A. Barata da Rocha

Prediction of the forming limit diagrams of anisotropic sheets in linear and non-linear loading

Abstract The formability of sheet metals is often evaluated from strain analysis using the concept of forming limit diagrams (FLDs). Numerous experimental results show that the formability of the material strongly depends on the loading history and on the plastic anisotropy of the rolled sheet. The limiting strains at the onset of localized necking can be predicted from a plastic instability analysis introduced by Marciniak and coworkers. However, the hypothesis of proportional loading is no longer valid for complex industrial stampings. Multistage forming operations often involve non-linear strain paths, and abrupt changes in the strain ratio can be observed. In the present work the occurrence of plastic instabilities in the general case of a rate-sensitive anisotropic material with orthotropic symmetry under non-proportional loading is analysed. Theoretical FLDs are determined for proportional loading, for a sequence of two proportional loadings, for a sequence of two proportional loadings and for non-proportional loading (curved strain paths). The simulations are carried out for a wide range of loading conditions, from uniaxial tension in the rolling direction to uniaxial tension in the transverse direction through biaxial stretching. The influence of the anisotropic behaviour of the sheet is studied using Hills theory of plastic anisotropy for both linear and non-linear strain paths in terms of the anisotropic coefficient measured during uniaxial tensile stretching in three different directions referred to the rolling direction (r o , r 45 and r 90 ). A good correlation is obtained between the theoretically and experimentally determined FLDs, and it is shown that important increases in formability may be achieved through careful specification of strain paths, blank-holder pressure and anisotropic blank orientation.

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.

Influence of damage on the plastic instability of sheet metals under complex strain paths

During the sheet metal forming operation, internal damage occurs as a result of nucleation growth and coalescence of cavities around particles. This phenomenon limits the strains which can be achieved before the appearence of localized necking. In this paper, damage is represented by initially equi-axed cavities and a void growth model is extended and linearized for complex strain paths. For a given void distribution, a statistical study pointed out the existence of weak sections in the material leading to localized plastic flow. The influence of the physical parameters of voids on the forming limit diagrams is shown.

On the Determination of Flow Stress Using Bulge Test and Mechanical Measurement

The standard uniaxial tensile test is a widely accepted method to obtain relevant properties of sheet metal materials. These fundamental parameters can be used in numerical modeling of sheet forming operations to predict and assess formability and failure analysis. However the range of strain obtained from tensile test is limited and therefore if one will need further information on material behavior, extrapolation of tensile data is performed. The bulge test is an alternative to obtain ranges of deformation higher than tensile test, thus being possible to obtain non-extrapolated data for material behavior. Several methods may be used to obtain stress-strain data from bulge test, but a common concept is behind them, which needs the measurement of bulge pressure, curvature of bulge specimen, its thickness at the pole and the application of membrane theory. Concerning such measurements, optical methods are being used recently but classical mechanical methods are still an alternative with its own strengths. This paper presents the use and development of a mechanical measuring system to be incorporated in a hydraulic bulge test for flow curve determination, which permits real-time data acquisition under controlled strain rates up to high levels of plastic deformation. Numerical simulations of bulge test using FEM are performed and a sensitivity analysis is done for some influencing variables used in measurements, thus giving some directions in the design and use of the experimental mechanical system. Also, first experimental results are presented, showing an efficient testing procedure method for real time data acquisition with a stable evaluation of the flow curve.

The respective influences of grain size and texture on the formability of a 1050 aluminium alloy

Abstract In order to clarify the relative influences of texture and grain size on the plastic response of a 1050 Al alloy, some tensile tests have been performed after various annealing treatments (designed to obtain different grain sizes) and initial and final textures have been measured. A micro–macro model has then been used in order to suppress the effect of texture from the macroscopic stress–strain curves. As for the description of textures, it has been shown that most of the obtained textures after annealing can be described as a mixture of rolling and recrystallisation textures (containing mainly the so-called Cube, Brass and Goss orientations) and that there is no clear correlation between texture intensity and grain size; after deformation, the Brass component is reinforced at the expense of the Goss orientation, whereas the evolution of the Cube component depends on the initial scatter around the various components. Concerning the tensile curves, it is observed first that the Hall–Petch relationship is not always verified (the smaller the grain size, the higher the yield stress) when the conventional stress/strain curves are examined. When the effect of texture is suppressed from these curves and ‘microstructural’ stress/strain curves are plotted, the Hall–Petch relationship becomes verified and the curve crossing phenomenon, sometimes observed, disappears. It can thus be concluded that the grain size is the only microstructural feature affecting the yield stress and that the hardening evolution is more or less independent of the texture evolution.

Study of Tool Trajectory in Incremental Forming

Single point incremental forming (SPIF) is an innovative flexible sheet metal forming process which can be used to produce complex shapes from various materials. Due to its flexibility, it attracts a more and more attention in the recent decades. Several studies show that besides the major operating parameters, namely feed rate, tool radius, and forming speed etc., tool path is also an important processing parameter to affect the final forming component. In view of that, the present paper studies the influence of tool paths on the work piece quality by the finite element method coupled with the Continuum Damage Mechanics (CDM) model. The formability of incremental forming in different tool paths is also analyzed.

Towards standard benchmarks and reference data for validation and improvement of numerical simulation in sheet metal forming

Abstract The last decade has witnessed many advances and a lot of improvement in FE codes for simulation of sheet metal forming processes. Such advances could be followed mainly by benchmarks proposed in Numisheet conferences. It was possible to notice that the scatter of results among numerical codes has decreased so significantly that recently scattering of experimental results among different corporations was evident. However in order to pursue further developments and validate numerical results it is fundamental to have reliable reference experimental data. This is one of the objectives of a current IMS project called 3DS-Digital Die Design System. In this paper such objectives are presented as well as some of the proposed benchmarks. It is intended to show part of the developed work concerning tool design and manufacturing methodology. Also an experimental case study about the use of piercing holes in parts and the use of counter-punch is presented. Finally some simulation results are also shown concerning one of the proposed benchmarks.

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.