Work hardening of materials with strong inclusions after prismatic punching

Work hardening of long range character for materials with strong inclusions was considered for the case in which plastic relaxation occurs by means of prismatic punching around the inclusions. The model used was a modification of the punching mechanism proposed by Ashby. The stress at an inclusion and the elastic energy arising from the presence of dislocation loops were calculated by using continuum mechanics. The balance between the driving force forprismatic punching produced by a decrease of the elastic energy due to prismatic punching and the retarding force arising from the frictional stress led to a stress-strain relationship after punching. It was found that work hardening was appreciable after considerable punching, although the derivation from linear hardening was significant. The elastically stiffer the inclusion the smaller is the strain required to initiate prismatic punching, but the larger is the increment of flow stress with plastic strain.