Evaluation of the Three-dimensional Welding Residual Stresses Based on the Eigenstran Methodology via X-Ray Measurements

In order to predict the lifetime of welded structures, it is important to evaluate threedimensional residual stresses nondestructively. However, X-ray diffraction is useful for measuring residual stresses only on the surface. Neutron diffraction is known to be an effective nondestructive method for measuring residual stresses till a depth of several tens of millimeters. Nevertheless, it is not a technique useful for on-site measurements. This is because neutron diffraction is achievable only within special irradiation facilities. In this paper, the authors have proposed a non-destructive method to estimate three-dimensional residual stresses by using X-ray measurements. In this method, the residual stresses for an entire structure are calculated from eigenstrains by using an elastic FEM (Finite Element Method) analysis. Eigenstrains can be estimated from elastic strains measured through X-ray diffraction using inverse analysis. The relationship between the three-dimensional eigenstrains and the surface elastic strains can be obtained if the Young’s modulus, Poisson’s ratio, and dimensions of the structure are known. This study aims to demonstrate the effectiveness of the proposed method on an actual butt-welded plate made of stainless steel SUS430. To evaluate the accuracy of this method, the residual stresses estimated using the method was compared with that measured using X-ray diffraction. In order to maximize the estimation accuracy of this inverse analysis, we considered the eigenstrain distributions along both the welding and thickness directions, as well elastic strains measured on the weld metal were used to estimate. Introduction It is important to predict crack propagation for observed cracks to prevent fatigue fractures and stress corrosion cracking (SCC) in welded structures. However, it is difficult to estimate crack growth rate without information on welding residual stresses. Three-dimensional welding residual stresses can be simulated qualitatively by using thermal elastic-plastic FEM analysis [1,2]. Nevertheless, it is recommended that each welded structure be quantitatively measured because individual differences in welding residual stress between them can be high. Currently, diffraction methods, including X-ray diffraction and neutron diffraction [3,4], are used as nondestructive measurement methods. However, it is impossible to measure three-dimensional stress distribution on-site by using these methods. Xray diffraction is useful to measure only surface residual stresses. Higher energy diffraction methods, including synchrotron and neutron diffractions, are available only within special irradiation facilities. Therefore, the targeted welded parts have to be destructively cut from an actual welded structure for measuring stress distribution. The cutting process releases some of the residual stresses, which affects the accuracy of the entire measurement process. As an alternative, the Bead Flush method, which is based on the eigenstrain methodology [5], has been proposed [6]. In this method, three-dimensional residual stresses are calculated by conducting Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 329-334 doi: http://dx.doi. org/10.21741/9781945291173-56 330 elastic FEM analysis on eigenstrains, which in turn are estimated through inverse analysis [7] on released strains measured using strain gauges during the removal of the weld reinforcement. Eigenstrains are defined as a sum of inelastic strains [5], but they are different from the sum of physical inelastic strains such as plastic, thermal, and transformation strains [8]. Here, the smoothening of excess weld metal can be regarded as a non-destructive process essentially because it can be eliminate a toe of weld that has the potential to become a crack starter. However, processing strains that arise on the machined surface owing to this method can worsen the accuracy of strain gauges that measure released strains. In order to overcome the disadvantages of the Bead Flush method, the first author has proposed the use of X-ray diffraction instead of strain gauges to estimate both the welding eigenstrains and processing strains [9]. The effectiveness of this method has been proved via numerical simulation. Besides, experimental demonstrations of this method have been conducted on an actual butt-welded plate made of 2Cr-1Mo ferritic steel [10]. However, the accuracy of estimating residual stresses along the perpendicular to the welding direction is not sufficient. Numerical simulation has confirmed the higher accuracy of this method when residual strains on machined surface measured by X-ray diffraction are used for estimation [11]. In the present study, the authors have estimated residual stresses of welded plates made of SUS430 by using this method on elastic strains measured over the weld metal [12]. For this estimation, it is assumed that welding eigenstrains are constant along the thickness direction even though the butt-welded joint has single U-groove before welding. The eigenstrain distribution along the welding direction is also neglected during inverse analysis. The residual stresses of welded joints made of SUS430 are estimated using this method after considering eigenstrain distributions along both the welding and thickness directions. Parameters to express eigenstrain distributions are determined following the Response Surface methodology. To evaluate the estimation accuracy, the residual stresses estimated using this method are compared with those measured by X-ray diffraction. Analytical Procedure The elastic strains {εe} of the concerned elements and the welding eigenstrains {ε} for the entire structure can be related through an intermediary an elastic response matrix [Re] as: {εe} = [Re] {ε} (1) The i-th column of the response matrix can be determined by imposing a unit eigenstrain on the i-th component of {εe} during elastic FEM analysis. Based on Eq. (1), the surface elastic strains before and after the removal of the weld reinforcement {εeb} and {εea} respectively can be expressed, as follows: {εeb} = [Rb] {ε} (2) {εea} = [Ra] {ε} + [Ra] {εpa} (3) where [Rb] and [Ra] respectively denote the response matrix before and after the removal. {εpa} is the processing strain that remains after the smoothening. By jointing Eq. (2) and Eq. (3), we obtain the following equations [18]: {εeb εea } = [R] {ε εpa} (4)