Double-sided module exhibits electrical and thermal characteristics that are superior to wire-bonded counterpart. Such structure, however, induces more than twice the thermo-mechanical stress in a single-layer structure. Compressive posts have been developed and integrated into the double-sided module to reduce the stress to a level acceptable by silicon dice. For a 14 mm x 21 mm module carrying 6.6 mm x 6.6 mm die, finite-element simulation suggested an optimal design having four posts located 1 mm from the die; the z-direction stress at the chip was reduced from 17 MPa to 0.6 MPa. / Ph. D.

Miniaturizing circuit size and increasing power density are the latest trends in modern power electronics development. In order to meet the requirements of higher frequency and higher power density in power electronics applications, planar interconnections are utilized to achieve a higher integration level. Power switching devices, passive power components, and EMI (Electromagnetic Interference) filters can all be integrated into planar power modules by using planar metallization, which is a technology involving electrical, mechanical, material, and thermal issues. By processing high dielectric materials, magnetic materials, or silicon chips using compatible manufacturing procedures, and by carefully designing structures and interconnections, we can realize the conventional discrete inductors, capacitors, and switch circuits with planar modules. Compared with conventional discrete components, the integrated planar modules have several advantages including lower profiles, better form factors, and less labor-intensive processing steps. In addition, planar interconnections reduce the wire bond inductive and resistive parasitic parameters, especially for high frequency applications. However, planar integration technology is a packaging approach with a large contact area between different materials. This may result in unknown failure mechanisms in power applications. Extensive research has already been done to study the performance, processing, and reliability of the planar interconnects in thin film structures. The thickness of the thin films used in integrated circuits (IC) or microelectronics applications ranges from the magnitude of nanometers to that of micrometers. In this work, we are interested in adopting planar interconnections to Integrated Power Electronics Modules (IPEM). In Integrated Power Electronics Modules (IPEMs), copper traces, especially bus traces, need to conduct current ranging from a few amps to tens of amps. One of the major differences between IC and IPEM is that the metal layer in IPEMs (normally >75µm) is much thicker than that of the thin films in IC (normally <1µm). The other major difference, which is also a feature of IPEM, is that the planar metallization is deposited on different brittle substrates. In active IPEM, switching devices are in a bare die form with no encapsulation. The copper deposition is on top of the silicon chips and the insulation polyimide layer. One of the key elements for passive IPEM and the EMI IPEM is the integrated inductor-capacitor (LC) module, which realizes equivalent inductors and capacitors in one single module. The deposition processes for silicon substrates and ceramic substrates are compatible and both the silicon and ceramic materials are brittle. Under high current and high temperature conditions, these copper depositions on brittle materials will cause detrimental failure spots. Over the last few years, the design, manufacture, optimization, and testing of the IPEMs has been developed and well documented. Up to this time , the research on failure mechanisms of conventional integrated power modules has led to the understanding of failures centered on wire bond or solder layer. However, investigation on the reliability and failure modes of IPEM is lacking, particularly that which uses metallization on brittle substrates for high current operations. In this study, we conduct experiments to measure and calculate the residual stresses induced during the process. We also, theoretically model and simulate the thermo-mechanical stresses caused by the mismatch of thermal expansion coefficients between different materials in the integrated power modules. In order to verify the simulation results, the integrated power modules are manufactured and subjected to the lifetime tests, in which both power cycling and temperature cycling tests are carried out. The failure mode analysis indicates that there are different failure modes for copper films under tensile or compressive stresses. The failure detection process verifies that delamination and silicon cracks happen to copper films due to compressive and tensile stresses respectively. This study confirms that the high stresses between the metallization and the silicon are the failure drivers in integrated power electronics modules.. We also discuss the driving forces behind several different failure modes. Further understanding of thesefailure mechanisms enables the failure modes to be engineered for safer electrical operation of IPEM modules and helps to enhance the reliability of system-level operation. It is also the basis to improve the design and to optimize the process parameters so that IPEM modules can have a high resistance to recognized failures. / Ph. D.

With continued feature size reduction in microelectronics and with more than a billion transistors on a single integrated circuit (IC), on-chip interconnection has become a challenge in terms of processing-, electrical-, thermal-, and mechanical perspective. Today’s high-performance ICs have on-chip back-end-of-line (BEOL) layers that consist of copper traces and vias interspersed with low-k dielectric materials. These layers have thicknesses in the range of 100 nm near the transistors and 1000 nm away from the transistors close to the solder bumps. In such BEOL layered stacks, cracking and/or delamination is a common failure mode due to the low mechanical and adhesive strength of the dielectric materials as well as due to high thermally-induced stresses. However, there are no available cohesive zone models and parameters to study such interfacial cracks in sub-micron thick microelectronic layers. This work focuses on developing framework based on cohesive zone modeling approach to study interfacial delamination in sub-micron thick layers. Such a framework is then successfully applied to predict microelectronic device reliability. As intentionally creating pre-fabricated cracks in such interfaces is difficult, this work examines a combination of four-point bend and double-cantilever beam tests to create initial cracks and to develop cohesive zone parameters over a range of mode-mixity. Similarly, a combination of four-point bend and end-notch flexure tests is used to cover additional range of mode-mixity. In these tests, silicon wafers obtained from wafer foundry are used for experimental characterization. The developed parameters are then used in actual microelectronic device to predict the onset and propagation of crack, and the results from such predictions are successfully validated with experimental data. In addition, nanoindenter-based shear test technique designed specifically for this study is demonstrated. The new test technique can address different mode mixities compared to the other interfacial fracture characterization tests, is sensitive to capture the change in fracture parameter due to changes in local trace pattern variations around the vicinity of bump and the test mimics the forces experienced by the bump during flip-chip assembly reflow process. Through this experimental and theoretical modeling research, guidelines are also developed for the reliable design of BEOL stacks for current and next-generation microelectronic devices.

This study is devoted to the thermo-mechanical constitutive modeling for saturated stiff clays and the development of a corresponding efficient stress integration algorithm. The mechanical behavior of natural Boom Clay in isothermal conditions was first characterized. The Modified Cam Clay model (MCC) was then applied to simulate the natural Boom Clay behavior. It has been found that the MCC gives poor-quality predictions of the natural Boom Clay behavior. Thereby, an adapted Cam Clay model (ACC-2) was developed by introducing a new yield surface and a new plastic potential as well as a Two-surface plastic mechanism. This model allows satisfactory prediction of the main features of the mechanical behavior of natural Boom Clay. Moreover, the constitutive equations of this model can be formulated mathematically as in a classic elasto-plastic model. Thus, the classic stress integration algorithm can be applied. The thermal effects were considered by assessing the performance of some advanced thermo-mechanical models (Cui et al., 2000; Abuel-Naga et al., 2007; Laloui and François, 2008; 2009). It appears that all the three models can capture the main features of the thermo-mechanical behavior of saturated clays. However, each constitutive model has its own limitations or unclear points from the theoretical point of view. The stress integration algorithm of the thermo-mechanical model proposed by Cui et al. (2000) at the stress point level was also developed using a specifically designed adaptive time-stepping scheme. The computation time required to achieve a given accuracy is largely reduced with the adaptive sub-stepping considered for both mechanical and thermal loadings. A Two-surface thermo-mechanical model (TEAM model) was developed based on the Two-surface plastic mechanism. The proposed model extends the model of Cui et al. (2000) to a Two-surface formulation, considering the plastic strain coupling between the thermal and the mechanical loading paths. The simulation of drained tests shows that this model can capture the main thermo-mechanical features of natural Boom Clay along different loading paths. The TEAM model was finally extended to undrained conditions. After setting up an appropriate effective stress principle and defining a volumetric strain condition, the undrained heating process was analyzed. The validity of the thermo-hydro-mechanical constitutive equations was examined based on the data from typical tests

<p dir="ltr">In structural metallic components, a material’s lifecycle begins with the processing route, to produce a desired structure, which dictates the in-service performance. The variability of microstructural features as a consequence of the processing route has a direct influence on the properties and performance of a material. In order to correlate the influence processing conditions have on material performance, large test matrices are required which tend to be time consuming and expensive. An alternative route to avoid such large test matrices is to incorporate physics-based process modeling and lifing paradigms to better understand the performance of structural materials. By linking microstructural information to the material’s lifecycle, the processing path can be modified without the need to repeat large-scale testing requirements. Additionally, when a materials system is accurately modeled throughout its lifecycle, the performance predictions can be leveraged to improve the design of materials and components.</p><p dir="ltr">Ni-based superalloys are a material class widely used in many critical aerospace components exposed to coupling thermal and mechanical loads due to their increased resistance to creep, corrosion, oxidation, and strength characteristics at elevated temperatures. Many Ni-based superalloys undergo high-temperature forging to produce a desired microstructure, targeting specific strength and fatigue properties in order to perform under thermo-mechanical loads. When in-service, these alloys tend to fail as a consequence of thermo-mechanical fatigue (TMF) from either inclusion- or matrix- driven failure. In order to produce safer, cheaper and more efficient critical aerospace components, the micromechanical deformation and damage mechanisms throughout a Ni-based superalloy’s lifecycle must be understood. This research utilizes process modeling as a tool to understand the damage and deformation of inclusions in a Ni-200 matrix throughout radial forging as a means to optimize the processing conditions for improved fatigue performance. In addition, microstructural sensitive performance modeling for a Ni-based superalloy is leveraged to understand the influence TMF has on damage mechanisms.</p><p dir="ltr">The radial forging processing route requires both high temperatures and large plastic deformation. During this process, non-metallic inclusions (NMIs) can debond from the metallic matrix and break apart, resulting in a linear array of smaller inclusions, known as stringers. The evolution of NMIs into stringers can result in matrix load shedding, localized plasticity, and stress concentrations near the matrix-NMI interface. Due to these factors, stringers can be detrimental to the fatigue life of the final forged component. By performing a finite element model of the forging process with cohesive zones to simulate material debonding, this research contributes to the understanding of processing induced deformation and damage sequences on the onset of stringer formation for Alumina NMIs in a Ni-200 matrix. Through a parametric study, the interactions of forging temperature, strain rate, strain per pass, and interfacial decohesion on the NMI damage evolution metrics are studied, specifically NMI particle separation, rotation, and cavity formation. The parametric study provides a linkage between the various processing conditions parameters influence on detrimental NMI morphology related to material performance.</p><p dir="ltr">The microstructural characteristics of Ni-based superalloys, as a consequence of a particular processing route, creates a variability in TMF performance. The micromechanical failure mechanisms associated with TMF are dependent on various loading parameters, such as temperature, strain range, and strain-temperature phasing. Insights on the complexities of micromechanical TMF damage are studied via a temperature-dependent, dislocation density-based crystal plasticity finite element (CPFE) model with uncertainty quantification. The capabilities of the model’s temperature dependency are examined via direct instantiation and comparison to a high-energy X-ray diffraction microscopy (HEDM) experiment under coupled thermal and mechanical loads. Unique loading states throughout the experiment are investigated with both CPFE predictions and HEDM results to study early indicators of TMF damage mechanisms at the grain scale. The mesoscale validation of the CPFE model to HEDM experimental data provides capabilities for a well-informed TMF performance paradigm under various strain-temperature phase profiles. </p><p dir="ltr">A material’s TMF performance is highly dependent on the temperature-load phase profile as a consequence of path-dependent thermo-mechanical plasticity. To investigate the relationship between microstructural damage and TMF phasing effects, the aforementioned CPFE model investigates in-phase (IP) TMF, out-of-phase (OP) TMF, and iso-thermal (ISO) loading profiles. A microstructural sensitive performance modeling framework with capabilities to isolate phasing (IP, OP, and ISO) effects is presented to locate fatigue damage in a set of statistically equivalent microstructures (SEMs). Location specific plasticity, and grain interactions are studied under the various phasing profiles providing a connection between microstructural material damage and TMF performance.</p>

Sous le Chili central et l’ouest de l'Argentine (29°-35°S), la plaque océanique Nazca, en subduction sous la plaque continentale Amérique du Sud, change radicalement de géométrie : inclinée à 30°, puis horizontale, engendrée par la subduction de la chaine de volcans de Juan Fernandez. Le but de mon étude est d'évaluer, la variation de nature et de propriétés physiques de la lithosphère chevauchante entre ces deux régions afin de mieux comprendre (1) sa structure profonde et (2) les liens entre les déformations observées en surface et en profondeur. Pour répondre à cette thématique, j’utilise une approche originale couplant la sismologie, la thermométrie, et la pétrologie. Je montre ainsi des images 3-D de tomographie sismique les plus complètes de cette région par rapport aux études précédentes, qui intègrent (1) de nombreuses données sismiques provenant de plusieurs catalogues, (2) un réseau de stations sismiques plus dense permettant de mieux imager la zone de subduction. J’apporte la preuve que la plaque en subduction se déshydrate dans deux régions distinctes : (1) le coin mantellique, et (2) le long de la ride subduite avant que celle-ci ne replonge plus profondément dans le manteau. La croûte continentale au-dessus du flat slab possède des propriétés sismiques très hétérogènes en relation avec des structures de déformation profondes et des domaines géologiques spécifiques. La croûte chevauchante d’avant-arc, au-dessus du flat slab, est décrite par des propriétés sismiques inhabituelles, liées à la géométrie particulière du slab en profondeur, et/ou liées aux effets du séisme de 1997 de Punitaqui (Mw 7.1). Mes résultats, confirmant les études antérieures, montrent que : - le bloc Cuyania situé plus à l’est, dans la zone d’arrière-arc est plus mafique et contient une croûte inférieure éclogitisée ; quant à, la croûte continentale inférieure sous l’arc Andin, est épaisse et non-éclogitisée, décrivant surement le bloc felsique de Chilenia. / Beneath central Chile and western Argentina, the oceanic Nazca slab drastically changes geometry from horizontal to dipping at an angle of 30°, and correlates with the subduction of the Juan Fernandez seamount ridge. The aim of our study is to assess, using a thermo-petrological-seismological approach, the differences of the overriding lithosphere between these two regions, in order to better understand the deep structure of the continental lithosphere above the flat slab, and the links between the deformations at the surface and at depth. We show the most complete regional 3-D seismic tomography images of this region, whereby, in comparison to previous studies, we use (1) a much larger seismic dataset compiled from several short-term seismic catalogs, (2) a much denser seismic station network which enables us to resolve better the subduction zone. We show significant seismic differences between the flat and normal subduction zones. As expected, the flat slab region is impacted by colder temperatures, and therefore by faster seismic velocities and more intense seismic activity, compared to the normal slab region. We show evidence that the flat slab dehydrates within the mantle wedge, but also along the subducting ridge prior to re-subducting. The forearc crust above the flat slab is described by unusual seismic properties, correlated to the slab geometry at depth, and/or, to the aftershock effects of the 1997 Mw 7.1 Punitaqui earthquake which occurred two years before the recording of our events. The continental crust above the flat slab has very heterogeneous seismic properties which correlate with important deformation structures and geological terranes at the surface. We confirm previous studies that have shown that the thick lower crust of the present day Andean arc is non-eclogitized and maybe representing the felsic Chilenia terrane, whereas to the east, the Cuyania terrane in the backarc is more mafic and contains an eclogitized lower crust.

Neste trabalho, propõe-se um modelo numérico-computacional representativo dos processos de tratamento térmico, que seja uma ferramenta eficiente e forneça meios para um entendimento efetivo do mecanismo de geração de tensões residuais durante a têmpera de aços. Foram investigados os fenômenos térmicos, mecânicos e de transformação de fase observados na têmpera, bem como o acoplamento entre esses três fenômenos. O modelo utiliza o Método dos Elementos Finitos (MEF) e o programa ABAQUS®, além de rotinas numéricas em FORTRAN responsáveis pela resolução do problema termo-mecânico-microestrutural acoplado. A utilização de sub-rotinas, que implementam uma alteração na formulação (matemática e numérica) do programa de Elementos Finitos, permite incluir no modelo as informações presentes em uma curva CRC (curva de resfriamento contínuo) do aço SAE 4140, implementando o cálculo de deformações da peça simulada de modo incremental e cumulativo. Os resultados mostram que a utilização das sub-rotinas desenvolvidas neste trabalho permitiu implementar, conjuntamente com o programa ABAQUS®, o cálculo das frações volumétricas, durezas, distorções e tensões que surgem em um tratamento térmico de têmpera, simulando as transformações martensítica, perlítica, bainítica e ferrítica. Os resultados dos modelos foram equivalentes aos relatados pela literatura, principalmente no que se refere às durezas e tensões associadas a cada transformação de fase. Em particular, os resultados indicam que a transformação martensítica está sempre associada à formação de tensões compressivas. Ensaios experimentais foram realizados a fim de validar os modelos computacionais propostos, utilizando-se um teste Jominy adaptado e instrumentado, de modo a permitir a amostragem da variação de temperaturas no material. Ensaios metalográficos permitiram correlacionar as frações volumétricas transformadas durante a têmpera do corpo de prova Jominy aos valores calculados pelo modelo numérico acoplado. / The objective of this work is to analyze residual strains and stresses and volumetric expansion due to phase transformations that occur during quenching of a steel body, as well as to predict these phase transformations. The coupled thermo-mechanical-phase transformation problem was analyzed, specifically in terms of the quenching process. Different computational models were presented, based on the finite element software ABAQUS® and on the use of FORTRAN subroutines. The continuous-cooling-transformation (CCT) diagrams of SAE 4140 steel are represented differently in each model, depending on the transformed phases and correspondent volumetric expansion. These subroutines include information from the CCT diagrams of SAE 4140 into a FORTRAN code. The subroutine calculates all the microstructures resulting from quenching (ferrite, pearlite, bainite, and martensite), depending on cooling rate. The numerical analysis conducted in this work provided results in terms of the temperature and stresses developed during quenching. The properties determined in this work are hardness, yield strength, volumetric fraction and distortion. Hardness has been predicted by the use of analytical equations. The finite element analyses were able to explain and reproduce phenomena observed during quenching of a steel cylinder. In particular, numerical results indicated that martensite formation is always related to a compressive stress field. The results of the models are in qualitative agreement with data provided by literature, particularly, in relation to the stresses originated by each different phase transformation during quenching process. Experimental testing was conducted, based on the analysis of the quenching of a Jominy probe, in order to validate the computational model developed in this work.

A need has been established in industry and academic publications to link an engine's maintenance costs throughout its operational life to its design as well as its operations and operating conditions. The established correlations between engine operation, design and maintenance costs highlight the value of establishing a satisfactory measure of the relative damage due to different operating conditions (operational severity). The methodology developed in this research enables the exploration of the causal, physics-based relationships underlying the statistical correlations in the public domain and identifies areas for further investigation. This thesis describes a physics-based approach to exploring the interactions, for commercial aircraft, of engine design, operation and through life maintenance costs. Applying the "virtual-workshop" workscoping concept to model engine maintenance throughout the operating life captures the maintenance requirements at each shop visit and the impact of a given shop visit on the timing and requirements for subsequent visits. Comparisons can thus be made between the cost implications of alternative operating regimes, flight profiles and maintenance strategies, taking into account engine design, age, operation and severity. The workscoping model developed operates within a physics-based methodology developed collaboratively within the research group which encompasses engine performance, lifing and operational severity modelling. The tool-set of coupled models used in this research additionally includes the workscoping maintenance cost model developed and implements a simplified 3D turbine blade geometry, new lifing models and an additional lifing mechanism (Thermo-mechanical fatigue (TMF)). Case studies presented model the effects of different outside air temperatures, reduced thrust operations (derate), flight durations and maintenance decisions. The use of operational severity and exhaust gas temperature margin deterioration as physics based cost drivers, while commonly accepted, limit the comparability of the results to other engine-aircraft pairs as the definition of operational severity, its derivation and application vary widely. The use of a single operation severity per mission based on high pressure turbine blade life does not permit the maintenance to vary with the prevalent lifing mechanism type (cyclic/steady state).

La connaissance du comportement au feu des structures est primordiale pour la maîtrise des risques en situation d’incendie. Pour le bois, matériau combustible, des travaux expérimentaux et de simulations numériques ont montré que ce matériau avait un comportement intéressant en situation d’incendie, car il se consume de façon maîtrisable. Cependant, ces travaux restent limités au regard de la complexité du comportement du matériau, des composants et des assemblages à base de bois. L’étude de la stabilité au feu des structures bois nécessite la connaissance de l’évolution des caractéristiques mécaniques et thermiques des liaisons (résistance et rigidité) dont dépend le comportement mécanique des structures. Pour une meilleure compréhension du fonctionnement mécanique des assemblages en situation d’incendie, la mise en place de modèles numériques, validés par essais, est nécessaire. Dans cette étude, l’objectif est d’utiliser un modèle numérique le plus précis possible afin de définir des méthodes simplifiées de calcul d’assemblages, facilement utilisables par les professionnels. Les résultats d’essais réalisés sur les assemblages bois-bois et bois-métal servant de base à la validation des modèles du comportement thermomécanique sont présentés. Il s’agit d’essais de traction longitudinale, transversale et d’essais de flexion sous conditions normales et sous actions thermiques normalisées. L’étude thermomécanique des assemblages est effectuée à partir de deux maillages tridimensionnels différents pour les calculs thermique et mécanique. Pour le modèle mécanique, les discontinuités sont prises en compte à travers des éléments de contact aux interfaces des pièces assemblées. Pour le calcul thermique, le maillage est continu et la résistance due au contact entre les éléments est ainsi négligée. Les modèles mécaniques et thermiques sont validés sur la base des résultats expérimentaux (courbes force-glissement et températures). Le modèle mécanique permet par ailleurs d’analyser la distribution des contraintes au sein des assemblages et d’évaluer l’influence de différents critères élasto-plastiques ou de rupture représentant le comportement mécanique du bois. Enfin, le modèle thermomécanique, a permis de simuler le comportement des assemblages testés en situation d’incendie. Le résultat utilisé pour valider le modèle thermomécanique est la durée de résistance au feu de l’assemblage. Cette durée est définie à l’aide des courbes glissement-temps obtenues par le modèle numérique. De bons résultats sont obtenus pour la prédiction des temps de rupture. L’évolution de la distribution des efforts sur les différents organes en fonction de la durée d’exposition au feu est aussi présentée. Ainsi, le modèle développé dans ce travail permet de bien représenter le comportement thermomécanique des assemblages étudiés. Il représente aussi un outil intéressant pour analyser le comportement au feu d’assemblages constitués de plusieurs organes métalliques. Il permet de servir de base pour développer une approche multiparamètre basée sur des plans d’expérience numérique. Ces travaux permettront de proposer des méthodes de dimensionnement simples, validés par les modèles numériques, et utilisables par les praticiens de la construction. / The knowledge of the behavior of structures under fire conditions is essential to control the risks during a fire. As timber is a combustible material, fire safety is of main importance for the development of its use in buildings. Although experimental and numerical studies exist in the literature, their number still limited regarding the variety of the configurations and the complexity of the mechanical behavior of the connections. Among the various structural components, the joints are characterized by a complex thermomechanical behavior due mainly to the geometrical configuration combining various materials (steel and timber). They govern the load-carrying capacity of the structure and its safety, as well in normal conditions as in fire situation. Due to their complex geometrical, physical and material configurations, the behavior of the connections in fire is one of the more difficult to predict. The development of generalized models requires the combination of research based both on the experimental results given by full scale tests and the development of sophisticated numerical models validated on these tests.The experimental results of tests realized on timber-to-timber and steel-to-timber connections used as a basis for the validation of the numerical models are presented. They concern tests of longitudinal and transversal tension and flexion under normal conditions and under standardized thermal actions. The thermomechanical analysis of the connections is made from two different three-dimensional meshings for the thermal and mechanical calculations. The thermal model is continuous to take account of the thermal continuity between the joint components. The mechanical model is discontinuous to consider the contact evolution between the joint components. The thermal model isused to predict the evolution of the temperature field inside the joint depending on the gas temperature. It is validated on the basis of measured temperatures during fire tests. The mechanical model is validated by comparison with the experimental results of joints in normal conditions. It allows the analysis of the distribution of stresses within the joints. The influence of various criteria to represent the mechanical behavior of timber is also studied. Finally, the thermomechanical model, based on previous both models, allowed to predict the behaviorof the tested connections in fire situation. The thermo-mechanical model is validated considering the fire resistance duration of some joints. This duration is defined by means of displacement-time curves obtained by the numerical model. The models showed a good capacity to simulate the failure times of the timber joints in fire situations. The application of the model gave the possibility to analyse the load distribution among the fasteners of the studied joints.The model developed in this work represents well the thermomechanical behavior of the tested connections. These developed and tested models can be used as general tool to analyze the behavior of a large variety of joint configurations to constitute a data base that can be used in safe and economic practice of fire engineering of wood joints.

Nonlinear finite element models of functionally graded beams with power-law variation of material, accounting for the von-Karman geometric nonlinearity and temperature dependent material properties as well as microstructure dependent length scale have been developed using the Euler-Bernoulli as well as the first-order and third- order beam theories. To capture the size effect, a modified couple stress theory with one length scale parameter is used. Such theories play crucial role in predicting accurate deflections of micro- and nano-beam structures. A general third order beam theory for microstructure dependent beam has been developed for functionally graded beams for the first time using a modified couple stress theory with the von Karman nonlinear strain. Finite element models of the three beam theories have been developed. The thermo-mechanical coupling as well as the bending-stretching coupling play significant role in the deflection response. Numerical results are presented to show the effect of nonlinearity, power-law index, microstructural length scale, and boundary conditions on the bending response of beams under thermo-mechanical loads. In general, the effect of microstructural parameter is to stiffen the beam, while shear deformation has the effect of modeling more realistically as a flexible beam.