Steady state dislocation densities in experimentally deformed calcite materials: Single crystals versus polycrystals

The theoretical relationship between dislocation density rho and applied stress sigma of the type sigma proportional to rho(0.5) is an essential part of many microphysical models for dislocation dynamics and creep. Thus, application of these microphysical models requires demonstration of this relation. In an attempt to determine the relation between rho and sigma for calcite, uniaxial compression tests were carried out on optical quality single crystals, at temperatures of 550-800 degrees C and strain rates of 3x10(-4)-3x10(-8) s(-1). The tests were performed with the compression direction parallel to [<40 (4)over bar 1>] (i.e., parallel to the intersection of two cleavage rhombs). Earlier data on crystals from the same batch already showed that, at the imposed conditions, steady state flow occurs by slip on the r- and f-glide systems, hence well within the dislocation creep regime. Dislocation densities measured by transmission electron microscopy achieved steady state values by similar to 2% strain. The steady state dislocation density can be related to the flow stress according to the empirical relation sigma=10(-)6.21(+/-0.86))rho(0.62(+/-0.07)) (sigma MPa, rho in m(-2)), in close agreement with the theoretically expected relation. Dislocation densities measured in experimentally deformed calcite polycrystals (previous and present studies) match the single-crystal data at high stress (> 40 MPa) but deviate from them toward low stress. The deviation appears to be more pronounced if the polycrystal has a smaller grain size. This can be explained using a theory of nonhomogeneous deformation in which strain incompatibility at grain boundaries is accommodated by ''geometrically necessary dislocations''. The contribution of these dislocations to the internal stress of the material (hence to the applied stress required for deformation at a given rate) is significant if the grain size is small. Consequently, a comparison of dislocation creep behavior of calcite materials with microphysical models based on dislocation dynamics should take into account the possible influence of grain size if stress levels are relatively low.