Investigation of Relationship between Instrumented Indentation Nominal Hardness and Reduced Elastic Modulus with Large Apex Angle Indenter

摘要

Based on dimensional analysis, finite element numerical calculation is undertaken on elastic-plastic solids to investigate the relationship between instrumented indentation nominal hardness H_n and reduced elastic modulus E_r for three different apex angle indenters. The half-included angles of axisymetric conical indenter models are 62.9°, 70.3° and 85.566° which are corresponding to the real indenters of cube corner indenter with 60° face angle, Berkovich indenter with 65.27° face angle and cube corner indenter with 85° face angle, respectively. The relationship between a nominal hardness/reduced elastic modulus (H_n/E_r) and elastic work/total indentation work (W_e/W_t) is established with a sixth-order polynomial form for each apex angle indenter. For rigid indenter of instrumented indentation model, reduced elastic modulus E_r=1/[(1+v~2)/E], where E and v are elastic modulus and Poisson's ratio of the indented material. Therefore, H_n/E_r-W_e/W_t relationship can be used to give estimates of E. Accuracy estimation for the each relationship of each half-included angle indenter shows that the large half-included angle of 85.566° gives better Er measurement error of +11.56% for a low yield strength material (e.g., materials for which σ_y=100MPa, n=0 and E=200GPa), while for the smaller half-included angle of 62.9° or 70.3° indenter, the measurement error is > ±12.74%. The research in this paper confirms that H_n/E_r-W_e/W_t relationship of large apex angle indenter such as 85.566° half-included angle is recommended to be used for estimating the elastic modulus E of indented material.