Error in compression stress-strain curve recording without extensometer and its correction method for non-standard small-sized specimens

Abstract

Compression tests employing small, non-standard specimens face challenges in accurate displacement measurement due to the unsuitability of contact extensometers and the high cost/complexity of video extensometers. The objective of this study is to develop a method for accurately measuring the true displacement of specimens during compression testing without the use of extensometers. Finite element analysis and compression tests on specimens with known elastic moduli identified three error components: frame deformation, contact gaps, and strain concentration at the fixture-specimen interface. Contact gaps can be eliminated through light preloading, leaving residual errors (denoted as Y) from frame compliance and interface strain concentration. Y was quantified by compressing small-diameter specimens of high-strength materials with known elastic moduli, specifically WC-11%Co cemented carbide, which was used in this study. The relationship between Y, load, and specimen diameter was established by subtracting the actual deformation of the small-diameter specimen from the total machine-recorded displacement. Subsequently, true specimen displacement was obtained by subtracting Y from the measured displacement. The method was validated on six metallic materials (Ni, W, Mo, Cu, Ti, #45 steel). Corrected stress-strain curves reduced elastic modulus errors to blow 10%. For example, Ni’s modulus improved from 26.5 GPa (uncorrected) to 195.4 GPa (96.7% of the true value), and W’s modulus increased from 34.2 to 370.2 GPa (92.6% of the true value). The proposed method requires only a single calibration test for specimens of identical diameter to establish Y-load-diameter mappings. Once integrated into testing systems, true displacement can be directly obtained, offering a cost-effective and operationally simple solution for small-specimen compression testing.