Abstract
The present study helps in providing a systematic approach towards the investigation of deep drawing and stretch forming processes for Inconel 625 alloy. Firstly, the flow stress nature and material properties of Inconel 625 super-alloy have been investigated and it has been found that temperature and deformation rate significantly affects the flow stress behavior. By using experimental flow stress data, four different constitutive models namely; modified Jhonson-Cook (m-JC), modified Zerilli-Armstrong (m-ZA), modified Arrhenius (m-A), Khan–Huang–Liang (KHL) model have been formulated of which m-A has been found to have the best predictability for flow stress. Hill 1948 and Barlat 1989 anisotropic yield criterion have also been applied and it has been found that Barlat 1989 criteria more accurately capture the yielding behavior of Inconel 625 alloy. The deep drawing analysis has been carried out using target and noise performance measures for different process parameters viz., temperature, punch speed and blank holding pressure. Uniformity in thickness has been major cause of concern, hence experiment at 473 K, 5 mm/min speed and 20 Bar pressure was found to have least variation in thickness. Furthermore, the forming limit diagram (FLD) and fracture curve (FC) obtained from stretch forming analysis along five different strain paths was found to be significantly affected by temperature. Further, user defined material (UMAT) subroutine have been incorporated in ABAQUS 6.13 software to have effect of m-A model and Barlat 1989 yield criteria in finite element analysis (FEA) of deep drawing and stretch forming processes.
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Abbreviations
- σ :
-
Flow Stress
- ε:
-
Plastic Strain
- \( \dot{\upvarepsilon} \) :
-
Deformation rate
- A:
-
Yield Stress
- B:
-
Strain-hardening coefficient
- m:
-
Thermal softening exponent
- n:
-
Strain hardening exponent
- Tm :
-
Melting temperature of Inconel 625 (1609 K)
- T:
-
Testing temperature
- Tref :
-
Reference temperature (298 K)
- R:
-
Universal gas constant
- Q:
-
Activation Energy
- A ′ :
-
Structural factor
- α:
-
Stress multiplier
- n1 :
-
Stress exponent
- C:
-
Strain rate hardening coefficient
- \( {D}_p^0 \) :
-
Random upper bound strain rate at 300 K (106 s−1)
- K:
-
Strength coefficient
- U:
-
Ultimate Strength
- %El:
-
Elongation percentage
- \( {\dot{\upvarepsilon}}_{\mathrm{ref}} \) :
-
Reference deformation rate (0.01 s−1)
References
Kotkunde N, Badrish A, Morchhale A, Takalkar P, Singh SK (2019) Warm deep drawing behavior of Inconel 625 alloy using constitutive modelling and anisotropic yield criteria. Int J Mater Form. https://doi.org/10.1007/s12289-019-01505-3
Thakur DG, Ramamoorthy B, Vijayaraghavan L (2009) Machinability investigation of Inconel 718 in high-speed turning. Int J Adv Manuf Technol 45(5-6):421. https://doi.org/10.1007/s00170-009-1987-x
Lin YC, Wen D-X, Deng J et al (2014) Constitutive models for high-temperature flow behaviors of a Ni-based superalloy. Mater Des 59:115–123. https://doi.org/10.1016/j.matdes.2014.02.041
Wen D-X, Lin YC, Li H-B et al (2014) Hot deformation behavior and processing map of a typical Ni-based superalloy. Mater Sci Eng A 591:183–192. https://doi.org/10.1016/j.msea.2013.09.049
Lin YC, Li K-K, Li H-B et al (2015) New constitutive model for high-temperature deformation behavior of inconel 718 superalloy. Mater Des 74:108–118. https://doi.org/10.1016/j.matdes.2015.03.001
Grzesik W, Niesłony P, Laskowski P (2017) Determination of material constitutive Laws for Inconel 718 Superalloy under different strain rates and working temperatures. J of Materi Eng and Perform 26(12):5705–5714. https://doi.org/10.1007/s11665-017-3017-8
Gujrati R, Gupta C, Jha JS et al (2019) Understanding activation energy of dynamic recrystallization in Inconel 718. Mater Sci Eng A 744:638–651. https://doi.org/10.1016/j.msea.2018.12.008
Zhou Y, Chen X-M, Qin S (2019) A strain-compensated constitutive model for describing the hot compressive deformation behaviors of an aged Inconel 718 Superalloy. High Temperature Materials and Processes 38:436–443. https://doi.org/10.1515/htmp-2018-0108
Lin YC, Chen X-M (2011) A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Mater Des 32:1733–1759. https://doi.org/10.1016/j.matdes.2010.11.048
Liu D, Zhang X, Qin X, Ding Y (2017) High-temperature mechanical properties of Inconel-625: role of carbides and delta phase. Mater Sci Technol 33:1610–1617. https://doi.org/10.1080/02670836.2017.1300365
Pandre S, Takalkar P, Morchhale A, Kotkunde N, Singh SK (2020) Prediction capability of anisotropic yielding behaviour for DP590 steel at elevated temperatures. Advances in Materials and Processing Technologies. https://doi.org/10.1080/2374068X.2020.1728647
Prasad KS, Kamal T, Panda SK et al (2015) Finite element validation of forming limit diagram of IN-718 sheet metal. Materials Today: Proceedings 2:2037–2045. https://doi.org/10.1016/j.matpr.2015.07.174
Kotkunde N, Deole AD, Gupta AK, Singh SK (2014) Experimental and numerical investigation of anisotropic yield criteria for warm deep drawing of Ti–6Al–4V alloy. Mater Des 63:336–344. https://doi.org/10.1016/j.matdes.2014.06.017
Jeswiet J, Geiger M, Engel U et al (2008) Metal forming progress since 2000. CIRP J Manuf Sci Technol 1:2–17. https://doi.org/10.1016/j.cirpj.2008.06.005
Yoon BB, Rao RS, Kikuchi N (1989) Sheet stretching: a theoretical-experimental comparison. Int J Mech Sci 31:579–590. https://doi.org/10.1016/0020-7403(89)90065-9
Kardan M, Parvizi A, Askari A (2018) Experimental and finite element results for optimization of punch force and thickness distribution in deep drawing process. Arab J Sci Eng 43(3):1165–1175. https://doi.org/10.1007/s13369-017-2783-9
Savaş V, Seçgin Ö (2010) An experimental investigation of forming load and side-wall thickness obtained by a new deep drawing die. Int J Mater Form 3(3):209–213. https://doi.org/10.1007/s12289-009-0672-9
Boissière R, Vacher P, Blandin JJ (2010) Influence of the punch geometry and sample size on the deep-drawing limits in expansion of an Aluminium alloy. Int J Mater Form 3(1):135–138. https://doi.org/10.1007/s12289-010-0725-0
Morchhale A (2016) Design and finite element analysis of hydrostatic pressure testing machine used for ductile Iron pipes. MER 6:23. https://doi.org/10.5539/mer.v6n2p23
Venkateswarlu G, Davidson MJ, Tagore GRN (2010) Influence of process parameters on the cup drawing of aluminium 7075 sheet. International journal of engineering, science and technology 2:
Ahmetoglu M, Broek TR, Kinzel G, Altan T (1995) Control of blank holder force to eliminate wrinkling and fracture in deep-drawing rectangular parts. CIRP Ann 44:247–250. https://doi.org/10.1016/S0007-8506(07)62318-X
Wallmeier M, Linvill E, Hauptmann M et al (2015) Explicit FEM analysis of the deep drawing of paperboard. Mech Mater 89:202–215. https://doi.org/10.1016/j.mechmat.2015.06.014
Prasad KS, Panda SK, Kar SK et al (2018) Prediction of fracture and deep drawing behavior of solution treated Inconel-718 sheets: numerical modeling and experimental validation. Mater Sci Eng A 733:393–407. https://doi.org/10.1016/j.msea.2018.07.007
Padmanabhan R, Oliveira MC, Alves JL, Menezes LF (2009) Stochastic analysis of a deep drawing process using finite element simulations. Int J Mater Form 2(1):347. https://doi.org/10.1007/s12289-009-0565-y
Choudhury IA, Ghomi V (2014) Springback reduction of aluminum sheet in V-bending dies. Proc Inst Mech Eng B J Eng Manuf 228:917–926. https://doi.org/10.1177/0954405413514225
Badrish A, Morchhale A, Kotkunde N, Singh SK (2020) Parameter Optimization in the Thermo-mechanical V-Bending Process to Minimize Springback of Inconel 625 Alloy. Arab J Sci Eng. https://doi.org/10.1007/s13369-020-04395-9
Djavanroodi F, Derogar A (2010) Experimental and numerical evaluation of forming limit diagram for Ti6Al4V titanium and Al6061-T6 aluminum alloys sheets. Mater Des 31:4866–4875. https://doi.org/10.1016/j.matdes.2010.05.030
He M, Li F, Wang Z (2011) Forming limit stress diagram prediction of aluminum alloy 5052 based on GTN model parameters determined by in situ tensile test. Chin J Aeronaut 24:378–386. https://doi.org/10.1016/S1000-9361(11)60045-9
Bleck W, Deng Z, Papamantellos K, Gusek CO (1998) A comparative study of the forming-limit diagram models for sheet steels. J Mater Process Technol 83:223–230. https://doi.org/10.1016/S0924-0136(98)00066-1
Panich S, Barlat F, Uthaisangsuk V et al (2013) Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels. Mater Des 51:756–766. https://doi.org/10.1016/j.matdes.2013.04.080
Badr OM, Rolfe B, Hodgson P, Weiss M (2015) Forming of high strength titanium sheet at room temperature. Mater Des 66:618–626. https://doi.org/10.1016/j.matdes.2014.03.008
Bong HJ, Barlat F, Lee M-G, Ahn DC (2012) The forming limit diagram of ferritic stainless steel sheets: experiments and modeling. Int J Mech Sci 64:1–10. https://doi.org/10.1016/j.ijmecsci.2012.08.009
Shu J, Bi H, Li X, Xu Z (2012) Effect of Ti addition on forming limit diagrams of Nb-bearing ferritic stainless steel. J Mater Process Technol 212:59–65. https://doi.org/10.1016/j.jmatprotec.2011.08.004
Roamer P, Van Tyne CJ, Matlock DK, et al (1997) Room temperature formability of alloys 625LCF, 718 and 718SPF. In: Superalloys 718, 625, 706 and various derivatives (1997). TMS, pp 315–329
Han HN, Kim K-H (2003) A ductile fracture criterion in sheet metal forming process. J Mater Process Technol 142:231–238. https://doi.org/10.1016/S0924-0136(03)00587-9
Jain M, Allin J, Lloyd DJ (1999) Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet. Int J Mech Sci 41:1273–1288. https://doi.org/10.1016/S0020-7403(98)00070-8
Jeswiet J, Micari F, Hirt G et al (2005) Asymmetric single point incremental forming of sheet metal. CIRP Ann 54:88–114. https://doi.org/10.1016/S0007-8506(07)60021-3
Embury JD, Duncan JL (1981) Formability maps. Annu Rev Mater Sci 11:505–521. https://doi.org/10.1146/annurev.ms.11.080181.002445
Takuda H, Mori K, Takakura N, Yamaguchi K (2000) Finite element analysis of limit strains in biaxial stretching of sheet metals allowing for ductile fracture. Int J Mech Sci 42:785–798. https://doi.org/10.1016/S0020-7403(99)00018-1
Prasad YVRK, Rao KP, Sasidhara S (2015) Hot working guide: a compendium of processing maps, second edition, first printing. ASM International, Materials Park, Ohio
E28 Committee Test Methods for Tension Testing of Metallic Materials. ASTM International
Hecker SS (1975) Simple technique for determining forming limit curves. Sheet Metal Industries 52:671–676
Dieter GE, Bacon DJ (1986) Mechanical metallurgy. McGraw-hill New York
Li D, Guo Q, Guo S et al (2011) The microstructure evolution and nucleation mechanisms of dynamic recrystallization in hot-deformed Inconel 625 superalloy. Mater Des 32:696–705. https://doi.org/10.1016/j.matdes.2010.07.040
Liu J, Cui Z, Li C (2008) Analysis of metal workability by integration of FEM and 3-D processing maps. J Mater Process Technol 205:497–505. https://doi.org/10.1016/j.jmatprotec.2007.11.308
Kuhlmann-Wilsdorf D (1989) Theory of plastic deformation: - properties of low energy dislocation structures. Mater Sci Eng A 113:1–41. https://doi.org/10.1016/0921-5093(89)90290-6
Rodriguez P (1984) Serrated plastic flow. Bull Mater Sci 6:653–663. https://doi.org/10.1007/BF02743993
Lin YC, Yang H, Chen X-M, Chen D-D (2018) Influences of initial microstructures on Portevin-Le Chatelier effect and mechanical properties of a Ni–Fe–Cr–Base Superalloy. Adv Eng Mater 20:1800234. https://doi.org/10.1002/adem.201800234
Hussaini SM, Singh SK, Gupta AK (2014) Formability of austenitic stainless steel 316 sheet in dynamic strain aging regime. Acta Metall Slovaca 20:71–81. https://doi.org/10.12776/ams.v20i1.187
Pandre S, Kotkunde N, Takalkar P, Morchhale A, Sujith R, Singh SK (2019) Flow stress behavior, constitutive modeling, and microstructural characteristics of DP 590 steel at elevated temperatures. J of Materi Eng and Perform 28(12):7565–7581. https://doi.org/10.1007/s11665-019-04497-y
Robinson JM, Shaw MP (1994) Microstructural and mechanical influences on dynamic strain aging phenomena. Int Mater Rev 39:113–122. https://doi.org/10.1179/imr.1994.39.3.113
Hosford WF, Caddell RM (2007) Metal forming by William F. Hosford. In: Cambridge Core. /core/books/metal-forming/DFD3C93FFFCB89A29076C55B8A4E1831. Accessed 5 Nov 2019
Johnson GR, Cook WH, Johnson G, Cook W A constitutive model and data for materials subjected to large strains, high strain rates, and high temperatures
Khan AS, Zhang H, Takacs L (2000) Mechanical response and modeling of fully compacted nanocrystalline iron and copper. Int J Plast 16:1459–1476. https://doi.org/10.1016/S0749-6419(00)00023-1
Sellars CM, McTegart WJ (1966) On the mechanism of hot deformation. Acta Metall 14:1136–1138. https://doi.org/10.1016/0001-6160(66)90207-0
Armstrong RW, Arnold W, Zerilli FJ (2009) Dislocation mechanics of copper and iron in high rate deformation tests. J Appl Phys 105:023511. https://doi.org/10.1063/1.3067764
Lin YC, Chen X-M (2010) A combined Johnson–Cook and Zerilli–Armstrong model for hot compressed typical high-strength alloy steel. Comput Mater Sci 49:628–633. https://doi.org/10.1016/j.commatsci.2010.06.004
Lin YC, Chen X-M, Liu G (2010) A modified Johnson–Cook model for tensile behaviors of typical high-strength alloy steel. Mater Sci Eng A 527:6980–6986. https://doi.org/10.1016/j.msea.2010.07.061
Samantaray D, Mandal S, Bhaduri AK (2009) A comparative study on Johnson Cook, modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict elevated temperature flow behaviour in modified 9Cr–1Mo steel. Comput Mater Sci 47:568–576. https://doi.org/10.1016/j.commatsci.2009.09.025
Prasad KS, Gupta AK (2014) A constitutive description to predict high-temperature flow stress in austenitic stainless steel 316. Procedia Mater Sci 6:347–353. https://doi.org/10.1016/j.mspro.2014.07.044
Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48. https://doi.org/10.1016/0013-7944(85)90052-9
Badrish AC, Morchhale A, Kotkunde N, Singh SK (2020) Experimental and finite element studies of springback using split-ring test for Inconel 625 alloy. Advances in Materials and Processing Technologies. https://doi.org/10.1080/2374068X.2020.1728644
Hill R (1990) Constitutive modelling of orthotropic plasticity in sheet metals. Journal of the Mechanics and Physics of Solids 38:405–417. https://doi.org/10.1016/0022-5096(90)90006-P
Banabic D (2010) Sheet metal forming processes: constitutive Modelling and numerical simulation. Springer-Verlag, Berlin Heidelberg
Barlat F, Brem JC, Yoon JW et al (2003) Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast 19:1297–1319. https://doi.org/10.1016/S0749-6419(02)00019-0
Sajun Prasad K, Panda SK, Kar SK, Sen M, Murty SVSN, Sharma SC (2017) Microstructures, forming limit and failure analyses of Inconel 718 sheets for fabrication of aerospace components. J of Materi Eng and Perform 26(4):1513–1530. https://doi.org/10.1007/s11665-017-2547-4
Charpentier PL (1975) Influence of punch curvature on the stretching limits of sheet steel. Metall Trans A 6(8):1665–1669. https://doi.org/10.1007/BF02641986
Bandyopadhyay K, Basak S, Prasad KS et al (2019) Improved formability prediction by modeling evolution of anisotropy of steel sheets. Int J Solids Struct 156–157:263–280. https://doi.org/10.1016/j.ijsolstr.2018.08.024
Morchhale A (2017) Study of positioning and dimensional optimization of angled stiffeners using finite element analysis of above ground storage tank. International Journal of Research in Mechanical Engineering 5:10–19
Acknowledgements
Authors pay their high regards towards Science and Engineering Research Board (SERB), Government of India for funding the project (file number - ECR/2016/001402). Authors are also thankful to BITS-Pilani, Hyderabad Campus for providing the UTM facility in Central Analytical Lab (CAL).
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Badrish, A., Morchhale, A., Kotkunde, N. et al. Influence of material modeling on warm forming behavior of nickel based super alloy. Int J Mater Form 13, 445–465 (2020). https://doi.org/10.1007/s12289-020-01548-x
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DOI: https://doi.org/10.1007/s12289-020-01548-x