Abstract
A new model for determining elastic/plastic indentation is presented. This model generalizes Johnson's incompressible core model to a compressible material and allows the indentation pressure to be transmitted via a misfitted inclusion core beneath the indenter which is surrounded by a hemispherical plastic zone. The internal stress field inside the core is obtained by applying Eshelby's spherical inclusion problem together with Hill's spherical-cavity expansion analysis. The plastic deformation considered here exactly ensures compatibility between the volume of a material displaced by the indenter and that accommodated by expansion. The analysis explains the essential relationships between the dimensions of the indentation and plastic zone and the dominant material properties; yield stress, hardness and elastic modulus. The solution is extended to evaluate the indentation fracture toughness by taking into account the reduced half-space constraint by the image force.
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Tanaka, K. Elastic/plastic indentation hardness and indentation fracture toughness: The inclusion core model. J Mater Sci 22, 1501–1508 (1987). https://doi.org/10.1007/BF01233154
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DOI: https://doi.org/10.1007/BF01233154