DD3MAT - a code for yield criteria anisotropy parameters identification.

Transcription

1 Journal of Physics: onference Series PAPER OPEN AESS DD3MA - a code for yield criteria anisotropy parameters identification. o cite this article: P D Barros et al 216 J. Phys.: onf. Ser View the article online for updates and enhancements. his content was downloaded from IP address on 2/7/218 at 8:34

2 Journal of Physics: onference Series 734 (216) 3253 IOP Pulishing DD3MA a code for yield criteria anisotropy parameters identification. P D Barros a, P D arvalho a, J L Alves, M Oliveira a and L F Menezes a a EMU, Mechanical Engineering Department, University of oimra, Polo II, Rua Luís Reis Santos, Pinhal de Marrocos, oimra, , Portugal MEMS, Microelectromechanical Systems Research Unit, University of Minho, ampus de Azurém, Guimarães, Portugal pedro.arros@dem.uc.pt Astract. his work presents the main strategies and algorithms adopted in the DD3MA inhouse code, specifically developed for identifying the anisotropy parameters. he algorithm adopted is ased on the minimization of an error function, using a downhill simplex method. he set of experimental values can consider yield stresses and r -values otained from in-plane tension, for different angles with the rolling direction (RD), yield stress and r -value otained for iaxial stress state, and yield stresses from shear tests performed also for different angles to RD. All these values can e defined for a specific value of plastic work. Moreover, it can also include the yield stresses otained from in-plane compression tests. he anisotropy parameters are identified for an AA2-3 aluminium alloy, highlighting the importance of the user intervention to improve the numerical fit. 1. Introduction Sheet metal forming processes are nowadays designed and optimized virtually using finite element analysis (FEA), which is consensually accepted as the main reason for the huge decrease in time-tomarket life cycle and for notale savings in terms of money, time and effort in the design, production and process set-up of new formed parts. However, the success of finite elements solvers on the design and optimization of sheet metal formed parts is strongly dependent on their aility to accurately descrie the material s mechanical ehaviour. Sheet metals generally exhiit anisotropic mechanical ehaviour due to the rolling process, characterized y the symmetry of the mechanical properties with respect to three orthogonal planes, i.e. orthotropic ehaviour. hus, different mechanical ehaviours are expected for different loading directions and conditions. Phenomenological models are the most widely used approach to descrie the elastoplastic response of metallic sheets, since they are computationally efficient when compared with microscopic models. he material s orthotropic ehaviour is modelled y the yield surface, used to descrie the yielding and the plastic flow of the material, ased on the hardening law selected. his dual role of the yield surface requires a particular care and accuracy in its modelling and numerical implementation. he material anisotropy parameters identification must e performed in a way that a given yield criterion should reproduce the materials mechanical ehaviour as close as possile. Moreover, since sheet metal forming processes are carried out with inhomogeneous deformation and under multiaxial strain paths it is important to use as much information as possile. In this work DD3MA in-house code is used to identify the anisotropy parameters for an AA2-3 aluminium alloy [1], considering three yield criteria [2], B1 [3] and PB6 [4]. he predicted in-plane distriution of the yield stresses and r -values evolution, as well as the yield surfaces, ontent from this work may e used under the terms of the reative ommons Attriution 3. licence. Any further distriution of this work must maintain attriution to the author(s) and the title of the work, journal citation and DOI. Pulished under licence y IOP Pulishing Ltd 1

3 Journal of Physics: onference Series 734 (216) 3253 IOP Pulishing are discussed to show that a more or less accurate fit of the experimental data is achieved, depending on the selected yield criterion and on the user intervention, through the selection of the weighting factor for each test result. 2. DD3MA yield criteria parameters identification code. he anisotropy parameters should e determined such that the yield criterion reproduces the material s mechanical ehavior as close as possile. he most used experimental results for the identification of anisotropy parameters are the yield stresses and r -values otained from in-plane tension, for different angles ( θ ) with the RD. In order to improve the description of the yield surface, it is also recommended to experimentally determine the iaxial yield stress and the iaxial anisotropy coefficient [5 7]. For the PB6 yield criterion, uniaxial compression experimental results are also necessary for descriing the strength differential effects. However, when performing compression tests for thin metallic sheets it is necessary to avoid uckling effects. his requires the use of small specimens, leading to supplementary difficulties in the acquisition and analysis of experimental results, particularly for high strain values [8]. he anisotropy parameters for the three selected yield criteria were otained with the DD3MA inhouse code. he procedure adopted is ased in an optimization prolem regarding the minimization of an error function, evaluating the difference etween the estimated values and the experimental ones, as follow ( ) ( ( ) ) ( ) F ( A ) = w ( ) 1 σ σθ A σθ + w θ θ 1 wr ( r r 1) θ σ σ A σ + θ θ θ A θ θ = wσ ( σ ( ) 1) ( ( ) 1) A σ + wr r A r where A represents the set of parameters associated with the selected yield criterion. σ θ, σ θ and r θ are the experimental yield stresses in tension, compression and r -values determined in uniaxial tension, respectively, otained from the uniaxial tests for a specific orientation ( θ ) with respect to RD. σ is the experimental yield stress otained from the equiiaxial tensile test, r is the experimental r -value otained from the disc compression test, and σθ ( A ), σθ ( A ) r θ ( A ), σ ( A ) and r ( A ) are the correspondent values predicted from the adopted yield criterion. Such procedure can e considered a generalization of the one proposed y Banaic et al., 5 [9]. he weighting factors, w σ, w θ σ, wr θ θ, w σ and w r are used to alance the influence of the experimental data. Nevertheless, the selection of the weighting factors is normally a manual procedure, strongly dependent on users expertise and knowledge. he identification procedure, defined in (1) also implies the pre-selection of an initial yield stress or the hardening law parameters, if a specific value of plastic work is defined to select the experimental values for the yield stresses. 3. Results and discussion he anisotropy parameters for the three previously mentioned yield criteria were identified for an AA2-3 aluminium alloy, for which the experimental values of σ θ, σ θ, r θ (at each 15º with RD), σ and r are availale [1]. Figure 1 shows the evolution of the yield stress and r -values with the angle from RD, for the three yield criteria, otained considering all weighting factors equal to 1. (laelled Set 1 ). As expected, shows a less accurate fit when compared with the other yield criteria, mainly for the yield stresses. PB6 presents a etter fit for the yield stresses, when compared with the, with the added enefit of also descriing the materials ehavior for compression stress states. Regarding the B1, oth yield stresses and r -values are gloally well descried. Nevertheless, it is possile to see that all yield criteria fail to capture the r -value at 45º and tend to overestimate the yield stresses for angles closer to the transverse direction (D). herefore, a new set of parameters was identified, through the selection of the weighting factors (shown in ale 1), i.e. with user intervention, laelled Set 2. Figure 2 shows the evolution of the yield stress and r -values with the angle from the RD, for the three yield criteria, considering the user intervention. For the B1, the description is enhanced mainly for yield stresses for angles closer to D and the predicted r -values at 45º and º are closer to the experimental ones. For the, the main improvement occurs for yield stresses closer to the rolling direction and the r -value at 45º. he PB6 also enefited from the user s input in the identification (1) 2

4 Journal of Physics: onference Series 734 (216) 3253 IOP Pulishing procedure since the yield stresses evolution in tension and compression are gloally closer to the experimental values. Figure 3 presents the yield surfaces for the three considered yield criteria in the σ1 σ 2 plane considering, or not, user intervention. hese results, together with ale 2, allows analyzing the material ehavior for stress states other than uniaxial tensile stress. presents lower experimental σ values, for oth sets, slightly more accurate for Set 2. he B1 yield criterion predicts accurate σ and r values for oth stets, ut Set 1 presents a r value lower than the experimental, while it is slightly higher for Set 2. Gloally, PB6 presents the σ and r values least accurate, since the introduction of the compression yield stress in the optimization procedure reduces the relative importance of these values in the ojective function. A summary of the parameters identified for the three yield criteria, considering oth sets, is presented in ale 3, highlighting the parameters interdependence. Yield stress [MPa] PB6 PB6 B1 r-value B1 PB6 PB6- Yield stress [MPa] () Figure 1. Experimental and predicted yield stresses and () r -values (Set 1). r-value PB6 PB6 PB6 PB6- B1 1.5 B () Figure 2. Experimental and predicted yield stresses and () r -values (Set 2). 4 4 σ 2 [MPa] - PB6 B1 σ 2 [MPa] - PB6 B σ 1 [MPa] σ 1 [MPa] () Figure 3. Predicted yield surfaces in the σ1 σ 2 plane Set 1 and () Set 2. 3

5 Journal of Physics: onference Series 734 (216) 3253 IOP Pulishing ale 1. Experimental and predicted yield stress and r -values for the iaxial test. B1 w r = 5 w 5 45 r = w 5 r = w 2 σ = w σ 6 = 1 w σ = 1 w σ = 1 w r = 5 w 2 45 σ = w σ = 2 w σ 15 = 2 w σ = 2 w σ = 2 PB6 w r = 7 w 2 45 σ = w σ = 3 w σ 15 = 4 w σ = 4 ale 2. Experimental and predicted yield stress and r -values for the iaxial test. Set 1 Set 2 B1 PB6 B1 PB6 σ (.6%) (-18.7%) (-19.6%) (-1.2%) (-17.3%) (-2.7%) r (-.74%).57 (-15.7%).78 (+15.8%).66 (-1.5%).76 (+12.7%).89 (+33.3%) B1 PB6 ale 3. Anisotropy parameters identified for the considered yield criteria. Set a 1 a 2 a 3 a c Set c 1 c 2 c 3 c 6 m Set k Note that, for metal sheets, the off plane parameters cannot e experimentally evaluated. hus, parameters a5, a 6 and k ( k = 6, 7,8,9,11), for the B1, c4, c 5 for the and 44, 55 for the PB6 take the corresponding isotropic values, i.e onclusions he results presented show the aility of DD3MA in-house to perform the identification of the anisotropy parameters for different yield criteria. he classical identification procedure adopted allows the user to control the importance of each test through the weighting factors. However, the users input and knowledge is only as good as the flexiility allowed y the yield criterion considered. Acknowledgments he authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and echnology (F) via the projects PD/EME-ME/11842/21 and UID/EMS/285/213.he first author is also grateful to the F for the PhD grant SFRH/BD/98545/213. References [1] J.W. Yoon, F. Barlat, K. hung, F. Pouroghrat, D.Y. Yang, Int. J. Plast. 16 () [2] F. Barlat, D.J. Lege, J.. Brem, Int. J. Plast. 7 (1991) [3] O. azacu, F. Barlat, Math. Mech. Solids 6 (1) [4] O. azacu, B. Plunkett, F. Barlat, Int. J. Plast. 22 (6) [5] D.J. Lege, F. Barlat, J.. Brem, Int. J. Mech. Sci. 31 (1989) [6] K. Pöhlandt, D. Banaic, K. Lange, in:, ESAFORM 2, Krakow, Poland., 2, pp [7] F. Barlat, J.. Brem, J.W. Yoon, K. hung, R.E. Dick, D.J. Lege, F. Pouroghrat, S.H. hoi, E. hu, Int. J. Plast. 19 (3) [8] M. ritschler, A. Butz, D. Helm, G. Falkinger, J. Kiese, Int. J. Mater. Form. 7 (214) [9] D. Banaic, H. Aretz, D.S. omsa, L. Paraianu, Int. J. Plast. 21 (5)