PSI - Issue 14

Vijay Sai et al. / Procedia Structural Integrity 14 (2019) 491–498

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Ch. Vijay Sai/ Structural Integrity Procedia 00 (2018) 000–000

1. Introduction Residual stresses are stresses resulting from Eigen strains that transcend the elastic domain, during the course of processes like welding. Essentially self-balanced and locked within a component, these stresses amplify the stress they are subjected during their service. Evidence is found, that these stresses aid a number of failure phenomena, as observed by Shi and Booth (2013) and Christopher et al. (2011) that ultimately result in the loss of structural integrity. Lundin (1982) and Ul-Hamid (2005) state that dissimilar weld joints, are particularly prone to failure. Apart from the metallurgical aspects that contribute to this phenomenon, the difference in base material properties also has bearing on the residual stress magnitude and distribution. It is therefore, important to study the nature and evolution of residual stresses in dissimilar weld joints. While experimental studies glean a part of the complex process, advances in Finite Element Methods, has made it possible to estimate the temperatures, strains and other variables to a reasonable accuracy, at every location, during the entire duration of the process. Such studies have been undertaken by Hyung Lee et al. (2013) and Wenchun and Wanchuk (2016) This paper, investigates the residual stress evolution in joints between Modified 9 Cr-1Mo Steel (P91), and Stainless steel 304 (SS304), which are widely used nuclear materials. Three dimensional, sequentially coupled thermo-metallurgical and mechanical analysis was conducted on plate butt weld and circumferential pipe welds. Temperature dependent thermal and mechanical properties were considered for the analysis. The variation of temperature and stress fields in the dissimilar joints is delineated in comparison to joints of P91 and SS304. 2. Evaluation of residual stress To evaluate residual stress, the process of welding was simulated mathematically, over the domain of the joint. Therefore, governing equations were solved for every time step, starting from initiation of welding process to cooling the component to room temperature. To simulate the welding torch of GTA process, Goldak’s double ellipsoidal heat source model was used. Fourier’s equation in the three dimensions and equations of cooling were used to determine the temperature field. Change in material properties, with temperature were considered during both heating and cooling. The thermal analysis was coupled with metallurgical analysis to solve Leblond and Koinsten-Marburger equations, to determine phase fractions in P91 steel. Martensite is formed in P91 steel during cooling. In the mechanical analysis, strains due to temperature and phase transformation were evaluated for every time step. Accounting the material properties, of an element, depending on its temperature and phase fractions, the nodal displacements were estimated. Stress-strain relationships were used to determine the stress at every time step, culminating with residual stress at the end of cooling to room temperature. The concentrated nature of the heat source, during welding results in non-uniform and steep temperature fields, and gives rise to eigen strains which result in residual stress. Thus the process of determining residual stress, involves geometrical and material modeling which are described further. The heat source was modeled by heat input fitting, which involves multiple two dimensional thermal analysis on cross-section of the considered joint to optimize the parameters of the heat source. The equations were solved using SYSWELD solver and package and simulated on Visual Weld interface. 2.1. Geometric modeling Butt weld joints between 100mm wide, 220 mm long and 3mm thick plates and 6” nominal diameter, schedule 10, 100 mm long pipes were three-dimensionally modeled. The physical entities were discretized using brick and wedge elements, with three degrees of freedom at each node. A two dimensional overlapping mesh was used to define the surface, for applying cooling equations. The weld trajectory was simulated using one-dimensional elements, between the two parts. For compatibility, two parts share common nodes at the joint. The three dimensional models are seen in Fig. 1. The mesh was refined in the vicinity of the weld zone, to improve accuracy, in regions with large temperature gradients. The size of the smallest element is 0.75 mm. Additionally, nodes of the corner elements of plate butt weld joint were restrained in all directions, to simulate clamping of the joint. Two corner nodes on top surface of pipe at one section were similarly restrained. This effectively hangs the pipe, during the simulation. The clamping conditions affect the residual stress in a joint, with a higher degree of restraint, resulting in higher residual stresses as observed by. Aalami-aleagha (2012).