The classical slip line field solution for a two-dimensional punch is found to give a constraint factor (2.57) which is too small when the specimen beneath the punch is extensive. A new approach based on elasticity provides a constraint factor of 2.75. The new method of analysis also enables residual stresses to be estimated and indicates that plastic flow occurs not only when the specimen is loaded, but also when it is unloaded. Several details concerning the performance of hardness indenters are explained by the new theory for the first time.

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