Viscoplastic Polycrystals Research Articles

Consideration of grain-size effect and kinetics in the plastic deformation of metal polycrystals

This work extends the constitutive model for the prediction of grain-size dependent hardening in f.c.c. polycrystalline metals proposed by Acharya and Beaudoin [1] (Grain-size effect in fcc viscoplastic polycrystals at moderate strains, 1999, in press) to include effects of temperature and strain rate dependence. A comparison is made between model predictions and compression data, taken at varying temperature and strain rate, for pure Ag having two different grain sizes. It is shown that an initial increase in yield stress and concomitant decrease in hardening rate for a fine-grained material, relative to a coarse-grained counterpart, can be captured through initialization of a state variable serving to describe stress response at prescribed reference conditions of temperature and strain rate. A grain-size dependence of hardening rate during parabolic (stage III) hardening is characterized by the evolution of net dislocation density in a finite element model of a polycrystal aggregate. Finally, observations from simulations of deformation of the polycrystal aggregate are introduced into an existing macroscopic constitutive model for metal plasticity based on the mechanical threshold.

Variational self-consistent estimates for viscoplastic polycrystals with highly anisotropic grains

A recently established variational procedure is used to compute self-consistent estimates for viscoplastic polycrystals with highly anisotropic ionic and HCP grains. For large values of the grain anisotropy M, the predictions for the macroscopic flow stress are found to scale as M γ , where γ depends on the number (less than 5) of independent slip systems that are available for plastic flow, but not on the strain-rate sensitivity. The predictions of other nonlinear extensions of the self-consistent scheme are inconsistent with this scaling law, suggesting that they may be less accurate than the variational estimates proposed here.

Second‐order and affine estimates for the behavior of viscous polycrystals

AbstractThe recently proposed second‐order and affine estimates for the effective behavior of nonlinear heterogeneous materials rely on the same linearization procedure and refer to some “thermoelastic comparison composite”. But both approaches differ in the way the overall nonlinear answer is defined, either through average stress‐strain relations or energy considerations. When combined with the linear self‐consistent model, they provide new tools for the predictions of the behavior of viscoplastic polycrystals (steady state creep). They are compared to each other and to other more classical estimates (incremental and tangent) in the following situations.: a 2D antiplane model problem for which efficient rigorous upper bounds are available, the creep of isotropic aggregates of FCC crystals and HCP crystals with different critical stresses on the basal and prismatic slip systems.

Second–order estimates of the self–consistent type for viscoplastic polycrystals

The ‘second–order’ homogenization procedure of Ponte Castaneda is used to propose new estimates of the self–consistent type for the effective behaviour of viscoplastic polycrystals. This is accomplished by means of appropriately generated estimates of the self–consistent type for the relevant ‘linear thermoelastic comparison composite’, in the homogenization procedure. The resulting nonlinear self–consistent estimates are the only estimates of their type to be exact to second order in the heterogeneity contrast, which, for polycrystals, is determined by the grain anisotropy. In addition, they satisfy the recent bounds of Kohn and Little for two–dimensional power–law polycrystals, which are known to be significantly sharper than the Taylor bound at large grain anisotropy. These two features combined, suggest that the new self–consistent estimates, obtained from the second–order procedure, may be the most accurate to date. Direct comparison with other self–consistent estimates, including the classical incremental and secant estimates, for the special case of power–law creep, appear to corroborate this observation.