Non-destructive estimation of three-dimensional inelastic strain via nonlinear inverse analysis using displacement

Abstract

The service life of mechanical structures is influenced by the inelastic strain generated during manufacturing and operation. Therefore, non-destructive estimation of three-dimensional inelastic strain is essential to ensure structure safety even during operation. Accordingly, an inverse problem method was proposed to estimate the inelastic strain over the entire component based on the eigenstrain theory using non-destructively measured surface displacement. However, this method assumes micro-deformation, in which the causal inelastic strain and resulting displacement are linearly related. In practice, the value of inelastic strain is large, which results in large deformation and a nonlinear effect on displacement determined by the magnitude of the inelastic strain. This study considers the inverse problem of estimating the creep strain in a turbine blade for power generation from the displacement caused by the creep strain and proposes a method to derive the exact solution even for large deformation problems. Numerical simulations using a simplified turbine model show that the estimates converge to the correct solution value with relatively high accuracy in the absence of measurement errors. Moreover, the result of the iterative calculations used in the proposed method converge around the correct value, even in the presence of measurement errors in the displacement by the laser displacement meter.

Non-destructive estimation of three-dimensional creep strain based on non-linear inverse analysis using displacement

“…This method was applied using the values of the surface displacements, and the estimation accuracy was evaluated by comparing the estimated creep strain with the correct values. This study is the first to demonstrate that the inverse analysis method proposed in previous research (Fujii et al, 2023) is effective for solving non-linear problems in 3-D models with torsion, such as those found in actual turbine rotor blades. Next, a non-linear inverse method with improved convergence was applied, and its convergence and estimation accuracy were compared.…”

“…However, most actual creep strains in turbine blades are large-deformation problems with relatively large creep-strain values, and the relationship between the cause and effect is non-linear. Therefore, the authors proposed a non-linear inverse analysis method that can provide relatively accurate estimates, even when the relationship between the cause and effect is non-linear (Fujii et al, 2023). This method converges the solution through iterative calculations that update the estimated value, and its effectiveness is demonstrated through numerical analysis.…”