- Bishop R
- Hill R
- Mott N

Proceedings of the Physical Society (1945) 57(3) 147-159

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A discussion is given of the indentation of ductile materials by cylindrical punches with conical heads. On the experimental side, experiments have been made with work-hardened and with annealed copper, with penetrations up to nine times the dameter of the punch. It is found that the load rises towards a maximum value which is not approached until the base of the cone has travelled four to five diameters into the copper block. Denoting ths maximum load by poA, where A is the area of the cross- section of the punch, it is found that p, for a lubricated punch is about twice the hardness, or five times the yield stress, of the work-hardened material. A theoretical methodis given for calculating Po, as follows : the pressures p, and p, required to enlarge a cylindrical and a spherical hole in a material showing any kind of strain hardening can be calculated. It is plausible to assume that p, should be between p, and p,, and since p, is only slightly greater than p,, an approximate theoretical estimate of p, is obtained. This is in good agreement with experiment. In the light of these results a qualitative discussion is given of hardness testing, and it is shown both on experimental and on theoretical grounds that with lubricated cones and work-hardened materials the hardness, i.e. load/indentation area, will not depend much on the angle of the cone unless this is less than 10"

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