On the Plastic Flow Beneath a Blunt Axisymmetric Indenter

A new approaclt to large strain plasticity problems i n which the material i s considered to behave i n a plastic-elastic fasltion, instead of as a plastic-rigid body, i s applied to the axisymmetric blunt indenter. The ratio of the mean stress on the pt~nclj face to tlte uniaxial flow stress of the material (constraint factor C ) i s found to be 2.82 for a n extensive specimen. However, i t i s slzown that a small part of the punclt face i s elastically loaded, and i f the loaded punch area i s assumed equal to the size of the plastic impression, the% the constraint factor to be used i s 3.00 instead of 2.82. Th i s i s the value to be used in interpreting the ordinary brine11 test. Hardness values are shown to be independent of the degree of friction on the face of a blunt indenter and of the elasticity of the indenter. The amount of material required beneath a n axisymmetric indenter i n order that there be no upward flow i s found to be about 2.6 times the diameter of the impression for steel. However, tlte exact value depends on Young's modulus of elasticity, Poisson's ratio, material hardness, and tlte depth of the impression relative to the diameter of the indenting sphere. W h e n two opposing axisymmetric indenters are employed, the influence of one on the other will be less t l u n one percent when their spacing i s approximately 11.5 times the indefttation diameter. .I blunt indenter m a y be defined a s one wlzick gives 710 npward flow i n a hardness test. Upward flow should be avoided i n kardness tesfing since i t causes the mean stress on tlte punch face to produce a given impression to be sensitive to friction and the tendency of the metal to strain harden. Upward flow m a y be prevented by use of a n extensive specimen relative to the depth of the impression, large indenter angle (160180 deg), and high indenter friction (roziglt surface and no lubricant). The$ow stress measured by a blunt indenter i s that correspouding to the onset of plastic flow. W h e n upward flow i s permitted, the flow stress measwed by a n indentation hardness test will correspond to a n appreciable plastic strain which increases a s the included a n g b of the indenter decreases. The quantity measured by a n indenter that performs wi th upward fEow i s , therefore, quite ambigzbous when the material tested strain hardens.