Summary. Previous attempts to deduce the stress distribution in the bending lithosphere near a consuming plate margin have relied on the observed bathymetry and an assumed constitutive relation for lithospheric behaviour, eg. perfectly elastic, viscous/perfectly plastic, or elastic perfectly plastic. From the point of view of rock mechanics, each of these approximations fails to describe one or more of several basic phenomena, including brittle failure of rock, temperature dependence of elasticity, and temperature and/or strain rate dependence of ductile behaviour. In order to formulate a more realistic constitutive relation, a limiting yield strength curve, which is primarily a function of temperature, is constructed from data from brittle failure and ductile flow experiments. The moments which can be supported by plates with this constitutive behaviour are compared to the moments calculated from bathymetric profiles. The comparison indicates that moments required by the bathymetric data are consistent with moments supported by plates with experimentally determined constitutive laws as extrapolated to geo- logically reasonable temperatures and strain rates. The stresses developed in such models are required to reach values greater than 100 MPat in the depth range 25-45 km. Geotherms necessary for strength curves consistent with moments calculated from the bathymetric data match those derived from heat flow data for the Aleutian, Bonin, Mariana and Tonga trenches. Of the trenches studied, only the geotherm inferred from the Kuril trench data is significantly different, perhaps implying that the Kuril plate is weaker than the others. The strength curves show that as a first approximation it is better to assume that bending moment is independent of curvature of the plate than to assume that bending moment and curvature are linearly related.

Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics

We summarize the progress made in providing experimental verification for the deformation map of polycrystalline olivine published by Stocker & Ashby in 1973 ( Rev. Geophys . 11, 391). Porosity-free polycrystalline deformation data, applicable to the mantle, were found to be obtainable only from high-pressure deformation studies. Combination of the results of such studies with hardness measurements and single crystal deformation studies on olivine provides narrow constraints on the flow of olivine resulting from dislocation mechanisms from room temperature to the melting point along a band of experimentally accessible strain rates. A good fit is obtained combining a Dorn law above 2 kbar differential stress, e/s -1 =5.7x10 11 ex{-128kcal/mol/RT (1-cr 1 -cr 2 /85000) 2 }, with a power law below 2 kbar, e = 70(cr 1 —cr 3 ) exp{— 122(kcal/mol)/RT}, where stress is measured in bars ( l bar = 10 5 Pa). Indirect data on a mechanism phenomenologically resembling the Goble creep regime are now available from two sources. The observed strain rates are only slightly faster than those predicted by Stocker & Ashby (1973). The 9 wet’ data, previously believed to show hydrolytic weakening, are found to fall within this Coble field. The asthenosphere is still expected to deform by the dislocation mechanism summarized by the two formulae given above, but higher stress deformation within the lithosphere is almost certainly dominated by this Coble creep regime once dynamic recrystallization sets in.

The mechanisms of creep in olivine

The experimental deformation of dunite

Gem quality single crystals of dry olivine were plastically deformed in compression at differential stresses between 50 and 1500 bars, with zero confining pressure, and at temperatures between 1428° and 1650°C. When these new data are combined with existing creep data for dry olivine-bearing rock, a flow law of the form e˙ = ƒ(σ) exp (−Q/RT) is obtained, whereƒ(σ) is an empirical function that is not simply proportional to σn for constant n and Q is equal to 125 ± 5 kcal/mol. The flow law covers the stress range 50–10,000 bars and the temperature range 1100°–1700°C and is consistent with all published data to 1 decade in strain rate.

C.B. Raleigh

Papers

Mechanisms of high-temperature, solid-state flow in minerals and ceramics and their bearing on the creep behavior of the mantle