Abstract
The crack growth rate of stress corrosion cracking is influenced by residual stress; therefore, if the three-dimensional residual stress in welded pipes can be accurately evaluated, their remaining service life may be predicted. While welding simulations offer a means of assessing residual stress, but weld joining techniques are known to yield significant individual variations even under similar welding conditions. Consequently, a residual stress evaluation grounded in actual measurement data is essential. A non-destructive method for estimating three-dimensional residual stress distribution in situ employs X-ray Diffraction alongside eigenstrain theory. In this approach, the eigenstrain of the entire structure is derived through inverse analysis of measured surface elastic strain values, with three-dimensional residual stresses subsequently calculated by inputting these estimated eigenstrains into a finite element (FE) model. However, to estimate three-dimensional eigenstrains from two-dimensional surface data, it is necessary to appropriately reduce the number of unknown variables. Function approximation serves as an effective method for this reduction, though its optimization is required, as the accuracy of the estimation depends on the function's shape. Previous studies have typically relied on empirical methods to determine the shape of this function. This study first elucidates, through numerical analysis, the challenges associated with empirically defining the approximate function shape of eigenstrain. Subsequently, a novel method is proposed, approximating the eigenstrain by employing a superposition of Chebyshev polynomials and Gaussian functions and optimizing the function’s shape with relatively few parameters. The proposed method’s effectiveness is demonstrated via numerical analysis, aiming to establish an approach that eliminates reliance on empirical assumptions.
