On the predictive capabilities of the shear modified Gurson and the modified Mohr-Coulomb fracture models over a wide range of stress triaxialities and Lode angles

The predictive capabilities of the shear-modified Gurson model [Nielsen and Tvergaard, Eng. Fract. Mech. 77, 2010] and the Modified Mohr-Coulomb (MMC) fracture model [Bai and Wierzbicki, Int. J. Fract. 161, 2010] are evaluated. Both phenomenological fracture models are physics-inspired and take the effect of the first and third stress tensor invariants into account in predicting the onset of ductile fracture. The MMC model is based on the assumption that the initiation of fracture is determined by a critical stress state, while the shear-modified Gurson model assumes void growth as the governing mechanism. Fracture experiments on TRIP-assisted steel sheets covering a wide range of stress states (from shear to equibiaxial tension) are used to calibrate and validate these models. The model accuracy is quantified based on the predictions of the displacement to fracture for experiments which have not been used for calibration. It is found that the MMC model predictions agree well with all experiments (less than 4% error), while less accurate predictions are observed for the shear-modified Gurson model. A comparison of plots of the strain to fracture as a function of the stress triaxiality and the normalized third invariant reveals significant differences between the two models except within the vicinity of stress states that have been used for calibration.     

A local viewpoint for evaluating the influence of stress triaxiality and Lode angle on ductile failure and hardening

All damage and failure models, describing either the evolution of microvoids, the development of shear bands or local rupture, rely on the knowledge of the hardening function at large plastic strains which, then, becomes an essential prerequisite for any failure prediction.     

Numerical simulation of 3D ductile cracks formation using recent improved Lode-dependent plasticity and damage models combined with remeshing

Damage to fracture transition has become a popular topic in the ductile fracture scientific community. Indeed, the transition from a damage continuous approach to a discontinuous fracture is not straightforward both from mechanical and numerical points of view. In the present study, a new improved Lode dependent phenomenological coupled damage model is used to investigate the ductile fracture in different mechanical tests. The remeshing and elements erosion techniques are employed to propagate the ductile cracks in 3D models using Forge® finite element code. This code is based on a mixed velocity–pressure formulation using the MINI element P1+/P1$P1+/P1$. In addition, the plasticity behavior is modeled by a Lode-dependent plasticity criterion. Applications to different mechanical tests at different loading configurations, using identified damage model parameters, show good agreement in terms of fracture prediction between experimental and numerical results.     

Site of ductile fracture initiation in cold forging: A finite element model

Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. In this study a new ductile fracture condition that based on the microscopic phenomena of void nucleation, growth and coalescence was proposed. Using this condition and combining with finite element model to predict the fracture locations in bulk metal forming, the results show that it is in close accordance with observations of some experimental specimens. However, in order to obtaining the high trustiness many experiments have to be carried out.     

On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule

It has been shown that the plastic response of many materials, including some metallic alloys, depends on the stress state. In this paper, we describe a plasticity model for isotropic materials, which is a function of the hydrostatic stress as well as the second and third invariants of the stress deviator, and present its finite element implementation, including integration of the constitutive equations using the backward Euler method and formulation of the consistent tangent moduli. Special attention is paid for the adoption of the non-associated flow rule. As an application, this model is calibrated and verified for a 5083 aluminum alloy. Furthermore, the Gurson-Tvergaard-Needleman porous plasticity model, which is widely used to simulate the void growth process of ductile fracture, is extended to include the effects of hydrostatic stress and the third invariant of stress deviator on the matrix material.     

On some topics for the numerical simulation of ductile fracture

In this work, we analyze some aspects of the macroscopic Gurson–Tvergaard–Needleman (GTN) constitutive model when it is addressed to solve ductile fracture problems by means of numerical simulations:     

Gradient plasticity with the tangential-subloading surface model and the prediction of shear-band thickness of granular materials

An extended gradient elastoplastic constitutive equation is formulated, which is capable of describing the plastic strain rate due to the rate of stress inside the yield surface and the inelastic strain rate due to the stress rate component tangential to the subloading surface by incorporating the tangential-subloading surface model. Based on the extended constitutive equation, the post-localization analysis of granular materials is performed to predict the shear-band thickness. It is revealed that the shear-band thickness is almost determined by the gradient coefficient characterizing the inhomogeneity of deformation, although the stress–strain curve is strongly dependent on material properties.