Strain rate sensitivity of hardness in indentation creep with conical and spherical indenters taking into consideration elastic deformations. (1st March 2021) - Mohammed, Yousuf S.; Stone, D.S.; Elmustafa, A.A.
Abstract: Using finite element analysis and analytical modeling, we investigate the strain rate sensitivity of the hardness in indentation creep ( m H ) and the relationship between m H and the strain rate sensitivity of the flow stress, mσ, for cone (self-similar) and spherical (non-self-similar) indenters. The present m H / m σ results extend previous results (Elmustafa et al, 2007a, b) for cones in terms of a universal curve that describes the ratio m H / m σ as a function of H / E ∗ / ∊ H starting from a value of 1, for small values of H / E ∗ / ∊ H (fully plastic) to zero at H / E ∗ / ∊ H ≈ 2.5 (fully elastic). We also investigated the effect of varying effective strain levels ( ∊ H ). For the cone, the strain level is determined by the angle β (25.3°, 22.5°, 19.7°) which is the angle the cone face makes with the specimen surface. mH /mσ becomes vanishingly small and the material undergoes full elastic deformation for H/E* ≈ 0.23 and 0.18 for the β angles of 25.3° and 19.7°, respectively, as compared to β angle of 22.5° for which H/E* ≈ 0.21 as shown by Elmustafa et al. (2007a). The simulation results of mH /mσ versus H/E * for various β angles collapsed to a single curve when H/E* is normalized to the tangent of the β angles. In the case of the spherical indenter, the strain level is a function of indent radius/indenter radius ratio ( a / R ) . Simulations were performed for depths between 0.01 and 0.5 R for the non-self similar spherical indentations. The results indicate that the ratio mH / mσ does not maintain a unique relation with H/E* and varies with the increase in the ratio of depth of penetration to the radius of the indenter, a / R . It is also concluded that the data collapsed to a single curve similar to the one produced for conical indentation and that mH / mσ approaches zero for a normalized (H/E * )/(a/R) of ≈ 0.4. It is also found that the normalized hardness data, when mH / mσ approaches zero, fits Johnson solution well. Nanoindentation experimental data of Al2 O3 samples using a spherical indenter tip displayed identical behavior similar to Johnson fully elastic behavior solution.