An inverse approach for constructing the residual stress field induced by welding

Y P Cao,N Hu,J Lu,Z H Yao,H Fukunaga

doi:10.1243/030932402760074562

Abstract

In this paper, an inverse approach based on the inherent strain method has been proposed for constructing the residual stress field induced by welding. Firstly, some smooth basis functions in the form of polynomials have been employed to approximate inherent strains. To select the basis functions properly, previous valuable knowledge about distributions of residual stresses for some typical welding structures should be considered. Furthermore, singular modes in the assumed inherent strain that do not cause residual stresses should be excluded. In this way, a stable profile of the inherent strain field can be assumed. Secondly, by employing the finite element method (FEM) and the least-squares technique, the inherent strain field can be identified from the experimental data at some key points. The proper selection of positions of experimental points has also been considered. Finally, the distribution of residual stresses can be constructed efficiently by using the obtained inherent strain field. Compared with the traditional inherent strain method, in the present work the sensitivity matrix for predicting inherent strains can be evaluated more effectively and experimental data needed in the identification procedure can be reduced significantly. Some typical examples have been presented to demonstrate the effectiveness of the present method.

Highlights

The residual stresses induced in the welding procedure can greatly affect the performance of structures
Due to the explicit form of the inherent strains in form of polynomial, some terms in the polynomials corresponding to the singular modes, which satisfy the compatibility condition explicitly, can be recognized and removed ; 3) Thirdly, to get a stable result, the proper selection of locations of experimental points is accounted for
When the number of components of inherent strain in the vector p are equal to the number of the unknown coefficients in the vector a, the distribution of inherent strain field in eqn (8) can be determined if the p vector are known using the following equation, a = L(x, y, p)

Summary

Introduction

The residual stresses induced in the welding procedure can greatly affect the performance of structures. The task in this inverse problem is to find the inherent strain ε* with the aid of the experimental data, and use it to get the residual stresses.

Results

Conclusion