Indentation of a Functionally Graded Plate by a Rigid Spherical Indenter in the Presence of a Semi-Elliptic Surface Crack

2012 ◽  
Author(s):  
Ali Nikbakht ◽  
Alireza Fallahi Arezoodar ◽  
Mojtaba Sadighi ◽  
Ali Tale Zadeh Lari
Keyword(s):  
Stress Distribution ◽  
Surface Crack ◽  
Volume Fraction ◽  
Crack Tip ◽  
Functionally Graded ◽  
Spherical Indenter ◽  
Elliptic Surface ◽  
Graded Materials ◽  
Cracked Plate ◽  
Abaqus Model

Graded materials, also known as functionally graded materials (FGMs), are multiphase composites mainly composed of a ceramic and a metal; thus, they exploit the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. These materials are mainly used as heat barriers. In addition, many of the present and potential applications of FGMs involve contact problems. On the other hand, the production process of FGMs is somewhat complex and leaves some defects in the produced structure. One of the most important defects in such structures is surface cracks. Here, the combination of the contact and crack problems is investigated in a functionally graded rectangular plate containing a semi–elliptic surface crack indented by a frictionless rigid spherical indenter. The plate is simply supported and the crack is located in the middle of the plate surface in the tension part. The crack surface is parallel to one of the plate edges. The gradient of mechanical properties variation is considered through the thickness of the plate and the volume fraction distribution of the constituting phases is modeled by a polynomial function and the Poisson’s ratio is kept constant. The analyzing of the problem is divided into two steps. At the first step, for an uncracked plate the equations of equilibrium are derived in terms of the displacement field and are solved numerically to find the contact rule. As the second step in studying the problem, the contact problem of a cracked plate is modeled by using ABAQUS finite element package. The aim of this step is to find the effect of the presence of the crack on the contact rule. The optimum mesh for the ABAQUS model is found by using the results of the first step. In order to do so, an ABAQUS model is created for the uncracked plate. The analytical results and the obtained results from ABAQUS for specified plate and indenter dimensions and material properties are compared. After finding the optimum mesh, a crack is added to the ABAQUS model of the plate under contact loading. The effects of gradient changes and indenter dimensions on the contact rule and stress distribution at the crack tip are then investigated by using the obtained ABAQUS model. The acquired results show that the influence of the material nonhomogeneity on the stress distribution around the crack tip and in the plate (uncracked and cracked) and contact rule can be quite significant. In general, increasing the overall volume fraction of the metal phase increases the load carrying capacity in an uncracked plate. In a cracked plate, the changes in material distribution as well as the changes of the indenter diameter does not affect the results that much.

Indentation of a transversely loaded functionally graded rectangular plate by a rigid spherical indentor

2012 ◽  
Vol 227 (4) ◽  
pp. 663-682 ◽  
Author(s):  
Ali Nikbakht ◽  
Mojtaba Sadighi ◽  
Alireza Fallahi Arezoodar
Keyword(s):  
Stress Distribution ◽  
Numerical Method ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Graded Materials ◽  
Stress Strain Relation ◽  
Finite Element Package ◽  
Spherical Indentor

Functionally graded materials are multiphase composites mainly composed of a ceramic and a metal; thus, they merge the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. Many of the present and possible applications of functionally graded materials involve contact loading. Here, the contact problem of a functionally graded simply supported plate with finite dimensions by a rigid spherical punch is studied by an analytical–numerical method. The contact rule will be derived by solving the equations of equilibrium analytically in terms of the displacement field components and by taking advantage of a numerical method in finding the contact parameters. The stress–strain relation is assumed to be linear and is represented by a refined volume fraction based model originally proposed by Tamura–Tomota–Ozawa model. The results of the analytical–numerical approach are validated by using ABAQUS finite element package. The analytical–numerical results are used to investigate the effect of parameters such as material distribution, punch radius, plate span and thickness on the contact rule and stress distribution in the plate. The obtained results show that the influence of the material non-homogeneity on the contact rule and stress distribution is quite significant. In addition, the acquired results illustrate that increasing the indentor diameter and the thickness of the plate increase the contact force for equal amount of indentation.

Solidification Processing of Functionally Graded Materials by Sedimentation

1999 ◽  
Author(s):  
J. W. Gao ◽  
S. J. White ◽  
C. Y. Wang
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Computer Code ◽  
Functionally Graded ◽  
Particle Volume ◽  
Particle Sedimentation ◽  
Graded Materials ◽  
Free Zone ◽  
Free Region

Abstract A combined experimental and numerical investigation of the solidification process during gravity casting of functionally graded materials (FGMs) is conducted. Focus is placed on the interplay between the freezing front propagation and particle sedimentation. Experiments were performed in a rectangular ingot using pure substances as the matrix and glass beads as the particle phase. The time evolutions of local particle volume fractions were measured by bifurcated fiber optical probes working in the reflection mode. The effects of various processing parameters were explored. It is found that there exists a particle-free zone in the top portion of the solidified ingot, followed by a graded particle distribution region towards the bottom. Higher superheat results in slower solidification and hence a thicker particle-free zone and a higher particle concentration near the bottom. The higher initial particle volume fraction leads to a thinner particle-free region. Lower cooling temperatures suppress particle settling. A one-dimensional solidification model was also developed, and the model equations were solved numerically using a fixed-grid, finite-volume method. The model was then validated against the experimental results, and the validated computer code was used as a tool for efficient computational prototyping of an Al/SiC FGM.

The Higher Order Crack Tip Fields of Exponential Gradient FGMs Plates with Reissner’s Effect

2013 ◽  
Vol 278-280 ◽  
pp. 491-494
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Asymptotic Expansion ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Deformation ◽  
Plate Bending ◽  
Graded Materials ◽  
Fundamental Significance ◽  
Asymptotic Expansion Method

The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials (FGMs) plates for a crack perpendicular to material gradient. The crack-tip higher order asymptotic fields of FGMs plates are obtained by the asymptotic expansion method. This study has fundamental significance as Williams’ solution.

scholarly journals A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3581 ◽  
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Creep Analysis of Functionally Graded Material Thick-Walled Cylinder

2013 ◽  
Vol 315 ◽  
pp. 867-871 ◽  
Author(s):  
Saifulnizan Jamian ◽  
Hisashi Sato ◽  
Hideaki Tsukamoto ◽  
Yoshimi Watanabe
Keyword(s):  
Cross Section ◽  
Volume Fraction ◽  
Rectangular Cross Section ◽  
Functionally Graded ◽  
Graded Materials ◽  
Incremental Approach ◽  
Creep Analysis ◽  
Graded Material ◽  
Ring Elements ◽  
Walled Cylinder

In this paper, creep analysis for a thick-walled cylinder made of functionally graded materials (FGMs) subjected to thermal and internal pressure is carried out. The structure is replaced by a system of discrete rectangular cross-section ring elements interconnected along circumferential nodal circles. The property of FGM is assumed to be continuous function of volume fraction of material composition. The creep behavior of the structures is obtained by the use of an incremental approach. The obtained results show that the property of FGM significantly influences the stress distribution along the radial direction of the thick-walled cylinder as a function of time.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

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