A comparative study on fracture toughness calculation models in spherical indentation tests (SITs) for ductile metals

Abstract

The study aimed to verify the effectiveness of fracture toughness calculation models in spherical indentation tests (SITs). Four representative models, the Haggag toughness (HT) model, critical indentation energy (CIE) model, critical stress-strain (CSS) model, and energy release rate (ERR) model, which were developed on different assumptions, were selected, and experiments were performed on 10 kinds of ductile metals. A comparison proved that none of the four models provide acceptable predictions for all experimental materials. The HT model provided the best fracture toughness KIC calculation for TC4, but failed for 6061 and some steels, while the other three models failed in predicting the KIC of TC4. The ERR model provided an overall acceptable prediction (with a maximum error around 20%, except for TC4) while the maximum errors in the other three models exceeded (or reached) 40% for steels and 6061. Errors were investigated from the effectiveness of empirical values used in each model, which proved that the stress ratio exhibits the best consistency and thus explained the reason why the ERR model provides the best fracture toughness calculations. The reason why the KIC of TC4 cannot be calculated with continuum-damage-mechanics based CIE and ERR models was also clarified through an investigation on its fracture (damage) mechanism through SEM observations. Further investigation proved that the fracture toughness can also be calculated from uniaxial tensile tests with an application of the CSS or ERR model, which verified the universality of these two models.