Geometric formulation of residual stress propagation in diamond lattice substrate

The stress residue in diamond lattice substrates significantly influences their mechanical properties during fabrication, testing, and application. However, its propagation mechanisms remain unclear, and traditional planar impact methods often underestimate surface damage owing to stress interference. This study reveals three distinct stress behaviors under dual-shock stimuli: rapid dissipation, triangular spreading, and surface localization. Specifically, the residual stress induced by shock waves of 50 MPa or higher affected up to 3.3 %, 10.1 %, and 4.1 % of the entire substrate area, depending on the propagation pattern. The corresponding propagation speeds were measured at 7.11, 5.49, and 2.31 km s⁻¹, respectively, highlighting distinct differences in kinetic behavior. By analyzing these stress propagation patterns through the lens of atomic potential energy barriers, we identified the most critical impact scenarios and their damage mechanisms. Each pattern uniquely affects the interior of the substrate, with point impacts at the atomic scale causing significantly higher damage concentrations compared to planar waves. Our findings offer valuable insights into the management of residual stress and enhancement of the durability of crystalline solids.