Deformation maps have found widespread use in the study of the rheology of Earth materials. The usual procedure is to construct a map in stress-temperature space, from which predominant creep mechanisms, strain rates and viscosities can be determined for a given grain size. The rheology of polycrystals, however, depends strongly on grain size, and consequently, a fuller description would entail the construction of three dimensional stress-grain-size-temperature diagrams. As these do not display clearly the parameters of interest, it is proposed to use deformation maps in stress-grain-size space at a given temperature. In several situations of geodynamic interest, grain size is a more critical parameter than temperature. Furthermore, stress-grain-size maps have the advantages of simplicity and clarity. For instance, the boundaries between Nabarro-Herring, Coble and power-law creep are straight lines, and so are constant strain rate and constant viscosity contours. The triple point at which the three boundaries converge is, under reasonable assumptions, a function of temperature only, and the slopes of the boundaries are independent of temperature. It is therefore possible to project, on a single map, data for various temperatures: the coordinates of the triple point contain all the necessary information for a synoptic representation of the rheology. As an example, deformation maps in stress-grain-size space are presented for olivine under laboratory and upper mantle conditions.

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Journal Physics of the Earth and Planetary Interiors
Ranalli, G. (1982). Deformation maps in grain-size-stress space as a tool to investigate mantle rheology. Physics of the Earth and Planetary Interiors, 29(1), 42–50. doi:10.1016/0031-9201(82)90136-4