Grain size distribution and flow stress in tectonites
Flow stresses in dynamically recrystallized tectonites are usually determined by using empirically calibrated grain size-stress relations. As grain size adjusts locally to stress, the validity of the procedure is dependent on the assumption that the local stress, at grain or subgrain level, is equal to the externally applied tectonic stress. The local stress, however, is a stochastic variable with a distribution related to the tectonic stress: once this fact is recognised, the question becomes that of deciding which measure of grain size, and therefore of local stress, gives the best estimate of the tectonic stress. Current procedures implicitly assume that such a measure is the mean grain size. It is shown here that, on the basis of the most general probabilistic considerations, the local stress, and therefore the grain size, can be expected to have a lognormal distribution, and consequently that the median grain size, and not the mean, is the best indicator of tectonic stress. The lognormality of grain size has been confirmed by observations, both on metals and on rocks. The use of the mean, rather than the median, grain size introduces a further source of uncertainty in flow stress determinations. An expression for the error in stress is derived, and found to depend on the coefficients of variation (i.e. dispersions) in the grain size distribution of calibrating curve and field tectonite. If these two are the same (or in the trivial case in which they are both very small), no error arises from the use of mean grain size. But, if this condition is not fulfilled, an error of up to 10-20% in flow stress may occur.