A local stress approach for ductile crack propagation (Integration into the GTN model framework and demonstrations)

Abstract

A local stress approach, employing failure conditions derived from notched round-bar tensile tests has successfully traced the ductile crack propagation in compact tension (CT) specimens. The failure condition is expressed using the failure stress index (FSI), which is a linear sum of equivalent and mean stresses. Material failure occurs when the FSI reaches a specific limit. The limit FSI, applicable to high-stress triaxiality ranges—particularly in the crack frontal region—was established based on the failure conditions observed at the center of the notched cross-section of round-bar specimens from two steel grades. We utilized the Gurson–Tvergaard–Needleman (GTN) model, incorporating a stress-controlled void nucleation term, as a framework to implement the limit FSI. The model can induce intense void nucleation and growth occurring just before failure, leading to final material failure. The model faithfully replicated the failure process of the notched round-bar specimens of two steel grades. Key model parameters include the void nucleation stress, and the correction coefficient related to the limit FSI, reducing the need to adjust other void growth parameters such as the initial void fraction. Ultimately, the model effectively traced the ductile crack propagation in CT specimens of two steel grades. A critical aspect of the analysis was the emergence of an FSI concentration zone ahead of the crack tip, termed the process zone. This zone indicates that void nucleation initiates not at the crack tip itself but within its frontal region. Additionally, scanning-electron-microscope examination of fracture surfaces revealed that similar fracture processes play in both notched round-bar and CT specimens. These findings reinforce the applicability of the limit FSI in predicting microscopic failures in the frontal region of mode I ductile cracks.