Development of a Method for Estimating Stress-strain Relationships Based on the Results of Indentation Tests that Eliminated the Size Effect Attributed to Ultra-small Loads

Abstract

For small samples for which tensile tests cannot be conducted, methods have been developed to estimate stress-strain relationships using indentation tests and analysis models that simulate these tests. However, precise modeling of factors such as wear at the indenter tip and friction coefficients between the indenter and material is challenging. A few examples are applied to small regions, such as single crystal grains, using small loads. In this study, we developed a method to estimate stress-strain relationships based on the work-hardening law from load-displacement curves and hardness measured by pyramidal indentation tests. Using the presented method, we evaluated the stress-strain relationships from nanoindentation test results obtained under a load of five mN and results from micro-Vickers hardness tests conducted under a load of 10 N. While micro-Vickers test results estimated curves similar to tensile test results, the estimation accuracy decreased for nanoindentation tests with lower loads. This reduction in accuracy is attributed to the size effect of hardness, which occurs under low-load conditions. To improve the estimation accuracy under low-load conditions, we determined correction coefficients to reduce the influence of the size effect by comparing the estimation results under both load conditions for ferritic single-phase materials fabricated within the compositional range of hypoeutectoid steel. As a result, it is now possible to estimate the stress-strain relationship using indentation tests from microregions, approaching the scale of single crystal grains, for materials within the compositional range of hypoeutectoid steel.