Em uma abordagem realística de estruturas e componentes mecânicos admite-se a existência de trincas. A presença destas, geralmente, está associada ao fenômeno da fadiga. Existem diversos modelos matemáticos que descrevem a propagação de uma trinca. De forma geral, os modelos de propagação de trinca são classificados pelo tipo de carregamento, que pode ter amplitude de tensão constante (CATC) ou amplitude de tensão variável (CATV). Neste trabalho foi utilizado o modelo do tipo CATC proposto por Collipriest. Para muitas aplicações de engenharia, até um certo momento, não se faz necessário uma grande acurácia nas previsões do comportamento das estatísticas, a cerca da evolução de uma trinca, mas uma previsão confiável, dentro de certos limites, desse comportamento. Este trabalho apresenta resultados teóricos, que consistem em obter cotas, inferiores e superiores, que “envelopam” os estimadores dos momentos estatísticos de primeira e de segunda ordem da função “tamanho de trinca” baseadas no método “Fast Crack Bounds”. Essas cotas são polinômios, definidos na variável número de ciclos, que consideram as incertezas nos parâmetros que descrevem os modelos de propagação de trinca. O método de simulação de Monte Carlo foi utilizado para obter as realizações da função tamanho de trinca a partir de um conjunto de 10.000 amostras randômicas dos parâmetros característicos do modelo de Collipriest. Essas realizações foram utilizadas para obter os estimadores dos momentos estatísticos do tamanho de trinca. A eficiência das cotas para os estimadores dos momentos estatísticos do tamanho de trinca é avaliada através de funções “desvio relativo” entre as cotas e as soluções numéricas aproximadas do problema de valor inicial (PVI) que descreve o modelo de Collipriest. Em geral, a solução dos PVI que descrevem os modelos de propagação de trincas é obtida através do uso de métodos numéricos, como o método de Runge-Kutta de quarta ordem explícito (RK4). Neste trabalho foi utilizado o software MATLAB para obter as soluções do PVI que descreve o modelo de Collipriest, avaliar o tempo computacional da metodologia proposta, além dos desvios das cotas em relação às soluções aproximadas, confirmando sua eficiência. / In a realistic approach of structures and mechanical components, cracks are admitted. Their presence is usually associated with the fatigue phenomenon. There are several mathematical models that describe the propagation of a crack. In general, the crack propagation models are classified by the type of load, which can have constant stress amplitude (CSA) or variable stress amplitude (VSA). In this work, the CSA type model proposed by Collipriest was used. For many engineering applications, until a certain point, it is not necessary to have great accuracy in predictions of the behavior of statistics, about the evolution of a crack, but a reliable prediction, within certain limits, of this behavior. This work presents theoretical results, which consist of obtaining lower and upper bounds that "envelop" the estimators of the first and second order statistical moments of the crack size function based on the Fast Crack Bounds method. These bounds are polynomials defined in the variable “number of cycles” that consider the Metais - Fadiga uncertainties in the parameters that describe the crack propagation models. The efficiency of the bounds for the statistical moments of crack size is evaluated through the deviation between the bounds and the approximate numerical solutions of the initial value problems (IVP) that describes the Collipriest model. In general, the solution of the IVPs describing crack propagation models is obtained through the use of numerical methods, such as the explicit fourth order Runge-Kutta method (RK4). In this work, the MATLAB software was used to obtain the solutions of the IVP that describes the Collipriest model, to evaluate the computational time of the proposed methodology, besides the deviations of the bounds in relation to the approximated solutions, confirming its efficiency.

CAPES / O estudo de um componente estrutural, é mais realístico quando se admite que o componente já possua trincas. A área que estuda este fenômeno é a mecânica da fratura. O componente que possui trinca e é submetido a esforços cíclicos, tende a falhar por fadiga. Este estudo apresenta cotas que “envelopam” a solução numérica aproximada da evolução da trinca. São estimados momentos estatísticos das cotas superior e inferior, afim de se obter resultados mais realísticos com relação a propagação da trinca, visto a existência de incerteza sobre os parâmetros dos modelos de evolução da trinca. As cotas são determinadas via metodologia Fast Crack Bounds, sendo está comparada com a solução numérica aproximada obtida pelo método de Runge-Kutta de quarta ordem. A randomização dos parâmetros do modelo, é executada através de Simulação de Monte Carlo. Para a quantificação da incerteza, da cota superior, inferior e da solução numérica, são considerados exemplos “clássicos” da mecânica da fratura, onde a função de correção do fator de intensidade de tensão é conhecida: placa com largura infinita, placa com largura finita e trinca central e placa com largura finita e trinca na aresta. O trabalho apresenta os desvios relativos do primeiro e segundo momento estatístico, bem como os ganhos computacionais na resolução do problema de valor inicial que descrevem a propagação da trinca. Em todos os casos analisados, a metodologia Fast Crack Bounds apresentou menor tempo computacional, quando comparada à solução numérica do problema, sendo no mínimo 411,23% mais eficaz para o parâmetro a0 , até 8.296,29% para o parâmetro KC . / The study of a structural component is more realistic when it is admitted that the component already has cracks. The area that studies this phenomenon is the fracture mechanics. The component which is cracked and subjected to cyclic stresses tends to fail due to fatigue. This study presents upper and lower bounds that "envelop" the approximate numerical solution of the evolution of the crack. The statistical moments of the upper and lower bounds are estimated, to obtain more realistic results in relation to the crack propagation, considering the existence of uncertainty about the parameters of the evolution models of the crack. Upper and lower bounds are determined using the Fast Crack Bounds methodology, being compared to the approximate numerical solution obtained by the fourth-order RungeKutta method. The randomization of the model parameters and execution through the Monte Carlo Simulation. For the quantification of the uncertainty, the upper and lower bounds and the numerical solution, "classic" examples of fracture mechanics are considered, where the correction function of the tensile strength factor is known: Infinite width plate, finite width plate a centered crack and finite width plate a bordercracked. The work presents the relative deviations of the first and second statistical moments, as well as the computational gains in solving the initial value problem that describe the propagation of the crack. In all cases analyzed, the Fast Crack Bounds methodology presented lower computational time when compared to the numerical solution of the problem, being at least 411.23% more effective for the parameter a0 , up to 8,296.29% for the parameter KC .

The compression behavior of a newly developed near eutectic Al-Si based cast alloy with three different microstructures has been investigated in the present work. Microstructures with modified and unmodified Si particles and matrix with different tempers are investigated. The main objective of this work is to understand the effect of heat treatment and modification on the fracture behavior of the alloy under compression. This alloy is subjected to compressive loading at different strain rates and temperatures during the operation of the engines. Hence, the effect of strain rates and temperatures is also considered. The compression tests are carried out at different strain rates from quasi-static to dynamic viz., 3*10-4 to 102/s and three different temperatures RT, 100°C and 200°C. Microstructure of the alloys studied predominantly consists of eutectic colonies of α-Al and Si with a few interspersed α-Al dendrites. Modified alloy has more globular Si particles than unmodified alloy. Heat treated alloys are found to have hardening precipitates S’ & Al7Cu4Ni and 3-7 atomic layer thick zones, which may be precursors to S’ phase. A variety of large intermetallics, viz., plate like particles Al4.5FeSi, Chinese script like particles Al19Fe4MnSi2 and bulky phase Al3NiCu are also observed in the alloys. Mechanical behavior of the alloys is found to be different for different microstructures. Modification improves strength and ductility. Heat treatment improves strength of the alloy at the expense of ductility. A transition in mechanical behavior is observed after a particular strain rate for all the alloys studied. This transition strain rate is dependent on heat treatment, Si particle size and temperature. This transition can be explained on the basis of dislocation-precipitate and dislocation-Si particle interactions. Work hardening behavior of the alloys depends on the matrix microstructure in the unmodified alloys, and both matrix and particles play a role in the modified alloy. A statistically robust quantitative micro structural analysis has been carried out after compressing the samples at various strain rates and temperatures. The unique contribution of this work is the understanding of combined effect of strain rate and temperature on Si particle fracture characteristics in the alloy with different microstructures. From the fracture characteristics of Si particles, it is concluded that both dislocation pile-up mechanism and fibre loading are responsible for particle fracture in the modified alloy, whereas the fibre loading mechanism alone is sufficient to explain the particle fracture characteristics in the unmodified alloy. Si particles in the modified condition are found to cleave along the lowest surface energy planes {112} & {110} and the particles with orientations {112} & {111} are more prone to fracture. In addition to Si particle fracture, elongated Fe rich intermetallic particles are also seen to show peculiar fracture behavior. The Al4.5FeSi intermetallics with (100) as the plane of the plate cleave along (100) planes. This is a novel finding in this work and could have immense implications on the role of Fe impurities in the fracture behavior of these alloys. Moreover, since these cleavage fractures are seen to be more than 200 microns in size (which implies that the real penny shaped crack would be even larger) their role cannot be assumed to be negligible, as was previously thought. The load sharing between the Al matrix and eutectic Si particles are simulated by microstructure based finite element modeling. The program OOF (Object-Oriented Finite element analysis) is used to generate the finite element meshes for real microstructures with different Si morphology. The experimentally obtained stress – strain properties of the alloy is given as an input to describe the plastic behavior of the Al matrix, in the finite element simulation. This analysis helps to understand the effect of particle size, shape, orientation & clustering and matrix temper on the stress transferred to the Si particles. Combination of Electron Back-Scattered Diffraction (EBSD) and frequency shift, polarized micro-Raman technique is applied to validate the stress states in Si particles with {111} orientations. The stress at fracture of Si particles is also estimated from Raman technique. Even though the alloys with different microstructures show different mechanical behavior, the sequence of fracture mechanisms is found to be same for all the alloys. The failure occurs in three stages: cracking of Si particles at low strains, micro-crack formation along the fractured particles, micro-crack coalescence and propagation leading to final failure. Thus, the proposed analysis links various deformation mechanisms ranging from nano precipitate-dislocation interactions to micro short-fiber theory of load sharing by eutectic silicon along with coupled effect of strain rate and temperature. In addition, negative strain rate sensitivity is also observed in the lower strain rate regimes (3*10-4, 10-3& 102/s) at RT and 100°C for all the three alloys, and serrated flow is also observed in the same strain rate and temperature regimes. Some of the features of serrated flow can be explained by the dynamic strain aging model and some other features by precipitate shearing.