The paper presents implementation of fracture prediction algorithm for a cold metal forming process simulation in the software QForm. Authors programmed the function for calculation of the criterion proposed by Bai and Wierzbicki. Obtained results of the simulation in QForm for a deep drawing process are compared with results of experiments. A good agreement between the simulation and experiment was achieved.Ministry of Education and Science of the Russian FederationDAA

Behrens, Bernd-Arno

Bouguecha, Anas

Gladkov, Yury

Peshekhodov, Ilya

Vucetic, Milan

The paper presents implementation of fracture prediction algorithm for a cold metal forming process simulation in the software QForm. Authors programmed the function for calculation of the criterion proposed by Bai and Wierzbicki. Obtained results of the simulation in QForm for a deep drawing process are compared with results of experiments. A good agreement between the simulation and experiment was achieved

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MATEC Web of Conferences 21, 12009 (2015)DOI: 10.1051/matecconf/20152112009C© Owned by the authors, published by EDP Sciences, 2015Implementation of the Bai & Wierzbicki fracture criterion inQForm and its application for cold metal forming and deepdrawing technologyYury Gladkov1,a , Ilya Peshekhodov2, Milan Vucetic2, Anas Bouguecha2, and Bernd-Arno Behrens21 Department of Metal Forming Technology, Bauman Moscow State Technical University (BMSTU),Russia2 Institute of Forming Technology and Machines (IFUM), Leibniz Universität Hannover, Garbsen,GermanyAbstract. The paper presents implementation of fracture prediction algorithm for a coldmetal forming process simulation in the software QForm. Authors programmed the functionfor calculation of the criterion proposed by Bai and Wierzbicki. Obtained results of thesimulation in QForm for a deep drawing process are compared with results of experiments.A good agreement between the simulation and experiment was achieved.1. IntroductionUse of simulation systems for design of cold metal forming processes is nowadays a key task in the workof an engineer in the field of forming technology. After all, a simulation system gives the possibility tocheck feasibility of a process before its realization. Also it allows comparing some process alternativesand carrying out optimization that ensures high efficiency of the developed technology and lower costof product.In turn, simulation systems should have a possibility to predict various kinds of defects, for example:laps and flow-throw defects, underfilling of dies in bulk metal forming, but also durability of tools andsufficiency of a force capacity of the chosen equipment in bulk and sheet metal forming. A direction toimprove simulation systems is prediction of a fracture due to depletion of the plasticity resource in coldforming (Fig. 1). Prediction of the remaining plasticity resource can help forecast strength and plasticproperties of a forged part [1].In the present paper the emphasis is put on a solution of the first problem: prediction of a fracture dueto depletion of the plasticity resource. Fracture and cracks which appear in this case, are not predictedby simulation software automatically. To predict formation of such imperfections it is required to createa criterion for depletion of a plasticity resource or a fracture criterion. It is possible to specify suchknown criteria as (named by surnames of scientists who offered them): Cockroft & Latham [2], Johnsona Corresponding author: gladyuri@yandex.ruThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152112009MATEC Web of ConferencesFigure 1. Examples of fracture in sheet (left) and bulk (right) metal formed part.& Cook [3], McClintock [4], Rice and Tracy [5], V.L. Kolmogorov [6], V.A. Ogorodnikov [7], G.D. Del[8], Yu.G. Kalpin [9], R.A. Vasin and P.A. Mossakovsky [10], and many others.Some of these criteria have found their application among standard fracture criteria in knowncommercial software for forming technology. So, for example, Cockroft & Latham criterion is includedin the program QForm [11, 12], Johnson & Cook is included in the program LS-DYNA. There are knownstudies on implementation of a fracture criterion in commercial software by third party research teams.Scientists have developed additional user subroutine which expands opportunities of the commercialprograms [1, 13, 14].The attention was attracted to studies of scientists led by Professor Tomasz Wierzbicki fromMassachusetts Institute of Technologies [15]. The criterion (hereinafter Bai & Wierzbicki criterion)considering stress state triaxiality  and Lode stress state parameter ̄ was proposed in [15]. Thisstudy inspired development of a new material testing procedure for deriving of a critical deformationdegree function ̄constp = f (, ̄) in the Institute of Forming Technology and Machines (IFUM), LeibnizUniversität in Hanover, Germany [16, 17]. The criterion is convenient for use as it is normalized upondefinition of a critical deformation degree ̄constp so that critical value for cracking condition is a valueof this criterion equal to 1. The criterion gives a fracture prediction in a wide spectrum of stress statesprocesses where the complex loading is restricted by a critical deformation degree surface [15].The purpose of the present research was development of the user subroutine for calculation of Bai& Wierzbicki criterion in the widely applicable commercial software product for forming simulationQForm [11, 18]. Its basis was results of the experimental works carried out in IFUM [16, 17]. Theresearch plan included the following: simulation of a deep drawing test case, implementation of the usersubroutine in the programming language Lua, testing of sensitivity of the developed subroutine to afinite element grid density, and definition of application potential of the criterion for solving of cold dieforming problems.The created subroutine can be applied by QForm users to estimate a quality of newly developedprocesses of cold sheet-metal forming for the purpose to decrease level rejection because of defectsdue to fracture. Also the subroutine may be used for prediction of strength and plastic properties of amaterial and possible cracking in the course of cold die forging.2. Simulation of cold sheet-metal forming: Input data and comparisonwith the experimentDeep drawing was performed on a hydraulic press with the nominal force of 630 kN. The blank holderforce was 320 kN. The process scheme is shown in Fig. 2. Figure 2a shows the workpiece made from asheet by thickness of 1.4 mm, overall dimensions of 240 × 162 mm, with edges of 127 mm (longitudinal)and 40 mm (transversal). A photo of the tool is shown in fig. 2b. The drawing punch has a right-angledshape with sizes of 76.4 × 156.4 mm and corner radiuses of 6 mm. The die dimensions are 160 × 80 mmand corner radiuses equal to 3 mm. Figure 2c shows the product after forming and Fig. 2e represents12009-p.2ICNFT 2015Figure 2. Deep drawing of the product “bucket”: a) primary blank, b) press tool, c) formed product, d) mesh sizein different zones, e) positioning of tools at the end of simulation, f) simulation result and real forged part photo.Table 1. Material characterization function parameters. AS BS nS AHS BHS mHS nHSHCT600XD 0.479 642 0.00596 0.660 757 1224 15.5 0.820positioning of tools (the drawing punch, the die, the blank holder) in the end of simulation. Specialsettings of the automatic generator of the tetrahedral finite element mesh in 3 areas have been used toprovide sufficient quality of simulation (Fig. 2d). The cylinder area (“box”) in an angle zone of theproduct has set that finite elements have a size about 0.2 mm that corresponds to 5–7 layers of elementsover thickness.Material characterization (Table 1): tests were conducted and the dependence of the flow stress  onthe equivalent plastic strain was obtained for the workpiece material HCT600XD [16, 19]: =  · (As · (Bs + p)ns ) + (1 − ) · (BHS − (BHS − AHS) · e−mHSnHSp (1)Comparisons and key sizes of the product both for experiment and simulation are shown in Fig. 3. Thesimulation error (for key sizes) does not exceed 3.3%. Force diagrams are shown in Fig. 3c: obtainedfrom the experiment [16], by simulation in Abaqus software [16] and by simulation in QForm software.The result closest to the experiment is obtained under simulation in QForm, version 7.3 with use ofelasto-plastic model of the material.12009-p.3MATEC Web of Conferencesa            b        c  Figure 3. Comparison of key dimensions and force: a) the photo of the formed part, b) the view of the part aftercompleting the simulation with results of measuring in the program QForm, c) deformation force diagrams obtainedfrom experiment [16], Abaqus software, and QForm software.The product obtained by simulation and a photo of the product fragment from the experiment areshown in Fig. 3b for visual comparison. Trace points (in QForm) and pointwise markers (in experiment)were used for correlation of the specific areas. Difference in force values between the experimental andsimulation results in both simulation programs stay within 5% error. The replica of the product shapeand a deforming force allows drawing a conclusion that the deep drawing process model in QFormreplicates the experiment with an adequate exactitude, and it is possible to use the model for designingand testing of Bai & Wierzbicki fracture criterion.3. Implementation of Bai & Wierzbicki criterion: Description andsimulation resultsCalculation of Bai & Wierzbicki criterion [15] in the developed subroutine is reduced to accumulationof an index of a formability depletion D:D =n∑i=0̄P̄critp· (2)Where on each simulation step i=0 ... n the increment of the equivalent deformation degree ̄p iscalculated numerically as the product of a strain velocity ̇p by value of a simulation time step t suchapproach is related by that in program QForm as the main simulation of the stress-strain state in nodesof the finite element grid is performed in deformation velocities: ̄p = ̄pt).Critical value of the deformation degree ̄critp = f(, ̄) is calculated as the function of a stress statetriaxiality  and athe normalized Lode coefficient ̄.̄critp =[0.5 · (D1e−D2· + D5e−D6·) − D3e−D4·] · ̄2 + 0.5 · (D1e−D2· − D5e−D6·) · ̄ + D3e−D4·,(3) = 1/3(1 + 2 + 3)eq· (4)12009-p.4ICNFT 2015a b cFigure 4. The screen layout with simulation results: a) the record corresponding to the tool movement of 20 mm(field “BnW” and window of the deformation force); b) photo of the product; c) the record corresponding to thetool movement of 25 mm (area of defect indication “Crack_View”).Values of coefficients D1 = 0.9702, D2 = 5.596E-6, D3 = 1.038, D4 = 0.9857, D5 = 1.803, D6 =2.742 are determined experimentally according to the procedure [17]. So, an input information fromthe simulation core for each node of the grid are the main and equivalent stresses 1, 2, 3, eq, andalso ̄, ̇p, t .In the course of simulations the filtering of the values which occur as fluctuation upon numericaldetermination of deformation components is possible. It has been discovered that the good result canbe obtained if the increment value D falling in the range 0 < ̄p̄critp < f ilter = 0.3, is used based onthe result of a previous step of simulation. The value of a fluctuation filtering level filter can be set withcoefficients D1, ... , D6.Results of simulation are the area with the name “BnW” (see Fig. 4a) (in which value of the criterionD is saved, the area “delta_BnW” (the criterion increment at the current step), the area “Eta” (the stressstate triaxiality  at a current step is saved here and the area with the name “Crack_View” (see Fig. 4c).Last area serves for indication of a zone where value D exceeds 1 that is a zone where crack occurrenceis predicted.To check the performance of the subroutine, the research was undertaken on how a finite elementgrid density influences results of simulation. Three alternatives of a finite element grid density wereconsidered with sizes of elements in a crack formation zone of 0.5 mm, 0.2 mm, and 0.1 mm. Sizes ofa zone of defect occurrence indication (the area “Crack_View”) on front and rear edges of the product,and also a distance at which the defect appeared on both sides of the product (i.e. “an open defect”appeared) were studied. Almost equal times of open defect occurrences confirm a stability of criterioncalculation algorithm. The sizes of defect indication zones differ by 30%. Upon that, it is clear that thedifference for the grids with a size of 0.2 mm and 0.1 mm can be neglected. This suggests usability ofcalculation with 0.2 mm finite element grid.4. Conclusions1. Simulation in QForm of a product obtained by sheet-metal forming replicates the correspondingexperiment data with an adequate accuracy (error is less 5%).2. A subroutine of fracture calculation by Bai & Wierzbicki criterion is developed.3. It is determined that the size of a finite element grid almost does not influence a defect occurrencetime on both sides of the product (no more 3%) that proves a stability of work of the criterioncalculation subroutine.12009-p.5MATEC Web of Conferences4. It is determined that the size of a finite element grid influences a size of a defect occurrenceindication zone (up to 30%). It is recommended to check the influence of a finite element grid ona size of a defect indication zone. It was found out that in the problem, it is possible to considera size of a finite element grid as sufficient if the element sizes equals to 0.2 mm in the examinedzone.5. The performed analysis of influence of the temperature increase in the cold forming process onvalues of the criterion, and also on volume character of a defect occurrence indication zone givesgrounds to consider the use of the developed subroutine for solution of similar problems in colddie forming processes in the future.The study was carried out at the Institute of Forming Technology and Machines (IFUM) of Leibniz UniversitätHannover. The financial support in the frame of the cooperative research grant “Mikhail Lomonosov III” providedby the Ministry of Education and Science of the Russian Federation and the German Academic Exchange Service(DAAD) is gratefully acknowledged. The authors also thank “Quantor Form" LLC for the granted license on QFormsoftware.References[1] A.V. Vlasov, The method of predicting the mechanical properties of the material after colddeformation on the results of mathematical modelling. Proceedings of the Conference on MetalForming. – Kramatorsk, DSEA, No 1(34), pp. 72 – 79 (Russian, 2013)[2] M.G. Cockcroft, D.J. Latham, Ductility and the workability of metals. J. of the Institute of Metals,96, pp. 33 – 39 (1968)[3] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strain,strain rates, temperatures, pressures // Eng. Frac. Mech., 21, pp.31 – 48 (1985)[4] F.A. McClintock, A criterion of ductile fracture by the growth of holes. Journal of AppliedMechanics, 35, pp. 363 – 371 (1968)[5] J.R. Rice, D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields. Journal of theMechanics and Physics of Solids, 17, pp. 201 – 217 (1969)[6] V.L. Kolmogorov, Mechanics of Metal Forming. Ekaterinburg, 836 p (Russian, 2001)[7] V.A. Ogorodnikov, Evaluation deformability of material at metal forming. Kiev: Vishya shcola,174 p. (Russian, 1983)[8] Del G.D. Plasticity of deformed material // Physics and technology of high pressure, No 11,pp. 28 – 32 (Russian, 1983)[9] Yu.G. Kalpin, V.I. Perfilov, P.A. Petrov, V.A. Ryabov, Yu.K. Filipov, Deformation resistance andplasticity in metal forming. Mashinostroenie, Moscow, 243 p. (Russian, 2011)[10] R.A. Vasin, P.A. Mossakovsky, Journal of Applied Mathematics and Mechanics 75 (2011)[11] Documentation and user guide of QForm on http://www.qform3d.co.uk[12] A.V. Belevich, D.M. Babin, Yu.A. Gladkov, A.V. Aborkin, Simulation and research of metalforming processes. Vladimir State University, 181 p. (Russian, 2012)[13] N.V. Biba, S.A. Stebunov, S.V. Smirnov. Application of adaptive damage theory for optimizationof cold bulk metal forming, Proceedings of the 7TH International Conference on NumericalMethods in Industrial forming processes, Toyohashi, Japan (2001)[14] O. Bylya, N. Biba, A. Vlasov, R. Vasin, The analysis of different damage accumulationmodels for simulation of hot and warm working of alfa+beta titanium alloys. Onhttp://qform3d.co.uk/db_files/47/280.pdf[15] Y. Bai, T. Wierzbicki A new model of metal plasticity and fracture with pressure and Lodedependence / International Journal of Plasticity 24, pp. 1071–1096 (2008)12009-p.6ICNFT 2015[16] B.-A. Behrens, M. Vucetic, I. Peshekhodov Effiziente Charakterisierung und Modellierungdes Fließ- und Versagensverhaltens von Dualphasenstählen. Umformtechnisces Kolloquium,Hannover, pp. 77–97 (German, 2014)[17] B.-A. Behrens, M. Vucetic, I. Peshekhodov Calibration of fracture initiation models for advancedhigh-strength sheet steels in a wide range of stress states using a uniaxial tensile testing machine.Proceedings of the IDDRG 2014 Conference, Paris, pp. 252–257 (2014)[18] N.V. Biba, S.A. Stebunov, Yu.A. Gladkov, P.S. Mordvincev QForm – unique software for metalforming simulation // KShP magazine, No 1, pp. 36–42 (Russian, 2011)[19] B.-A. Behrens, A. Bouguecha, M. Vucetic, I. Peshekhodov Characterisation of the quasi-staticflow and fracture behaviour of dual – phase steel sheets in a wide range of plane stress states.Archives of Civil and Mechanical Engineering 12, No. 4, pp. 397–406 (2012)12009-p.7

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Implementation of the Bai and Wierzbicki fracture criterion in QForm and its application for cold metal forming and deep drawing technology

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Implementation of the Bai and Wierzbicki fracture criterion in QForm and its application for cold metal forming and deep drawing technology

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