Thermal Output (continued)

Thermal output is caused by two concurrent and algebraically additive effects in the strain gage installation. First, the electrical resistivity of the grid conductor is somewhat temperature dependent; and, as a result, the gage resistance varies with temperature. The second contribution to thermal output is due to the differential thermal expansion between the grid conductor and the test part or substrate material to which the gage is bonded. With temperature change, the substrate expands or contracts; and, since the strain gage is firmly bonded to the substrate, the gage grid is forced to undergo the same expansion or contraction. To the extent that the thermal expansion coefficient of the grid differs from that of the substrate, the grid is mechanically strained in conforming to the free expansion or contraction of the substrate. Because the grid is, by design, strain sensitive, the gage exhibits a resistance change proportional to the differential expansion.

Each of the two thermally induced resistance changes may be either positive or negative in sign with respect to that of the temperature change, and the net thermal output of the strain gage is the algebraic sum of these. Thus, expressed in terms of unit resistance change, the thermal output becomes:

where, in consistent units:

= unit change in resistance from the initial reference resistance, , due to thermal output.
= thermal coefficient of resistance of the grid conductor.
= gage factor of the strain gage.
= transverse sensitivity of the strain gage.
= Poisson's ratio (0.285) of the standard test material used in calibrating the gage for its gage factor.
= difference in thermal expansion coefficients between substrate and grid, respectively.
= temperature change from an arbitrary initial reference temperature.

In this publication, the gage factor of the strain gage (as specified by the package technical data sheet) is identified as , to distinguish it from the gage factor setting of the measuring instrument, denoted here by . This distinction is important, since the gage factor setting of the instrument may sometimes, as a matter of convenience or utility, be different from that of the gage.

The correction factor for transverse sensitivity [ ] is included in Eq. (504.1) to account for the fact that the strain in the gage grid due to differential thermal expansion is equal-biaxial, while the gage factor, , refers to the strain sensitivity as calibrated in a uniaxial stress state, with a principal strain ratio of 1/(-0.285).

It should not be assumed from the form of Eq.(504.1) that the thermal output is linear with temperature change, because all of the coefficients within the brackets are themselves functions of temperature. The equation clearly demonstrates, however, that thermal output depends not only on the nature of the strain gage, but also on the material to which the gage is bonded. Because of this, thermal output data are meaningful only when referred to a particular type of strain gage, bonded to a specified substrate material.

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