Flow laws of polyphase aggregates from end‐member flow laws

Abstract

An incompressible finite element model has been used to study the plane strain deformation of two‐phase aggregates deformed by dislocation creep. Input for the model includes the power law flow laws of the two end‐member phases and their volume fractions and configuration. The model calculates the overall flow law of the aggregate as well as the stress and strain rate variations within it. The input flow laws were experimentally determined for monomineralic aggregates of clinopyroxene and plagioclase. Results were calculated for a temperature of 1000°C, strain rates from 10−4 to 10−12S−1, and stresses of 1–1000 MPa. For these conditions, the end‐member flow laws intersect on a log stress versus log strain rate plot at 10−8S−1. Some runs were made on finite element grids fit to an actual diabase texture (∼64% pyroxene, ∼ 36% plagioclase.) Other runs were made on idealized geometries to test the effects of varying the volume fraction of two phases, shape of inclusions, and relative strengths of inclusion and matrix. Important results include the following: (1) The model results satisfy the requirement that the aggregate strength must lie between the bounds set by the end‐member flow laws and those set by assumptions of uniform stress and uniform strain rate. (2) The calculated diabase flow law matches well with that experimentally determined. (3) The aggregate strength within the uniform stress and uniform strain rate bounds is primarily affected by volume fraction, although certain phase geometries can also affect the strength. (4) Although the flow law for an aggregate of power law phases need not be a simple power law, we find it to be a good approximation. We have developed two simple methods of estimating the strength of an aggregate, given the end‐member flow law parameters and volume fractions; both give results that agree with the finite element model calculations. (1) One method takes into account the phase geometry and gives a strength for the aggregate at any strain rate. (2) The other method can be used even if the phase geometry is unknown and gives expressions for the aggregate flow law parameters.