This paper provides estimates for the stress, strain-rate and spin field statistics in viscoplastic polycrystals. They are obtained by combining the fully optimized second-order (FOSO) homogenization method with the self-consistent estimate for linear polycrystalline aggregates. The FOSO linearization method allows the consistent estimation of the field statistics in nonlinear composites and polycrystals directly from those in suitably optimized linear comparison composites (LCC). For the LCC, a novel generalized approach is used to extract the field statistics of the stress, the strain-rate and also of the continuum-spin fields (including the second moments). Then, the stress-field statistics are used to extract the plastic-spin statistics, which, together with the continuum-spin statistics, provide consistent estimates for the microstructural-spin statistics. Applications to power-law viscoplastic FCC polycrystals and ice-like HCP polycrystals are considered, and the overall and intragranular field fluctuations are computed and found to increase with nonlinearity exponent and grain anisotropy. In particular, the covariance tensors of the continuum-spin fluctuations within the grains of viscoplastic polycrystals, which are characterized here for the first time by means of nonlinear homogenization methods, are found to be quite significant, even when the corresponding averages of the continuum-spin in the grains are negligible, and thus have a strong influence on the corresponding microstructural-spin fluctuations.

本文提供了粘塑性多晶体中应力，应变率和自旋场统计的估计值。它们是通过将完全优化的二阶（FOSO）均质化方法与线性多晶聚集体的自洽估计值相结合而获得的。FOSO线性化方法允许直接从适当优化的线性比较复合材料（LCC）中的场强统计数据中估算非线性复合材料和多晶中的场统计数据。对于LCC，使用一种新颖的广义方法来提取应力，应变率以及连续旋转场（包括第二矩）的场统计信息。然后，使用应力场统计数据来提取塑性旋转统计数据，并将其与连续旋转统计数据一起，为微观结构自旋统计提供一致的估计。考虑了幂律粘塑性FCC多晶和冰状HCP多晶的应用，计算了整体和晶内场的波动，发现它们随非线性指数和晶粒各向异性的增加而增大。特别是，这里首次通过非线性均化方法表征的粘塑性多晶体晶粒内连续自旋涨落的协方差张量非常显着，即使连续统一体的相应平均值也是如此。晶粒中的自旋可忽略不计，因此对相应的微结构自旋起伏有很大的影响。计算出整体和晶内场的波动，发现其随非线性指数和晶粒各向异性的增加而增大。特别是，这里首次通过非线性均化方法表征的粘塑性多晶体晶粒内连续自旋涨落的协方差张量非常显着，即使连续统一体的相应平均值也是如此。晶粒中的自旋可忽略不计，因此对相应的微结构自旋起伏有很大的影响。计算出整体和晶内场的波动，发现其随非线性指数和晶粒各向异性的增加而增大。特别是，这里首次通过非线性均化方法表征的粘塑性多晶体晶粒内连续自旋涨落的协方差张量非常显着，即使连续统一体的相应平均值也是如此。晶粒中的自旋几乎可以忽略不计，因此对相应的微结构自旋波动有很大的影响。