Use of Inverse Solutions for Residual Stress Measurements

[+] Author and Article Information
Gary S. Schajer

Department Mechanical Engineering,  University of British Columbia, Vancouver, Canada

Michael B. Prime

Engineering Sciences and Applications Division,  Los Alamos National Laboratory, Los Alamos, NM

J. Eng. Mater. Technol 128(3), 375-382 (Mar 10, 2006) (8 pages) doi:10.1115/1.2204952 History: Received January 24, 2005; Revised March 10, 2006

For most of the destructive methods used for measuring residual stresses, the relationship between the measured deformations and the residual stresses are in the form of an integral equation, typically a Volterra equation of the first kind. Such equations require an inverse method to evaluate the residual stress solution. This paper demonstrates the mathematical commonality of physically different measurement types, and proposes a generic residual stress solution approach. The unit pulse solution method that is presented is conceptually straightforward and has direct physical interpretations. It uses the same basis functions as the hole-drilling integral method, and also permits enforcement of equilibrium constraints. In addition, Tikhonov regularization is shown to be an effective way to reduce the influences of measurement noise. The method is successfully demonstrated using data from slitting (crack compliance) measurements, and excellent correspondence with independently determined residual stresses is achieved.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Contour plots of kernel function integrals. (a) Sachs’ method, (b) layer removal, (c) hole-drilling (11), (d) slitting.

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Figure 2

Unit pulse functions used for the residual stress solution

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Figure 3

Physical interpretation of matrix coefficients Gij for the hole-drilling method

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Figure 4

Strain versus slit depth for a residual stress measurement using the slitting method

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Figure 5

Residual stress profiles. Solid line=calculated from Fig. 4 data using Eqs. 18,23. Dashed line=calculated from bending strains.

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Figure 6

Residual stress profiles calculated using different amounts of regularization. Misfit norms=0.07, 0.7 (optimal), and 70 microstrain.

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Figure 7

Strain misfits calculated using different amounts of regularization. Misfit norms: (a)=0.07, (b)=0.7 (optimal), and (c)=7.0 microstrain.



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