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A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory

We examine FCC nickel undergoing simple shear by using three different numerical frameworks formulated at three different size scales. The three frameworks included embedded atom method potentials used in molecular dynamics simulations, crystal plasticity used in finite element simulations, and a macroscale internal state variable formulation used in finite element simulations. Simple shear simulations were performed in which the specimen aspect ratio was varied to give insight into the homogeneous and inhomogeneous aspects of large deformation. This study revealed that the `apparent' yield stress was sensitive to the specimen aspect ratio except when the length-to-height ratio reached about 8 : 1, the yield stress remained constant. The three numerical frameworks gave similar qualitative responses related to inhomogeneous stress and strain distributions in the corner regions of the specimens and also similar responses in the centralized homogeneous deformation region. However, when comparing the shear stress distribution for the finite element analyses to the atomistic simulations, a much narrower distribution arose for the finite element analyses due to the lack of thermal vibrations experienced in the atomistic simulations at 300 K. A 10 K an atomistic simulation which dampened out the high frequency thermal vibrations verified this reasoning. Three different sizes of blocks of atoms were also used in the atomistic simulations and the results showed very similar stress and strain distributions with respect to each other indicating that no size scale effect is evidenced when normalized by the global shear stress. However, a size scale effect exists related to the global (volume average) shear stress in the specimen. As the specimen size increased, the yield stress decreased. Finally, when comparing the three different numerical frameworks, the location of maximum dislocation nucleation occurred at the location of the maximum plastic spin, stress gradients, and strain gradients.