Biaxial gage factors for piezoresistive strain gages

Theoretical considerations of piezoresistive strain gages show that the change in electrical resistivity depends on the biaxial state of strain at the surface of the specimen to which the gage is bonded. In particular, whenV is the initial voltage across the gage and ( \( \in _{11} , \in _{22} , \in _{12} \) ) is the surface-strain state at the point of attachment, the gage-voltage change ΔV is given by \(\frac{{\Delta V}}{V} = G_{11} \in _{11} + G_{22} \in _{22} + G_{12} \in _{12} \) whereG ₁₁,G ₂₂ andG ₁₂ are the biaxial gage factors. Experiments were conducted on a nominally one-dimensional gage. Kulite type DLP-120-500, bonded to a standard ASTM flat tensile specimen of CR 1018 steel. For this gage, typical values were found to beG ₁₁?26,G ₂₂??1.4 andG ₁₂??1.1. SinceG ₂₂ andG ₁₂ are less than 6 percent ofG ₁₁, it is concluded that contributions from these two factors (called transverse and shear sensitivities) will be significant only when the gage is oriented such that \( \in _{11}<< \left( { \in _{22} , \in _{22} } \right)\) . However, in the interest of completeness and accuracy, all biaxial gage factors should be reported.