Impression creep by an annular punch

The diffusion problem of impression creep of a half-space by an annular punch is analyzed. The results indicate that, at low stresses, the impression velocity is proportional to the punching stress. For the same punching stress the impression velocity increases without limit as the annular thickness approaches zero. The limiting case for a solid punch agrees with previous results, namely, (1) the impression velocity for interface diffusion the impression velocity is inversely to the square of the punch radius, and (2) that for bulk diffusion the impression velocity is inversely proportional to the punch radius. For a thin annular punch, the impression velocity reduces to that of impression creep by a straight punch, i.e., the impression velocity for interface diffusion is inversely proportional to the square of the thickness of the annular punch, and that for bulk diffusion it is inversely proportional to the thickness of the annular punch. In fact, the straight punch is a good approximation (larger by less than 5%) if the inner radius/outer radius ratio is larger than 0.1 for interface diffusion and 0.2 for bulk diffusion.