A Gurson model improved by cohesive traction-separation law to realize transition from ductile to brittle fracture

The objective of this study is to improve Gurson model by combining with cohesive traction-separation law to realize crack propagation associated with transition from ductile to brittle fracture. To embed the cohesive cracks into the Gurson model, five kinds of conditional equations are solved for the crack opening displacement and the plastic strain. One of the conditional equations correspond to the local balance equations between the cohesive tractions and the principal stresses and the others are the yield function, the isotropic hardening law, evolutional equation of void volume fraction and inequality constraint. The enhanced Gurson model allows us to represent the nucleation and propagation of the ductile crack along with the void nucleation and growth. Moreover, it is realized by the embedded cohesive traction-separation law that the stress rapidly drops down when the crack accelerates due to the transition from the ductile to brittle fracture. Throughout the numerical examples at several temperatures, it is confirmed that the proposed model enables us to realize load-displacement curves depending on temperature along with the ductile-brittle transition. Also, the proposed model has represented changes of crack propagation rate and void volume fraction by depending on temperature. Furthermore, the proposed model has capability of reproducing the crack propagation associated with the transition from the ductile to brittle fracture at -60 °C. © 2020 Japan Welding Society. All rights reserved.