of radius. The cylinder is assumed to be made of many isotropic sub-cylinders (layers) across the thickness. Functionally graded properties are created by suitable arrangement of layers and governing equations are expanded in longitudinal direction by means of trigonometric function expansion. The Galerkin Finite Element and Newmark Methods are used to analyze the cylinder. The dynamic behavior of temperature distribution, mechanical displacement and thermal stresses is obtained and discussed. The second sound and elastic wave propagation are determined for various kinds of variation in the mechanical properties. The comparison of present results with published data shows the excellent agreement.     

W/Cu功能梯度材料的制备及热循环应力分析

采用水煮溶解造孔剂法, 即先制备孔隙呈梯度分布的钨骨架、后渗铜的方法, 制备了W/ Cu 功能梯度材料, 并对钨铜在纵截面的分布进行了检测, 数据表明在纵截面上钨铜呈梯度分布。利用水淬法模拟其服役状况并用有限差分方法对产生的非稳态热应力进行了分析。结果表明, 热应力的最大值总是出现在两端, 由于富钨端相对密度较低, 裂纹总是在该端出现, 模拟结果与实验结果相一致。      

First order reaction kinetics for transient creep in NiAl hardened austenitic steel

Abstract

Transient creep of an NiAl hardened austenitic steel was analysed in the temperature range of 823 to 923 K at stresses ranging from 150 to 450 MPa in the frame work of first order reaction kinetics. The present analysis is aimed: to correlate various transient creep parameters with steady state creep rate following first order reaction rate theory to obtain correlation constants; and to arrive at a unified equation to describe primary and steady state regimes of the creep curves in terms of correlation coefficients thus derived. Good correlation of transient creep parameters with steady state creep rate has been obtained over the test conditions studied indicating that the basic mechanism of deformation is the same for all the three stages of creep. Unified equation that fits the experimental creep strain time data for different test conditions over transient and steady state regimes has been obtained in terms of correlation coefficients.     

Investigating Creep Performance and Predicting Rupture Time for Rotating FGM Disc under Different Thermal Gradients

A mathematical model is developed to describe the steady state creep in a rotating Al-SiC_p disc having a non-linear thickness profile and distribution of SiC particles along the radial direction. The model is used to investigate the effect of imposing three different kinds of radial temperature profiles viz. linear, parabolic and exponential with fixed values of inner and outer surface temperatures, on the creep stresses and strain rates. It is noticed that by increasing the temperature exponent (n_T), the radial stress (over the entire radius) and tangential stress (near the inner radius) increase in the disc. However, the tangential stress decreases near the outer radius. The radial and tangential strain rates in the functionally graded (FG) disc reduce significantly with the increase in exponent n_T. Besides reduction in the magnitude, the distribution of strain rates also become relatively more uniform throughout with the increase in n_T. It is concluded that FG disc operating under exponential temperature profile performs better. It is also revealed that amongst several FG discs operating under radial thermal gradients, with different values of temperature exponent (n_T) but having the same average and fixed outer surface temperature, the FGM disc with lower value of n_T exhibits the maximum creep life.     

Semi‐analytical analysis for multi‐directional functionally graded plates: 3‐D elasticity solutions

Semi‐analytical 3‐D elasticity solutions are presented for orthotropic multi‐directional functionally graded plates using the differential quadrature method (DQM) based on the state‐space formalism. Material properties are assumed to vary not only through the thickness but also in the in‐plane directions following an exponential law. The graded in‐plane domain is solved numerically via the DQM, while exact solutions are sought for the thickness domain using the state‐space method. Convergence studies are performed, and the present hybrid semi‐analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate. Finally, effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed. Copyright © 2009 John Wiley & Sons, Ltd.