Correction for transverse Strain Effects

 Transverse Sensitivity Transverse sensitivity in a strain gage refers to the behavior of the gage in responding to strains which are perpendicular to the primary sensing axis of the gage. Ideally, it would be preferable if strain gages were completely insensitive to transverse strains. In practice, most gages exhibit some degree of transverse sensitivity; but the effect is ordinarily quite small, and of the order of several percent of the axial sensitivity. In plane wire strain gages, transmission of strain into the wire from a direction perpendicular to the wire axis is nearly negligible. As a result, the transverse sensitivity of these gages is due almost entirely to the fact that a portion of the wire in the end loop lies in the transverse direction. Because of this, the sign of the transverse sensitivity for a plane wire gage will always be positive, and the magnitude of the effect can be calculated quite closely from the geometry of the grid. This statement does not apply to the small “wraparound” gages having the wire wound on a flattened core. Such gages often exhibit negative transverse sensitivities. In foil strain gages, on the other hand, the transverse sensitivity arises from much more complex phenomena, and it is affected by almost every aspect of grid design and gage construction. In addition to end loop effects, the foil gridlines, having a large ratio of width to thickness, are strained significantly by transverse strains. The magnitude of transverse strain transmission into the gridlines is determined by the relative thicknesses and elastic moduli of the backing and foil, by the width-to-thickness ratio of the foil gridlines, and, to a lesser degree, by several other parameters, including the presence or lack of an encapsulating layer over the grid. Depending upon the foil material and its metallurgical condition, the contribution to transverse sensitivity from the transmission of transverse strain into the gridlines can be either positive or negative. Because of this, the overall transverse sensitivity of a foil strain gage can also be either positive or negative. While the transverse sensitivity of a foil gage is thus subject to a greater degree of control in the design of the gage, the compromises necessary to optimize all aspects of gage performance generally limit the attainable reduction in transverse sensitivity. Errors Due to Transverse Sensitivity Errors in strain indication due to transverse sensitivity are generally quite small since the transverse sensitivity itself is small. However, in biaxial strain fields characterized by extreme ratios between principal strains, the percentage error in the smaller strain can be very great if not corrected for transverse sensitivity. On the other hand, in the particular case of uniaxial stress in a material with a Poisson’s ratio of 0.285, the error is zero because the gage factor given by the manufacturer was measured in such a uniaxial stress field and already includes the effect of the Poisson strain. It is important to note that when a strain gage is used under any conditions other than those employed in the gage-factor calibration, there is always some degree of error due to transverse sensitivity. In other words, any gage which is: (a) installed on a material with a different Poisson’s ratio; or (b) installed on steel, but subjected to other than a uniaxial stress state; or (c) even installed on steel with a uniaxial stress state, but aligned with other than the maximum principal stress, exhibits a transverse-sensitivity error which may require correction. The historical practice of quoting gage factors which, in effect, mask the presence of transverse sensitivity, and which are correct in themselves for only a specific stress field in a specific material, is an unfortunate one. This approach has generally complicated the use of strain gages, while leading to errors and confusion. Although the uniaxial stress field is very common, it is not highly significant to the general field of experimental stress analysis. There is no particular merit, therefore, in combining the axial and transverse sensitivities for this case.