Insensitivity of Grain Boundary Stress Fields to Area Variations

The atomistic simulations in this article substantiate that grain boundary stress fields remain unaffected by changes in their area, aligning with the Olson-Cohen theory which supports that such area insensitivity is an inherent outcome of the combined effect of coherency and anti-coherency dislocations. Twist grain boundaries are employed in alpha-iron as a model in atomistic simulations, revealing and contrasting the dislocations and stresses of these grain boundaries when their area varies from infinity to a few square nanometers. It is discovered that the grain boundary stresses remain relatively constant, always short-ranged. Furthermore, within the framework of the Frank-Bilby equation, the line directions and spacing of coherency and anti-coherency dislocation arrays in a grain boundary are predicted, the stresses of these dislocations are subsequently calculated numerically, and these stresses are superimposed together to form the grain boundary stress field. The numerical calculations verify that stress fields of grain boundaries are not sensitive to changes of their area, corroborating our atomistic simulations. The preliminary atomistic simulations of various homophase and heterophase boundaries further affirm this area insensitivity. Atomistic simulations and numerical calculations demonstrate that the area insensitivity of grain boundary stress fields can be attributed to the net boundary dislocation content of zero and that all real grain boundaries with finite areas have short-range stress fields and finite boundary energy.image (c) 2024 WILEY-VCH GmbH