DEFORMATION BEHAVIOUR OF GRADIENT MATERIALS BASED ON AI-A1203 PARTICULATE COMPOSITE

Abstract

A Functionally Graded Material (FGM, or sometimes also called "gradient material") is characterized by a gradual change of material properties with position. The property gradient in the material is caused by a position-dependent variation of constituents, microstructure and consequently, the mechanical properties. Functionally graded materials based on composites are a special class distinct from the normal composites, which have properties uniform along the dimensions while the FGMs have properties tailored to vary with position depending on the needs of a particular application. A unique example is that of ceramic tiles used as thermal barrier on the outer surface of space vehicles presently where the temperature reaches up to 2100 K. Because of the difference of thermal expansion coefficients of the inner shell of metal and the ceramic at the surface, there is a steep change in the thermal stresses at the surface of contact. Such thermal stresses cause the ceramic tiles to peel off or crack with disastrous consequences. The ceramic materials cannot be used alone because of its low toughness and strength and the metal alone cannot be used as it cannot withstand high temperatures. The best replacement for these ceramic tiles may be the functionally graded metal-ceramic composite, with outer layer made of ceramic entirely and the volume fraction of ceramic decreases continuously till the all metal layer starts. Since there is no sharp interface between metal and ceramic and there is a gradual change in the coefficient of thermal expansion, no steep change in thermal stresses will set in to cause delamination. Thus the FGMs are the new class of composite materials being researched and developed for such critical applications where gradient in properties is a requirement. Gradient in properties is important in several other applications also, as in the case of automobile cylinder and piston, better tribological properties are required at one surface, while better toughness is required on the other. In order to make good use of engineering materials, it is required to understand their behaviour sufficiently well to be able to predict their performance. For composites, this means developing models which represent reasonably closely the known experimental response of real composites to applied stresses and environmental conditions. For structural applications, the prediction of the mechanical behaviour of any given composite ii accurately with the help of modelling is important for designing and developing composites in order to ensure the material designed is likely to meet the service requirements of the application concerned. The solidification processing of metal or alloy based gradient materials results in porosity which affects the mechanical behaviour of the material adversely and so, the modelling of such gradient material will be unrealistic unless porosity is taken into account. Although, it is generally accepted that tensile properties decrease with an increase in porosity content but the effect of other porosity parameters like shape, size and distribution on the mechanical properties are yet to be investigated. The application of any material is dictated by its suitability for the given application, cost of production and reliability of knowledge about its behaviour. To popularize the use of FGMs, cheaper manufacturing processes for the mass production of FGMs are required. These manufacturing processes should be reproducible, reliable and cost effective. Presently, there are no reliable and inexpensive ways of fabricating FGMs that also allows for bulk production of large parts. Current methods of fabrication include solidification processing, chemical vapor deposition, spray atomization and codeposition and powder metallurgy techniques (Gao and Wang, 2000). Amongst these various techniques, the most economical and attractive processing route is offered by solidification processing. The process involves the addition of reinforcing particle phase to molten metal or alloy and mixing them uniformly, followed by application of suitable differential forces to cause segregation of particles required for the desired gradient in the particle concentration for a given application. The preservation of the spatially graded distribution through solidification is the final step. Chapter-I of the thesis provides the general context of the present investigation. The detailed literature review given in chapter-2, indicates that although the processing of FGMs in the laboratory scale has reached considerable level of maturity, there is still a need for developing a reliable, reproducible and cost effective manufacturing process for the bulk production of the FGMs. The literature available on modelling the properties of Particle Reinforced Metal Matrix Composites (PMMCs) and Functionally Graded Materials (FGMs) has instances of application of a number of mathematical and finite element models for estimating the properties of PMMCs and FGMs, but there is need to proceed further in view of certain deficiencies. iii The simplest models available for the elastic properties of composites are rules of mixture, Halpin-Tsai equations,1-lashim Shtrikman bounds etc. These models estimate the upper and lower bounds for the modulus of elasticity, modulus of rigidity and Poisson's ratio. The Finite Element Method (FEM) models available for estimating the elastic properties are mostly based on the unit cell. In the unit cell models the composite is modelled as a unit cell or periodic array of identical unit cells, each containing a reinforcement particle dimensioned to represent the overall reinforcement volume fraction. In practice however particulate reinforced metal matrix composites have highly heterogeneous microstructures. Porosity is one of the most important parameter affecting the deformation behaviour of composites. The formation of porosity and its effect on the mechanical properties of PMMCs have been the subject of several experimental studies. It is generally accepted that tensile properties decrease with increasing porosity content. However, the effect of parameters such as shape, size and distribution of porosity on mechanical properties of a composite is still not well understood. Although the properties of FGMs are being investigated experimentally as well as by the modelling techniques, the estimation of local as well as global properties of FGMs is still a challenge. A reliable estimation of elastic as well as nonlinear properties of FGMs is important to make these.materials acceptable for industrial use. FGMs have also, been ~:w modelled in the past using the unit cell models like those developed for uniform composites. The current modelling strategies often do not explicitly couple the heterogeneous microstructure with the structural global analysis. FGMs were originally conceived for super heat resistant applications involving severe thermo-mechanical loading, such as the outer wall and the engine parts of the future spacecrafts. Conventional super heat resistant materials, such as those found in the exterior of space shuttles, consist of heat resistant ceramic tiles bonded to metal structures. In view of this it is felt that a model which is capable of estimating thermal stress distribution inside the FGM should also be investigated. In the context of the gaps in literature review, the present study has been formulated with the following objectives: 1. To develop a simple and practical modelling technique capable of describing the heterogeneous microstructure of PMMCs more faithfully with flexibility to distribute a given volume fraction of the particles of different shapes and sizes, randomly in the matrix and estimate the elastic as well as nonlinear iv deformation behaviour on the basis of the behaviour of the constituent materials. 2. To incorporate in the model the effect of volume fraction of porosity and also, their shapes, sizes and orientations relative to the direction of loading for a given volume fraction and study their effect on the mechanical properties. 3. To study through the same model the deformation behaviour, both local and global, of gradient materials and uniform composites by distributing the particles with some desired gradation in volume fraction or uniformly so that the properties as determined through the same model could be compared between different types of particle distribution. 4. To estimate and study the temperature distribution and thermal stresses as encountered in certain applications under thermo-mechanical loading. 5. To develop FGM based on Al-A1203 by centrifugal casting technique and determine the particle distribution in order to model this composite and compare the hardness behaviour with the local yield stress in order to judge the capability of the model to predict deformation behaviour of .real life composites. Chapter-3 describes the experimental work on fabrication of set-up for centrifugal casting and synthesis of gradient materials from aluminium based composite containing alumina particles with the assistance of differential of centrifugal force field operating on particles and the surrounding molten metal. In the present work, solid cylindrical ingots of FGMs have been cast in a rotating mold solidifying the.melt-particle slurry. FGM ingots with different alumina mass percentages have been synthesized and their transverse and horizontal sections have been prepared for metallographic studies to study the distribution of particles under optical and scanning electron microscope. Hardness measurements have been conducted on the FGM samples using Vickers hardness testing machine to characterize local mechanical properties. Aluminium alloy is selected for use as the matrix materials due to its (a) low density, (b) low melting point, (c) reasonably high thermal conductivity, (d) good processing flexibility, (e) easy availability, (f) low cost, (g) high toughness and (h) good malleability. Alumina is selected as reinforcement material due to high thermal and wear resistance, chemical inertness, high hardness and availability at reasonable price. v Chapter-4 describes modelling of M.MCs by finite element method as followed in this study. First the metal matrix composite with uniformly distributed particles has been modelled by two dimensional Finite Element Method (FEM) using FEM too] ANSYS 5.4. Iit the present modelling effort, plane stress condition is assumed. For the modelling of MMCs with uniform random distribution of particles, a square area consisting of 10000 elements (plane42, four-node) having the same size as that of particle (average particle size) is considered. Out of these 10000 elements, 10000 *Vf (Vf is the average particle volume fraction) elements are randomly selected with the help of a FORTRAN programme in such a way that these elements are uniformly distributed over the whole matrix. These elements are assigned the properties corresponding to the reinforcement. Remaining elements are assigned the properties of the matrix .material. One of the most important features of the present modelling technique is the random distribution of the particles in the matrix. Randomness in the distribution of particles produces a near realistic distribution of the particles in the matrix. The effect of randomness on the material properties has also been established in the present study. It has been found that the random distribution of particles has negligible effect on the mechanical properties on the global scale, although it may affect the local behaviour of the composites. The properties of the uniform composites with different particle volume fractions and with different shapes and sizes of particles have been investigated. The present'iiodel is used to estimate the elastic properties of particle reinforced metal matrix composites with uniformly distributed particles for different average particle contents. The results from the present model for elastic behaviour are verified with the existing results for elastic properties of composites for the same average particle volume fractions. The present model has also been used to estimate the nonlinear behaviour of the particle reinforced metal matrix composites. with uniform random distribution of particles. The results from the present model for the nonlinear behaviour have also been compared with the results of existing models for uniform composites with different average particle contents. The present work is concerned with uniaxial stress-strain behaviour of the composites with elastically deforming particles reinforced in ductile matrix. The stress-strain behaviour of the matrix is characterized by elastic-perfectly plastic behaviour. In the present work the same model which has been used to estimate the elastic as well as non linear behaviour of uniform composites is further modified to make it suitable vi for FGMs. In the case of model for uniform composite the element size particles are uniformly and randomly distributed over the whole matrix. In the case of FGMs the particle distribution is still random locally but follows a prescribed distribution so as to mimic the FGM. This has been achieved with the help of a FORTRAN program which generates the required variation in the particle concentration over the matrix. Elastic as well as nonlinear behaviour of FGM models with variation of particle volume fraction from one end to the other for different average particle contents have been investigated in the present work. FGMs having different average particle contents and tailored variation in particle concentration in one direction have been investigated. The response of FGM models with variation in particle concentration in both the directions has also been investigated. Polynomial and linear distributions are used for modelling the variation in particle concentration in the FGM models. The local variation in the FGM properties has also been investigated with the help of the present model. FGM models with constant average particle content and with different types of variations in particle concentration have also been investigated. It has been found that during the manufacturing of particle reinforced metal matrix composites (PMMCs) using the processing route, such as melt-stirring or powder metallurgy, some defects occur in the resulting material. These defects lower quality and the performance characteristics of the composites. One of the most important defects is the porosity which affects the mechanical properties of the composites adversely. The presence of porosity within a component leads to the reduction in the load bearing area of the material as well as inhomogeneity is stress distribution and hence is observed to reduce both Young's modulus and strength. It is generally accepted that tensile properties decrease with increasing porosity content. However, the effect of parameters, such as shape, size, distribution and volume fraction of porosity on the mechanical properties and fracture behaviour is not yet well understood. In the present work, the present modelling technique has also been used to create pores with different shapes and sizes, uniformly distributed with random distribution in the whole matrix. Uniform composite models as well as FGM models with different average porosity contents and different average particle contents have been investigated for elastic as well as nonlinear behaviour. The effects of pore size on the elastic as well as nonlinear behaviour have also been studied. The results of the present model are compared with the existing models and experimental results. vii In gradient materials based on composites containing metal and' ceramics, the difference in thermal expansion coefficients between the constituents causes steep change in thermal stresses at the contact surface. It is necessary to examine whether the thermal stresses generated may cause the ceramic to de-bond and peel off or crack from the metal as it happens in case of ceramic tiles attached on the surface of metal shell. It has been claimed that FGMs should reduce such thermal stresses and resist super high temperatures but it is necessary to develop modelling techniques to determine the thenno-mechanical stresses due to thermal or/and mechanical loads. The objective is to find out a continuous material distribution which minimizes the thermal stresses under the required conditions. The present model may also be used to determine the thermal stresses in metal matrix composites when subjected to temperature gradients. The distribution of thermal stresses in uniform composite models, layered composites and functionally graded material models as estimated through the model described above, have been compared. The results and discussion are given in two chapters, 5 and 6. Chapter-5 describes the results on fabrication of gradient composites and characterization of their local mechanical behaviour through measurement of hardness. Al-A1203 based FGM ingots with average weight percentage of alumina particles of 10%, 20% and 30% have : been successfully synthesized by using centrifugal casting method. Alumina content decreases gradually in the radial direction from the centre towards the outer radius of the circular section of the cast ingots at any height below the shrinkage cavity. Alumina content also decreases gradually in the axial direction from the top to the bottom of the cast ingots. The decrease in alumina content from the centre towards the outer wall is not in agreement with the theory that the higher centrifugal force acting on relatively denser alumina particles during rotation will force them relatively towards the outer wall because of higher density, leaving behind the relatively lighter aluminium melt. The decreasing alumina content from the top to the bottom of cast ingots is also surprising in view of higher density of alumina particles relative to the melt. The fact that a larger amount of alumina particles is observed at higher heights from the bottom and towards the inner side along the radius is due to the flotation of the bubble-particle combine due to their lower combined density. Clusters of particles are not commonly observed in the cast FGM ingots synthesized in this study, as evident, from optical micrographs. It is possible that centrifugal force acting on the bubble-particle viii combinations has helped to keep these combined entities separate from each other on the basis of their density. However, the centrifugal force at the rotational speed used does not appear adequate to detach particles from bubbles. Vickers hardness distribution of the cast ingot follows the particle distribution but there are sometimes some abrupt changes locally in the hardness distribution, which has been attributed to inhomogeneous cast structure of the matrix in cast FGM ingots. Annealing of the cast FGM ingots results in the elimination of inhomogeneous cast structure and the radial hardness distributions become relatively smooth in FGM ingots. In Chapter-6, the results of 2-D FEM model on the mechanical properties of particle reinforced composites are given. The model is based on the random distribution of particles, which produces a realistic distribution. Uniform composite models with randomly distributed particles containing particle vol% from 10% to 90% in a step of 10% are obtained. The effect of random distribution of particles on the modulus of elasticity for uniform composite has been investigated through this model with a domain size of 5 mm x 5 mm. It has been concluded that though there may be . variation in material properties at the micro level due to random distribution of particles, the properties at the global level remain unchanged for a given average particle volume fraction for uniform distribution of particles. It is also concluded the use of a domain size of 5 mm x 5 mm is adequate. For composite samples of the size taken in the present study or bigger, random distribution of particles produces the same macroscopic properties irrespective of the local variation in particle positions in different composite models due to the random distribution of particles. The results for modulus of elasticity of the present modelling technique for uniform composite are compared with the well established rule of mixture (ROM) and inverse rule of mixture (IROM). ROM and IROM may be assumed as the most conservative upper and lower bounds for the modulus of elasticity of uniform composite. It was observed that the results of the present modelling technique are well within the bounds given by the rule of mixture and the inverse rule of mixture. The results predicted by the present model for modulus of elasticity are also compared with the well known Hashim-Shtrikman (1963) bounds. The results from the present modelling technique are found to be well within the Hashim-Shtrikman bounds. The present model results for modulus of elasticity are also compared with those given by Halpin—Tsai (1968) equation. It has been concluded that the present model results are in good agreement with the ix Halpin-Tsai equation with the parameter ( = 2. From the results of the present modelling technique a simple equation for estimating modulus of elasticity has been suggested. The results for modulus of rigidity for the uniform composites with different average particle contents have also been obtained through the model. It has been concluded that the results for the modulus of rigidity with the present modelling technique are well within the bounds of rule of mixture and inverse rule of mixture and also within the bounds given by Hashim-Shtrikman (1963). Non linear analysis has been carried out with the present model to predict nonlinear behaviour of the uniform composites with different average particle contents. It has been concluded that the strain required for a composite to undergo transition from elastic to plastic behaviour decreases as the level of reinforcement increases, These results are similar to those obtained by Bao and coworkers (1991) with their unit cell model. Yield stress is estimated for different average particle contents by the crossover method. An empirical relation showing the dependence of yield stress on the particle content has been obtained from the results of the model by curve fitting. The relation between the particle content and the ratio of flow stress of a composite (o) to that of the matrix (cro ) has been obtained under the plane strain conditions for different shapes and orientation of particles by Bao and coworkers (1991) for their unit cell model. It is observed that for lower particle contents their results compare quite well with those obtained in the present study. For higher particle contents, the result of the present model gives higher value for the flow stress ratio. The present model may have resulted into clustering of the particles at higher particle contents and contributed to the difference in results with unit cell model. The clustering of the particles causes a rapid increase in flow stress ratio of the composites at higher particle content. The effect of the shape of the particles on the uniform composite has also been investigated. It is concluded that the shape of the particles affect both the modulus of elasticity and yield stress and the particles elongated in the direction of loading results in higher modulus of elasticity and yield strength. Numerical results have been obtained for the variation of modulus of elasticity of uniform composites with increasing particle vol% from 0 to 100, with three different porosity contents of 2.5, 5.0 and 7.5 vol%. It is concluded that porosity lowers the Young's modulus of the composites. The results of the present model for modulus of elasticity have been compared with Sprigg's equation. Nonlinear analysis has also been carried out to predict the effect of porosity on the yield strength using four different types x of pores represented by 1*1, 1*4, 2*2 and 4*], The notation m*n represents the pore introduced by the removal of m x n elements where m represents the length of m grid elements along the direction perpendicular to that of loading (x-axis) and n represents the length of n grid elements in the direction of loading (y-axis). These results indicate that for 7.5 vol% of porosity, the yield strength of a composite containing 30 vol% of particle decreases from 77 MPa to 47.8 MPa when the pore type changes from 1 *4 to 4*], which are the least and most damaging pore types considered in the present work. Thus, there could be 38% reduction in the yield strength depending on the shape, size and orientation of pores for the same porosity content. Similarly, for the elastic modulus, there is 33% reduction when the pore type changes from 1 *4 to 4 *1 for 7.5 vol% of porosity. These results also show that for the same porosity type (type 1 *4) the reduction in the modulus of elasticity is only 5.3% when the porosity content increases from 2.5 to 5 vol%. Also the results for yield strength show that there is only 9% reduction in the yield stress for the same porosity type (type 1 *4) when the porosity content increases from 2.5 to 5 vol%. These results clearly indicate the dominance of the porosity type on the mechanical properties of the composites. Thus, the average porosity content is not a reliable parameter to predict the mechanical properties as the shape and orientation of pores are also important in determining the damage. The existence of large pores perpendicular to the loading direction is more damaging than the overall porosity content. It has been observed that the ratio of yield stresses with and without porosity decreases with the level of reinforcement. The results of the present model for the effect of porosity on the mechanical properties have been compared with those given by Tekmen and coworkers (2003) and Ghosh (1986). The results of the present model are found to be well in agreement with these experimental results. FGM models with variation of particle concentration in the direction of x-axis from 0 vol% at one end and 100 vol% at the other end following a polynomial distribution have been investigated. It has been observed that the global average values of modulus of elasticity in the gradation direction (x-axis direction) are lower than that in the uniform composite for the same average particle content. While in the perpendicular direction (y-axis) these values are higher than that in the corresponding uniform composite. FGM models with gradation in both x-axis and y-axis directions have also been studied. It has been observed that the global average values of modulus of elasticity for the FGM models with gradation in both directions are almost equal to that obtained for uniform composites with the same average particle vol%. Nonlinear analysis has been performed on FGM models with gradation in x-direction. In the y-direction FGM models exhibit better yield properties in comparison to those in uniform composite with the same average particle contents. It is observed that in the x-direction FGM models show the same yield stress as that of the matrix up to almost 70 vol% of particle content. In the x-direction the modulus of elasticity of the FGM models is also lower than that of the uniform composites for the same average particle contents. Variation in local values of modulus of elasticity has also been obtained for the FGM models for different amount of average particle contents. It is found that the variation in modulus of elasticity within the model follows closely the variation in particle concentration. FGM models with average particle content of 30 vol% but following different types of polynomial and linear gradation have also been investigated. Thermal analysis has also been performed in the present study. Three different types of materials combinations are considered in the present analysis. In the first case a layered composite plate of alumina and aluminium is considered. In the second. case a uniform composite with particle content of 30 vol% has been studied. In the third, case, FGM model with variation in particle concentration from 0 vol% at one end to 100 vol% at the other end and with 30 vol% average particle content has been considered. It is concluded that in the case of uniform composite and FGM, there is smooth change in the temperature and thermal stresses. In the case of layered composite there is steep change in the thermal stresses at the metal ceramic interface. FGM with 100 vol% ceramic at one side may, thus, be used for high temperature applications to smoothen the thermal stress distribution. The FGM samples synthesized experimentally in the present study have also been modelled in the present study. The results for modulus of elasticity and yield stress have' been obtained at different layers below the shrinkage cavity perpendicular and along the gradation direction. In the cast composites particles are generally associated with porosity. Higher particle concentration is associated with higher porosity. The effect of the gradation of porosity on the FGM samples has also been investigated. It is observed that the linear variation in porosity does not affect the properties of FGMs significantly. The hardness distributions at different height have been compared with the local yield stresses determined from the model. Chapter-7 outlines the conclusions drawn from the present i