Use of calcite twin lamellae to infer differential stress

Abstract

The equation that relates the resolved shear stress coefficient ( S 1 ), differential stress (Δσ), and the critical resolved shear stress ( t c ) necessary to produce twin gliding is t r = S t * Δσ. If we assume an infinite number of possible crystal orientations, it is possible to determine the percentage of grains that has a given value of the resolved shear stress coefficient ( S 1 ) on one, two, or three twin sets. Therefore, if the percentage of grains exhibiting one, two, or three twin sets is known, the differential stress can be determined in terms of the critical resolved shear stress using the above equation. The method has been developed for the case of randomly oriented grains deformed in an irrotational, uniaxial stress field. The method also assumes that all twinning is observable and has occurred in only those orientations where twinning is theoretically possible. Twin gliding has previously been shown to be a mechanism of creep in calcite, and in many cases the method may actually overestimate the magnitude of the differential stress. The validity of this technique of differential stress magnitude determination has been tested by its application to six experimentally deformed samples of Indiana limestone. The calculated differential stresses are within 21 percent of the experimental values for strains of less than 3 to 4 percent. At larger strain values reasonably accurate differential stress values may also be determined, but this requires a greater degree of interpretation. Comparison of samples that contain naturally deformed crystals of both calcite and dolomite suggests that the critical resolved shear stress for dolomite is approximately five times greater than that for calcite.