Fig. 4
Finite element simulations showing the dependency of peak stress level at grain boundary–twin intersections on twin thickness. a Finite element model of a spherical nanotwinned grain containing alternative twins (colored in blue) and matrixes (colored in purple) located at the center of a cube (colored in gray). The cube edge is two times larger than the grain diameter. The crystal orientation of the twins and the cube are indicated in the model. b Calculated stress concentration factors, defined as the maximum value of the resolved shear stress occurring at the grain boundary–twin intersections normalized by its value at the center of the nanotwinned grain, increases with the twin thickness for three nanotwinned materials Pd, Cu, and diamond. The stress concentration factor versus twin thickness relations for each material is fitted to a square root scaling law. The direction of the applied displacement has an inclination angle of 30° with respect to the X axis. c, d Contours showing the resolved shear stress along the direction on (111) planes subtracted by its value at the center of the grain for two different normalized twin thicknesses c λ/d = 0.083 and d 0.25. The maximum resolved shear stress at the intersections is higher for the larger twin thickness
