M.C. Butuc

A theoretical study on forming limit diagrams prediction

Abstract The paper develops a theoretical study on forming limit diagrams using a new general code for forming limit strains prediction. Treating the Marciniak and Kuckzinsky (M–K) theory by a new approach, the code consists of the main part and several subroutines, which allow the implementation of any hardening law, yield function or constitutive equation, changing the respective subroutine. The strong influence of the constitutive law incorporated in the analysis on the predicted limit strains is shown by use of different yield functions like von Mises isotropic yield function, quadratic and non-quadratic criterion of Hill (Hill, 1948 and Hill, 1979) and Barlat Yld96 yield function. The difference in the stress–strain curve based on two hardening models (namely Swift hardening law and Voce equation), up to the maximum equivalent strain is presented and the effect on the predicted limit strains is also studied. In this work an aluminum alloy sheet metal AA6016-T4 is studied. Yield surface shapes, yield stress and R-value directionalities simulated by the respective yield functions were investigated and compared with experimental data. A successful correlation is observed between the experimental FLDs and the computed limit strains when the shape of the yield locus is described by Yld96 criterion and the hardening law represented by Voce equation.

A more general model for forming limit diagrams prediction

Abstract The present paper is devoted to the development of a more general code for the prediction of forming limit diagrams (FLDs). For this purpose, the Marciniak–Kuczynski (M–K) theory is treated with a new approach. The code is composed of a main part and several subroutines, which allow the implementation of different hardening laws, yield functions or constitutive equations. The Newton–Raphson numerical method is used to solve the theoretical treatments of localized necking taking into account linear and complex strain paths.

The performance of Yld96 and BBC2000 yield functions in forming limit prediction

Abstract The objective of the work presented here is to assess the performance of two non-quadratic yield functions for orthotropic sheet metals under plane stress conditions, namely Yld96 and BBC2000, on forming limit prediction. The similitude and the differences between both of them are discussed. The Newton–Raphson numerical method respectively the minimisation of an error-function has been used for the numerical identification of the Yld96 and BBC2000 coefficients. The necking phenomenon was modelled by using the Marciniack–Kuczinsky (M–K) theory. In the present study an aluminium alloy sheet metal AA5XXX is considered. Yield surface shapes, yield stress and r -value directionalities of Yld96 and BBC2000 were investigated and compared with the experimental data. A successful correlation is observed between the experimental FLDs and the computed limit strains when, the shape of yield locus is described by Yld96 criterion respectively BBC2000 criterion and the hardening law represented by Voce equation.

Experiments and Modeling of Low Carbon Steel Sheet Subjected to Double Strain Path Changes

Low carbon steel was deformed under double strain path changes consisting in three successive tension tests carried out in different directions with respect to the material symmetry axes. The influences of the strain amounts and severity of strain path change in the reloading yield stress and subsequent strain hardening were investigated in detail. The trends captured using the homogeneous anisotropic hardening approach, which is based on a homogeneous yield function, are in good agreement with the experimental results.

A Comparative Study Between Strain And Stress Based Forming Limit Analysis By Applying Several Phenomenological Yield Criteria

The present work aims at analyzing a comparative study between the strain‐based forming limit criterion (FLD) and the stress‐based forming limit criterion (FLSD), under linear and complex strain paths. The selected material is an AA5182‐0 aluminium alloy. Some relevant remarks about stress‐based forming limit criterion concept are presented.

A Theoretical Study of the Effect of the Double Strain Path Change on the Forming Limits of Metal Sheet

The present paper aims at a theoretical study of the forming limits of a sheet metal subjected to double strain path changes by using as reference material the AA6016-T4 aluminum alloy sheet. The simulation of plastic instability is carried out through the Marciniak-Kuczynski analysis. The initial shape of the yield locus is given by the Yld2000-2d plane stress yield function. The strain hardening of the material is described by the Voce type saturation law. Linear and several complex strain paths involving single and double strain path changes are taken into account. The validity of the model is assessed by comparing the predicted and experimental forming limits under linear and selected one strain path change. A good accuracy of the developed software on predicting the forming limits is found. A sensitive analysis of the influence of the type and value of the double prestain in the occurrence of the plastic flow localization is performed. A remarkable effect of the double strain path change on the sheet metal forming limits is observed.

Plastic Instability in Complex Strain Paths Predicted by Advanced Constitutive Equations

The present paper aims at predicting plastic instabilities under complex loading histories using an advanced sheet metal forming limit model. The onset of localized necking is computed using the Marciniak-Kuczinsky (MK) analysis [1] with a physically-based hardening model and the phenomenological anisotropic yield criterion Yld2000-2d [2]. The hardening model accounts for anisotropic work-hardening induced by the microstructural evolution at large strains, which was proposed by Teodosiu and Hu [3]. Simulations are carried out for linear and complex strain paths. Experimentally, two deep-drawing quality sheet metals are selected: a bake-hardening steel (BH) and a DC06 steel sheet. The validity of the model is assessed by comparing the predicted and experimental forming limits. The remarkable accuracy of the developed software to predict the forming limits under linear and non-linear strain path is obviously due to the performance of the advanced constitutive equations to describe with great detail the material behavior. The effect of strain-induced anisotropy on formability evolution under strain path changes, as predicted by the microstructural hardening model, is particularly well captured by the model.

Mechanical behaviour of TWIP steel under shear loading

Twinning induced plasticity steels (TWIP) are very good candidate for automotive industry applications because they potentially offer large energy absorption before failure due to their exceptional strain hardening capability and high strength. However, their behaviour is drastically influenced by the loading conditions. In this work, the mechanical behaviour of a TWIP steel sheet sample was investigated at room temperature under monotonic and reverse simple shear loading. It was shown that all the expected features of load reversal such as Bauschinger effect, transient strain hardening with high rate and permanent softening, depend on the prestrain level. This is in agreement with the fact that these effects, which occur during reloading, are related to the rearrangement of the dislocation structure induced during the predeformation. The homogeneous anisotropic hardening (HAH) approach proposed by Barlat et al. (2011) [1] was successfully employed to predict the experimental results.

Plastic instability in complex strain paths and finite element simulation for localised necking prediction in sheet metal forming technology

Formability of sheet metals is a measure of its ability to deform plastically, being mainly limited by the occurrence of flow localisation or instability. Plastic instability numerical models have been used to predict such behaviour and recent and more accurate constitutive plasticity models have been applied in these calculations. Combination of Forming Limit Diagram (FLD) analysis with Finite Element (FE) simulations often fail to give the right answer, if complex strain paths are not included. This paper presents a Plastic Instability Model developed to predict localised necking under complex strain paths, which may be used as FLD prediction code or as a FE post-processing tool for necking prediction. It is shown that considering the non-Linear Strain Paths in the analysis, more accurate failure predictions are achieved. An experimental component with necking occurrence is studied. The numerical simulation of this component by FEM is performed and necking is predicted by developed code.