Two stochastic mean-field polycrystal plasticity methods

In this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients L^c are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L^c tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D^c = frac(1, 2) (L^c + L^{c T}) are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.