A comparison of Gurson and Cocks–Ashby porosity kinetics and degradation functions

Abstract

Effects of porosity play a key role in ductile fracture and many modern metals are less than fully dense with a finite porosity created either unintentionally (as in additively manufactured or powder processed materials) or intentionally (as in metallic meta-materials and foams). This study compares the Gurson and Cocks–Ashby models’ predictions of porosity evolution (kinetics) and material degradation against unit cell simulations of a strain-rate dependent material under varying triaxiality. Previous comparisons do not address varying triaxiality and direct comparisons between the Gurson and Cocks–Ashby models are limited. This study also uses triaxiality, flow stress, strain rate, and strain-rate sensitivity from unit cell simulations as inputs to each model to give an accurate depiction of the models’ performance under complex evolving loading and material states. A fitting procedure for porosity evolution is also shown. This study shows the overall predictive power of the Gurson model over the Cocks–Ashby model. It also highlights the accuracy of the Cocks–Ashby porosity evolution model and Cocks–Ashby degradation function when each model is calibrated independently.