Use of inverse solutions for residual stress measurements

Article Abstract:

The mathematical commonality of physically different destructive measurement types is demonstrated and a generic procedure for achieving effective and reliable solutions is presented. The proposed procedure uses unit pulses as basis functions to solve the integral equations and this method is conceptually straightforward and has direct physical interpretations and permits enforcement of equilibrium constraints.

Measurement, Continuum mechanics, Integral equations

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Uncertainty, model error, and order selection for series-expanded, residual-stress inverse solutions

Article Abstract:

A comprehensive uncertainty analysis and order selection methodology, with detailed development for the slitting method is presented to measure the spatial variation of residual stresses. Using Monte Carlo numerical simulations, it is demonstrated that accurate uncertainty estimates require the estimation of model error, the ability of the chosen series expansion to fit the actual stress variation.

Science & research, Research, Monte Carlo method, Monte Carlo methods

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Residual stress solution extrapolation for the slitting method using equilibrium constraints

Article Abstract:

The three slitting residual stress calculations, truncated Legendre series, regularized Legendre series and regularized unit pulses are investigated. It is found that they give generally similar calculated stress results, particularly in the central depth region, away from the boundary areas where the depth is either very small or very large.

Numerical analysis, Stress analysis (Engineering)

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