Abstract
We propose an inverse method, using a circular disk in diametrical compression, for the simultaneous determination of two elastic constants,E andv, from a single displacement map. Moiré interferometry combined with the phase-shifting technique provides a full-field displacement field. An overdeterministic approach using the least-squares method is implemented to fit the experimentally determined displacements to the theoretical solution. An implementation guideline is provided, considering the effects of accidental rigid-body motions, random noise and imperfect position of the origin. Accuracy and repeatability of the proposed method are verified experimentally.
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References
Hertz, H., Zeitschrift für Mathematik und Physik, Vol. 28 (1883).
Mitchell, J., “Elementary Distributions of Plane Stress,”Proceedings of the London Mathematical Society,32,35–61 (1901).
Muskhelishvili, N., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands, 330–334 (1963).
Sokolnikoff, I., Mathematical Theory of Elasticity, Krieger Publishing, Malabar, 283–284 (1983).
Sciammarella, C., Theoretical and Experimental Study on Moiré Fringes, Ph.D. Dissertation,Illinois Institute of Technology, Chicago, IL, 185–192 (1960).
Durelli, A. andFerrer, L., “New Methods to Determine Elastic Constants,”Materials Research and Standards,3,988–991 (1963).
Cárdenas-García, J., “The Moiré Circular Disk: Two Inverse Problems,”Mechanics Research Communications,28(4),381–388 (2001).
Post, D., Han, B., andIfju, P., High Sensitivity Mojré: Experimental Analysis for Mechanics and Materials, Springer-Verlag, New York (1994).
Post, D., Han, B., andIfju, P., “Moiré Methods for Engineering and Science — Moiré Interferometry and Shadow Moiré,”Photomechanics for Engineers, Pramod Rastogi, editor, Chapter 7,Springer-Verlag, New York (2000).
Han, B., Post, D., andIfju, P., “Moiré Interferometry for Engineering Mechanics: Current Practice and Future Development,”Journal of Strain Analysis,36(1),101–117 (2001).
Huntley, J., “Automated Fringe Pattern Analysis in Experimental Mechanics: A Review,”Journal of Strain Analysis,33(2),105–125 (1998).
Robinson, D., andReid, G., Interferogram Analysis, IOP Publishing, Bristol, 141–229 (1993).
Timoshenko, S. andGoodier, J., Theory of Elasticity, 3rd edition, McGraw-Hill, New York, 122–127 (1970).
Sanford, R., “Application of the Least-sauares Method to Photoelastic Analysis,”EXPERIMENTAL MECHANICS,20(6), 192–197 (1980).
Sanford, R. andDally, J., “A General Method for Determining Mexed-mode Stress Intensity Factors from Isochromatic Fringe Patterns,”Engineering Fracture Mechanics,11(4),621–633 (1979).
Dally, J. andRiley, W., Experimental Stress Analysis, 3rd edition, McGraw-Hill, New York, 616–619 (1991).
Gander, W. andHrebicek, J., Solving Problems in Scientific Computing Using Maple and MATLAB®, 3rd edition, Springer-Verlag, New York, 136–139 (1997).
Metals Handbook, Volume 2: Properties and Selection: Non-Ferrous Alloys and Special Purpose Materials, 10th edition, ASM International, Materials Park, OH (1990).
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Wang, Z., Cárdenas-García, J.F. & Han, B. Inverse method to determine elastic constants using a circular disk and moiré interferometry. Experimental Mechanics 45, 27–34 (2005). https://doi.org/10.1007/BF02428987
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DOI: https://doi.org/10.1007/BF02428987