Two expanding cavity models (ECMs) are developed for describing indentation deformations of elastic power-law hardening and elastic linear-hardening materials. The derivations are based on two elastic-plastic solutions for internally pressurized thick-walled spherical shells of strain-hardening materials. Closed-form formulas are provided for both conical and spherical indentations, which explicitly show that for a given indenter geometry indentation hardness depends on YoungÕs modulus, yield stress and strain-hardening index of the indented material. The two new models reduce to JohnsonÕs ECM for elastic-perfectly plastic materials when the strain-hardening effect is not considered. The sample numerical results obtained using the two newly developed models reveal that the indentation hardness increases with the YoungÕs modulus and strain-hardening level of the indented material. For conical indentations the values of the indentation hardness are found to depend on the sharpness of the indenter: the sharper the indenter, the larger the hardness. For spherical indentations it is shown that the hardness is significantly affected by the strainhardening level when the indented material is stiff (i.e., with a large ratio of YoungÕs modulus to yield stress) and/or the indentation depth is large. When the indentation depth is small such that little or no plastic deformation is induced by the spherical indenter, the hardness appears to be independent of the strain-hardening level. These predicted trends for spherical indentations are in fairly good agreement with the recent finite element results of Park and Pharr.
Boron carbide disks with three different grain sizes were consolidated from submicrometer-sized boron carbide powder using the plasma pressure compaction technique. Static and dynamic indentations were performed to determine their loading-rate dependence on mechanical properties. Dynamic indentations resulted in a decrease in hardness and fracture toughness, and induced more severe damage compared with static indentations. Using Raman spectroscopy, the mechanism responsible for loss of strength under dynamic loads was identified as the solid-state structural phase transformation in the dynamically loaded regions. The influence of processing conditions and the resulting microstructure on the observed rate dependency of mechanical properties are discussed.
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