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<p>Functionally graded materials offer a way of obtaining materials with superior properties. Decarburization has been used in other steels to create graded materials. These materials offer high strength and improved ductility when compared homogeneous materials of the same type. In this thesis, graded martensitic stainless steel was explored as a way to provide a very high strength material with medium ductility by partially decarburizing the materials. Different processing treatments were tried and the resulting materials characterized and mechanically tested to compare homogeneous and graded martensitic stainless steels. Mechanical testing demonstrated that decarburization has a positive effect on the tensile, rolling and Charpy impact properties. A model was also developed that attempted to capture the deformation behaviour of graded materials. Present data was not available to verify the models validity but the model was used to predict trends of a how different gradients affect fracture stresses and strains. These trends were used in an attempt to find optimum carbon distributions and maximize strength or ductility, as examples.</p> / Master of Materials Science and Engineering (MMatSE)

Yes / In recent times, the subject of effective cooling have become an interesting research topic for electronic and mechanical engineers due to the increased miniaturization trend in modern electronic systems. However, fins are useful for cooling various low and high power electronic systems. For improved thermal management of electronic systems, porous fins of functionally graded materials (FGM) have been identified as a viable candidate to enhance cooling. The present study presents an analysis of a convective–radiative porous fin of FGM. For theoretical investigations, the thermal property of the functionally graded material is assumed to follow linear and power-law functions. In this study, we investigated the effects of inhomogeneity index of FGM, convective and radiative variables on the thermal performance of the porous heatsink. The results of the present study show that an increase in the inhomogeneity index of FGM, convective and radiative parameter improves fin efficiency. Moreover, the rate of heat transfer in longitudinal FGM fin increases as b increases. The temperature prediction using the Adomian decomposition method is in excellent agreement with other analytical and method.

Functionally graded materials (FGMs) are an advanced class of material which seeks to leverage the strengths of one material to mitigate the weaknesses of another. This allows for operation in extreme environments or conditions where materials properties must change at various locations within a structure. Fabrication of this advanced class of material is limited due to geometric, economic, and material constraints inherent in the various methods. For this reason, a model was developed to discretize continuous gradient curves to allow for the use of a step-wise approximations to such gradients. These alternative step-wise gradients would allow for the use of numerous manufacturing techniques which have improved composition control, cost of processing, cost of equipment, and equipment availability. One such technique, tape casting, was explored due to its robustness and ability to create layered ceramics. Since ceramics are inherently brittle materials, they serve to be strengthened by the thermal residual stresses that form in the creation of these step-wise graded composites. With models to calculate these residual stresses and determine step-wise approximations of various compositional gradients, the process of designing these layered ceramics can be significantly improved.

Functionally graded materials (FGMs) are composites with continuous material property variations. The distinct interfaces between the reinforcement and the matrix in classical composites are potential damage initiation sites. The concept of FGM aims at avoiding the material mismatch at the interfaces. Functionally graded materials originated from the need for a material that has high-toughness at very high operating temperatures that occur in rocket nozzles and aeroplane engines. One of the early applications of graded materials can be thus found in thermal barrier coatings of gas turbine blades. Recent applications of FGMs include optoelectronics, ballistic impact resistance structures, wear resistant coatings and others. Although the manufacturing and applications of FGMs are well developed the basic mechanics of failure is not well understood, which is important in developing engineering design methodologies. Modern day design practice uses the concepts of fracture mechanics and the fracture properties of graded materials is not well understood. Most studies in the literature have assumed that the material response of the bulk functionally graded material to be elastic even though the constituents are nominally ductile. Some asymptotic analysis available in the literature have described the effect of ductility on the fracture parameters. However, these analysis are not complete in the sense that they have some undetermined constants. The present thesis aims at performing whole-field finite element (FE) simulations of a crack embedded in a ductile functionally graded material subjected to an anti-plane shear (mode-3) loading. A J2-deformation theory based power-law hardening nonlinear material response is assumed. The material property variation is assumed to be in the radial-direction (r-FGM), tangential to the crack (x-FGM), normal to the crack plane (y-FGM) and also at an arbitrary angle to the crack-plane (xy-FGM). Yet another power law described the material property variation. The competition between the indices of the hardening and material property variation is understood by performing a parametric analysis by varying both systematically. Our results indicate that the first most singular term of the asymptotic series remains unaffected. For some values of the material property variation index, the second asymptotic term is affected. The semi-closed form solutions available in the literature were unable to decipher the relative range of dominance of the first and second terms. From the present whole-field FEM analysis were able to extract this relative range of dominance. Our results indicate the range of dominance of the first term is least for FGMs when the material property variation is in the direction to the crack (x-FGM), and it is more for y-FGM.

Functionally graded materials (FGMs) are composites that have continuously varying material properties, which eliminate undesirable stress concentrations that might otherwise occur in layered composites. The concept of inhomogeneously varying properties is observed in nature; examples include bones, teeth, shells and timber. Modern engineering applications of FGMs include thermal barrier coatings, wear-resistant coatings, biomedical implants and MEMS devices. Syntactic foams, particle filled nano-composites are examples of inhomogeneous materials of current interest. Analyses and experiments available in the literature have focused on characterizing the inhomogeneous material modulus and density variations. Common techniques employed are nano-indentation and wave propagation studies. There are a few fracture mechanics analyses and experiments available in the literature; most of which are devoted to measuring the fracture toughness of graded materials. A few fracture analyses of graded materials are devoted to deriving asymptotic stress, strain and displacement fields around stationary and steadily growing cracks in inhomogeneous materials. Only a few studies exist that deal with understanding the effect of material property inhomogeneity on the spontaneous crack propagation. In the present thesis the effect of material property inhomogeneity on the dynamic fracture mechanics of cracks in FGMs is described. Numerical analysis of the elastodynamic initial boundary value problem is performed using a spectral scheme. Spectral scheme is a special numerical technique developed to simulate spontaneous, planar crack propagation in a variety of materials. The method is numerically efficient as it can be implemented on parallel machines with ease. The numerical scheme is versatile and can handle any state-and rate-dependent traction-separation laws (cohesive zone models) or frictional laws. Spectral scheme has successfully been used in simulating intersonic crack propagation, earthquake slip dynamics and also direct silicon wafer bonding process used in realizing 3D MEMS structures. In the present work, the spectral formulation accounts for the inhomogeneous variation in the material wave speeds in the medium. The effect of inhomogeneity on spontaneous crack propagation due to in-plane mixed-mode loading is also addressed here. A parametric study has been performed by varying the inhomogeneity length scales independently in the top and bottom half-spaces. The effect of inhomogeneity in shear wave speed on the dynamic stress intensity factors (SIFs) of a crack propagating in a quasi-steady-state along the interface between the two functionally graded half-spaces is studied. A symmetric hardening FGM offers the maximum fracture resistance, while the fracture resistance is minimum for a symmetric softening FGM. Our simulation shows that increasing the inhomogeneity in the wave speed leads to eliminate the overshoot in the dynamic stress intensity factor. The magnitude of the steady-state (long-time) SIF increases indicating an increase in the fracture resistance. The effect of the inhomogeneous wave speed on the mode-3 crack propagation characteristics is demonstrated by taking snapshots of the crack opening at a time interval. The magnitude of the crack sliding displacement is found to increase with increase in the inhomogeneity. The effect of the material property inhomogeneity on the mode-1 crack propagation is simulated to track the crack opening displacements. The inhomogeneity is assumed to be symmetric about the weak-plane. Our spectral scheme developed here for functionally graded material with exponential variation in the material properties is capable of simulating independent bimaterial combinations. When the graded material becomes progressively stiffer and denser (hardening), the crack opening displacement in reduced, indicating an increase in the fracture resistance. On the other hand, for the softening FGMs the crack opening displacement increases indicating a reduction in fracture toughness. It is noted that the cohesive fracture resistance on the weak-plane remains same in all the FGMs.

Functionally graded materials (FGMs) are inhomogeneous materials in which the material properties vary with respect to space. Research has been done by scientific community in developing techniques like photothermal radiometry (PTR) to measure the thermal conductivity and volumetric heat capacity of FGMs. One of the problems involved in the technique is to solve the inverse problem, i.e., estimating the thermal properties after the frequency scan has been obtained. The present work involves finding the unknown thermal conductivity and volumetric heat capacity of the FGMs by using finite volume method. By taking the flux entering the sample as periodic and solving the discretized 1-D thermal wave field equation at a frequency domain, one can obtain the complex temperatures at the surface of the sample for each frequency. These complex temperatures when solved for a range of frequencies gives the phase vs frequency scan which can then be compared to original frequency scan obtained from the PTR experiment by using a residual function. Brute force and gradient descent optimization methods have been implemented to estimate the unknown thermal conductivity and volumetric specific heat of the FGMs through minimization of the residual function. In general, the spatial composition profile of the FGMs can be approximated by using a smooth curve. Three functional forms namely Arctangent curve, Hermite curve, and Bezier curve are used in approximating the thermal conductivity and volumetric heat capacity distributions in the FGMs. The use of Hermite and Bezier curves gives the flexibility to control the slope of the curve i.e. the thermal property distribution along the thickness of the sample. Two-layered samples with constant thermal properties and three layered samples in which one of the layer has varying thermal properties with respect to thickness are considered. The program is written in Fortran and several test runs are performed. Results obtained are close to the original thermal property values with some deviation based on the stopping criteria used in the gradient descent algorithm. Calculating the gradients at each iteration takes considerable amount of time and if these gradient values are already available, the problem can be solved at a faster rate. One of the methods is extending automatic differentiation to complex numbers and calculating the gradient values ahead; this is left for future work.

Functionally low-literate consumers may often struggle to complete everyday adult tasks, such as reading food labels. Food labels are an important source of information for consumers, and assist them to make informed and wise food purchase decisions. However, the manner in which functionally low-literate consumers read, understand and apply this information to their decisionmaking, is different to literate consumers, and minimal research has been conducted regarding functionally low-literate consumers and their use of food labels in South Africa. This study was conducted in a predominantly low-literate and low-income rural area of Valspan, South Africa. Therefore, using food labels to make healthy and financially sound food choices may be considered especially important for this group of consumers. The current study served to conduct an in-depth literature review of functionally low-literate consumers‟ use of food labels in a rural area; explore whether and how functionally low-literate consumers use (read, understand and apply to decision-making) food label information; explore and describe the differences between the demographic characteristics of low-literate consumers and their use (reading, understanding and application) of food labels; make recommendations to educators on how functionally low-literate consumers can improve their use of food labels in a rural area; as well as to make recommendations on how food labels can be adapted to be more user-friendly to functionally low-literate consumers. Data was collected, using 292 interviewer administrated questionnaires, using purposive criterion sampling. The inclusion criteria for respondents were that they: had to be older than 18 years, living in Valspan and must have completed between grades 5 and 8 at school. Data analysis was done, using descriptive statistics, T-tests, ANOVA‟s, Spearman‟s rank order correlations and two-way frequency tables. Effect sizes were taken into consideration for all differences and associations. The results showed that respondents in this study did read food labels. They were also able to understand some simple aspects of the food label, but struggled with other aspects. When respondents struggled to understand food labels, they were selective about who they would ask to assist them, favouring the help of familiar family members and friends. Regarding the respondents‟ ability to apply food label information to their decision-making, respondents were able to identify several store logos, probably due to their tendency to pictorial thinking. Food-related calculations were relatively well completed; however, certain calculation-related terminology was not well understood by respondents. Food label symbols were not well identified, indicating that respondents did not have a good understanding of the meaning of these symbols. Literacy is vital to the use of food labels, as respondents who showed higher literacy levels showed a tendency towards better understanding of food label information, food label symbols and store logos. They also tended to be better equipped to correctly execute product-related calculations. Regarding demographics, respondents who spoke English and Afrikaans and who had a higher income had a tendency to better understand food label information, than respondents who spoke other languages and belonged to lower-income groups. If food labels are adapted, so that even lowliterate consumers are able to efficiently use food labels, they will be able to make informed and wise food product choices. This situation would be beneficial to low-literate and low-income consumers, marketers and retailers, as products with usable labels may consequently become the preferred choice of low-literate consumers and money wary low-income consumers. Additionally, marketers and retailers would be able to capitalise on the mass purchasing power that this target market represents. / M. Consumer Science, North-West University, Potchefstroom Campus, 2014

Functionally low-literate consumers may often struggle to complete everyday adult tasks, such as reading food labels. Food labels are an important source of information for consumers, and assist them to make informed and wise food purchase decisions. However, the manner in which functionally low-literate consumers read, understand and apply this information to their decisionmaking, is different to literate consumers, and minimal research has been conducted regarding functionally low-literate consumers and their use of food labels in South Africa. This study was conducted in a predominantly low-literate and low-income rural area of Valspan, South Africa. Therefore, using food labels to make healthy and financially sound food choices may be considered especially important for this group of consumers. The current study served to conduct an in-depth literature review of functionally low-literate consumers‟ use of food labels in a rural area; explore whether and how functionally low-literate consumers use (read, understand and apply to decision-making) food label information; explore and describe the differences between the demographic characteristics of low-literate consumers and their use (reading, understanding and application) of food labels; make recommendations to educators on how functionally low-literate consumers can improve their use of food labels in a rural area; as well as to make recommendations on how food labels can be adapted to be more user-friendly to functionally low-literate consumers. Data was collected, using 292 interviewer administrated questionnaires, using purposive criterion sampling. The inclusion criteria for respondents were that they: had to be older than 18 years, living in Valspan and must have completed between grades 5 and 8 at school. Data analysis was done, using descriptive statistics, T-tests, ANOVA‟s, Spearman‟s rank order correlations and two-way frequency tables. Effect sizes were taken into consideration for all differences and associations. The results showed that respondents in this study did read food labels. They were also able to understand some simple aspects of the food label, but struggled with other aspects. When respondents struggled to understand food labels, they were selective about who they would ask to assist them, favouring the help of familiar family members and friends. Regarding the respondents‟ ability to apply food label information to their decision-making, respondents were able to identify several store logos, probably due to their tendency to pictorial thinking. Food-related calculations were relatively well completed; however, certain calculation-related terminology was not well understood by respondents. Food label symbols were not well identified, indicating that respondents did not have a good understanding of the meaning of these symbols. Literacy is vital to the use of food labels, as respondents who showed higher literacy levels showed a tendency towards better understanding of food label information, food label symbols and store logos. They also tended to be better equipped to correctly execute product-related calculations. Regarding demographics, respondents who spoke English and Afrikaans and who had a higher income had a tendency to better understand food label information, than respondents who spoke other languages and belonged to lower-income groups. If food labels are adapted, so that even lowliterate consumers are able to efficiently use food labels, they will be able to make informed and wise food product choices. This situation would be beneficial to low-literate and low-income consumers, marketers and retailers, as products with usable labels may consequently become the preferred choice of low-literate consumers and money wary low-income consumers. Additionally, marketers and retailers would be able to capitalise on the mass purchasing power that this target market represents. / M. Consumer Science, North-West University, Potchefstroom Campus, 2014

Este trabalho apresenta a aplicação do Método de Otimização Topológica (MOT) considerando restrição de tensão mecânica em dois problemas de Engenharia: o projeto de estruturas mecânicas sujeitas a restrição de tensão e o projeto da distribuição de material em estruturas constituídas por Materiais com Gradação Funcional (MsGF). O MOT é um método numérico capaz de fornecer de forma automática o leiaute básico de uma estrutura mecânica para que esta atenda a um dado requisito de projeto, como o limite sobre a máxima tensão mecânica no componente. Os MsGF são materiais cujas propriedades variam gradualmente com a posição. Este gradiente de propriedades é obtido através da variação contínua da microestrutura formada por dois materiais diferentes. Neste trabalho o MOT foi implementado utilizando o modelo de material Solid Isotropic Microstructure with Penalization (SIMP) e o campo de densidades foi parametrizado utilizando a abordagem Aproximação Contínua da Distribuição de Material (ACDM). O modelo de material e utilizado em conjunto com um localizador de tensões, de modo a representar as tensões nas regiões com densidade intermediária. O projeto de estruturas tradicionais através do MOT possui dois problemas centrais aqui tratados: o fenômeno das topologias singulares, que consiste na incapacidade do algoritmo de otimização de retirar material de certas regiões da estrutura, onde a tensão mecânica supera o limite de tensão quando os valores da densidade tendem a zero, e o problema do grande número de restrições envolvidas, pois que a tensão mecânica é uma grandeza local e deve ser restrita em todos os pontos da estrutura. Para tratar o primeiro problema é utilizado o conceito de relaxação. Para o segundo são utilizadas duas abordagens: uma é a substituição das restrições locais por uma restrição global e a outra é a aplicação do Método do Lagrangeano Aumentado. Ambas foram implementadas e aplicadas para o projeto de estruturas planas e axissimétricas. No projeto da distribuição de material em estruturas constituídas por MsGF é utilizado um modelo de material baseado na interpolação dos limites de Hashin-Shtrikman. A partir deste modelo as tensões em cada fase são obtidas a partir das matrizes localizadoras de tensão. Para tratar o fenômeno das topologias singulares é proposto um índice estimativo de falha, baseado nas tensões de von Mises em cada fase da microestrutura, que evita tal problema. O grande número de restrições é tratado através da restrição global de tensão. Em ambos os problemas as formulações são apresentadas e sua eficiência é discutida através de exemplos numéricos. / This work presents the Topology Optimization Method (TOM) with stress constraint applied to two Engineering problems: the design of mechanical structures subjected to stress constraint and the design of material distribution in structures made of Functionally Graded Materials (FGMs). The TOM is a numerical method capable of synthesizing the basic layout of a mechanical structure accomplishing to a given design requirement, for example the maximum stress in the structure. The FGMs are materials with spatially varying properties, which are obtained through a continuum change of the microstructuremade of two different materials. In this work, the TOM was implemented with Solid Isotropic Microstructure with Penalization (SIMP) material model and the density field was parameterized with the Continuous Approximations of Material Distribution. To obtain the intermediate density stresses, the material model is applied together with a stress localization matrix. The design of mechanical structures through the TOM has two major problems: the singular topology phenomenon, which is characterized by the optimization algorithm impossibility of removing material from certain regions, where the stress overpasses the limiting stress when the density goes to zero, and the large number of constraints, once the stress is a local value that must be constrained everywhere in the structure. To deal with the first problem, it is applied the \"-realaxation concept, and for the second one two approaches are considered: one is to change the local stress constraint into a global stress constraint and the other is to apply the Augmented Lagrangian Method. Both approaches were implemented and applied to the design of plane and axisymmetric structures. In the design of material distribution in structures made of FGMs a material model based on Hashin-Shtrikman bounds is applied. From this model, stresses in each phase are obtained by the stress localization matrix. To deal with the singular topology phenomenon it is proposed a modified von Mises failure criteria index that avoids such problem. A global stress constraint is applied to deal with the large number of constraints. In both problems formulations are presented and their performance are discussed through numerical examples.