A CFD-FEM Model of Residual Stress for Electron Beam Welding Including the Weld Imperfection Effect
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the State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology(HUST), Luoyu Rd, Wuhan 1037, P.R. China. RENZHI HU, JINGSHENG WANG, MANLELAN LUO, ANGUO HUANG, and SHENGYONG PANG are with the State Key Laboratory of Material Processing and Die & Mould Technology, Huazhong University of Science and Technology(HUST), Luoyu Rd, Wuhan 1037, P.R. China. Contact e-mail: [email protected] BING WU is with the Science and Technology on Power Beam Processes Laboratory, AVIC Manufacturing Technology Institute, Beijing, P.R. China. Manuscript submitted August 16, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
INTRODUCTION
ELECTRON beam welding (EBW) is a key technology used for joining components in large-scale aeronautical and aerospace structures. Residual stresses from EBW must be assessed to reduce welding deformations and structural failures in the welds. During the welding process, due to the extremely high temperature caused by the electron beam, the instability of the keyhole may produce some imperfections. Hence, an accurate model for predicting the residual stress from EBW is important in engineering. Numerous mathematical models of the residual stress induced by EBW were developed in past decades based on heat conduction[1–5] and thermal stress calculations.[6–10] For instance, Elmer et al.[1] calculated the heat conduction of EBW from a distributed, point, or
line heat source. Hemmer et al.[3] presented a model based on a combination of the moving line source solution and the solution for a cylindrical cavity moving though a plate of finite thickness. Piotr et al.[5] used an invariable heat source model to simulate the temperature field during EBW. Liu et al.[7] proposed a three-dimensional model to investigate the residual stress of a 50-mm-thick plate that was welded by an electron beam. Zhao et al.[10] used the contour and X-ray methods to measure the internal and surface longitudinal stresses in a thick welded plate caused by EBW; they used the finite element method (FEM) to simulate the welding process. Cowles et al.[8] developed a three-dimensional (3D) model to predict the residual stress of EBW in a high-pressure drum rotor and compared the simulated results with an experiment. These researches are mostly based on the permanent heat source model, especially, for the analysis of thermal stress and residual stress calculations. However, residual stress from EBW is not only associated with heat transfer, as fluid flow and keyhole dynamics also occur in the process. This is because the keyhole and weld pool dynamics of EBW determine the process defects and weld joint geometries. Theoretically, a residual stress model including these effects should provide more accurate results. Usually, the computational fluid dynamics (CFD) model has been used to simulate high-energy beam welding, such as laser welding[11–14] and EBW. Recently, there have been several reports on fluid flow modeling of EBW. By assuming that the keyhole is stationary, Wei[15,16] and Rai[17,18
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