The J-laying technique for the construction of offshore pipelines requires a fast welding process that can produce sound welds in the horizontal-vertical position. The suitability of narrow gap gas metal arc welding (NG-GMA W) process for this application was previously demonstrated. The present programme studied the influence of process parameters on the fusion characteristics of NG-GMA welding in a range of different shielding gas compositions and welding positions. Statistical techniques were employed for both designing the experimental programme and to process the data generated. A partial factorial design scheme was used to investigate the influence of input variables and their interaction in determining weld bead shape. Modelling equations were developed by multiple linear regression to represent different characteristics of the weld bead. Transformation of the response variable based on the Cox-Box method was commonly used to simplify the model format. Modelling results were analysed by graphical techniques including surface plots and a multiplot approach was developed in order to graphically assess the influence of up to four input variables on the bead shape. Conditions for acceptable bead formation were determined and the process sensitivity to minor changes in input parameters assessed. Asymmetrical base metal fusion in horizontalvertical welding is discussed and techniques to improve fusion presented. At the same time, the interaction between the power supply output characteristic and the bead geometry was studied for narrow gap joints and the effect of shielding gas composition on both process stability and fusion of the base metal was assessed. An arc instability mode that is strongly influenced by arc length, power supply characteristic and shielding gas composition was demonstrated and its properties investigated. An optimized shielding gas composition for narrow gap process was suggested.

A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V\-S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then γc(G)≥g(G)-2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results.

A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V\-S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then γc(G)≥g(G)-2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results.

The research presented in this thesis covers two critical problems regarding lined pipes: dynamic impact and welding. A lined pipe consists of an inner layer (the liner) made of corrosion resistant alloy (CRA), e.g. AISI304 stainless steel, and an outer layer made of low carbon steel, e.g. carbon-manganese steel, C-Mn. To manufacture the lined pipe, a special heat treatment, known as tight fit pipe (TFP), based on cooling the liner to -200°C, heating the backing pipe to +500°C and inserting the liner inside the outer pipe, was used in this work. Both welding and impact with external objects are responsible for accumulating high levels of plastic strains and residual stresses which could lead to failure in the pipe sometime after the impact or the welding. The special welding process used in lined pipes typically consists of the overlay welding (inner welding) of the liner with the C-Mn steel pipe for each segment and the girth welding (outer welding) of the two segments. To simulate this welding process using the ABAQUS code, nonlinear heat-transfer and mechanical finite-element (FE) analyses have been conducted. A distributed power density of the moving welding torch and a non-linear heat transfer coefficient accounting for both radiation and convection have been used in the analysis and implemented in ABAQUS user-subroutines. The modelling procedure has been validated first against previously published experimental results for stainless steel and carbon steel pipe welding separately. The model has been then used to determine the isotherms induced by the one-pass weld overlay and the one-pass girth welding and to clarify their influence on the transient temperature field and residual stress in the lined pipe. Furthermore, the influence of the cooling time between weld overlay and girth welding and of the welding speed have been examined thermally and mechanically as they are key factors that can affect the quality of lined pipe welding. The same FE numerical procedure to analyse line pipe welding is then applied to simulate six cases experimentally tested in the lab within this project. Furthermore, two cases have been analysed first, namely a reference case, in which the effect of the TFP pre-heat treatment is neglected, and a second one where the pre-heat treatment has been taken into consideration. During welding, the FE thermal history and mechanical strain results for both cases correlate well with the experimental ones in the region with the highest residual stresses, because the effect of initial residual stresses is cancelled in the regions subject to very high temperatures. After welding, the numerical and experimental results have proved that the initial residual stresses due to the TFP pre-heat treatment are reasonably important in the liner whereas they are practically negligible in the C-Mn pipe. The same reference case is then compared numerically and experimentally with further five parametric cases to study the effect of welding properties (weld overlay and girth welding materials), geometric parameters (using weld overlay and liner) and welding process parameters (heat input). The numerical temperature fields and residual stresses are in good agreement with their experimental counterparts for all cases. The dynamic impact problem is a crucial one for lined pipes because of the reduction in the thickness of the outer pipe ensured by the internal protection from corrosion given by a thinner liner. In this case, the lined pipe is more affected by potential impact with external objects (so-called 'third party interference' in the Oil and Gas industry). In general, a dent produced by a freely dropped weight is responsible to a large extent of catastrophic failure in pipelines. Therefore, in this work, 3D FE models have been developed to simulate the mechanism of vertical free drop of a weight from different heights resulting in damage in the pipe. Models have been executed using a three-dimensional non-linear explicit-dynamics FE code, ABAQUS/EXPLICIT. In order to precisely simulate the response of the pipe to subsequent impacts and spring back, an elastic-plastic constitutive law is adopted using the isotropic Hooke's law and a Von Mises yield criterion, with work hardening based on an isotropic hardening rule associated with the equivalent plastic strain rate. Strain-rate dependent properties are specified for both materials, C-Mn and AISI304, to take into account the change in velocities during impact. The numerical strain results are reasonably consistent with the experimental ones recorded by four strain gauge rosettes positioned symmetrically around the dent centre. Numerical and experimental results are comprehensively analysed and discussed also in terms of practical implications in the industry.

A total dominating set of a graph G with no isolated vertex is a set 5 of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set in G. In this paper, we present several upper bounds on the total domination number in terms of the minimum degree, diameter, girth and order.

A demanda crescente por energia tem motivado a procura por petróleo e gás natural em ambientes com condições extremas, como operações em águas profundas e o transporte de fluídos corrosivos. Avanços tecnológicos recentes favorecem o uso de tubos de aço contendo uma camada interna resistente a corrosão (comumente chamados de Lined ou Clad Pipes) para o transporte de tais fluidos agressivos. Além disso, as tubulações submarinas são sujeitas a condições de instalação muito severas e, um caso de interesse, é o procedimento de reeling que permite com que a fabricação e inspeção da tubulação seja feita em terra. Apesar de possuir vantagens econômicas, a avaliação da integridade estrutural e especificação dos tamanhos toleráveis de trinca em juntas soldadas, nestas condições, torna-se uma tarefa complexa, devido a natureza dissimilar dos materiais e ao grande nível de deformação plástica no processo. Dessa maneira, este trabalho tem por objetivo o desenvolvimento de um procedimento de avaliação de forças motrizes elasto-plásticas em tubos contendo juntas soldadas circunferenciais sujeitos a flexão, para uma extensa gama de configurações geométricas. Dois métodos distintos foram desenvolvidos e analisados: a metodologia EPRI e o procedimento que utiliza a curva de tensão vs. deformação equivalente. As análises numéricas 3D fornecem os parâmetros de fratura necessários para a resolução do problema e a acurácia dos procedimentos é verificada a partir de estudos de casos e análises paramétricas. / The increasing demand for energy has motivated the oil and natural gas exploration in very hostile environments, including very deep water operation and the transport of corrosive fluids. Technological advances favor the use of high strength steel pipelines either clad or mechanically lined with a corrosion resistant alloy (CRA), such as Alloy 625, for the transport of corrosive hydrocarbons. Moreover, these pipelines are subjected to severe installation conditions and a case of interest is the pipe reeling process, which allows pipe welding and inspection to be conducted at onshore facilities. While cost effective, fracture assessments and specification of critical flaw sizes for the girth welds of lined/clad pipes are more complex due to the dissimilar nature of these materials and the high levels of plastic strain imposed during installation. In particular, effective analyses of crack driving forces in undermatched or partially mismatched pipe girth welds remain essential to determine more accurate acceptable flaw sizes for the piping system based upon conventional ECA procedures. This work focuses on the development of a procedure to determine the elastic-plastic crack driving forces for pipe girth welds with circumferential surface cracks subjected to bending load for a wide range of geometries and weld mismatch levels based upon based methodologies: the GE-EPRI framework and the equivalente stress vs. strain curve. The study also addresses the potential effects of an undermatching girth weld on critical flaw sizes. The extensive nonlinear, 3-D numerical analysis provide the fracture parameters for cracked pipes and cylinders with mismatched girth welds which will be applied in case studies and parametric analyses in order to verify the accuracy of the methods.

A demonstração feita por Erdos da existência de grafos com cintura e número cromático grandes é uma das primeiras aplicações do método probabilístico. Essa demonstração fornece um limite para o número de vértices de um grafo desse tipo, que é exponencial na cintura quando o número cromático é fixado. O foco deste texto, no entanto, são as construções determinísticas de grafos com cintura e número cromático grandes e os números de vértices dos grafos obtidos. As construções elementares conhecidas fornecem apenas grafos com um número Ackermanniano de vértices. O texto começa com uma breve repetição das demonstrações probabilísticas da existência de grafos e hipergrafos com cintura e número cromático grandes. Depois, a busca por construções determinísticas é motivada apresentando-se algumas construções para o caso particular de grafos livres de triângulo e com número cromático grande. São construídos os grafos de Tutte, Zykov, Mycielski e Kneser, os grafos de shift e os de planos projetivos finitos. Os números de vértices dessas construções são computados e comparados. De fato, a construção a partir de planos projetivos finitos tem um número polinomial de vértices. A parte principal do texto são as construções de grafos e hipergrafos com cintura e número cromático grandes. A primeira construção apresentada foi feita por Kriz. Ela foi a primeira construção para grafos com cintura e número cromático grandes que não envolvia hipergrafos. A segunda construção apresentada foi feita por Nesetril e Rödl. Essa construção antecede a de Kriz. Ela utiliza a amalgamação entre grafos e hipergrafos para obter um hipergrafo uniforme com cintura e número cromático grandes. A terceira e última construção apresentada foi encontrada por Alon, Kostochka, Reiniger, West e Zhu. Essa construção consegue obter hipergrafos uniformes com cintura e número cromático grandes diretamente a partir de um grafo, que é uma certa árvore aumentada. Em particular, essa construção obtém grafos com cintura e número cromático grandes sem envolver hipergrafos. Os números de vértices dos hipergrafos obtidos por essas construções são computados e comparados. / The proof by Erdos of the existence of graphs with high girth and high chromatic number is one of the first applications of the probabilistic method. This proof gives a bound on the number of vertices of such graphs, which is exponential on the girth if the chromatic number is fixed. The focus of this text is however on the deterministic construction of graphs with high girth and high chromatic number and on the number of vertices of the obtained graphs. The elementary known constructions can only give us graphs with an Ackermannian number of vertices. We begin by briefly repeating the probabilistic proofs of the existence of graphs and hypergraphs with high girth and high chromatic number. Then we motivate the search for deterministic constructions of such graphs by showing some constructions for the special case of triangle-free graphs with high chromatic number. We construct Tutte, Zykov, Mycielski and Kneser graphs, the shift graphs and graphs built from finite projective planes. We count and compare the number of vertices of the graphs obtained by each of these constructions. In fact, the construction based on finite projective planes gives us graphs with a polynomial number of vertices. The main part of the text consists of constructions of graphs and hypergraphs with high girth and high chromatic number. The first construction we present is due to Kriz. This was the first construction to give graphs with high girth and high chromatic number without using hypergraphs. The second construction we present is due to Nesetril and Rödl. This construction precedes the one by Kriz. It uses amalgamations between graphs and hypergraphs to obtain uniform hypergraphs with high girth and high chromatic number. The third and last construction we show was found by Alon, Kostochka, Reiniger, West and Zhu. This construction manages to build uniform hypergraphs with high girth and high chromatic number directly from a single graph, which is an augmented-tree. In particular, it constructs graphs with high girth and high chromatic number without using hypergraphs. We count and compare the number of vertices of the hypergraphs obtained by these constructions.

Métodos acurados de avaliação de tenacidade à fratura, incluindo curvas de resistência ao rasgamento dúctil de juntas soldadas de dutos e risers rígidos, tornam-se essenciais em procedimentos de avaliação de defeitos em regiões de soldas e zonas termicamente afetadas, nas quais defeitos não detectados podem se propagar devido às grandes tensões e deformações envolvidas na instalação e/ou operação dessa classe de estruturas. Este trabalho apresenta uma investigação experimental da tenacidade à fratura de uma junta soldada de um duto rígido de aço API 5L X80 (curvas J-Ãa). A motivação para este trabalho decorre da demanda crescente na aplicação de dutos de alta resistência na indústria de óleo e gás, em particular dutos submarinos e risers rígidos em catenária. Para tal, foram empregados corpos de prova de tração SE(T) fixados por garras, e flexão três pontos SE(B) contendo entalhe no centro da solda, para determinação das curvas J-R pelo método do corpo de prova único utilizando a técnica da flexibilidade no descarregamento, além das funções de flexibilidade e fatores n referentes aos corpos de prova SE(T) e SE(B) em função do nível de dissimilaridades mecânicas, o que permite obter valores mais assertivos das propriedades de tenacidade à fratura de juntas soldadas. / Accurate measurements of fracture resistance properties, including crack growth resistance curves for pipeline girth welds, become essential in defect assessment procedures of the weldment region and the heat affected zone, where undetected crack-like defects (such as lack of penetration, deep undercuts, root cracks, etc.) may exhibit further crack extension due to high tensile stresses and strains during installation and in-service operation. This work presents an investigation of the ductile tearing properties for a girth weld made of an API 5L X80 pipeline steel using experimentally measured crack growth resistance curves (J-Ãa curves). Use of these materials is motivated by the increasing demand in the number of applications for manufacturing high strength pipes for the oil and gas industry including marine applications and steel catenary risers. Testing of the pipeline girth welds utilized sidegrooved, clamped SE(T) specimens and 3P bend SE(B) specimens with a weld centerline notch to determine the crack growth resistance curves based upon the unloading compliance (UC) method using a single specimen technique. Recently developed compliance functions and n-factors applicable for SE(T) and SE(B) fracture specimens with homogeneous material and overmatch welds are introduced to determine crack growth resistance data from laboratory measurements of load-displacement records. This experimental characterization provides additional toughness data which serve to evaluate crack growth resistance properties of pipeline girth welds using SE(T) and SE(B) specimens with weld centerline cracks.

Métodos acurados de avaliação de tenacidade à fratura, incluindo curvas de resistência ao rasgamento dúctil de juntas soldadas de dutos e risers rígidos, tornam-se essenciais em procedimentos de avaliação de defeitos em regiões de soldas e zonas termicamente afetadas, nas quais defeitos não detectados podem se propagar devido às grandes tensões e deformações envolvidas na instalação e/ou operação dessa classe de estruturas. Este trabalho apresenta uma investigação experimental da tenacidade à fratura de uma junta soldada de um duto rígido de aço API 5L X80 (curvas J-Ãa). A motivação para este trabalho decorre da demanda crescente na aplicação de dutos de alta resistência na indústria de óleo e gás, em particular dutos submarinos e risers rígidos em catenária. Para tal, foram empregados corpos de prova de tração SE(T) fixados por garras, e flexão três pontos SE(B) contendo entalhe no centro da solda, para determinação das curvas J-R pelo método do corpo de prova único utilizando a técnica da flexibilidade no descarregamento, além das funções de flexibilidade e fatores n referentes aos corpos de prova SE(T) e SE(B) em função do nível de dissimilaridades mecânicas, o que permite obter valores mais assertivos das propriedades de tenacidade à fratura de juntas soldadas. / Accurate measurements of fracture resistance properties, including crack growth resistance curves for pipeline girth welds, become essential in defect assessment procedures of the weldment region and the heat affected zone, where undetected crack-like defects (such as lack of penetration, deep undercuts, root cracks, etc.) may exhibit further crack extension due to high tensile stresses and strains during installation and in-service operation. This work presents an investigation of the ductile tearing properties for a girth weld made of an API 5L X80 pipeline steel using experimentally measured crack growth resistance curves (J-Ãa curves). Use of these materials is motivated by the increasing demand in the number of applications for manufacturing high strength pipes for the oil and gas industry including marine applications and steel catenary risers. Testing of the pipeline girth welds utilized sidegrooved, clamped SE(T) specimens and 3P bend SE(B) specimens with a weld centerline notch to determine the crack growth resistance curves based upon the unloading compliance (UC) method using a single specimen technique. Recently developed compliance functions and n-factors applicable for SE(T) and SE(B) fracture specimens with homogeneous material and overmatch welds are introduced to determine crack growth resistance data from laboratory measurements of load-displacement records. This experimental characterization provides additional toughness data which serve to evaluate crack growth resistance properties of pipeline girth welds using SE(T) and SE(B) specimens with weld centerline cracks.

A demanda crescente por energia tem motivado a procura por petróleo e gás natural em ambientes com condições extremas, como operações em águas profundas e o transporte de fluídos corrosivos. Avanços tecnológicos recentes favorecem o uso de tubos de aço contendo uma camada interna resistente a corrosão (comumente chamados de Lined ou Clad Pipes) para o transporte de tais fluidos agressivos. Além disso, as tubulações submarinas são sujeitas a condições de instalação muito severas e, um caso de interesse, é o procedimento de reeling que permite com que a fabricação e inspeção da tubulação seja feita em terra. Apesar de possuir vantagens econômicas, a avaliação da integridade estrutural e especificação dos tamanhos toleráveis de trinca em juntas soldadas, nestas condições, torna-se uma tarefa complexa, devido a natureza dissimilar dos materiais e ao grande nível de deformação plástica no processo. Dessa maneira, este trabalho tem por objetivo o desenvolvimento de um procedimento de avaliação de forças motrizes elasto-plásticas em tubos contendo juntas soldadas circunferenciais sujeitos a flexão, para uma extensa gama de configurações geométricas. Dois métodos distintos foram desenvolvidos e analisados: a metodologia EPRI e o procedimento que utiliza a curva de tensão vs. deformação equivalente. As análises numéricas 3D fornecem os parâmetros de fratura necessários para a resolução do problema e a acurácia dos procedimentos é verificada a partir de estudos de casos e análises paramétricas. / The increasing demand for energy has motivated the oil and natural gas exploration in very hostile environments, including very deep water operation and the transport of corrosive fluids. Technological advances favor the use of high strength steel pipelines either clad or mechanically lined with a corrosion resistant alloy (CRA), such as Alloy 625, for the transport of corrosive hydrocarbons. Moreover, these pipelines are subjected to severe installation conditions and a case of interest is the pipe reeling process, which allows pipe welding and inspection to be conducted at onshore facilities. While cost effective, fracture assessments and specification of critical flaw sizes for the girth welds of lined/clad pipes are more complex due to the dissimilar nature of these materials and the high levels of plastic strain imposed during installation. In particular, effective analyses of crack driving forces in undermatched or partially mismatched pipe girth welds remain essential to determine more accurate acceptable flaw sizes for the piping system based upon conventional ECA procedures. This work focuses on the development of a procedure to determine the elastic-plastic crack driving forces for pipe girth welds with circumferential surface cracks subjected to bending load for a wide range of geometries and weld mismatch levels based upon based methodologies: the GE-EPRI framework and the equivalente stress vs. strain curve. The study also addresses the potential effects of an undermatching girth weld on critical flaw sizes. The extensive nonlinear, 3-D numerical analysis provide the fracture parameters for cracked pipes and cylinders with mismatched girth welds which will be applied in case studies and parametric analyses in order to verify the accuracy of the methods.