On the Plastic Flow Beneath a Blunt Axisymmetric Indenter

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Abstract
A new approach to large strain plasticity problems in which the material is considered to behave in a plastic-elastic fashion, instead of as a plastic-rigid body, is applied to the axisymmetric blunt indenter. The ratio of the mean stress on the punch face to the uniaxial flow stress of the material (constraint factor C) is found to be 2.82 for an extensive specimen. However, it is shown that a small part of the punch face is elastically loaded, and if the loaded punch area is assumed equal to the size of the plastic impression, then the constraint factor to be used is 3.00 instead of 2.82. This is the value to be used in interpreting the ordinary brinell 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 an axisymmetric indenter in order that there be no upward flow is found to be about 2.6 times the diameter of the impression for steel. However, the exact value depends on Young’s modulus of elasticity, Poisson’s ratio, material hardness, and the depth of the impression relative to the diameter of the indenting sphere. When two opposing axisymmetric indenters are employed, the influence of one on the other will be less than one percent when their spacing is approximately 11.5 times the indentation diameter. A blunt indenter may be defined as one which gives no upward flow in a hardness test. Upward flow should be avoided in hardness testing since it causes the mean stress on the punch face to produce a given impression to be sensitive to friction and the tendency of the metal to strain harden. Upward flow may be prevented by use of an extensive specimen relative to the depth of the impression, large indenter angle (160–180 deg), and high indenter friction (rough surface and no lubricant). The flow stress measured by a blunt indenter is that corresponding to the onset of plastic flow. When upward flow is permitted, the flow stress measured by an indentation hardness test will correspond to an appreciable plastic strain which increases as the included angle of the indenter decreases. The quantity measured by an indenter that performs with upward flow is, therefore, quite ambiguous when the material tested strain hardens.

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