Localized Necking Model for Punching Fracture Simulation in Unstiffened and Stiffened Panels

The ductile fracture of thin-shell structures was studied here using a localized necking model. The punching experiments for unstiffened and stiffened panels were compared with numerical predictions using a combined ductile fracture and localized necking model using shell elements. The plasticity and fracture model parameters of JIS G3131 SPHC steel were identified by performing calibration experiments on standard flat bars, notched tension, central hole tension, plane strain tension, and shear specimens. The plasticity beyond the onset of necking was modeled using the Swift hardening law. The damage indicator framework with a combined Hosford–Coulomb fracture model and the domain of shell-to-solid equivalence (DSSE) were adopted to characterize the fracture initiation. The model parameters were calibrated based on the loading paths to fracture initiation, which were extracted from a non-linear finite element (FE) analysis. The presented HC–DSSE model was validated using punch tests and was able to predict fracture initiation with good accuracy.

Prediction of Strain Path Changing Effect on Forming Limits of AA 6111-T4 Based on A Shear Ductile Fracture Criterion

Strain path changing is a phenomenon in the stamping of complex panels or multiple-step stamping processes. In this study, the influence of the strain path changing effect was investigated and assessed for an aluminum alloy of 6111-T4 with a shear ductile fracture criterion. Plastic deformation of the alloy was modeled by an anisotropic Drucker yield function with the assumption of normal anisotropy. Then the shear ductile fracture criterion was calibrated by the fracture strains at uniaxial tension, plane strain tension and equibiaxial tension under proportional loading conditions. The calibrated fracture criterion was utilized to predict forming limit curves (FLCs) of the alloy stretched under bilinear strain paths. The analyzed bilinear strain paths included biaxial tension after uniaxial tension, plane strain tension and equibiaxial tension. The predicted FLCs of bilinear strain paths were compared with experimental results. The comparison showed that the shear ductile fracture criterion could reasonably describe the effect of strain path changing on FLCs, but its accuracy was poor for some bilinear paths, such as uniaxial tension followed by equibiaxial tension and equibiaxial tension followed by plane strain tension. Kinematic hardening is suggested to substitute the isotropic hardening assumption for better prediction of FLCs with strain path changing effect.

Hole-Expansion: Sensitivity of Failure Prediction on Plastic Anisotropy Modeling

The influence of yield function parameters on hole-expansion (HE) predictions are investigated for an anisotropic AA6022-T4 aluminum sheet. The HE experiment is performed in a fully-instrumented double-action hydraulic press with a flat-headed punch. Full strain fields are measured by a stereo-type digital image correlation (DIC) system. The stress state gradually changes from uniaxial to plane-strain tension to biaxial tension in the radial direction. Besides HE, the plastic anisotropy of AA6022-T4 is characterized by uniaxial tension and plane-strain tension experiments. Uniaxial tension is considered as the most important, since it is the stress state along the hoop direction in the hole. For the finite element (FE) simulation, the Yld2000-2d non-quadratic anisotropic yield function is used with two different parameter sets, calibrated by: (1) uniaxial tension only (termed Calib1) and, (2) both uniaxial and plane-strain tension (Calib2). The strain field predictions show a good agreement with the experiments only for Calib2, which takes into account plane-strain as well uniaxial tension. This indicates the importance of biaxial modes, and in particular plane-strain tension, for the adopted yield function to produce accurate HE simulations.

Effect of the third invariant on the formation of necking instabilities in ductile plates subjected to plane strain tension

In this paper, we have investigated the effect of the third invariant of the stress deviator on the formation of necking instabilities in isotropic metallic plates subjected to plane strain tension. For that purpose, we have performed finite element calculations and linear stability analysis for initial equivalent strain rates ranging from 10^−4 s−1 to 8 · 10^4 s−1. The plastic behavior of the material has been escribed with the isotropic Drucker yield criterion [11], which depends on both the second and third invariant of the stress deviator, and a parameter c which determines the ratio between the yield stresses in uniaxial tension and in pure shear \sigma_T /\tau_Y . For c = 0, Drucker yield criterion [11] reduces to the von Mises yield criterion [32] while for c = 81/66, the Hershey-Hosford (m = 6) yield criterion [19, 22] is recovered. The results obtained with both finite element calculations and linear stability analysis show the same overall trends and there is also quantitative agreement for most of the loading rates considered. In the quasi-static regime, while the specimen elongation when necking occurs is virtually insensitive to the value of the parameter c, both finite element results and analytical calculations using Considère criterion [10] show that the necking strain increases as the parameter c decreases, bringing out the effect of the third invariant of the stress deviator on the formation of quasi-static necks. In contrast, at high initial equivalent strain rates, when the influence of inertia on the necking process becomes important, both finite element simulations and linear stability analysis show that the effect of the third invariant is reversed, notably for long necking wavelengths, with the specimen elongation when necking occurs increasing as the parameter c increases, and the necking strain decreasing as the parameter c decreases.

A simple and computationally efficient stress integration scheme based on numerical approximation of the yield function gradients: Application to advanced yield criteri

In this paper, we have modi?ed the stress integration scheme proposed by Choi and Yoon (2019), which is based on the numerical approximation of the yield function gradients, to implement in the ?nite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p (Barlat et al., 2005), CPB06ex2 (Plunkett et al., 2008) and Yld2011-27p (Aretz and Barlat, 2013) criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon (2019), and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the ?finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations.

Plane strain tension fracture at high strain rate

Under plane stress conditions, most micromechanical and phenomenological models predict a minimum in ductility for plane strain tension stress state. Therefore, the stress state of plane strain tension plays a crucial role in many forming and crash applications and the reliable measurement of the strain to fracture for plane strain tension is particularly crucial when calibrating modern fracture initiation models. Recently, a new experimental technique has been proposed for measuring the strain to fracture for sheet metal after proportional loading under plane strain conditions. The basic configuration of the new setup includes a dihedral punch which applies out-of-plane loading onto a Nakazima-type of discshaped specimen with two symmetric holes and an outer diameter of 60 mm. In the present work, the applicability of the test is extended to high strain rates. High strain rates of about 100/s to 200/s are obtained using a drop weight tower device with an original sensor for load measurements. Quasi static tests are also performed for comparison, keeping the same specimen geometry, image recording parameters and set-up. The effective strains at fracture are compared from quasi-static to high strain rate loading for three different materials, i.e one aluminium alloy and two steels.