This study introduces a multiscale model for analyzing nonlinear thermo-viscoelastic responses of particulate composites. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermal and mechanical properties and time-dependent response of the composites. The particle and matrix constituents are made of isotropic homogeneous viscoelastic bodies undergoing small deformation gradients. Perfect bonds are assumed along the sub-cell⁰́₉s interfaces. The coupling between the thermal and mechanical response is attributed to the dissipation of energy due to the viscoelastic deformation and temperature dependent material parameters in the viscoelastic constitutive model. The micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the sub-cells. The effective mechanical properties and coefficient of thermal expansion are derived by satisfying displacement- and traction continuities at the interfaces during the thermo-viscoelastic deformations. The effective thermal conductivity is formulated by imposing heat flux- and temperature continuities at the subcells⁰́₉ interfaces. The expression of the effective specific heat at a constant stress is also established. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic materials is developed. The algorithm is then incorporated within each sub-cell of the micromechanical model together with the macroscopic energy equation to determine the effective coupled thermoviscoelastic response of the particulate composite. The numerical formulation is implemented within the ABAQUS, general purpose displacement based FE software, allowing for analyzing coupled heat conduction and deformations of composite structures. Experimental data on the effective thermal properties and time dependent responses of particulate composites available in the literature are used to verify the micromechanical model formulation. The multiscale model capability is also examined by comparing the field variables, i.e., temperature, displacement, stresses and strains, obtained from heterogeneous and homogeneous composite structures, during the transient heat conduction and deformations. Examples of coupled thermoviscoelastic analyses of particulate composites and functionally graded structures are also presented. The present micromechanical modeling approach is found to be computationally efficient and shows good agreement with experiments in predicting the effective thermo-mechanical response of particulate composites and functionally graded materials. Our analyses forecast a better design for creep resistant and less dissipative structures using particulate composites and functionally graded materials.

In some applications the stress across the entire cross-section of a component is not uniform but varies with position. For example, maximum shear stress is highest at the inner surface of a thick-walled cylinder subjected to uniform internal pressure and it decreases continuously towards the outer surface. In such applications it would be more appropriate for the component, too, to have varying strength across the cross-section matching with the stress profile it is subjected to. The present work deals with obtaining such a functionally graded material (FGM), characterizing it and testing its mechanical properties in compression. Differential aging heat treatment was used to produce the functionally graded material in a precipitation hardenable Al-4.6%Cu alloy by changing the microstructure. Temperature gradient furnace was used to achieve the gradation in microstructure from one end of the sample to the other end by differential aging of the solution treated sample. Mechanical properties can be varied in any precipitation hardenable alloy by means of producing various precipitates, which will form during the aging sequence. In Al-4.6%Cu alloy one end of the solution treated sample was aged for 38 hours at 170°C and the other end at 70°C by means of a temperature gradient furnace in which the coil density varies along the axis of the furnace. Thus we achieved a difference in mechanical properties from 70°C side to 170°C side as the precipitation during differential aging varied from GP zones at one end to θ' precipitate at the other end. Characterization was done on isothermally aged samples and in FGM using XRD (X-ray diffraction) and TEM (Transmission Electron Microscopy). XRD result showed that the final equilibrium precipitate θ was not formed in any of the heat-treated samples. TEM result showed the various precipitation sequences from GP zones to θ' in the isothermally aged samples and the same was confirmed in the gradient sample by cutting the samples form 70°C side towards the 170°C side and doing TEM on each sample. The properties of FGM in compression were studied using a 9mmx9mmxl8mm-compression sample using DARTEC machine and it was compared with those of isothermally aged samples. For 70°C the 0.2% proof stress was 141MPa and for 170°C it was 226MPa. The corresponding ductility values at the point of inflection on the engineering stress-strain curve for 70°C sample was higher (33%) than the 170°C (22%) sample. For the gradient sample it gave a proof stress of 163MPa and a ductility value of 30%.

Today, nonhomogeneous materials are used in many technological applications. Nonhomogeneity can be introduced intentionally in order to improve the thermomechanical performance of material systems. The concept of functionally graded materials (FGMs) is an example of such an application. Nonhomogeneity can also be an intrinsic property of some of the natural materials such as natural soil. The main interest in this study is on the contact mechanics of nonhomogeneous surfaces. There is an extensive volume of literature on the contact mechanics of nonhomogeneous materials. In most of these studies, the elastic gradation is assumed to exist in depth direction. But, it is known that elastic gradation may also exist laterally. This may either occur naturally as in the case of natural soil or may be induced as a result of the applied processing technique as in the case of FGMs. The main objective in this study is therefore to examine the effect of the lateral nonhomogeneities on the contact stress distribution at the surface of an elastically graded material. In the model developed to examine this problem, a laterally graded surface is assumed to be in sliding contact with a rigid stamp of arbitrary profile. The problem is formulated using the theory of elasticity and reduced to a singular integral equation. The integral equation is solved numerically using a collocation approach. By carrying out parametric studies, the effects of the nonhomogeneity constants, coefficient of friction and stamp location on the contact stress distribution and on the required contact forces are studied.

ABSTRACT CONTACT MECHANICS OF GRADED MATERIALS WITH TWODIMENSIONAL MATERIAL PROPERTY VARIATIONS G&ouml / kay, Kemal M.S., Department of Mechanical Engineering Supervisor: Asst. Prof. Dr. Serkan Dag September 2005, 62 pages Ceramic layers used as protective coatings in tribological applications are known to be prone to cracking and debonding due to their brittle nature. Recent experiments with functionally graded ceramics however show that these material systems are particularly useful in enhancing the resistance of a surface to tribological damage. This improved behavior is attributed to the influence of the material property gradation on the stress distribution that develops at the contacting surfaces. The main interest in the present study is in the contact mechanics of a functionally graded surface with a two &ndash / dimensional spatial variation in the modulus of elasticity. Poisson&rsquo / s ratio is assumed to be constant due to its insignificant effect on the contact stress distribution [30]. In the formulation of the problem it is assumed that the functionally graded surface is in frictional sliding contact with a rigid flat stamp. Using elasticity theory and semi-infinite plane approximation for the graded medium, the problem is reduced to a singular integral equation of the second kind. Integral equation is solved numerically by expanding the unknown contact stress distribution into a series of Jacobi polynomials and using suitable collocation points. The developed method is validated by providing comparisons to a closed form solution derived for homogeneous materials. Main numerical results consist of the effects of the material nonhomogeneity parameters, coefficient of friction and stamp size and location on the contact stress distribution.

In the last decade aluminium started to be considered as an alternative to steel to produce car body panels, especially considering the strict demands to decrease fuel consumption which require vehicle weight reduction. In order to keep their leading role, steel companies have to produce stronger materials to reduce the thickness of steel sheets used in cars and are now considering non-conventional steel making processes. The purpose of this PhD research was to investigate the possibility of strengthening thin sheets of interstitial free steel (IF steel) by using carbon rich films deposited on the steel surface using Physical Vapour Deposition (PVD). These films then act as a carbon reservoir which upon heat treatment release carbon in the IF steel and strengthen it. Coated tensile coupons 200 μm thick were annealed at different temperatures under high vacuum. Tensile tests show that a 100 MPa increase in yield stress can be obtained after annealing at 430 ˚C for 1h in high vacuum. The effects of annealing environment, film thickness and prestrain on carbon diffusion were also investigated. It was shown that carbon diffusion from the film to the IF steel substrate is limited by the film transformation into cementite at temperatures equal or higher than 530 ˚C. All tensile curves showed a plastic instability known as Lüders plateau, which is undesirable as it results in surface markings on the deformed part. FEM analyses were performed to find ways to suppress the Lüders plateau, proving that increasing strain-hardening or having a graded instead of uniform carbon content through thickness can suppress or limit Lüdering. The possibility of creating a through thickness gradient of microstructure was investigated as it could suppress Lüdering and result in higher strength. For these tests, FeC coated coupons were induction heated to 820 ˚C followed by water quenching. After only 2 minutes of heat treatment the yield stress was increased by 250 MPa and the ultimate tensile strength reached 400 MPa. With an annealing of 4 minutes, the Lüders plateau was fully suppressed and the microstructure consisted in ferrite grains and TiC nanocarbides. This work demonstrates that FeC films can be effectively used to diffuse carbon into steel and that a significant increase in mechanical properties can be obtained after a heat treatment of only a few minutes.

The challenges in the deposition of dissimilar materials are mainly related to the large differences in the physical and chemical properties of the deposited and substrate materials. These differences readily cause residual stresses and intermetallic phases. This has led to the development of functionally graded materials which exhibit spatial variation in composition. Laser direct metal deposition due to its flexibility, it offers wide variety of dissimilar and functionally graded materials deposition. Despite considerable advances in process optimization, there is a rather limited understanding of the role of metallurgical factors in the laser deposition of dissimilar and functionally graded alloys. The aim of this work is to understand and explain mechanisms occurring in diode laser deposition of dissimilar materials and functionally graded materials. The first part of this work addressed diode laser deposition of Inconel 718 nickel alloy to Ti-6Al-4V titanium alloy. Here, the effect of laser pulse parameters and powder mass flow rates on the stress formation and cracking has evaluated by experiment and numerical techniques. Results showed that the clad thickness was an important factor affecting the cracking behaviour. In the second part of this study, an image analysis technique has been developed to measure the surface disturbance and the melt pool cross section size during laser direct metal deposition of Inconel 718 on a Ti-6Al-4V thin wall. It was noted that under tested conditions the overall melt pool area increased with the increase in powder flow rate; the powder carrier gas flow rates also seemed to play important roles in determining the melt pool size. In the third part of this study, a parametric study on the development of Inconel 718 and Stainless steel 316L continuously graded structure has been carried out. Results suggested that microstructure and other mechanical properties can be selectively controlled across the deposited wall. The results presented in this dissertation can be used as a metallurgical basis for further development of dissimilar and functionally graded manufacturing using LDMD technique, guiding future manufacturing engineers to produce structurally sound and microstructurally desirable laser deposited samples.

abstract: Multi-material fabrication allows for the creation of individual parts composed of several materials with distinct properties, providing opportunities for integrating mechanisms into monolithic components. Components produced in this manner will have material boundaries which may be points of failure. However, the unique capabilities of multi-material fabrication allow for the use of graded material transitions at these boundaries to mitigate the impact of abrupt material property changes. The goal of this work is to identify methods of creating graded material transitions that can improve the ultimate tensile strength of a multi-material component while maintaining other model properties. Particular focus is given towards transitions that can be produced using low cost manufacturing equipment. This work presents a series of methods for creating graded material transitions which include previously established transition types as well as several novel techniques. Test samples of each transition type were produced using additive manufacturing and their performance was measured. It is shown that some types of transitions can increase the ultimate strength of a part, while others may introduce new stress concentrations that reduce performance. This work then presents a method for adjusting the elastic modulus of a component to which graded material transitions have been added to allow the original design properties to be met. / Dissertation/Thesis / Supplementary code from appendices / Masters Thesis Engineering 2020

Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering, e.g., stiffened floors, fuselage, railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their areas of applications and possibly make them lighter without sacrificing strength is to make them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. In this thesis, we study free vibrations of FGM circular beams by using a logarithmic shear deformation theory that incorporates through-the-thickness logarithmic variation of the circumferential displacement, and does not require a shear correction factor. The radial displacement of a point is assumed to depend only upon its angular position. Thus the beam theory can be regarded as a generalization of the Timoshenko beam theory. Equations governing transient deformations of the beam are derived by using Hamilton's principle. Assuming a time harmonic variation of the displacements, and by utilizing the generalized differential quadrature method (GDQM) the free vibration problem is reduced to solving an algebraic eigenvalue problem whose solution provides frequencies and the corresponding mode shapes. Results are presented for different spatial variations of the material properties, boundary conditions, and the aspect ratio. It is found that the radial and the circumferential gradation of material properties maintains their natural frequency within that of the homogeneous beam comprised of a constituent of the FGM beam. Furthermore, keeping every other variable fixed, the change in the beam opening angle results in very close frequencies of the first two modes of vibration, a phenomenon usually called mode transition. / Master of Science / Curved and straight beams of various cross-sections are one of the simplest and most fundamental structural elements that have been extensively studied because of their ubiquitous applications in civil, mechanical, biomedical and aerospace engineering. Many attempts have been made to enhance their material properties and designs for applications in harsh environments and reduce weight. One way of accomplishing this is to combine layerwise two or more distinct materials and take advantage of their directional properties. It results in a lightweight structure having overall specific strength superior to that of its constituents. Another possibility is to have volume fractions of two or more constituents gradually vary throughout the structure for enhancing its performance under anticipated applications. Functionally graded materials (FGMs) are a class of composites whose properties gradually vary along one or more space directions. In this thesis, we have numerically studied free vibrations of FGM circular beams to enhance their application domain and possibly use them for energy harvesting.

The focus of this dissertation is on the development of an additive manufacturing system and methodology for fabricating structures with functionally graded porous internal properties and complex three-dimensional external characteristics. For this purpose, a multi-scale three-dimensional printing system was developed, with capabilities and fabrication methodologies refined in the context of, but not limited to, manufacturing of porous bone substitutes. Porous bone implants are functionally graded structures, where internally, the design requires a gradient in porosity and mechanical properties matching the functional transition between cortical and cancellous bone regions. Geometrically, the three-dimensional shape of the design must adhere to the anatomical shape of the bone tissue being replaced. In this work, control over functionally graded porous properties was achieved by integrating specialized modules in a custom-made additive manufacturing system and studying their effect on fabricated constructs. Heterogeneous porous properties were controlled by: (i) using a micro-syringe deposition module capable of embedding sacrificial elements with a controlled feature size within the structure, (ii) controlling the amount of binder dispersed onto the powder substrate using a piezoelectric printhead, (iii) controlling the powder type or size in real-time, and/or (iv) selecting the print layer stacking orientation within the part. Characterization methods included differential scanning calorimetry (DSC)-thermo gravimetric analysis (TGA) to establish the thermal decomposition of sacrificial elements, X-ray diffraction (XRD) and dispersive X-ray spectroscopy (EDAX) to investigate the chemical composition and crystallinity, scanning electron microscopy (SEM) and optical microscopy to investigate the physical and structural properties, uniaxial mechanical loading to establish compressive strength characteristics, and porosity measurements to determine the bulk properties of the material. These studies showed that the developed system was successful in manufacturing embedded interconnected features in the range of 100-500 $ \mu m $, with a significant impact on structural properties resulting in bulk porosities in the range of 30-55% and compressive strength between 2-50 MPa. In this work, control over the the three-dimensional shape of the construct was established iteratively, by using a silhouette extraction image processing technique to determine the appropriate anisotropic compensation factors necessary to offset the effects of shrinkage in complex-shaped parts during thermal annealing. Overall shape deviations in the range of +/- 5-7 % were achieved in the second iteration for a femoral condyle implant in a sheep model. The newly developed multi-scale 3DP system and associated fabrication methodology was concluded to have great potential in manufacturing structures with functionally graded properties and complex shape characteristics.

Functionally graded materials processed by the thermal spray techniques such as electron beam physical vapor deposition and plasma spray forming are known to have an orthotropic structure with reduced mechanical properties. Debonding related failures in these types of material systems occur due to embedded cracks that are perpendicular to the direction of the material property gradation. These cracks are inherently under mixed-mode loading and fracture analysis requires the extraction of the modes I and II stress intensity factors. The present study aims at developing semi-analytical techniques to study embedded crack problems in graded orthotropic media under various boundary conditions. The cracks are assumed to be aligned parallel to one of the principal axes of orthotropy. The problems are formulated using the averaged constants of plane orthotropic elasticity and reduced to two coupled integral equations with Cauchy type dominant singularities. The equations are solved numerically by adopting an expansion - collocation technique. The main results of the analyses are the mixed mode stress intensity factors and the energy release rate as functions of the material nonhomogeneity and orthotropy parameters. The effects of the boundary conditions on the mentioned fracture parameters are also duly discussed.