A two-stage homogenization for modelling of elastic-plastic functionally graded composites

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Witold Ogierman
Keyword(s):  
Volume Fraction ◽  
Mean Field ◽  
Functionally Graded ◽  
Two Stage ◽  
Graded Materials ◽  
Content Type ◽  
Elastic Plastic ◽  
Functionally Graded Composites ◽  
Homogenization Approach ◽  
Arbitrary Volume

Purpose The purpose of this study is to develop a homogenization approach that ensures both high accuracy and time-efficient solution for elastic-plastic functionally graded composites. Design/methodology/approach The paper presents a novel two-stage hybrid homogenization approach that combines advantages of the mean field homogenization and homogenization based on the finite element method (FEM). The groundbreaking nature of the developed approach is associated with division of the hybrid homogenization procedure into two stages, which allows to very efficiently determine the solution for arbitrary volume fraction of the reinforcement. This paper concerns also on modelling of composites with randomly distributed prolate and oblate particles. For this purpose, the hybrid homogenization was implemented in the framework of the discrete orientation averaging procedure involving pseudo-grain discretization method. Findings Agreement between the results obtained using the proposed approach and the standard FEM-based homogenization is very good (up to the volume fraction of 0.3). Originality/value The proposed two-stage homogenization approach allows to obtain the solution for materials with arbitrary volume fraction of the reinforcement very efficiently; therefore, it is highly beneficial for the two-scale modeling of nonlinear functionally graded materials and structures.

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.

Functionally Graded Polymeric Composites Having Micro-Tailored Structure Formed by Electric Field

Materials ◽  
2003 ◽  
Author(s):  
Geun Hyung Kim ◽  
Daniel K. Moeller ◽  
Yuri M. Shkel
Keyword(s):  
Mechanical Properties ◽  
Electric Field ◽  
Functionally Graded Materials ◽  
Applied Electric Field ◽  
Polymeric Composites ◽  
Functionally Graded ◽  
Graded Materials ◽  
Functionally Graded Composites ◽  
Liquid Suspensions ◽  
Redistribution Effect

A solid composite having locally micro-tailored structure can be produced by curing liquid polymeric suspensions in an electric field. The redistribution effect of the field-induced forces exceeds the effect of centrifugation, presently employed to manufacture functionally graded materials. Moreover, unlike centrifugational sedimentation, one can electrically rearrange the inclusions in desired targeted areas. The applied electric field can be employed to produce a composite having uniformly oriented structure or only modify the material in selected regions. This technology enables polymeric composites to be locally micro-tailored for given design objectives. We discuss electrical and rheological inteactions in liquid suspensions. Relationships between microstructure and mechanical properties of the obtained functionally graded composites are presented.

Modeling of functionally graded materials to estimate effective thermo-mechanical properties

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Royal Madan ◽  
Shubhankar Bhowmick
Keyword(s):  
Experimental Data ◽  
Functionally Graded Materials ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Content Type ◽  
Wide Range ◽  
Metal Metal ◽  
Novel Material ◽  
First Time

Purpose Functionally graded materials are a special class of composites in which material are graded either continuously or layered wise depending upon its applications. With such variations of materials, the properties of structure vary either lengthwise or thickness wise. This paper aims to investigate models for effective estimation of material properties, as it is necessary for industries to identify the properties of composites or functionally graded materials (FGM’s) before manufacturing and also to develop novel material combinations. Design/methodology/approach Available models were compared for different material combinations and tested with experimental data for properties such as Young’s modulus, density, coefficient of thermal expansion (CTE) and thermal conductivity. Combinations of metal–ceramic and metal–metal were selected such that their ratios cover a wide range of materials. Findings This study reveals different models will be required depending on the material used and properties to be identified. Practical implications The results of the present work will help researchers in the effective modeling of composites or FGM’s for any analysis. Originality/value This paper presents a comparison and review of various analytical methods with experimental data graphically to find out the best suitable method. For the first time, the Halpin-Tsai model was extended in the analysis of the CTE which shows good approximations.

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.

Simulation-based verification of homogenization approach in predicting effective thermal conductivities of wavy orthotropic fiber composite

2019 ◽  
Vol 08 (04) ◽  
pp. 1950015
Author(s):  
C. Mahesh ◽  
K. Govindarajulu ◽  
V. Balakrishna Murthy
Keyword(s):  
Volume Fraction ◽  
Fiber Composite ◽  
Micromechanical Model ◽  
Two Stage ◽  
Micromechanics Models ◽  
Simulation Based ◽  
Homogenization Approach ◽  
Homogenized Model ◽  
Good Agreement ◽  
Thermal Conductivities

In this work, applicability of homogenization approach is verified with the micromechanics approach by considering wavy orthotropic fiber composite. Thermal conductivities of [Formula: see text]-300 orthotropic wavy fiber composite are determined for micromechanical model and compared with the results obtained by two stage homogenized model over volume fraction ranging from 0.1 to 0.6. Also, a methodology is suggested for reducing percentage deviation between homogenization and micromechanical approaches. Effect of debond on the thermal conductivities of wavy orthotrophic fiber composite is studied and compared with perfectly aligned fiber composite for different volume fraction. It is observed that results obtained by the homogenization approach are in good agreement with the results obtained through micromechanics approach. Maximum percentage deviation between homogenized and micromechanics models is 2.13%.

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.

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.

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