Analytical determination of residual stresses in a butt‐weld of two thin rectangular plates

Abstract

Based upon the direct integration method, the technique for analysis of residual stresses in a thin rectangular plate consisting of two butt-welded plates is presented. The material of plate is assumed to be elastic-plastic. The welded joint is modeled by a locally distributed field of longitudinal and transversal residual strains.

Axisymmetric residual stresses in a solid cylinder of finite length

“…The formulation and solution of the inverse problems is based on the so-called conventional-plastic strain hypothesis [ 21 , 22 ] implying the base material of a solid to be elastic, while the expected zone of residual stress distribution exhibits specific elastic–plastic behavior so that the total strain can be represented in the following form: where is the total strain tensor, is the tensor of elastic strains occurring within the entire solid, and denotes the tensor of incompatible strain [ 23 ] distributed within the area affected by the impacts causing the residual stress–strain state. This approach has been efficiently employed for the analysis of residual stresses due to welding residual strains in infinite layers with rectilinear and circular welds [ 24 , 25 ], butt-welded cylindrical vessels [ 26 , 27 ], and rectangular plates [ 28 ]. Special attention in the latter paper was given to the end effects in the butt-welded rectangular plate by performing the exact analysis based on the direct integration method [ 29 ].…”

Analysis of residual stresses in a long hollow cylinder

“…This solution strategy allows one to construct an exact analytical solution without unjustified increasing degree of the governing differential equations. This direct integration method has also been employed for analysis of the welding residual stresses in an infinite layer [41e43] and butt-welded rectangular plates [44].…”