Nanometer Scale Mechanical Behavior of Grain Boundaries
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Nanometer Scale Mechanical Behavior of Grain Boundaries Chien-Kai Wang, Huck Beng Chew, and Kyung-Suk Kim School of Engineering, Brown University, Providence, RI 02912, U.S.A. ABSTRACT A nonlinear field projection method has been developed to study nanometer scale mechanical properties of grain boundaries in nanocrystalline FCC metals. The nonlinear field projection is based on the principle of virtual work, for virtual variations of atomic positions in equilibrium through nonlocal interatomic interactions such as EAM potential interaction, to get field-projected subatomic-resolution traction distributions on various grain boundaries. The analyses show that the field projected traction produces periodic concentrated compression sites on the grain boundary, which act as crack trapping or dislocation nucleation sites. The field projection was also used to assess the nanometer scale failure processes of Cu 65 grain boundaries doped with Pb. It was revealed that the Pb dopants prevented the emission of dislocations by grain boundary slip and embrittles the grain boundary. INTRODUCTION Nanocrystalline materials are polycrystals with nanometer-scale grain sizes, and have been the subject of widespread research over the past few decades. There is now general consensus among the scientific community that the mechanical strength and toughness of these nanocrystalline materials are structurally characterized by their large volume fraction of grain boundaries. However, the intrinsic relationship between the nanometer scale mechanical properties of grain boundaries and their macroscopic failure behavior are still not well understood. Studies have attempted to ascertain the strength characteristics of grain boundaries and the effects of dopants on grain boundary embrittlement via their electronic structure changes and local density of states [1,2]. However, these ab-initio calculations cannot quantitatively characterize the mechanical strength and toughness of the grain boundary, since the fracture energy of the grain boundary is dependent on the separation process [3-5]. Therefore, an accurate assessment of the nanometer scale failure processes of the grain boundaries is required to characterize the mechanical strength of nanocrystalline materials. Despite the availability of computational tools such as molecular dynamics simulations, determination of the grain boundary traction-separation characteristics is highly nontrivial due to the discreteness of the atomic system which results in inconsistencies in the definition of stress. In molecular dynamics, for example, the virial stress is widely used to interpret physical continuum properties. Figure 1 shows the interpolated V 22 virial stresses along a 65 symmetric tilt grain boundary in Cu, connected by linear interpolation. Observe that the linear interpolation of conventional virial stress distribution do not satisfy the basic equilibrium requirement in the absence of far-field loading, i.e. sum of forces = 0. Therefore, to assess the strength and the toughness of the grain b
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