In order to accurately model the plastic deformation of Aluminum sheet at elevated temperatures, a model is required that incorporate the temperature and strain rate dependency of the material. In this article, two physically based models are compared: Bergstr¨om and Alflow model. Although both models can be fit quite well to monotonic tensile tests of 5754-O alloy, large differences appear if strain rate jumps are applied. The Alflow model also represents the negative strain rate sensitivity behavior of Al-Mg alloys at temperatures below 125±C

Boogaard, A.H. van den

Huetink, J.

Kurukuri, S.

English

In order to accurately model the plastic deformation of Aluminum sheet at elevated temperatures, a model is required that incorporate the temperature and strain rate dependency of the material. In this article, two physically based models are compared: Bergström and Alflow model. Although both models can be fit quite well to monotonic tensile tests of 5754-O alloy, large differences appear if strain rate jumps are applied. The Alflow model also represents the negative strain rate sensitivity behavior of Al-Mg alloys at temperatures below 125±C

van den Boogaard, A.H.

Huetink, H.

University of Twente Research Information

IX Internatinal Conference on Computational PlasticityCOMPLAS IXE. Oñate and D.R.J. Owen (Eds)c©CIMNE, Barcelona, 2007FINITE ELEMENT SIMULATION OF ALUMINUM SHEETWARM FORMING USING ALFLOW HARDENING MODELS. Kurukuri∗, A. H. van den Boogaard† and J. Huétink†∗Netherlands Institute for Metals Research (NIMR)P. O. Box 5008, 2600 GA Delft, The Netherlandse-mail: s.kurukuri@nimr.nl, web page: http://www.nimr.nl†University of Twente, Faculty of Engineering TechnologyP. O. Box 217, 7500 AE Enschede, The NetherlandsWeb page: http://www.tm.ctw.utwente.nl/onderzoek/DiekA/index.htmlKey words: Aluminum, warm forming, material model, Alflow hardening.Summary. In order to accurately model the plastic deformation of Aluminum sheet at elevatedtemperatures, a model is required that incorporate the temperature and strain rate dependencyof the material. In this article, two physically based models are compared: Bergström and Alflowmodel. Although both models can be fit quite well to monotonic tensile tests of 5754-O alloy,large differences appear if strain rate jumps are applied. The Alflow model also represents thenegative strain rate sensitivity behavior of Al-Mg alloys at temperatures below 125◦C.1 INTRODUCTIONMass reduction has long been identified as a key priority for improving automotive fuel econ-omy. However, replacing steel in the structure and body with lighter materials such as aluminumcan be costly and is not simple or straightforward, because it has much lower formability at roomtemperature than typical sheet steel. The formability of automotive aluminum sheet alloys (suchas 5754-O) can be greatly improved by warm forming. Since elevated temperature produces de-creased flow stress and increased ductility in the sheet, which can allow deeper drawing andmore stretching to form panels without design modifications. An extra benefit of warm form-ing is that the stretcher lines due to PLC effect occur when 5xxx alloys are deformed at roomtemperature do not appear at elevated temperatures. However, experience with temperaturecontrolled forming process is lacking and numerical models would be beneficial in optimizing theprocess simulations. A large number of constitutive models of the plastic behavior of aluminumsheet are available for finite element modeling. However, their applicability is usually limitedin terms of varying strain, strain rate, temperature and changing microstructure, particularlyin warm forming we cannot ignore the strain rate and temperature influence. Material modelsbased on consideration of the underlying physical processes are expected to have a larger rangeof usability in this respect. This report focuses on the implementation of one such physicallybased hardening model developed by Nes, Marthinsen and co-workers. It is referred to as Alflow1and it uses the dislocation density as a way to model plastic deformation. The Alflow model is1S. Kurukuri, A. H. van den Boogaard and J. Huétinkbased upon a model for sub-structure evolution and consequent work hardening during plasticdeformation proposed by Nes2 and dedicated to aluminum alloys. The model can directly takeinto account the chemical composition and the fabrication process influence on the stress-straincurve by changes of solute level, particle fraction and grain size.2 CONSTITUTIVE MODELIn the present study, the anisotropic yield function of Vegter is used. The Vegter yieldcriterion3 is defined in principle stress space for plane stress situations meant for planar anisotropicmaterial, i.e., the yield function depends on the angle between the principal axes and the rollingdirection. For a particular angle θ, four experiments are necessary to determine the modelparameters: a simple shear test, a uniaxial tensile test, a plane strain tensile test and an equi-biaxial tensile test. Between the measured stress points a Bezier curve is used to describe theyield locus. Extensive information is given in3.3 MICROSTRUCTURE EVOLUTION AND DISLOCATION MECHANICSBASED WORK HARDENING MODELThe model approach relies on multi parameter description for the microstructure evolution.At small strains the stored dislocations are arranged in a cell structure characterized by the cellsize, δ and the dislocation density within the cells, ρi. At large strains the dynamic recoveryof dislocation becomes important and the cell walls collapse into sub-boundaries of well definedmisorientations, ϕ. Extensive presentations of the model are given in1,2. The microstructureevolution is covered by the following three differential equations:dρidγ=dρi+dγ+dρi−dγ,dδdγ=dδ−dγ+dδ+dγanddϕdγ=dϕ+dγ+dϕ−dγ. (1)Here, γ is the resolved shear strain, which is defined as the algebraic sum of resolved shearsof each slip system in the Taylor theory and interpreted as an average of the grains in thiscontext.dρi+dγ,dδ−dγanddϕ+dγare storage terms, describing different ways of athermal storage ofdislocations, whereasdρi−dγdescribes the dynamic recovery of cell interior dislocations by dipoleannihilation anddδ+dγis subgrain growth at elevated temperatures. Explicit expressions for theseterms can be found in1 . The Alflow model expresses the critical resolved shear stress of the slipsystems within each grain as a function of its microstructure:τ = τt + τp + τcl + α1Gb[Γ1(qcδ√ρi)√ρi + Γ2(qcδ√ρi)qcδ]+ α̂2Gb[Γ2 (0)1δ+1D](2)Here τt is the thermal component of stress due to rate and temperature dependent interactionswith short range obstacles, Orowan stress, τp due to non-deformable particles, τcl clusteringstressrespectively. Details may be found in1,2. In applications of the model the stress tensorat a macroscopic continuum scale is required representing contributions from many grains ofvarious crystallographic orientation and microstructure. The equivalent stress and strain can be2S. Kurukuri, A. H. van den Boogaard and J. Huétinkcalculated as: σeq = Mτ and εeq = γ/M , here M is the Taylor factor and τ (γ) follows from themicrostructure evolution predicted by the Alflow model.4 RESULTSFigure 1 shows the simulated engineering stress-strain curves plotted for the Alflow model,together with experimental data for various temperatures and strain rates4. It can be seen thatthe model is more or less capable of describing the experiments. A large difference between theAlflow and Bergström models is observed if a jump in the strain rate is applied. In Figure 2,stress-strain curves are plotted for deformation at 250◦C. If a strain rate change from 0.002 to0.02 or from 0.02 to 0.002 is applied, with the Bergström model the constant strain curve isonly slowly approached after continuous straining, whereas the Alflow model better representthe experiments4. In Figure 3, even though the difference is small, it is clearly observed thatthe Alflow model can represent the negative strain rate sensitivity of Al-Mg alloys at low tem-peratures that is attributed to dynamic strain ageing caused by solutes, whereas hardly can findthis behavior with the Bergström model. 80 120 160 200 240 0  0.05  0.1  0.15  0.2engineering stress (MPa)engineering strain (−)100 °C175 °C250 °Cε̇ = 0.002 s−1experimentAlflow 80 120 160 200 240 0  0.05  0.1  0.15  0.2engineering stress (MPa)engineering strain (−)100 °C175 °C250 °Cε̇ = 0.02 s−1experimentAlflowFigure 1: Engineering stress-strain curves experiments and model 100 125 150 175 200 0  0.05  0.1  0.15  0.2true stress (MPa)true strain (−)ε̇ = 0.002 s−1ε̇ = 0.02 s−1T = 250°CAlflow model 100 125 150 175 200 0  0.05  0.1  0.15  0.2true stress (MPa)true strain (−)ε̇ = 0.002 s−1ε̇ = 0.02 s−1T = 250°CBergström modelFigure 2: True stress-strain curves with and without strain rate jumps at 125◦C3S. Kurukuri, A. H. van den Boogaard and J. Huétink 120 160 200 240 0  0.05  0.1  0.15  0.2engineering stress (MPa)engineering strain (−)100°C175°CAlflow modelε̇ = 0.02 s−1ε̇ = 0.002 s−1 120 160 200 240 0  0.05  0.1  0.15  0.2engineering stress (MPa)engineering strain (−)100°C175°CBergström modelε̇ = 0.02 s−1ε̇ = 0.002 s−1Figure 3: Strain rate influence on stress-strain curves5 CONCLUSIONSIn order to accurately model the plastic deformation of Aluminum sheet at elevated tem-peratures, a model is required that incorporate the temperature and strain rate dependencyof the material. In this article, two physically based models are compared: Bergström andAlflow model. Although both models can be fit quite well to monotonic tensile tests of 5754-Oalloy, large differences appear if strain rate jumps are applied. Alflow model also representsthe negative strain sensitivity behavior of Al-Mg alloys at temperatures below 125◦C. Deepdrawing simulations need to be carried out yet for further validation of the Alflow model withexperiments.6 ACKNOWLEDGEMENTThe work, presented in this article, was performed as a part of project MC1. 02106 in theframework of the Strategic Research program of the Netherlands Institute for Metals Researchin the Netherlands (www.nimr.nl).REFERENCES[1] E. Nes and K. Marthinsen. Modelling the evolution in microstructure and properties duringplastic deformation of FCC metals and alloys – an approach towards a unified model. Mater.Sci. Engng. A, 322, 176–193, (2002).[2] E. Nes. Modelling of work hardening and stress saturationin FCC metals. Prog. Mater. Sci.Forum, 41, 129–193, (1998).[3] H. Vegter and A. H. van den Boogaard. A yield function for anisotropic sheet material byinterpolation of biaxial stress states. Int. J. Plasticity, 22, 557–580, (2006).[4] A. H. van den Boogaard and J. Huétink. Simulation of aluminium sheet forming at elevatedtemperatures. Comput. Methods Appl. Mech. Engrg., 195, 6691–6709 (2006).4

Finite element simulation of aluminum sheet warm forming using alflow hardening model

van den Boogaard, Antonius H.

Huetink, Han

NARCIS 

A yield function for anisotropic sheet material by interpolation of biaxial stress states.

Modelling of work hardening and stress saturationin FCC metals.

Modelling the evolution in microstructure and properties during plastic deformation of FCC metals and alloys – an approach towards a uniﬁed model.

Simulation of aluminium sheet forming at elevated temperatures.

http://purl.utwente.nl/publications/59636

Finite element simulation of aluminum sheet warm forming using alflow hardening model

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