Extension of the modified Bai‐Wierzbicki model for predicting ductile fracture under complex loading conditions

Abstract

The ductile fracture behaviour of metallic materials is strongly dependent on the material's stress state and loading history. This paper presents a concept of damage initiation and failure indicators and corresponding evolution laws to enhance the modified Bai‐Wierzbicki model for predicting ductile damage under complex loading conditions. The proposed model considers the influence of stress triaxiality and the Lode angle parameter on both damage initiation and the subsequent damage propagation. The model parameters are calibrated for C45E + N steel using a series of mechanical tests and numerical simulations. The enhanced approach is applied to the modelling of various mechanical tests under proportional and non‐proportional loading conditions and successfully predicts the ductile damage behaviour in these tests.

Influence of Pore Characteristics on Anisotropic Mechanical Behavior of Laser Powder Bed Fusion–Manufactured Metal by Micromechanical Modeling

“…[38,39] The initiation criterion can be specified by providing the equivalent plastic strain at the onset of ductile damage as a function of stress triaxiality, Lode angle, and strain rate. [40,41] However, such a modeling approach, in general, features a macroscopic phenomenological nature, owning great predictive capability in application but also requiring a significant amount of effort for parameter identification by experiments at various stress states and loading conditions. Although such criteria can be used in combination with CP models, the data required are difficult to obtain, as experiments covering a range of stress triaxialities must be conducted at the microscopic scale.…”

The differences of damage initiation and accumulation of DP steels: a numerical and experimental analysis

“…In the framework of continuum damage mechanics, the modified Bai Wierzbicki (MBW) model has been proposed by Lian et al (2013) and widely applied to describe the damage and fracture behaviours of various grades of steels (Lian et al 2013;Münstermann et al 2017;Wu et al 2017;Novokshanov et al 2015;Shen et al 2020;Liu et al 2020). Like in other damage mechanics models, the significant influences of stress state on the ductile fracture are considered through defining a strain based criterion which is usually a weighted function of two particularly important variables, the stress triaxiality η and the Lode-angle parameter θ that are related to the three stress invariants.…”

“…Additionally, a set of critical values for the damage variable was applied, at which material fracture was assumed in the numerical simulation. Wu et al changed that considerably by implementing a locus for the fracture, as well as considering non proportional loading paths until the inception of ductile damage (Wu et al 2017). A further development of the MBW model was made by Shen et al to characterise the influence of loading orientation, which was used to describe the anisotropic ductile damage and fracture behaviour of pipeline steels (Shen et al 2020).…”

Numerical Evaluation of Surface Roughness Influences on Cold Formability of Dual‐Phase Steel

“…To combine these ideas, a hybrid approach called the "modified Bai-Wierzbicki (MBW) model was introduced. [8][9][10] This model allows us to include the damage softening effect before fracture as well as define a strain limit as a function of stress state to identify its fracture criterion. Therefore, after yielding, instead of modeling the material in two stages-failed and not-failed-one can classify it into three stages: plasticity, damage softening, and failed.…”