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The concept of strength envelopes, developed in the 1970s, allowed quantitative predictions of the strength of the lithosphere based on experimentally determined constitutive equations. Initial strength envelopes used an empirical relation for frictional sliding to describe deformation along brittle faults in the upper portion of the lithosphere and power law creep equations to estimate the plastic flow strength of rocks in the deeper part of the lithosphere. In the intervening decades, substantial progress has been made both in understanding the physical mechanisms involved in lithospheric deformation and in refining constitutive equations that describe these processes. The importance of a regime of semibrittle behavior is now recognized. Based on data from rocks without added pore fluids, the transition from brittle deformation to semibrittle flow can be estimated as the point at which the brittle fracture strength equals the peak stress to cause sliding. The transition from semibrittle deformation to plastic flow can be approximated as the stress at which the pressure exceeds the plastic flow strength. Current estimates of these stresses are on the order of a few hundred megapascals for relatively dry rocks. Knowledge of the stability of sliding along faults and of the onset of localization during brittle fracture has improved considerably. If the depth to the bottom of the seismogenic zone is determined by the transition to the stable frictional sliding regime, then that depth will be considerably more shallow than the depth of the transition to the plastic flow regime. Major questions concerning the strength of rocks remain. In particular, the effect of water on strength is critical to accurate predictions. Constitutive equations which include the effects of water fugacity and pore fluid pressure as well as temperature and strain rate are needed for both the brittle sliding and semibrittle flow regimes. Although the constitutive equations for dislocation creep and diffusional creep in single‐phase aggregates are more robust, few data exist for plastic deformation in two‐phase aggregates. Despite the fact that localization is ubiquitous in rocks deforming both in brittle and plastic regimes, only a limited amount of accurate experimental data are available to constrain predictions of this behavior. Accordingly, flow strengths now predicted from laboratory data probably overestimate the actual rock strength, perhaps by a significant amount. Still, the predictions are robust enough that uncertainties in geometry, mineralogy, loading conditions and thermodynamic state are probably the limiting factors in our understanding. Thus, experimentally determined rheologies can be applied to understand a broad range of topical problems in regional and global tectonics both on the Earth and on other planetary bodies.

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Laboratory measurements of rock strength provide limiting values of lithospheric stress, provided that one effective principal stress is known. Fracture strengths are too variable to be useful; however, rocks at shallow depth are probably fractured so that frictional strength may apply. A single linear friction law, termed Byerlee's law, holds for all materials except clays, to pressures of more than 1 GPa, to temperatures of 500°C, and over a wide range of strain rates. Byerlee's law, converted to maximum or minimum stress, is a good upper or lower bound to observed in situ stresses to 5 km, for pore pressure hydrostatic or subhydrostatic. Byerlee's law combined with the quartz or olivine flow law provides a maximum stress profile to about 25 or 50 km, respectively. For a temperature gradient of 15°K/km, stress will be close to zero at the surface and at 25 km (quartz) or 50 km (olivine) and reaches a maximum of 600 MPa (quartz) or 1100 MPa (olivine) for hydrostatic pore pressure. Some new permeability studies of crystalline rocks suggest that pore pressure will be low in the absence of a thick argillaceous cover.

Abstract. Creep experiments on fine-grained ice reveal the existence of three creep regimes: (1) a dislocation creep regime, (2) a superplastic flow regime in which grain boundary sliding is an important deformation process, and (3) a basal slip creep regime in which the strain rate is limited by basal slip. Dislocation creep in ice is likely climblimited, is characterized by a stress exponent of 4.0, and is independent of grain size. Superplastic flow is characterized by a stress exponent of 1.8 and depends inversely on grain size to the 1.4 power. Basal slip limited creep is characterized by a stress exponent of 2.4 and is independent of grain size. A fourth creep mechanism, diffusional flow, which usually occurs at very low stresses, is inaccessible at practical laboratory strain rates even for our finest grain sizes of--3 •m. A constitutive equation based on these experimental results that includes flow laws for these four creep mechanisms is described. This equation is in excellent agreement with published laboratory creep data for coarse-grained samples at high temperatures. Superplastic flow of ice is the rate-limiting creep mechanism over a wide range of temperatures and grain sizes at stresses • 0.1 MPa, conditions which overlap those occurring in glaciers, ice sheets, and icy planetary interiors.