The ductile damage mechanisms dominating in modern high-strength steels have emphasised the significance of the onset of damage and the subsequent damage evolution in sheet metal forming processes. This paper contributes to the modelling of the plasticity and ductile damage behaviour of a dual-phase steel sheet by proposing a new damage mechanics approach derived from the combination of different types of damage models. It addresses the influence of stress state on the plasticity behaviour and onset of damage of materials, and quantifies the microstructure degradation using a dissipation-energy-based damage evolution law. The model is implemented into ABAQUS/Explicit by means of a user material subroutine (VUMAT) and applied to the subsequent numerical simulations. A hybrid experimental and numerical approach is employed to calibrate the material parameters, and the detailed program is demonstrated. The calibrated parameters and the model are then verified by experiments at different levels, and a good agreement between the experimental and numerical results is achieved.

Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in \(\sim \)0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods.

While strength and toughness properties of construction steels are major mechanical properties with respect to the safety assessment of components, increasingly often requirements are defined on the processing properties of materials, in particular cold formability properties. So far, the cold formability of structural steels is characterized in terms of three-point bending tests, which result in very expensive experimental effort and limited understanding of the material behaviour under various stress states. In this paper, the cold formability of a structural steel S355J2 + N is characterized under various stress states in a laboratory scale by a recently proposed hybrid damage mechanics approach. A damage initiation criterion that considers the influence of stress triaxiality and Lode angle is used to describe the onset of material degradation in a microstructural scale in the approach. Subsequent damage evolution is followed to further quantify the accumulation of damage till the final fracture. A series of laboratory tests is designed to calibrate the model parameters as well as to verify the calibration. Good agreement of experimental and numerical force–displacement responses proves the predicative capability of the model. With the laboratory findings, the industrial scale three-point bending test is simulated to predict the forming limit. In addition, the numerical study reveals that the stress state of the critical element in three-point bending test coincides with plane-strain tension, which results in a simpler method to characterize the bendability to reduce the experimental effort.