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Research Papers

Inverse Calculation of Uniaxial Stress-Strain Curves From Bending Test Data

[+] Author and Article Information
G. S. Schajer, Y. An

Department of Mechanical Engineering, University of British Columbia, Vancouver, V6T 1Z4 Canada

J. Eng. Mater. Technol 131(4), 041001 (Sep 03, 2009) (6 pages) doi:10.1115/1.3120409 History: Received December 10, 2008; Revised February 04, 2009; Published September 03, 2009

Uniaxial tension and compression stress-strain curves are simultaneously evaluated from load and surface strain data measured during a bending test. The required calculations for the uniaxial results are expressed as integral equations and solved in that form using inverse methods. This approach is taken to reduce the extreme numerical sensitivity of calculations based on equations expressed in differential form. The inverse solution method presented addresses the numerical sensitivity issue by using Tikhonov regularization. The use of a priori information is explored as a means of further stabilizing the stress-strain curve evaluation. The characteristics of the inverse solution are investigated using experimental data from bending and uniaxial tests.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Four-point bending of a rectangular beam specimen

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Figure 2

Bending stress profile in an ideal ductile material

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Figure 3

Bending stress profile in a general material

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Figure 4

Load versus strain measurements for the bending specimen (compressive strains ê shown with reversed sign)

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Figure 5

Uniaxial stress-strain curves. Thin line, measured from the tension test; thick line, computed from the bending test data, assuming a ductile material.

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Figure 6

Uniaxial stress-strain curves for a ductile material computed from experimental data with estimated standard force error Pstd=0.23 N: (a) no regularization, misfit Prms=0; (b) with regularization, misfit Prms=0.23 N; (c) Prms=0.47 N; and (d) Prms=1.26 N

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Figure 7

Regularized stress-strain curves for general and ductile materials

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Figure 8

Unregularized stress-strain curves for general and ductile materials

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