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TECHNICAL PAPERS

Residual Stress Solution Extrapolation for the Slitting Method Using Equilibrium Constraints

[+] Author and Article Information
Gary S. Schajer1

Department of Mechanical Engineering, 6250 Applied Science Lane,  University of British Columbia, Vancouver, Canada V6T 1Z4schajer@mech.ubc.ca

Michael B. Prime

Engineering Sciences and Applications Division,  Los Alamos National Lab., Los Alamos, NM 87545

1

Corresponding author.

J. Eng. Mater. Technol 129(2), 227-232 (Jul 20, 2006) (6 pages) doi:10.1115/1.2400281 History: Received April 17, 2006; Revised July 20, 2006

Established methods for calculating residual stresses from the strains measured when using the slitting method give results for the stresses that exist within the depth range of the slit. Practical considerations typically limit this range to about 90–95% of the specimen thickness. Force and moment equilibrium can provide additional information that may be used to estimate the residual stresses in the “no-data” region within the remaining ligament beyond the maximum slit depth. Three different numerical methods to calculate the residual stress profile over the entire specimen thickness are investigated. They are truncated Legendre series, regularized Legendre series, and regularized unit pulses. In tests with simulated strain data and with strain data measured on a cold compressed 7050-T7452 Aluminum hand forging, the three methods gave generally similar stress results in the central region of the specimen. At small depths, where the strain sensitivity to the residual stresses is low, the two regularized calculation methods tended to give more stable results. In the area of very large depth beyond the maximum depth of the slit, the regularized Legendre series solution generally gave the most realistic stress results.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the slitting method

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Figure 2

Calculated residual stresses for a simulated bending specimen with central elastic region between 0.40 and 0.60 normalized depth. The regularized solutions use “smooth” regularization, and the truncated Legendre series contains terms up to 12th order.

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Figure 3

Calculated residual stresses for a simulated bending specimen with central elastic region between 0.45 and 0.55 normalized depth. The regularized solutions use “smooth” regularization, and the truncated Legendre series contains terms up to 11th order.

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Figure 4

Calculated residual stresses for a simulated quenched specimen. The regularized solutions use “smooth” regularization, and the truncated Legendre series contains terms up to 7th order.

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Figure 5

Calculated residual stresses for a simulated quenched specimen. The regularized solutions use “flat” regularization, and the truncated Legendre series contains terms up to 7th order.

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Figure 6

Calculated residual stresses for a quenched aluminum specimen. The regularized solutions use “smooth” regularization, and the truncated Legendre series contains terms up to 11th order.

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