Cold rolled carbon steel 1018C is widely used in pressurized fuel pipelines. For those structures, stress corrosion cracking (SCC) can pose a significant problem because cracks initiate late in the lifetime and often unexpectedly, but grow fast once they get started. To ensure a safe operation, it is crucial that any damage can be detected before the structural stability is reduced by large cracks. In the early stages of SCC, microstructural changes occur which increase the acoustic nonlinearity of the material. Therefore, an initially monochromatic Rayleigh wave is distorted and measurable higher harmonics are generated. Different levels of stress corrosion cracking is induced in five specimens. For each specimen, nonlinear ultrasonic measurements are performed before and after inducing the damage. For the measurements, oil coupled wedge transducers are used to generate and detect tone burst Rayleigh wave signals. The amplitudes of the received fundamental and second harmonic waves are measured at varying propagation distances to obtain a measure for the acoustic nonlinearity of the material. The results show a damage-dependent increase in nonlinearity for early stages of damage, indicating the suitability for this nonlinear ultrasonic method to detect stress corrosion cracking before structural failure.

Interrogating metals with ultrasonic waves can be used to evaluate their microstructural and mechanical properties. These techniques analyze ultrasonic wave features in order to make inferences on the medium of interest. Current research is being conducted to determine higher order elastic properties and characterize material degradation of 7075-T651 aluminum with ultrasonics. This thesis topic will use acoustoelasticity, the stress dependency of acoustic velocity, to accomplish these goals. Acoustoelasticity is a manifestation of the inherent nonlinearity in the interatomic binding energy, which appears mathematically as higher order elastic terms in the stress strain constitutive relation. The acoustoelasticity will be determined for longitudinal and shear waves propagating through a sample under uni-axial stress. Experimentally, specific techniques and tooling will be designed to insure accurate measurements of acoustic wave velocity as a function of stress. Using acoustoelasticity the third order elastic constants of 7075-T651 aluminum will be determined. Further, Al samples will be fatigue damaged and acoustoelasticity and third order elastic constants will be mapped versus damage. Literature will be used to verify measured values of acoustoelasticity as well as provide theoretical models for acoustoelastic dependence on damage.

Fretting, which can occur when two bodies in contact undergo a low amplitude relative slip, can drastically reduce the fatigue performance of a material. The extent of fretting damage is dependent on the material combination and is affected by many parameters, making it difficult to design against fretting. Some of these parameters include contact force, displacement amplitude, and contacting materials. This work develops a method for quantifying the extent of damage from fretting as a function of these parameters for a thin sheet of AISI 301 stainless steel in the full hard condition in contact with both ANSI A356 aluminum and AISI 52100 steel contacting bodies. Fretting experiments were conducted on a Phoenix Tribology DN55 Fretting Machine using a fixture which was developed for holding thin specimens. The displacement amplitude and normal force were systematically varied in order to cover a range that could typically be experienced during service. The tribological behavior was studied by analyzing friction force during cycling and inspecting the resulting surface characteristics. Fretting damaged specimens were cycled in tension in a servohydraulic test system to failure. The decrease in fatigue life caused by fretting damage was determined by comparing the stress-life (S-N) response of the fretted specimens to the S-N response of the virgin material, thus characterizing the severity of the fretting damage. The conditions that lead to the greatest reduction in life were identified in this way. Using the fracture mechanics based NASGRO model, an Equivalent Initial Flaw Size (EIFS) was used to quantify the level of fretting damage, thus separating the life of the component into crack nucleation and subsequent propagation. This method and data will allow engineers to design more robust components that resist fretting damage, thus increasing the safety and reliability of the system.

In this thesis, we pursue a simulation-based approach whereby microstructure-sensitive finite element simulations are performed within a statistical perspective to examine the VHCF life variability and assess the surface initiation probability. The methodology introduced in this thesis lends itself as a cost-effective platform for development of microstructure-property relations to support design of new or modified alloys, or to more accurately predict the properties of existing alloys.

Uma parte significativa da vida de um componente mecânico pode ocorrer com a propagação de trincas em fadiga. Atualmente, dispõe-se de vários modelos matemáticos para descrever o comportamento do crescimento da trinca. Esses modelos são classificados em duas categorias em termos da amplitude de tensão: constante (CAC) e variável (CAV). Em geral, esses modelos de propagação são formulados como um problema de valor inicial (PVI) e, a partir disso, a curva de evolução da trinca é obtida através da aplicação de um método numérico. Nesta dissertação apresentou-se a aplicação da metodologia “Fast Bounds Crack” para o estabelecimento das funções cotas superior e inferior para modelos de evolução do tamanho de trinca. O desempenho desta metodologia foi avaliado através do desvio relativo e tempo computacional, em relação às soluções numéricas aproximadas obtidas pelo método de Runge-Kutta de 4º ordem explícito (RK4). Atingiu-se um desvio relativo máximo de 5,92% e o tempo computacional foi, para os exemplos resolvidos, 130000 vezes superior ao tempo obtido pelo método do RK4. Realizou-se, ainda, uma aplicação de Engenharia para a obtenção de uma solução numérica aproximada, a partir da média aritmética das cotas superior e inferior obtidas na metodologia aplicada neste trabalho, quando não se conhece a lei de evolução. O erro relativo máximo encontrado nessa aplicação foi de 2,08% o que comprova a eficiência da metodologia “Fast Bounds Crack”. / A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".

Uma parte significativa da vida de um componente mecânico pode ocorrer com a propagação de trincas em fadiga. Atualmente, dispõe-se de vários modelos matemáticos para descrever o comportamento do crescimento da trinca. Esses modelos são classificados em duas categorias em termos da amplitude de tensão: constante (CAC) e variável (CAV). Em geral, esses modelos de propagação são formulados como um problema de valor inicial (PVI) e, a partir disso, a curva de evolução da trinca é obtida através da aplicação de um método numérico. Nesta dissertação apresentou-se a aplicação da metodologia “Fast Bounds Crack” para o estabelecimento das funções cotas superior e inferior para modelos de evolução do tamanho de trinca. O desempenho desta metodologia foi avaliado através do desvio relativo e tempo computacional, em relação às soluções numéricas aproximadas obtidas pelo método de Runge-Kutta de 4º ordem explícito (RK4). Atingiu-se um desvio relativo máximo de 5,92% e o tempo computacional foi, para os exemplos resolvidos, 130000 vezes superior ao tempo obtido pelo método do RK4. Realizou-se, ainda, uma aplicação de Engenharia para a obtenção de uma solução numérica aproximada, a partir da média aritmética das cotas superior e inferior obtidas na metodologia aplicada neste trabalho, quando não se conhece a lei de evolução. O erro relativo máximo encontrado nessa aplicação foi de 2,08% o que comprova a eficiência da metodologia “Fast Bounds Crack”. / A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".

Thermomechanical fatigue life prediction is important in the design of Ni-base superalloy components in gas turbine engines and requires a stress-strain analysis for accurate results. Crystal viscoplasticity models are an ideal tool for this stress-strain analysis of Ni-base superalloys as they can capture not only the anomalous yielding behavior, but also the non-Schmid effect, the strain rate dependence, and the temperature dependence of typically large grained directionally-solidified and single crystal alloys. However, the model is difficult to calibrate even for isothermal conditions because of the interdependencies between parameters meant to capture different but similar phenomena at different length scales, many tied to a particular slip system. The need for the capacity to predict the material response over a large temperature range, which is critical for the simulation of hot section gas turbine components, causes the determination of parameters to be even more difficult since some parameters are highly temperature dependent. Rapid parameter determination techniques are therefore needed for temperature-dependent parameterizations so that the effort needed to calibrate the model is reduced to a reasonable level. Specific parameter determination protocols are established for a crystal viscoplasticity model implemented in ABAQUS through a user material subroutine. Parameters are grouped to reduce interdependencies and a hierarchical path through the groups and the parameters within each group is established. This dual level hierarchy creates a logical path for parameter determination which further reduces the interdependencies between parameters, allowing for rapid parameter determination. Next, experiments and protocols are established to rapidly provide data for calibration of the temperature-dependencies of the viscoplasticity. The amount of data needed to calibrate the crystal viscoplasticity model over a wide temperature range is excessively large due to the number of parameters that it contains which causes the amount of time spent in the experimentation phase of parameter determination to be excessively large. To avoid this lengthy experimentation phase each experiment is designed to contain as much relevant data as possible. This is accomplished through the inclusion of multiple strain rates in each experiment with strain ranges sufficiently large to clearly capture the inelastic response. The experimental and parameter determination protocols were exercised by calibrating the model to the directionally-solidified Ni-bas superalloy DS-CM247LC. The resulting calibration describes the material's behavior in multiple loading orientations and over a wide temperature range of 20 °C to 1050 °C. Several parametric studies illustrate the utility of the calibrated model.

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.

A maioria das máquinas e componentes mecânicos estão sujeitos a solicitações dinâmicas as quais podem ocasionar falhas por fadiga. Um dos métodos para a previsão de falhas por fadiga é a Mecânica da Fratura Linear Elástica (MFLE). Na MFLE existem diversos modelos que descrevem a propagação de uma trinca, com suas diferentes abordagens e concepções. De forma geral, distinguem-se os modelos de propagação de trinca para carregamentos com amplitude de tensão constante e variável. Dentre os modelos de amplitude de tensão constante destaca-se a Lei de Paris, que consiste de um Problema de Valor Inicial (PVI), sendo que sua solução, em poucos casos, é determinada de forma exata. Assim, o objetivo deste trabalho é propor uma nova metodologia para solucionar alguns modelos de propagação de trinca de amplitude de tensão constante, como os modelos de Paris-Erdogan, Forman, Walker, McEvily e Priddle sem a necessidade da utilização de métodos numéricos para a solução. Essa metodologia foi desenvolvida estabelecendo cotas, superior e inferior, que delimitam o comportamento das soluções dos modelos de propagação de trinca. Para isso, através da literatura, foram delimitados os modelos a serem avaliados com base em dois aspectos principais: modelos que incorporem em suas equações as regiões I a III da propagação de trinca, e modelos que levem em consideração parâmetros como a razão de tensão, a tenacidade à fratura e o fator intensidade de tensão inicial para propagação de trinca. Para verificação da precisão e eficácia da nova metodologia, foi calculado o desvio relativo entre as cotas e a solução numérica aproximada, utilizando o método de Runge-Kutta de 4a ordem (RK4), e observou-se que as cotas são válidas como forma de aproximação do comportamento da evolução da trinca para todos os modelos estudados. Também foi avaliado o desempenho da utilização das cotas em relação à solução pelo método RK4 através do tempo de computação, e foi observado que com a utilização das cotas, consegue-se um monitoramento dinâmico dos resultados. / Most machines and mechanical components are subject to dynamic loads that can lead to fatigue failures. One of the methods for the prediction of fatigue failures is the Linear Elastic Fracture Mechanics (LEFM). In the LEFM there are several models that describe the propagation of a crack, with their different approaches and conceptions. In general, a distinction is made between the crack propagation models under constant and variable amplitude load. One of the constant amplitude load models is the Paris law, consisting of an Initial Value Problem (IVP), whose solution, in a few cases, can be obtained in closed form. Thus, the objective of this work is to propose a new methodology to solve some models of crack propagation under constant amplitude load, as the models of Paris-Erdogan, Forman, Walker, McEvily and Priddle, without requiring the use of numerical methods for the solution. This methodology was developed by establishing upper and lower bounds that delimit the behavior of the solutions of the models of crack propagation. For that, through literature, were delimited the models to be assessed on the basis of two main aspects: models that incorporate in their equations the regions I to III of the crack propagation, and models that take into account parameters such as the stress ratio, fracture toughness and threshold stress intensity factor for crack propagation. For verification of the accuracy and effectiveness of the new methodology, the relative deviation between bounds and approximate numerical solution was calculated, using the Runge-Kutta 4th order (RK4), and it was observed that the bounds are valid as a way of obtaining approximate solutions to all models. The performance of the use of bounds regarding the RK4 method solution was also evaluated through the computation time.

A maioria das máquinas e componentes mecânicos estão sujeitos a solicitações dinâmicas as quais podem ocasionar falhas por fadiga. Um dos métodos para a previsão de falhas por fadiga é a Mecânica da Fratura Linear Elástica (MFLE). Na MFLE existem diversos modelos que descrevem a propagação de uma trinca, com suas diferentes abordagens e concepções. De forma geral, distinguem-se os modelos de propagação de trinca para carregamentos com amplitude de tensão constante e variável. Dentre os modelos de amplitude de tensão constante destaca-se a Lei de Paris, que consiste de um Problema de Valor Inicial (PVI), sendo que sua solução, em poucos casos, é determinada de forma exata. Assim, o objetivo deste trabalho é propor uma nova metodologia para solucionar alguns modelos de propagação de trinca de amplitude de tensão constante, como os modelos de Paris-Erdogan, Forman, Walker, McEvily e Priddle sem a necessidade da utilização de métodos numéricos para a solução. Essa metodologia foi desenvolvida estabelecendo cotas, superior e inferior, que delimitam o comportamento das soluções dos modelos de propagação de trinca. Para isso, através da literatura, foram delimitados os modelos a serem avaliados com base em dois aspectos principais: modelos que incorporem em suas equações as regiões I a III da propagação de trinca, e modelos que levem em consideração parâmetros como a razão de tensão, a tenacidade à fratura e o fator intensidade de tensão inicial para propagação de trinca. Para verificação da precisão e eficácia da nova metodologia, foi calculado o desvio relativo entre as cotas e a solução numérica aproximada, utilizando o método de Runge-Kutta de 4a ordem (RK4), e observou-se que as cotas são válidas como forma de aproximação do comportamento da evolução da trinca para todos os modelos estudados. Também foi avaliado o desempenho da utilização das cotas em relação à solução pelo método RK4 através do tempo de computação, e foi observado que com a utilização das cotas, consegue-se um monitoramento dinâmico dos resultados. / Most machines and mechanical components are subject to dynamic loads that can lead to fatigue failures. One of the methods for the prediction of fatigue failures is the Linear Elastic Fracture Mechanics (LEFM). In the LEFM there are several models that describe the propagation of a crack, with their different approaches and conceptions. In general, a distinction is made between the crack propagation models under constant and variable amplitude load. One of the constant amplitude load models is the Paris law, consisting of an Initial Value Problem (IVP), whose solution, in a few cases, can be obtained in closed form. Thus, the objective of this work is to propose a new methodology to solve some models of crack propagation under constant amplitude load, as the models of Paris-Erdogan, Forman, Walker, McEvily and Priddle, without requiring the use of numerical methods for the solution. This methodology was developed by establishing upper and lower bounds that delimit the behavior of the solutions of the models of crack propagation. For that, through literature, were delimited the models to be assessed on the basis of two main aspects: models that incorporate in their equations the regions I to III of the crack propagation, and models that take into account parameters such as the stress ratio, fracture toughness and threshold stress intensity factor for crack propagation. For verification of the accuracy and effectiveness of the new methodology, the relative deviation between bounds and approximate numerical solution was calculated, using the Runge-Kutta 4th order (RK4), and it was observed that the bounds are valid as a way of obtaining approximate solutions to all models. The performance of the use of bounds regarding the RK4 method solution was also evaluated through the computation time.