METHOD TO GENERATE ACCURATE ELASTIC AND HYPERELASTIC UNIAXIAL TENSION STRESS–STRAIN DATA WITHOUT AN EXTENSOMETER

Abstract

Uniaxial tension tests on dumbbells are routinely used to determine the stress–strain response of engineering materials. The simplest way to calculate strain is from grip displacement during extension, but this introduces significant error when dumbbells are gripped at the wider end sections to avoid the sample breaking prematurely in the grips. Mechanical and optical extensometers alleviate this problem by directly measuring strain in the gauge section. However, the equipment introduces significant additional hardware and software costs, and some experimental setups obstruct or prevent direct measurement of strain. The strain following systems also struggle both with the loss in mark intensity and changes of the shape of the marked point as the strain level is increased. To address these shortcomings, a novel analytical model to correct stress–strain data based on grip displacement is proposed. The model is implemented in Fortran and applied to hyperelastic materials which are assumed isotropic, but in principle the method is not restricted to elastomers. The model is validated with three studies on dumbbells: (i) a finite-element analysis for strains up to 660%; (ii) an experimental test with unfilled natural rubber up to 300% strain using a video extensometer; and (iii) a high temperature experimental test to fracture where the strain is corrected for a filled rubber. The model errors range from 2.2% to 3.1%, which is well within material and experimental uncertainties; hence, the model provides an accurate, inexpensive means of determining stress–strain behavior from grip displacement.