Analysis of Vickers Hardness by the Finite Element Method

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Abstract
A particular formulation of the three-dimensional finite element method specifically for analyzing the Vickers hardness test is established. The Vickers hardness of 0.46 percent carbon steel and 70/30 brass is calculated using the proposed method using the stress-strain curve obtained from a tensile test. The calculated values correlate well with the experimental results for 0.46 percent steel and 70/30 brass. In addition, the analysis predicts the extension of the plastic zone induced by indentation, the stresses at the maximum load, and the residual stresses present after complete removal of the load. At the maximum load there are no tensile stresses in the vicinity of the indenter. However, after removal of the load, large tensile residual stresses are present on the diagonal edge beneath the indentation in the direction perpendicular to the diagonal edge. These results imply that it is necessary to reconsider the accuracy and validity of the conventional indentation method used for the determination of Klc for brittle materials such as ceramics.

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