A large deformation viscoplastic polycrystal theory is formulated. It is restricted to loading conditions since elasticity is entirely neglected. The single crystal behavior is based on crystallographic slip, and the slip rate is a non-linear function of the resolved shear stress. The time independent plasticity is obtained as a limit when the rate sensitivity tends to zero. The polycrystal behavior is obtained from the single crystal constitutive relation by solving integral equations derived from the field equations. A self-consistent approach is developed, where each grain is assumed to be a single ellipsoidal inclusion in a homogeneous equivalent medium. An interaction formula is derived and the local strain rates are calculated by resolving a nonlinear system of equations. Applications to texture predictions in tension, compression, rolling and torsion are finally considered.
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