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To address the problem of poor accuracy associated with using instrumented indentation tests to determine Vickers hardness, and the problem of selection of the most appropriate instrumented indentation approach, the finite element method was adopted to determine theoretical Vickers hardness values of different materials. On the basis of these theoretical values, a theoretical accuracy analysis of three representative methods was conducted for determining Vickers hardness via instrumented indentation: ISO method, Kang method and Ma method. Moreover, the results of the analysis were experimentally verified. The results show that with increasing ratio between the unloading work W e  and total unloading work W t  (i. e., W e /W t ), the theoretical error of Vickers hardness determined using each of the investigated instrumented indentation methods initially decreases and then increases. Compared to the other two instrumented indentation methods, the Ma method gave the lowest theoretical error of Vickers hardness. When the W e /W t  ratio ranged from 0.01 to 0.3, with different values of the plane strain elastic modulus ratio η and strain-hardening ratio n, the errors of Vickers hardness determined using each of the investigated methods were all discrete. By contrast, when W e /W t  ranged from 0.3 to 0.81, the errors were relatively concentrated. This work provides a theoretical basis for the further study of new methods for determining Vickers hardness via instrumented indentation testing.

Comparison of three methods for determining Vickers hardness by instrumented indentation testing