Mathematical Modeling of the Deformation Zone Under an Impression Creep Indenter Using Upper-Bound Theory
摘要
This work presents a novel analytical approach using the upper-bound method for the impression creep test. A cylindrical velocity field for the deformation zone is proposed and the depth and radius of the deformation zone are determined by minimizing the relative punch pressure expression. The impression creep test relies on the analysis of the indenter penetration depth over time. This depth is directly related to the plastic deformation zone beneath the indenter which is used to calculate the conversion factors to correlate results with conventional creep tests and to determine the minimum sample size. Therefore, from a metallurgical perspective, the depth and volume of the deformation zone are important in this test. The material flow pattern, as depicted by the velocity field expressions, exhibits excellent agreement with the findings obtained from finite element analysis. Thus, this study presents a novel approach to estimating a constant friction factor by combining the analytical model with metallographic measurements of the deformation zone beneath the indenter. Additionally, by utilizing the measured steady-state punch velocity from the impression creep test along with the obtained constant friction factor, the average strain rate can be calculated. This method eliminates the limitations associated with the unknown or wide range of conversion factors presented in the literature and offers a more reliable and robust approach for analyzing material behavior in impression creep tests.