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A life prediction method is developed for spot-welds subject to fatigue loading. Stress intensity factors are used with the Walker equation to develop two crack growth approaches to the problem. The predictions fit data for lap joint configurations well, but not so for peel joint geometries. / Master of Science

A lifetime prediction scheme is proposed based on the assumption that the lifetime (time to failure) of rocks under load is governed by the growth of microstructual defects (microcracks). The numerical approach is based on linear elastic fracture mechanics. The numerical calculation scheme is implemented as a cellular automat, where each cell contains a microcrack with length and orientation following certain distributions. The propagation of the microcrack is controlled by the Charles equation, based on subcritical crack growth. The zone inside the numerical model fails if the microcrack has reached the zone dimension or the stress intensity factor of the crack reached the fracture toughness. Macroscopic fractures are formed by these coalesced propagating microcracks, and finally lead to failure of the model. In the numerical approaches, elasto-plastic stress redistributions take place during the forming of the macroscopic fractures. Distinct microcrack propagation types have been programmed and applied to the proposed numerical models. These numerical models are studied under different loading conditions. Numerical results with excellent agreement with the analytical solutions are obtained with respective to predicted lifetime, important parameters for the microcracks, fracture pattern and damage evolution. Potential applications of the proposed numerical model schemes are investigated in some preliminary studies and simulation results are discussed. Finally, conclusions are drawn and possible improvements to the numerical approaches and extensions of the research work are given. / 本文认为微结构缺陷（微裂纹）的扩展决定了受力岩石的寿命（破坏时间）。基于此假设，提出了岩石寿命预测方法。利用线弹性断裂力学理论，通过FLAC进行了数值模拟。数值模型中每个单元定义一条初始裂纹，其长度与方向服从特定分布。基于亚临界裂纹扩展理论，由Charles方程决定微裂纹的扩展（速度）。如微裂纹发展至单元边界，或应力强度系数到达断裂韧度，则单元破坏。宏观裂纹由微裂纹所联合形成，并最终贯穿模型导致破坏。在形成宏观裂纹的过程中，发生弹塑性应力重分布。在数值模型中，编制了不同类型的微裂纹扩展方式，并在不同的受力条件下加以分析。数值模型的岩石寿命，裂纹形状，破坏方式以及一些重要的参数的数值模拟结果与解析解有较好的一致性。对本文所提出的数值模型的初步实际应用进行了分析，并讨论了计算结果。最后讨论了本文所提出的岩石寿命预测方法的可能改良与发展，并对进一步的研究工作给出建议。

Fatigue in concrete is a complex phenomenon involving formation of microcracks, their coalescence into major crack and simultaneous formation of the fracture process zone ahead of the crack tip. Complex phenomena are best dealt through an energy approach and hence it is reasonable to use the theory of thermodynamics. Fracture mechanics and damage mechanics are two theories that are based on physically sound principles and are used to describe failure processes in materials. The former deals with the study of macroscopic cracks, whereas the latter defines the state of microcracking. In this study, the concepts from these theories are utilized to improve our understanding and modeling of fatigue process in concrete. In this thesis, a closed form expression for the thermodynamic function entropy is proposed and examined for its size independency and its use as a material property to characterize failure of concrete under fatigue. In the thermodynamic formalism, dissipative phenomena are described by a dissipation potential or its dual, from which evolution laws for internal variables could be defined. In this work, closed form expressions for dual of dissipation potential are derived using concepts of dimensional analysis and self-similarity within the framework of fracture mechanics and damage mechanics. Consequently, a fatigue crack propagation law and a fatigue damage evolution law are proposed respectively. A method is proposed in this study to correlate fracture mechanics and damage mechanics theories by equating the potentials obtained in each theory. Through this equivalence, a crack could be transformed into an equivalent damage zone and vice versa. Also, damage state corresponding to a given crack in a member can be quantified in terms of a damage index. An analytical way of computing size independent S-N curves is proposed, using a nonlocal damage theory by including aggregate size and specimen size in the formulation. It is realized from this study that fracture mechanics and damage mechanics theories should be used in a unified manner in order to accurately model the process of fatigue in concrete. Furthermore, based on the models developed in this study, several damage indicators for fatigue of concrete are proposed. The advantages and limitations of each of these indices are presented such that, the relevant damage index could be used, based on available parameters. Additionally, deterministic sensitivity studies are carried out to determine the most important parameters influencing fatigue life of a concrete member.

Assessing long-term rock stability is an important aspect in the analysis of slopes, dam and bridge foundations, and other infrastructure. Rock behavior over tens to thousands of years must be anticipated when predicting the performance of, for example, an underground containment facility for nuclear waste. At such long time scales, the time dependence of rock failure, typically ignored in short time scale analyses, has a significant effect and must be included in the analysis. Since time-dependent rock behavior is thought to be caused by the subcritical growth of microcracks, a time-dependent analysis should incorporate a method of simulating subcritical crack growth. In this thesis, a rock bridge damage model was developed using the finite element program Abaqus to simulate subcritical crack growth for all three modes of crack tip displacement in three-dimensional rock masses. Since subcritical crack growth is not among the damage initiation and evolution criteria available in Abaqus, its effect was included in the model through the USDFLD user subroutine. Material properties for the damage model were obtained through laboratory fracture toughness testing of Escabrosa limestone from Kartchner Caverns. Tests included the grooved disk test for mode I, the punch-through shear with confining pressure test for mode II, and the circumferentially-notched cylindrical specimen test for mode III. The subcritical crack growth parameters n and A were calculated for all three modes using the constant stress-rate method. Fracture test results were compared with a previous study by Tae Young Ko at the University of Arizona, which tested Coconino sandstone and determined that the subcritical crack growth parameters were consistent among modes. This thesis expands upon Ko's work by adding the characterization of a second rock material in all three modes; results indicate that for Escabrosa limestone the subcritical crack growth parameters are not consistent among modes. Additionally, the Escabrosa limestone composing the caverns ranges from a more homogeneous, even-grained texture to a more heterogeneous texture consisting of coarse-grained veins and solution cavities set in a fine-grained matrix. To determine if the veined regions are more susceptible to fracturing and act as the nuclei of rock bridge failure, the fracture toughness tests were conducted separately for each texture. Results indicate that the more heterogeneous limestone has a higher fracture strength, fracture toughness, and subcritical crack growth index n than the more homogeneous limestone. This is in agreement with previous studies that determined that a more complex and heterogeneous microstructure produces a larger microcrack process zone and a more tortuous crack path, leading to higher fracture energies and larger values of n. Application of the rock bridge damage model to a simplified Kartchner cave room with a single roof block provided visualization of decreasing rock bridge size and produced time-to-failure estimates of 1,251 to 65,850 years. Multiple models were run to study the effect of (i) using material properties from each of the two textures identified in the Escabrosa limestone and (ii) varying the in-situ stress ratio, K. Both the value of K and the choice of Escabrosa texture had a large effect on the estimated time-to-failure, indicating that for future modeling of Kartchner accurate estimation of the in-situ stress ratio is as important as field identification of homogeneous vs. heterogeneous textures.

ABSTRACT As industries are upgrading rapidly from a lower steel grade to higher ones it has become necessary to study the effect of changing from lower steel grades to higher grades. This thesis reports on fatigue life and behaviour, economic implications and material composition of these higher strength steels (HSS) as compared to the conventional grades. Three grades are commercially available in South Africa: 300W, 350W and 460W. These different steel grades (conventional and HSS) with the same moment capacities where subjected to constant dynamic stresses and the fatigue crack growth of the overloading and unloading were monitored and compared with each other. The influences of the overloading and unloading made standard grades perform better under repeated loading than the HSS, since HSS have been proved to have poor ductility, resulting in lower number of cycles to failure. An 85% increase in material cost was generated as HSS replaces the conventional lower steel grades. Reduction in number of cycles to failure in HSS was over 500%. A space analysis for a multi-storey building with 10 beam floors was conducted for the various steel grades using a software package. The buckling and linear behaviours of these structures were compared. Although the deflections were not too far apart, it was shown clearly that grade lower steel grades performed better than the higher grades. An optimization was conducted using the parameters discussed in the text or obtained from experiment and computer modelling, in order to aid in the selection criterion of general purpose steel. Grade 300W was the optimal grade although the result was based mainly on the cost and fatigue behaviour of the three grades.

Esse trabalho trata da análise de corpos multi-fraturados utilizando o método dos elementos de contorno. Este método numérico é conhecido por ser robusto e preciso neste tipo de problema e também por requerer pequeno esforço computacional na criação da malha de elementos para o crescimento das fissuras. Duas metodologias para a análise do comportamento das fissuras são consideradas. A primeira é a já consagrada metodologia dual. Por meio desta técnica equações integrais distintas são aplicadas às faces da fissura. Estas equações integrais são escritas em termos de deslocamentos e forças de superfície. A segunda metodologia é a que emprega a formulação singular onde a fissura é considerada como um vazio no domínio sendo as faces da fissura separadas por uma pequena distância. No tocante ao crescimento das fissuras foi desenvolvido um procedimento especial para a determinação da direção de crescimento das fissuras o qual mostrou-se muito eficiente levando a resultados precisos. O crescimento das fissuras é efetuado considerando o fator de intensidade de tensão atuante na extremidade de cada fissura. Dessa forma, as fissuras mais solicitadas apresentam maior comprimento de propagação tornando a análise mais realista. Os fatores de intensidade de tensão são calculados por meio de duas técnicas. A primeira é a já conhecida técnica de correlação de deslocamentos a qual relaciona os deslocamentos atuantes nas faces da fissura. Uma técnica alternativa é também utilizada a qual emprega o campo de tensões presente na extremidade da fissura. Após a determinação dos fatores de intensidade de tensão quatro diferentes teorias de interação de modos podem ser utilizadas para a determinação do ângulo de propagação. Foram analisadas estruturas sendo os resultados comparados aos previstos analiticamente e também numericamente. As respostas obtidas foram satisfatórias validando assim a metodologia proposta neste trabalho / This work deals with analysis of multi-fractured bodies using boundary element method. This numerical method is known to be robust and accurate in this kind of problem and by small computational effort to create elements mesh of crack growth. Two methodologies to analyze of crack behavior are considerate. The first is consecrated dual methodology. Through this technique different kind of integral equations are applied to crack boundaries. These integrals equations are written in displacements and traction variables. Second methodology is singular formulation. Through this technique crack is represented like a hole in body and the crack boundaries is separated by a small gap. For crack growth was created a special proceeding to determination crack growth direction. This method is very efficient and your results are accurate. Crack growth is made through the stress intensity factor performed in crack tip. Then the cracks more requested going to propagate with a larger length’s growth turning this model very realistic. The stress intensity factors are calculated through two techniques in this work. First is the known correlation displacement technique which related displacement in crack boundaries. An alternative technique is also used which consider stress field in crack tip. After determination of stress intensity factors four different theories are used to calculate the crack growth angle. In this work were analyzed structures with results are compared with analytical and numerical answers. The results obtained went very satisfactory validating the methodology proposed

A austenita retida está sempre presente na microestrutura de camada cementada de aços, em maior ou menor quantidade. Como é uma fase dúctil comparada à martensita, sua presença tem sido alvo de muita controvérsia. Este trabalho apresenta um estudo sobre a influência da austenita retida na propagação de trincas curtas por fadiga em camada cementada de aço SAE 8620. Foram feitos ensaios de fadiga por flexão em quatro pontos, a temperatura ambiente, em corpos de prova sem entalhe com três níveis de amplitude de tensão e razão de tensões de 0,1. Através de diferentes ciclos de cementação e tratamentos térmicos, foram obtidas camadas cementadas com quatro níveis de austenita retida na microestrutura. O teor de austenita retida foi medido através da técnica de difração de Raios-X. Trincas superficiais foram monitoradas por meio da técnica de réplicas de acetato. Como resultados foram obtidos tamanho de trinca em função do número de ciclos e taxa de crescimento de trincas curtas. Corpos de prova com maiores níveis de austenita retida apresentaram maior vida em fadiga. / The retained austenite is always present in case carburized steel microstructure in small or high percentages. Since it is a ductile phase, its presence has long been a controversial subject. The influence of retained austenite on short fatigue crack propagation in case carburized SAE 8620 steel was studied in this work. Four-point-bend fatigue tests were carried out at room temperature in specimens without notch using three levels of stress range and a stress ratio of 0.1. Four different amount of retained austenite in the case carburized microstructure were obtained through different cycles of carburizing and heat treating. The retained austenite content was measured by X-ray technique, and the surface short crack growth was monitored by means of acetate replication technique. Crack length versus number of cycles and crack growth rate versus mean crack length were obtained as results. Specimens with higher levels of retained austenite in the carburized case showed longer fatigue life.

Neste trabalho desenvolveremos um modelo estatístico em uma escala micrométrica de interações entre as componentes do sistema que pretende descrever a propagação de trincas em materiais submetidos a tensões cíclicas. Apesar de sua extrema simplicidade, este modelo é capaz de reproduzir um resultado experimental bastante difundido entre engenheiros e especialistas, conhecido como lei de Paris, cujo enunciado estabelece que a taxa de crescimento de uma trinca sob carregamento cíclico é proporcional a uma potência da variação em seu correspondente fator de intensidade de tensões sendo largamente utilizada em aplicações práticas. Estamos particularmente interessados em estudar a introdução de desordem em determinados parâmetros associados ao material investigando as modificações impostas por este tipo de abordagem ao comportamento estatístico do modelo. Nossos principais resultados serão obtidos numericamente a partir de uma aproximação do tipo campo efetivo que ignora a correlação existente entre as diversas trincas que podem se formar ao longo do sistema durante o processo. Simulações numéricas do modelo serão igualmente consideradas ao analisarmos situações mais gerais do processo de propagação em que efeitos associados à regeneração de trincas podem desempenhar um importante papel na descrição do comportamento mecânico de um material. / In this work we consider a statistical model in a micrometric scale of interactions between the components of the system which intends to describe the failure of materials subjected to cyclic-load fatigue. Although quite simple, this model is able to reproduce an important experimental result widespread among engineers and experts, known as Paris law, which states that the growth rate of a crack at subcritical load is proportional to a power of the change in its stress-intensity factor and it is largely used in engineering practice. We are particularly interested to study the introduction of disorder in some parameters of the material investigating the modifications caused by this kind of approach in the statistical properties of the model. Our main results will be obtained numerically assuming an effective-field like approximation which neglects the correlation between the different cracks emerging throughout the system during the breaking process. Numerical simulations of the model are also performed in order to describe more general situations of propagation where the effects of crack self-healing can play an important role in the material strength.

O objetivo desta pesquisa foi verificar a influência de diferentes tamanhos de partículas de carga na tenacidade à fratura (KIc), nos parâmetros do crescimento subcrítico de trinca (n e f0) e de Weibull (m e 0), na longevidade estimada pelo diagrama tensão-probabilidade-tempo (SPT) e no limite de fadiga cíclica (LFC) de compósitos resinosos experimentais. Quatro compósitos foram preparados contendo 78% em massa (59% em volume) de conteúdo inorgânico, constituído por 67% de pó de vidro com diferentes tamanhos de partículas (d50 = 0,5; 0,9; 1,2 e 1,9 µm) e 11% de sílica pirogênica. Dados de KIc obtidos pelo método single-edge notched beam (25x5x2,8 mm; n=15) foram submetidos a ANOVA/teste de Tukey (p < 0,05). n e f0 foram determinados através do ensaio de fadiga dinâmica (10-2 a 102 MPa/s) utilizando um dispositivo de flexão biaxial (12x1,2 mm; n=10). Para determinar m e 0, mais 20 espécimes de cada compósito foram testados na taxa de 100 MPa/s. Os diagramas SPT foram obtidos a partir dos dados da fadiga dinâmica e análise de Weibull. No ensaio de fadiga cíclica, um dispositivo de flexão biaxial (12x1,2 mm) foi utilizado para se obter a resistência à flexão inicial (RFI; n=14) e o LFC (n=20). LFC foi obtido pelo método escada após 105 ciclos. Para todos os testes, os espécimes foram armazenados em água destilada a 37oC por 24h. Foi realizada a fractografia dos espécimes fraturados nas taxas 10-2 e 10-1 MPa/s da fadiga dinâmica e nos ensaios para determinação da RFI e LFC. Houve relação direta entre d50 e KIc (C0,5: 1,2±0,1b; C0,9: 1,3±0,1ab; C1,2: 1,3±0,1ab; C1,9: 1,4±0,2a, em MPa.m0,5). C0,5 (31,2±6,2a) e C1,9 (34,7±7,4a) apresentaram valores de n superiores a C0,9 (20,3±3,0b) e C1,2 (17,3±1,8b). C1,2 (166,42±0,01a) apresentou o maior valor de f0 (em MPa), seguido pelo C1,9 (159,82±0,02b), C0,9 (159,59±0,02c) e C0,5 (158,40±0,02d). Não houve diferença estatística entre os valores de m (6,6 a 10,6) e 0 (170,6 a 176,4 MPa) dos compósitos. As reduções na tensão de fratura para uma probabilidade de falha de 5% após 10 anos estimadas pelo diagramas SPT foram de aproximadamente 22% para C0,5 e C1,9 e 36% para C0,9 e C1,2. Não houve diferença estatística entre as médias de RFI (155,4 a 170,7 MPa). C0,5 (93,0±18,6a) apresentou o maior LFC (em MPa), seguido pelo C1,2 (91,8±11,1ab), C1,9 (87,2±3,0b) e C0,9 (82,5±8,0c). Defeitos sub-superficiais e superficiais foram as principais origens de fratura. A trinca se propagou pela matriz polimérica ao redor das partículas (deflexão de trinca) e todas as superfícies apresentaram características de fratura frágil. Como conclusão, compósitos com partículas maiores apresentaram maior KIC, enquanto que partículas menores contribuíram para um maior LFC. Compósitos com distribuição granulométrica mais ampla, independentemente do d50, apresentaram maior resistência ao SCG. Nos demais parâmetros e propriedades avaliados (m, 0 e RFI) não houve influência do tamanho das partículas. / The aim of this study was to verify the influence of different filler sizes in the fracture toughness (KIc), subcritical crack growth (n e f0) and Weibull (m e 0) parameters, longevity estimated by the strength-probability-time (SPT) diagram and cyclic fatigue limit (CFL) of experimental resin composites. Four composites were prepared, each one containing 78 w% (59 vol%) of inorganic content, in which 67 w% were glass powder with different filler sizes (d50 = 0.5; 0.9; 1.2 e 1.9 µm) and 11 w% were pyrogenic silica. KIc data was obtained by the single-edge notched beam test and submitted to ANOVA/Tukey tests (p < 0.05). n and f0 were determined by the dynamic fatigue test (10-2 a 102 MPa/s) using a biaxial flexural device (12x1.2 mm; n=10). 20 specimens of each composite were tested at 100 MPa/s to determine Weibull parameters. SPT diagrams were constructed using the dynamic fatigue and Weibull data. For the cyclic fatigue test, a biaxial flexural device (12x1.2 mm) was used to obtain the initial flexural strength (IFS; n=14) and CFL (n=20). CFL was determined by staircase method after 105 cycles. For all tests, the specimens were stored in distilled water at 37oC for 24h. It was done the fractography of the fractured specimens that was subjected to the 10-2 e 10-1 MPa/s rates of the dynamic fatigue and to the IFS and CFL tests. There was a direct relation between d50 e KIc (C0.5: 1.2±0.1b; C0.9: 1.3±0.1ab; C1.2: 1.3±0.1ab; C1.9: 1.4±0,2a, in MPa.m0,5). C0.5 (31.2±6.2a) and C1.9 (34.7±7.4a) presented higher n values than C0.9 (20.3±3.0b) and C1.2 (17.3±1.8b). C1.2 (166.42±0.01a) showed the highest f0 value (in MPa), followed by C1.9 (159.82±0.02b), C0.9 (159.59±0.02c) and C0.5 (158.40±0.02d). There were no statistical differences among the m (6.6 to 10.6) and 0 (170.6 to 176.4 MPa) values of the composites. The reductions in fracture stress at 5% failure probability for a lifetime of 10 years estimated by the SPT diagrams were approximately 22% for C0.5 and C1.9 and 36% for C0.9 and C1.2. There were no statistical differences among the IFS means (155.4 to 170.7 MPa). C0.5 (93.0±18.6a) showed the highest CFL (in MPa), followed by C1.2 (91.8±11.1ab), C1.9 (87.2±3.0b) and C0.9 (82.5±8.0c). Near-surface and surface flaws were the main fracture origins. The crack propagated by the polymeric matrix around the fillers (crack deflection) and all the fracture surfaces showed brittle fracture features. As conclusion, composites with large fillers presented the highest KIC, while the small fillers contributed to increase the CFL. Composites with broader granulometric size distribution, regardless of d50, showed higher resistance to SCG. There was no influence of the composites filler sizes in the others parameters and properties evaluated (m, 0 and IFS).