Atomistic calculation of internal stress in nanoscale polycrystalline materials

Internal stress in polycrystalline materials is an intrinsic attribute of the microstructure that affects a broad range of material properties. It is usually acquired through experiment in conjunction with continuum mechanics modelling, but its determination at nanometre and submicron scales is extremely difficult. Here, we report a bottom-up approach using atomistic calculation. We obtain the internal stress in polycrystalline copper with nanosized grains by first computing the stress associated with each atom and then sorting the stress into those associated with different self-equilibrating length scales, i.e. sample scale and grain cell, which gives type I, II and III residual stresses, respectively. The result shows highly non-uniform internal stress distribution; the internal stress depends sensitively on grain size and the grain shape anisotropy. Statistical distributions of the internal stresses, along with the means and variance, are calculated as a function of the mean grain size and temperature. The implementation of this work in assisting the interpretation of experimental results and predicting material properties is discussed.