Geophysical Journal (1 989) 97, 199-207 A continuum theory for lattice preferred orientation

A 2-D model for the development of lattice preferred orientation (LPO) in aggregates of crystals (such as high T/T, olivine) which deform with a single dominant slip system is presented. In two dimensions, an arbitrary LPO can be described by an orientation distribution function (ODF) g($, t) , such that g($, t)d $ represents the fraction of crystals for which the orientation of the slip plane lies between $ and $ + d $ at time t. A differential equation which describes the evolution of the ODF during an arbitrary deformation history is described. This evolution is controlled by the vorticity number A ( t) = sZ/i of the deformation, where 252(t) is the vorticity and i ( t) is the strain rate. For A = 0 (uniaxial compression or pure shear), the ODF of an initially isotropic aggregate consists of two growing peaks oriented symmetrically about the extensional axis. For 1A1 = 1 (simple shear), the ODF consists of two unequal peaks which migrate relative to the extensional axis, and which eventually merge into a single peak centred on the shear plane orientation. If IAl exceeds a critical value-1.15, the ODF periodically returns to its initial isotropic state. The theory gives an excellent fit to data from olivine aggregates deformed in uniaxial compression, and an acceptable fit to data from ice aggregates deformed in simple shear. Key words: crystalline plasticity, lattice preferred orientation, slip systems