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TN-504
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Strain Gage Thermal Output
and Gage Factor Variation with Temperature |
Appendix - Surface Curvature Effects on Thermal OutputFrank F. Hines ( Proceedings, Western Regional Strain Gage Committee , Nov. 9, 1960, pp. 39-44.) has demonstrated that when a strain gage is installed on a sharply curved surface the thermal output manifested by such an installation is different than for the same gage mounted on a flat surface. The curvature-induced change in thermal output, referred to here as the incremental thermal output, is due to the fact that the strain-sensitive grid of the gage is above the surface of the test member by the thickness of the gage backing and adhesive layer. It can be shown that under these conditions a temperature change causes a different strain in the grid than would occur with the grid bonded to a plane surface. The result is an altered thermal output from the data provided in the gage package. The curvature-induced incremental thermal output is a second-order effect which can ordinarily be ignored; but it can become significant when the radius of curvature is very small. As a rule of thumb, the incremental thermal output can be neglected when the radius of curvature is 0.5 in (13 mm) or greater. With smaller radii, correction may be necessary, depending upon the required strain-measurement accuracy. Employing the same basic approach and approximations used by Hines in his derivation, but generalizing the treatment to allow for any combination of adhesive and backing properties, an expression for estimating the incremental thermal output can be written as follows:
where, in consistent units,
Approximate values for the adhesive and backing
parameters in Eq. (504.A-1) are given in Table A-1
for representative Micro-Measurements adhesives and
gage series. The sign of the incremental thermal
output is obtained from Eq. (504.A-1) when the signs
of
Table A-1Adhesive and Backing Parameters for Use with Eq. 504.A-1
= 0.35 for all combinations.Because the adhesive and backing parameters given in Table A-1 are approximate, and are affected by gage installation technique and other variables, the curvature correction defined by Eq.(504.A-1) is limited in accuracy. When the surface curvature is severe enough so that the curvature induced incremental thermal output may be important, the actual thermal output should be measured as described earlier . In other words, the strain gage should be bonded to the test part as for strain measurement, a thermocouple or resistance temperature sensor should be installed adjacent to the gage, and the test part then subjected to test temperatures (while free of mechanical and thermal stresses) to record the "true" thermal output. As an aid in judging the approximate magnitude of the curvature-induced thermal output, Eq. (504.A-1) has been evaluated for several representative combinations of Micro-Measurements adhesives and gage series. Parameters from Table A-1 were substituted into the equation, along with 
= 6.0E-6 (assuming a steel test material), and the
results plotted in Fig. A-1. Note, in the figure,
that the ordinate gives the incremental thermal
output per unit of temperature change from the
initial reference temperature - that is,
/
.
Fig. A-1 - Equation (A-1) evaluated and plotted for various standard Micro-Measurements strain gage backing materials when bonded to a steel substrate. 
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Eq.(504.A-1)
= radius of curvature of test surface at gage site.
= adhesive and backing thickness, respectively.
= thermal expansion coefficients of adhesive and
backing, respectively.
, in (mm)
, ppm/° F (ppm/° C)
, in (mm)
, ppm/° F (ppm/° C)