Theoretical Analysis of the Temperature and Strain Rate Effects on the Forming Limit Diagram of AA3104

Document Type : Research Article

Authors

1 Ph.D. Student of Mechanical Engineering/ Guilan University

2 Iran University of Science and Technology

3 Department of Mechanical Engineering, Bandar Anzali Branch

Abstract

Forming limit diagram is one of the most applicable methods for prediction of the plastic instability in sheet metal forming in which is very much affected by the influences of strain rate and temperature. In this paper, taking the temperature and strain rate effects into account, the true stress-true strain and forming limit curves of AA3104 aluminum alloy are analytically investigated by considering the Marciniak-Kuckzynski method and Johnson-cook model. The obtained theoretical results based on the Ludwik model are validated with the experimental ones. Furthermore, according to the stress[1]strain curves based on the Ludwik equation, Johnson-Cook coefficients are calculated for sheet metal AA3104. The stress-strain respond and forming limit diagram are produced over a range of strain rates (10-5 to 10-3 S-1) and temperatures (50-400 o C ). The results show that the stress-strain curve decreases with increasing temperature and increases with increasing strain rate. Also the forming limit diagram increases with increasing temperature and decreases with increasing the strain rate. The results exhibit a positive sensitivity of the temperature on the limit strain due to the thermal softening and the negative strain rate sensitivity on the forming limit diagram AA3104 due to the behavior of crystallographic structure of the material.

Keywords

Main Subjects

References

[1] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures  and  pressures,  Engineering  fracture mechanics, 21(1) (1985) 31-48.
[2]  W. Van Haaften, B. Magnin, W. Kool, L. Katgerman, Constitutive  behavior  of  as-cast AA1050, AA3104, and AA5182, Metallurgical and Materials Transactions A, 33(7) (2002) 1971-1980.
[3]  A.S.  Khan,  M.  Baig,  Anisotropic  responses, constitutive  modeling  and  the  effects  of  strain-rate and temperature on the formability of an aluminum alloy, International Journal of Plasticity, 27(4) (2011) 522-538.
[4] J.V.  Laukonis,  A.K.  Ghosh,  Effects  of  strain path  changes  on  the  formability  of  sheet  metals, Metallurgical  Transactions  A,  )21(9  (1978)  -9481 1856.
[5]  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) 789800.
[6] A.K. Ghosh, S.S. Hecker, Failure in thin sheets stretched over rigid punches, Metallurgical Transactions A, 6(5) (1975) 1065-1074.
[7] M.  Gerdooei,  B.  Dariani,  Strain-rate-dependent forming limit diagrams for sheet metals, Proceedings of  the  Institution  of  Mechanical  Engineers,  Part  B: Journal of Engineering Manufacture, 222(12) (2008) .9561-1561
[8] B. Dariani, G. Liaghat, M. Gerdooei, Experimental investigation  of  sheet  metal  formability  under various strain rates, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 223(6) (2009) 703-712.
[9]  M. Jie, C. Cheng, L. Chan, C. Chow, Forming limit diagrams  of  strain-rate-dependent  sheet  metals, International Journal of Mechanical Sciences, 51(4) (2009) 269-275.
[10]   S. Kim, H. Huh, H. Bok, M. 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.
[11]   M. Safari, S. Hosseinipour, H. Azodi, An investigation into the effect of strain rate on forming limit diagram using  ductile  fracture  criteria,  Meccanica,  47(6) (2012) 1391-1399.
[12]   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) 212-222. (in Persian)
[13]  T.C. Cheng, R.S. Lee, The influence of grain size and strain rate effects on formability of aluminium alloy sheet  at  high-speed  forming,  Journal  of  Materials Processing Technology, 253 (2018) 134-159.
[14]   D. Li, A.K. Ghosh, Biaxial warm forming behavior of  aluminum  sheet  alloys,  Journal  of  Materials Processing Technology, 145(3) (2004) 281-293.
[15]   X.-q. Cao, P.-p. Xu, F. Qi, W.-x. Wang, Theoretical prediction  of  forming  limit  diagram  of  AZ31 magnesium  alloy  sheet  at  warm  temperatures, Transactions of Nonferrous Metals Society of China, 26(9) (2016) 2426-2432.
[16]  J. Zhou, Y. Mu, B. Wang, A damage-coupled unified viscoplastic  constitutive  model  for  prediction  of forming  limits  of  22MnB5  at  high  temperatures, International  Journal  of  Mechanical  Sciences,  133 (2017) 457-468.
[17]   T. Naka, G. Torikai, R. Hino, F. Yoshida, The effects of temperature and forming speed on the forming limit diagram  for  type  5083  aluminum–magnesium  alloy sheet,  Journal  of  Materials  Processing  Technology, 113(1-3) (2001) 648-653.
[18]  X.  Chu,  L.  Leotoing,  D.  Guines,  E.  Ragneau, Temperature  and  strain  rate  influence  on  AA5086 Forming  Limit  Curves:  Experimental  results and  discussion  on  the  validity  of  the  MK  model, International  Journal  of  Mechanical  Sciences,  78 (2014) 27-34.
[19]  O. El 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 (2014) 736741.
[20]  C.  Zhang,  X.  Chu,  D.  Guines,  L.  Leotoing,  J. Ding, G. Zhao, Dedicated linear–Voce model and its application  in  investigating  temperature  and  strain rate effects on sheet formability of aluminum alloys, Materials & Design, 67 (2015) 522-530.
[21]   Z.  Marciniak,  K.  Kuczyński,  Limit  strains  in  the processes of stretch-forming sheet metal, International journal of mechanical sciences, 9(9) (1967) 609-620.
[22]    J.  Hutchinson,  K.  Neale,  Sheet  necking-II.  Timeindependent behavior, in:  Mechanics of sheet metal forming, Springer, 1978, pp. 127-153.
[23]    J. Hutchinson, K. Neale, Sheet necking-III. Strainrate effects, in:  Mechanics of sheet metal forming, Springer, 1978, pp. 269-285.
[24]    J.  Hutchinson,  K.  Neale,  A.  Needleman,  Sheet necking—I. Validity  of  plane  stress  assumptions  of the long-wavelength approximation, in:  Mechanics of sheet metal forming, Springer, 1978, pp. 111-126.
[25]    R.  Sowerby,  J.  Duncan,  Failure  in  sheet  metal  in biaxial tension, International Journal of Mechanical Sciences, 13(3) (1971) 217-229.
[26]    M. Ganjiani, A. Assempour, An improved analytical approach for determination of forming limit diagrams considering the effects of yield functions, Journal of materials  processing  technology,  )3-1(281  (2007) .706-895.
[27]    A.B. Da Rocha, F. Barlat, J. Jalinier, Prediction of the  forming  limit  diagrams  of  anisotropic  sheets  in linear and non-linear loading, Materials science and engineering, 68(2) (1985) 151-164.
[28]    R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond. A, 193(1033) (1948) 281-297.
[29]    S.M.  Mirfalah  Nasiri,  A.  Basti,  R.  Hashemi, Numerical  analysis  of  the  effect  of  advanced  yield criterion  on  prediction  of  strains  and  stresses  in anisotropic  aluminum  sheets,  Modares  Mechanical Engineering, 15(8) (2015) 393-401. (in Persian)
[30]    H. Aretz, F. Barlat, New convex yield functions for orthotropic metal plasticity, International Journal of non-linear mechanics, 51 (2013) 97-111.
[31]    C.  Zhang,  L.  Leotoing,  D.  Guines,  E.  Ragneau, Theoretical  and  numerical  study  of  strain  rate influence on AA5083 formability, Journal of materials processing technology, 209(8) (2009) 3849-3858.
[32]    P. Wu, M. Jain, J. Savoie, S. MacEwen, P. Tuğcu, K. Neale, Evaluation of anisotropic yield functions for aluminum sheets, International Journal of Plasticity, 19(1) (2003) 121-138.
[33]    F. Stachowicz, Effect of annealing temperature on plastic flow properties and forming limit diagrams of titanium and titanium alloy sheets, Transactions of the Japan institute of metals, 29(6) (1988) 484-493.
[34]   S.C.  Soare,  Theoretical  considerations  upon  the MK  model  for  limit  strains  prediction:  The  plane strain case, strain-rate effects, yield surface influence, and  material  heterogeneity,  European  Journal  of Mechanics-A/Solids, 29(6) (2010) 938-950.
 
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 3
June 2020
Pages 555-570

Files

Share

How to cite

Statistics