Hardening effects on formability limit prediction based on gurson-type damage models and bifurcation analysis

In this work, ductility limits of metallic materials, associated with the occurrence of strain localization, are predicted using the GTN damage model coupled with bifurcation theory. The resulting approach is implemented into the finite element code ABAQUS within the framework of large plastic strains and a fully three-dimensional formulation. A parametric study with respect to damage and hardening parameters is conducted in order to identify the most influential material parameters on strain localization. The analysis shows that the damage parameters have a significant impact on the predicted ductility limits, while the effect of hardening parameters on strain localization depends on the choice of void nucleation mechanism

Analysis of strain localization with a nonlocal plasticity model

In the present paper a nonlocal plasticity model is described, intended to reproduce the mechanical behaviour of stiff fine-grained soils, including the objective simulation of strain localization; the phenomenon of accumulation of deformations in narrow zones in the form of shear bands or fractures. A number of analyses have been performed to assess the developed formulation. Relevant aspects have been addressed such as the thickness of the shear band, its orientation, and the onset of localization in a boundary value problem (BVP). Results provide useful insigths into relevant aspects of the numerical simulation of strain localization

Strain localization in a shear transformation zone model for amorphous solids

We model a sheared disordered solid using the theory of Shear Transformation Zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi, et al.(Phys. Rev. Lett. 98 185505 2007), finding that the model generates solutions that fit the data,exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.Comment: 8 figures, references added, typos correcte

Strain localization analysis using a multiscale model

In order to analyze the formability of steels in sheet metal forming, a ductility loss criterion is coupled with a multiscale model. The behavior at the mesoscopic (grain) scale is modeled by a large strain micromechanical constitutive law, which is then used in a self-consistent scale transition scheme. Hardening at the slip system level is taken into account through mean dislocation densities considered as internal variables. The determination of active slip systems and the calculation of plastic slip activity are achieved with help of a regularization technique drawn from viscoplastic formulations. The model is shown to be able to correctly simulate the macroscopic behavior for single-phase steels during both monotonic and sequential loading paths. Finally, Rice's localization criterion, based on the ellipticity loss of the elastic-plastic tangent modulus, is introduced and applied to determine forming limit diagrams (FLDs). The model allows us to obtain correct FLDs for monotonic as well as sequential loading paths. Pre-strain impact on FLDs is qualitatively reproduced as well.ArcelorMittal CNR

Fracture of disordered solids in compression as a critical phenomenon: III. Analysis of the localization transition

The properties of the Hamiltonian developed in Paper II are studied showing that at a particular strain level a ``localization'' phase transition occurs characterized by the emergence of conjugate bands of coherently oriented cracks. The functional integration that yields the partition function is then performed analytically using an approximation that employs only a subset of states in the functional neighborhood surrounding the most probable states. Such integration establishes the free energy of the system, and upon taking the derivatives of the free energy, the localization transition is shown to be continuous and to be distinct from peak stress. When the bulk modulus of the grain material is large, localization always occurs in the softening regime following peak stress, while for sufficiently small bulk moduli and at sufficiently low confining pressure, the localization occurs in the hardening regime prior to peak stress. In the approach to localization, the stress-strain relation for the whole rock remains analytic, as is observed both in experimental data and in simpler models. The correlation function of the crack fields is also obtained. It has a correlation length characterizing the aspect ratio of the crack clusters that diverges as (\xi \sim (\ep_{c}-\ep)^{-2}) at localization.Comment: 11 pages, 3 figure