Peridynamics is a nonlocal theory that applies an integral term to represent the material response. Without a spatial differential term involved, peridynamics possesses certain advantages for solving discontinuity-involved problems. However, due to the reduction of stiffness, the deformation near the boundary region by peridynamics has a low accuracy compared to the local elastic deformation. Previous peridynamics boundary condition treatment enriches the stiffness on the boundary region by adding an artificial layer outside the domain boundary. However, this requires the deformation of the pseudo-layer to be pre-determined. In addition, the accuracy of the response on the physical domain depends largely on the accuracy of the pre-determined deformation on the pseudo-layer. Considering the fact that peridynamics reduces to local elasticity as the horizon size goes to zero, and previous researches indicate the potential advantage of boundary enrichment via the horizon varying approach, in this paper, peridynamics with a variable horizon is utilized as an efficient way to reduce the boundary-induced inaccuracy. Firstly, the pseudo-layer boundary condition treatments are discussed by using the symmetrical enrichment function and other extrapolation functions. Then, the variable horizon boundary condition treatment is introduced and a robust improvement of deformation accuracy on the boundary region is observed compared to other boundary condition treatments for both one- and two-dimensional examples. The variable horizon approach requires no additional pseudo-layer and the boundary conditions are applied directly on the physical boundary. Thus, the variable horizon approach is easy to implement and its computational cost is reduced.

In order to clarify the role of different post-weld heat treatment processes in the manufacturing process, welding tests, post-weld heat treatment tests, and finite element analysis (FEA) are carried out for 12C1MoV steel pipes. The simulated temperature field and residual stress field agree well with the measured results, which indicates that the simulation method is available. The influence of post-weld heat treatment process parameters on residual stress reduction results is further analyzed. It is found that the post weld dehydrogenation treatment could not release residual stress obviously. However, the residual stress can be relieved by 65% with tempering treatment. The stress relief effect of “post weld dehydrogenation treatment + temper heat treatment” is same with that of “temper heat treatment”. The higher the temperature, the greater the residual stress reduction, when the peak temperature is at 650–750 °C, especially for the stress concentration area. The longer holding time has no obvious positive effect on the reduction of residual stress.

The key to accurately predict welding residual stress is to explore the solid-phase transition law of SA508-3 steel and establish the phase transition model under continuous cooling conditions. The effects of cooling rate on phase transformation and strain response of SA508-3 steel were investigated in this paper. The established programs accurately predict the evolution of microstructure at different cooling rates, the relationship between the bainite volume fraction and temperature is fitted by a modified bainite transformation model and is validated by optical microscopy and dilatometric test. The strain evolution of SA508-3 steel is predicted at different cooling rates and is verified by the dilatometric test. In addition, the effects of bainite transformation and martensite transformation on the strain response of SA508-3 steel are intensively discussed. This work casts light on the simulation of metallurgical effects at different cooling region during welding.

This paper investigates the evolution of temperature and stress during induction heating local postweld heat treatment (PWHT) of ultra-thick pressure vessels (with a thickness typically exceeding 300 mm) through electromagnetic-thermo-mechanical coupling simulations and experimental validation, aiming to develop an effective heat treatment method for ultralarge equipment. The effects of various inductive heating parameters including the cable winding width, the number of turns, the spacing, the winding method, the current density, and the current frequency on the temperature uniformity during the heat treatment holding time are studied. The results indicate that the maximum temperature difference is directly proportional to current density, but inversely proportional to frequency, winding width, and the number of turns. After local PWHT, the residual stress on the outer surface of backward-oriented pressure vessels can be effectively reduced, but the stress relief on the inner wall is relatively small. Furthermore, the influence of heated bandwidth on the reduction of residual stress is considered. If reducing residual stress on the inner wall is considered, the width of the heated band should exceed 3Rt. If aforementioned width cannot be achieved, the local PWHT by primary plus secondary heating method can be used to further reduce the residual stress. This research sheds light on the application of inductive heating in ultralarge pressure vessels.