Effect of frictional force on the steady state axisymmetric deformations of a viscoplastic target

Abstract

We study steady state axistmmetric deformations of a thick viscoplastic target being penetrated by a fast-moving long rigid cylindrical rod with a hemispherical nose. The deformations of the target appear steady to an observer situated on the penetrator nose tip and moving with it. The objective of this work is to investigate the effect of the frictional force acting on the target/penetrator interface upon the deformations of the target. It is postulated that the frictional force at a point on the target/penetrator interface is proportional to the normal traction there and depends upon the speed of the target particle relative to the penetrator. It is found that the frictional force affects significantly the variation of the tangential speed and the second invariant of the strain-rate tensor on the penetrator nose surface, but minimally the distribution of the normal stress there, since the dominant component of the normal stress is the hydrostatic pressure which is affected little by the consideration of friction forces.