Subsurface hardening in erosion-damaged copper as inferred from the dislocation cell structure, and its dependence on particle velocity and angle of impact

Previously published measurements of the cell diameters d of dislocation cells underneath copper surfaces exposed to particle erosion were evaluated in terms of the subsurface stresses τ to which they correspond. These were compared with the elastic stresses expected underneath spherical indenters impacting on the surface with different speeds. The inferred stresses differ markedly from theoretical predictions, not only in regard to the dependence on speed and angle of impact but even in regard to their decay along the z axis, the direction normal to the surface. Instead of τ decreasing as z − n with n continuously rising from 0 at a shallow depth to 2 at large depths, as predicted from elastic theory, the stresses follow a z −1 dependence throughout the measured range. All data are satisfactorily explained by the relationship 1/d = (7/z)v 2 5 sin α ≈ τ/100 (using MKS units), where v stands for the velocity of the impacting particles, namely rather irregularly shaped alumina particles 50 μm in diameter, and α is the angle of impact. No theoretical explanation has so far been found to account for this result. It is noted, however, that previously a z −1 decay of stress had already given excellent results in a theoretical interpretation of the subsurface shear strain underneath a surface subject to sliding wear. Further, sin α is the direction cosine for the normal force component, whereas a velocity dependence of v 2 5 is found from elastic theory for the depth scaling of the elastic stress due to a spherical indenter. Suggestions are made for further experiments.