آنالیز حد شکل‌پذیری ورق‌های فلزی براساس پدیده گلویی موضعی ورتکس و معیار آسیب نرم

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکترا، دانشکده مهندسی مکانیک، پردیس دانشگاهی، دانشگاه گیلان، رشت، ایران

2 گیلان*مهندسی مکانیک

3 دانشگاه گیلان*مکانیک

4 عضو هیئت علمی و مدیر گروه مکانیک دانشگاه بین المللی امام خمینی

چکیده

در این مقاله یک روش عددی برای مدلی که توانایی بیان حد شکل‌پذیری ورق‌های فولادی را بر اساس نرخ کرنش، گلویی‌شدن موضعی و آسیب نرم را داشته باشد ارائه شده است. با کاربرد معادله توانی کرنش سختی فلزات که وابسته به نرخ کرنش می‌باشد در تئوری ورتکس، ضمن اینکه پدیده گلویی‌شدن موضعی را می‌توان بررسی کرد اثر نرخ کرنش را نیز می‌توان لحاظ نمود. هدف دیگر این مقاله آنالیز حد شکل‌پذیری ورق‌های فولادی بر اساس معیار آسیب نرم وابسته به حالت تنش است. نتایج مدل عددی ارائه‌شده در زیربرنامه نرم افزار المان محدود آباکوس با نتایج آزمایشگاهی در ورق‌های فولادی ساده کربنی رده 13 و 14 برای اعتبارسنجی مقایسه گردید و مشخص شد که این مدل عددی دارای دقت بسیار بالایی می‌باشد. همچنین بر اساس این نتایج، نمودارهای حد شکل‌دهی ورق‌های فولادی وابسته به نرخ کرنش می‌باشد. به طوری که با افزایش نرخ کرنش سطح نمودارهای حد شکل‌دهی افزایش یافته و این افزایش سطح در نرخ کرنش‌های بالا نسبت به نرخ کرنش‌های پایین قابل‌ملاحظه می‌باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analysis of Forming Limit of Sheet Metals Considering Vertex Localized Necking and Ductile Damage Criterion

نویسندگان [English]

  • Farid Hosseini Mansoub 1
  • Ali Basti 2
  • aboulfazl darvizeh 3
  • Asghar Zajkani 4
1 Mechanical Faculty, University Campus 2, University of Guilan, Rasht, Iran
2 Mechanical Faculty, University of Guilan, Rasht, Iran
3 Mechanical Faculty, University of Guilan, Rasht, Iran
4 Mechanical Engineering Department, Imam Khomeini International University
چکیده [English]

In the present paper, a predictive strain-rate-dependent model of localized necking is developed by using a modified Vertex theory. A novel ductile damage-based criterion is proposed to control the necking parameters including on stress triaxiality, strain hardening exponent, and Lode parameters. As a characterization parameter, elastic modulus is eventually chosen to measure the ductile damage during the process of plastic deforming. Furthermore, a vectorized user-defined material subroutine is developed to finite element simulation by ABAQUS software, according to original formulations, to create a linkage between related essential models. A typical strain rate-dependent metal is selected to validate the modified Vertex theory. To examine the accuracy of the results from the present simulated study, the applicability is considered to compare with the experimental results. Tests of forming are also performed for steel 13 and steel 14 sheets to measure forming limit diagram. It should be noted that the simulated forming limit diagrams are in good agreement with the experimental data. However, this correlation at low strain rates is better than high strain rates. However, this increase will be infinitesimal for the lower strain rates as compared to the higher ones.

کلیدواژه‌ها [English]

  • Ductile damage
  • Stress state
  • Strain rate
  • Forming limit diagrams
  • Vertex theory

مراجع

[1] H. Takuda, K. Mori, N. Hatta, The application of some criteria for ductile fracture to the prediction of the forming limit of sheet metals, Journal of Materials Processing Technology, 95(1) (1999) 116-121.
[2] X. Ma, F. Li, J. Li, Q. Wang, Z. Yuan, Y. Fang, Analysis of forming limits based on a new ductile damage criterion in St14 steel sheets, 2015.
[3]R. Hill, On discontinuous plastic states, with special reference to localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 19-30 (1952) (1) 1.
[4] R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, 6(3) (1958) 236-249.
[5] G. Borré, G. Maier, On linear versus nonlinear flow rules in strain localization analysis, Meccanica, 24(1) (1989) 36-41.
[6] J. Rudnicki, J. Rice, Condition for the Localization of Deformation in Pressure-Sensitive Dilatant Materials, 1975.
[7] C.L. Chow, M. Jie, X. Wu, Localized Necking Criterion for Strain-Softening Materials, Journal of Engineering Materials and Technology, 127(3) (2005) 273-278.
[8] M.K. Neilsen, H.L. Schreyer, Bifurcations in elastic-plastic materials, International Journal of Solids and Structures, 30(4) (1993) 521-544.
[9] C.L. Chow, M. Jie, X. Wu, A Damage-coupled Criterion of Localized Necking Based on Acoustic Tensor, International Journal of Damage Mechanics, 16(3) (2007) 265-281.
[10] L. Szabó, Comments on loss of strong ellipticity in elastoplasticity, International Journal of Solids and Structures, 37575-3806 (2000) (28)37.
[11] D. Bigoni, T. Hueckel, Uniqueness and localization—I. Associative and non-associative elastoplasticity, International Journal of Solids and Structures, 28(2) (1991) 197-213.
[12] N.S. Ottosen, K. Runesson, Properties of discontinuous bifurcation solutions in elasto-plasticity, International Journal of Solids and Structures, 27(4) (1991) 401-421.
[13] K.L. Nielsen, Ductile damage development in friction stir welded aluminum (AA2024) joints, Engineering Fracture Mechanics, 75(10) (2008) 2795-2811.
[14] Z. Marciniak, K. Kuczyński, Limit strains in the processes of stretch-forming sheet metal, International Journal of Mechanical Sciences, 9(9) (1967) 609-620.
[15] Z. Marciniak, K. Kuczyński, T. Pokora, Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension, International Journal of Mechanical Sciences, 15(10) (1973) 789-800.
[16] A. Zajkani, A. Bandizaki, An efficient model for diffuse to localized necking transition in rate-dependent bifurcation analysis of metallic sheets, International Journal of Mechanical Sciences, 133(Supplement C) (2017) 794-803.
[17] A. Zajkani, A. Bandizaki, A path-dependent necking instability analysis of the thin substrate composite plates considering nonlinear reinforced layer effects, The International Journal of Advanced Manufacturing Technology,  (2017.(
[18]S. Stören, J.R. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, 23(6) (1975) 421-441.
[19] Y. Bai, T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, International journal of plasticity, 24(6) (2008) 1071-1096.
[20] C.H.M. Simha, S. Xu, W. Tyson, Non-local phenomenological damage-mechanics-based modeling of the Drop-Weight Tear Test, Engineering Fracture Mechanics, 118 (2014) 66-82.
[21] S.B. Kim, H. Huh, H.H. Bok, M.B. Moon, Forming limit diagram of auto-body steel sheets for high-speed sheet metal forming, Journal of Materials Processing Technology, 211(5) (2011) 851-862.
[22] S. Balasubramanian, L. Anand, Elasto-viscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures, Journal of the Mechanics and Physics of Solids, 50(1) (2002) 101-126.
[23] J.H. Kim, J.H. Sung, K. Piao, R. Wagoner, The shear fracture of dual-phase steel, International Journal of Plasticity, 27(10) (2011) 1658-1676.
[24] Y. Lou, J.W. Yoon, H. Huh, Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality, International Journal of Plasticity, 54 (2014) 56-80.
[25] X. Sun, K.S. Choi, W.N. Liu, M.A. Khaleel, Predicting failure modes and ductility of dual phase steels using plastic strain localization, International Journal of Plasticity, 25(10) (2009) 1888-1909.
[26] G. Gruben, E. Fagerholt, O.S. Hopperstad, T. Børvik, Fracture characteristics of a cold-rolled dual-phase steel, European Journal of Mechanics-A/Solids, 30(3) (2011) 204-218.
[27] K. Chung, N. Ma, T. Park, D. Kim, D. Yoo, C. Kim, A modified damage model for advanced high strength steel sheets, International Journal of Plasticity, 27(10) (2011) 1485-1511.
[28] H. Huh, S.-B. Kim, J.-H. Song, J.-H. Lim, Dynamic tensile characteristics of TRIP-type and DP-type steel sheets for an auto-body, International Journal of Mechanical Sciences, 50(5) (2008) 918-931.
[29] S. Curtze, V.-T. Kuokkala, M. Hokka, P. Peura, Deformation behavior of TRIP and DP steels in tension at different temperatures over a wide range of strain rates, Materials Science and Engineering: A, 507(1) (2009) 124-131.
[30] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, in:  Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 1983, pp. 541-547.
[31] A.H. Clausen, T. Børvik, O.S. Hopperstad, A. Benallal, Flow and fracture characteristics of aluminium alloy AA5083–H116 as function of strain rate, temperature and triaxiality, Materials Science and Engineering: A, 364(1). 260-272 (2004).
[32] B. Erice, F. Gálvez, D. Cendón, V. Sánchez-Gálvez, Flow and fracture behaviour of FV535 steel at different triaxialities, strain rates and temperatures, Engineering Fracture Mechanics, 79 (2012) 1-17.
[33] M. Jie, Generalized criteria for localized necking in sheet metal forming, 2003.
[34] M. Saradar, A. Basti, M. Zaeimi, Numerical study of the effect of strain rate on damage prediction by dynamic forming limit diagram in high velocity sheet metal forming, Modares Mechanical Engineering, 14(16) (2015.( (in persian)
[35] W. Hosford, A generalized isotropic yield criterion, Journal of Applied Mechanics, 39(2) (1972) 607-609.
[36] H.-Y. Wu, P.-H. Sun, H.-W. Chen, C.-H. Chiu, Rate and Orientation Dependence of Formability in Fine-Grained AZ31B-O Mg Alloy Thin Sheet, Journal of Materials Engineering and Performance, 21(10) (2012) 2124-2130.
[37] D. Kim, H. Kim, J.H. Kim, M.-G. Lee, K.J. Kim, F. Barlat, Y. Lee, K. Chung, Modeling of forming limit for multilayer sheets based on strain-rate potentials, International Journal of Plasticity, 75(Supplement C) (2015) 63-99.
[38] O.E. Fakir, L. Wang, D. Balint, J.P. Dear, J. Lin, Predicting Effect of Temperature, Strain Rate and Strain Path Changes on Forming Limit of Lightweight Sheet Metal Alloys, Procedia Engineering, 81(Supplement C) (2014) 736-741.
[39] P. Verleysen, J. Peirs, J. Van Slycken, K. Faes, L. Duchene, Effect of strain rate on the forming behaviour of sheet metals, Journal of Materials Processing Technology, 211(8) (2011) 1457-1464.
نشریه مهندسی مکانیک امیرکبیر
دوره 53، شماره 2 (Special Issue)
اردیبهشت 1400
صفحه 1307-1320

فایل ها

هم رسانی

ارجاع به این مقاله

آمار