Determination of the triaxial distribution of residual stresses in welded joints of structural elements with rectilinear seams and estimation of their influence on joint strength in the presence of crack-type defects

Abstract

On the basis of a three-dimensional theory, we consider a mathematical model of a welded joint of plane structural elements with rectilinear seams. These joints are simulated by a plane layer with rectilinear seam with residual stresses. Using the method of direct integration of key equations without additional potential functions, we obtain expressions for components of the stress tensor for a set of given inconsistent residual strains localized in the weld. We investigate the influence of residual stresses on the static strength of this welded joint with sharp defects simulated by external surface cracks. Using a twoparameter criterion for brittle-ductile fracture, we calculate the load factors for a welded joint with a crack in the weld.Welded joints with rectilinear seams are widely used in various elements of welded structures. Among them are plate-like structural elements, pipes, in particular, main pipelines, etc. The negative influence of nonrelaxed residual stresses on strength and load-carrying ability of welded structures, especially in the presence of sharp concentrators, is well known. Locality of residual plastic strains causes, in the general case, a triaxial stressed state of structural elements in the zone of the weld. To estimate this state, it is necessary to solve a three-dimensional problem. In the process of long-term operation and in the manufacture of structures, various sharp defects can appear in zones of welded joints, which are usually simulated by cracks. Analysis of the results of investigation presented in domestic works (see, e.g., [4]) shows that, in zones of axial (longitudinal) welds in cylindrical pipes (main pipelines), the distribution of welding stresses slightly differs from an analogous distribution in plates, i.e., in this case, the effect of curvature of a pipe is insignificant. In the general case, this distribution is triaxial. For its analysis in zones of welds, we use a mathematical model of a plane layer with rectilinear seam. For structures in long-term operation, a calculated-experimental method is used. The method is based on mathematical models of bodies with residual stresses and inverse problems with the use of experimental data. The essence of the method is presented, e.g., in [3,5,8,9]. In [7], based on this method, the strength of a part of the pipeline with a circumferential crack in a weld is considered. In the case where the circumferential crack lies outside the weld and a part of the pipeline is subjected to the action of torques, the process of propagation of the crack in linear and nonlinear cases is investigated in [14] on the basis of finite-element analysis. Calculated-Experimental Determination of Residual Stresses in Joints with WeldConsider an infinite plane layer of thickness 2h in the Cartesian coordinate system X 1 , X 2 , X 3 . We introduce the dimensional coordinates system x = X 1 /h, y = X 2 /h , z = X 3 /h , with axis y directed along the

Calculation of Stresses near Holes in Welded Plates Taking Account of the Residual Deformations

“…Results of the calculations. For testing, let us consider a rectangular plate with half-sides a and b with residual deformations (1), ( 2), ( 7 The given graphs practically coincide with the data of the calculations obtained in [6] for this problem using another method.…”

“…, has also shown a complete convergence of the results of the calculation with the data [6] obtained by way using other methods.…”

“…Therefore, approximate methods of determining the residual weld stresses are common in the literature. The theoretical-experimental method [6] is among them, which generalizes the approaches known in the literature. The essence of this method is based on the fact that in the process of welding, plastic deformations are localized in the weld area and these deformations for line welds of large length are functions only of the distance to the center of the weld.…”

“…In this work, the calculation-and-experimental method [6] was used to determine the residual stresses in the plates. The algorithm for determining the stresses the near the holes in the plates due to residual deformations is based on the method of integral equations.…”

“…Let us consider a plate of an arbitrary shape with a line weld, whose center is located on the Оу axis. According to [6], it is assumed that plastic deformations, which arose in the plate after welding, are expressed as follows: 0 0 0 0 0 0 ( ), ( ), ( )…”