Analysis of Piezoresistance Gauges for Stress in Divergent Flow Fields
Publication: Journal of Engineering Mechanics
Volume 123, Issue 1
Abstract
An analytical procedure is presented for interpreting resistance histories from three piezoresistance gauges in a plane at a “point” to uniquely determine the normal stress at that point for nonuniaxial strain loading. The response of the elements can be plastic, and the analysis is valid for unloading and reloading. The only restrictions are that the elements must be aligned with the principal directions of the flow field, and the coupling between matrix strains and gauge strains must be specified. The gauges' piezoresistance properties, constitutive properties, and the coupling relations form a set of highly nonlinear simultaneous equations that can be solved for the normal stress and in-plane strains. A computer program named PIEZOR3 performs this task. Finite-element calculations are used to generate resistance histories from which the original stresses and strains can be computed with PIEZOR3. The computational examples demonstrate the accuracy of the procedure and quantify the uncertainties in the resolved stresses arising from uncertainties in mechanical, piezoresistance, and strain-coupling parameters.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Brar, N. S., and Gupta, Y. M.(1987). “Piezoresistance response of ytterbium foil gauges shocked to 45 kbar in fused silica matrix.”J. Appl. Phys., 61(4), 1304–1310.
2.
Chen, D. Y., Gupta, Y. M., and Miles, M. H.(1984). “Quasistatic experiments to determine material constants for the piezoresistance foils used in shock wave experiments.”J. Appl. Phys., 55(11), 3984–3993.
3.
Dynasen. (1980). Shock pressure sensors and impact facilities. Goleta, Calif.
4.
Gupta, Y. M.(1983a). “Stress measurements using piezoresistance gauges: modeling the gauge as an elastic-plastic inclusion.”J. Appl. Phys., 54(11), 6093–6098.
5.
Gupta, Y. M.(1983b). “Analysis of manganin and ytterbium gauge data under shock loading.”J. Appl. Phys., 54(11), 6256–6266.
6.
Gupta, S. C., and Gupta, Y. M.(1985). “Piezoresistance response of longitudinally and laterally oriented ytterbium foils subjected to impact and quasi-static loading.”J. Appl. Phys., 57(7), 2464–2473.
7.
Gupta, Y. M., and Gupta, S. C.(1987a). “Incorporation of strain hardening in piezoresistance analysis: application of ytterbium foils in a PMMA matrix.”J. Appl. Phys., 61(2), 489–498.
8.
Gupta, S. C., and Gupta, Y. M.(1987b). “Experimental measurements and analysis of the loading and unloading response of longitudinal and lateral manganin gauges shocked to 90 kbar.”J. Appl. Phys., 62(7), 2603–2609.
9.
Hallquist, J. O. (1983). “NIKE2D—a vectorized, implicit, finite deformation, finite element code for analyzing the static and dynamic response of 2-D solids.”UCID-19677, Lawrence Livermore National Laboratory, Livermore, Calif.
10.
Holmes, B. S. (1983). “Measuring pressure from short laser pulses.”Shock waves in condensed matter, J. R. Asay, R. A. Graham, and G. K. Straub, eds., North-Holland Publishing Co., New York, N.Y., 339–342.
11.
Holmes, B. S.(1985). “Pressure measurement in laser-supported plasmas with piezoresistance gages.”Experimental Mech., 25(1), 32–42.
12.
Holmes, B. S., and Aidun, J. B. (1985). “Piezoresistant response of vapor-deposited ytterbium.”Shock waves in condensed matter, Y. M. Gupta, ed., Plenum Publishing Corp., New York, N.Y., 519–524.
13.
Ito, Y. M., and Muki, Y. (1990). “Numerical simulation of piezoresistance gage response.”DNA-TR-87-130, Defense Nuclear Agency, Washington, D.C.
14.
Keough, D. D., DeCarli, P. S., Florence, A. L., Mak, R., Walter, D. F., and Rosenberg, J. T. (1986). “Investigation of the credibility of in-situ measurements of radial and tangential stress in a salt test bed.”Tech. Rep. to DNA, Contract DNA001-82-C-0248, SRI International, Menlo Park, Calif.
15.
Miller, S. A., Rosenberg, J. T., and Florence, A. L. (1987). “Dynamic load/unload response of vapor-deposited ytterbium stress transducers.”1987 ASME Appl. Mech., Bio Engrg., and Fluid Engrs. Conf., ASME, New York, N.Y.
16.
Miller, S. A. (1987). “Piezoresistant response of rolled ytterbium foils to double-shock loading.”Shock waves in condensed matter, S. C. Schmidt and N. C. Holmes, eds., North-Holland Publishing Co., New York, N.Y., 605–608.
17.
Seaman, L. (1979). “Plasticity analysis for isotropic material.”Tech. Rep. PLTR-003-79, SRI International, Menlo Park, Calif.
18.
Stout, R. B., and Larson, D. B. (1987). “Multi-component stress history measurements and analysis.”Rep. No. UCRL-96319, 4th Containment Symp., U.S. Department of Energy, Washington, D.C.
19.
Vishay Intertechnology. (1971a). Micro-measurements product bulletin PB-109 manganin gages. Romulus, Mich.
20.
Vishay Intertechnology. (1971b). Micro-measurements catalog 500 strain gage technical data. Romulus, Mich.
21.
Wilkins, M. (1964). “Calculation of elastic-plastic flow.”Methods in computational physics 3, fundamental methods in hydrodynamics, B. Alder, ed., Academic Press, New York, N.Y., 211–263.
22.
Wong, M. K. W. (1991). “Experiments and analysis to understand the response of lateral piezoresistance gauges under dynamic loading,” PhD thesis, Washington State Univ., Pullman, Wash.
Information & Authors
Information
Published In
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jan 1, 1997
Published in print: Jan 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.