Convex Analysis: (pms-28)

The effect of non-linear recovery on springback prediction

Large-strain monotonic and cyclic loading tests of AZ31B magnesium alloy sheets were performed with a newly developed testing system, at different temperatures, ranging from room temperature to 250 °C. Behaviors showing significant twinning during initial in-plane compression and untwinning in subsequent tension at and slightly above room temperature were recorded. Strong yielding asymmetry and nonlinear hardening behavior were also revealed. Considerable Bauschinger effects, transient behavior, and variable permanent softening responses were observed near room temperature, but these were reduced and almost disappeared as the temperature increased. Different stress–strain responses were inherent to the activation of twinning at lower temperatures and non-basal slip systems at elevated temperatures. A critical temperature was identified to account for the transition between the twinning-dominant and slip-dominant deformation mechanisms. Accordingly, below the transition point, stress–strain curves of cyclic loading tests exhibited concave-up shapes for compression or compression following tension, and an unusual S-shape for tension following compression. This unusual shape disappeared when the temperature was above the transition point. Shrinkage of the elastic range and variation in Young’s modulus due to plastic strain deformation during stress reversals were also observed. The texture-induced anisotropy of both the elastic and plastic behaviors was characterized experimentally.

https://www.mdpi.com/1996-1944/7/2/1271/pdf

Mechanical Behavior of AZ31B Mg Alloy Sheets under Monotonic and Cyclic Loadings at Room and Moderately Elevated Temperatures

The prediction of earing during cup-drawing of the anisotropic aluminum alloy Al-6022-T4 is studied through a combination of experiments and analysis. At first, the anisotropy of the material is established experimentally, using uniaxial and plane-strain tension, as well as disk compression experiments. The material is seen to possess mild anisotropy, which however evolves with deformation. Two plastic potentials, Yld89 and Yld2000-2D are then calibrated to that data. The latter potential is flexible enough to represent the experimental plastic work contours almost exactly. Subsequently, the cup-drawing experiments are detailed, including descriptions of the equipment and tooling, measurements during forming as well as measurements of thickness and earing in the drawn-cups. Three analytical models for predicting the maximum drawing force are compared to the experiments. The cups exhibit maximum thinning around the punch-radius, as well as four ears. The ears are oriented along the RD and TD directions, with the TD ears being higher than the RD ones. A simple analytical model is seen to closely capture these results. The experiments are then simulated with shell finite elements in DYNAFORM, which uses the explicit solver of LS-DYNA. The simulations permitted the inverse determination of the friction between the blank and the tooling. The thickness and earing profile predictions from the numerical model are in good agreement with the experiments.

Earing in cup-drawing of anisotropic Al-6022-T4 sheets

Development and application of the material constitutive model in springback prediction of cold-bending

The paper deals with constitutive modeling of highly anisotropic sheet metals and presents FEM based earing predictions in a round cup drawing simulation of highly anisotropic aluminum alloys where more than four ears occur For that purpose the BBC2008 yield criterion, which is a plane-stress yield criterion formulated in the form of a finite series, is used Thus defined criterion can be expanded to retain more or less terms, depending on the amount of given experimental data To be used in sheet metal forming simulations the constitutive model, derived in accordance with the associated flow theory of plasticity, has been implemented in a general purpose finite element code ABAQUS/Explicit via VUMAT subroutine, considering alternatively different number of parameters in the BBC2008 yield criterion, where possible number of parameters are any multiple of number 8 For the integration of the constitutive model the explicit NICE (Next Increment Corrects Error) integration scheme has been used The CPU time consumption for an explicit deep drawing simulation, which is based on the developed constitutive model, has been proven to be, due to effectiveness of the used integration scheme, fully comparable to the performance experienced when the simulation is performed with ABAQUS built-in constitutive models and implicit integration schemes Two aluminum alloys, namely AA5042-H2 and AA2090-T3, have been considered for a validation of the constitutive model The respective BBC2008 model parameters have been identified for both alloys with a developed numerical procedure, based on a minimization of the specified cost function For both materials, the simulation predictions based on the BBC2008 model prove to be in very good agreement with the experimental results Further, in order to show the flexibility of the BBC2008 model in modeling of highly anisotropic sheet metal response, we have introduced a highly anisotropic fictitious material which yields, according to the theory, twelve ears in cup drawing As it is shown in the paper the BBC2008 model is able to predict twelve ears in cup drawing simulation with the formulation containing 16 parameters for anisotropy description only The flexibility and accuracy of the constitutive model together with the robust identification and integration procedure guarantee the applicability of the BBC2008 yield criterion in industrial applications

Capability of the BBC2008 yield criterion in predicting the earing profile in cup deep drawing simulations

Consistent tangent operator for cutting-plane algorithm of elasto-plasticity

The paper deals with constitutive modelling of highly anisotropic sheet metals. It presents FEM based earing predictions in cup drawing simulation of highly anisotropic aluminium alloys where more than four ears occur. For that purpose the BBC2008 yield criterion, which is a plane‐stress yield criterion formulated in the form of a finite series, is used. Thus defined criterion can be expanded to retain more or less terms, depending on the amount of given experimental data. In order to use the model in sheet metal forming simulations we have implemented it in a general purpose finite element code ABAQUS/Explicit via VUMAT subroutine, considering alternatively eight or sixteen parameters (8p and 16p version). For the integration of the constitutive model the explicit NICE (Next Increment Corrects Error) integration scheme has been used. Due to the scheme effectiveness the CPU time consumption for a simulation is comparable to the time consumption of built‐in constitutive models. Two aluminium alloys, namely AA5042‐H2 and AA2090‐T3, have been used for a validation of the model. For both alloys the parameters of the BBC2008 model have been identified with a developed numerical procedure, based on a minimization of the developed cost function. For both materials, the predictions of the BBC2008 model prove to be in very good agreement with the experimental results. The flexibility and the accuracy of the model together with the identification and integration procedure guarantee the applicability of the BBC2008 yield criterion in industrial applications.

/pdf/earing-prediction-in-cup-drawing-using-the-bbc2008-yield-2j1x7k3won.pdf

Earing Prediction in Cup Drawing using the BBC2008 Yield Criterion

Shear test-based identification of hardening behaviour of stainless steel sheet after onset of necking

Springback, the phenomenon that is governed by strain recovery after removal of forming loads, is of great concern in sheet metal forming. There is no doubt that physically reliable numerical modelling of the forming process and predictions of springback obtained by respective computer simulations are crucial to control this problem. Unfortunately, by currently available approaches springback still cannot be adequately predicted in general. This paper is an attempt of building a corresponding constitutive model, which will simultaneously consider sheet anisotropy, damage evolution and strain path dependent stiffness degradation during metal forming. First, for the identification of the parameters in the built constitutive model a particular experimental procedure is deliberately developed. To solve the arisen inverse problem an optimization procedure is employed. The proposed approach to constitutive modelling is validated in the end by a simulation of the springback in the formed HSS steel. The simulation results prove to be in good agreement with the experimental ones. From the performed comparisons it is clearly indicated, that only simultaneous modelling of material properties can be the true key to obtain accurate prediction of springback in sheet metal forming.

Bojan Starman

Papers

Capability of the BBC2008 yield criterion in predicting the earing profile in cup deep drawing simulations

Consistent tangent operator for cutting-plane algorithm of elasto-plasticity

Earing Prediction in Cup Drawing using the BBC2008 Yield Criterion

Shear test-based identification of hardening behaviour of stainless steel sheet after onset of necking

Modelling of springback in sheet metal forming