Development of similarity-based scaling criteria for creep age forming of large/extra-large panels


A scaling method is developed for the creep age forming (CAF) process to downscale manufacturing of large/extra-large panels to lab-scale experimental trials for industrial application. Similarity theory is applied to identify both the geometrical and physical (non-geometrical) similarities between large-size prototypes and scaled-down models in all process stages of CAF, including loading, stress-relaxation and unloading (springback). A constitutive model is incorporated into the theory in order to identify the similarity in the highly non-linear stress-relaxation behaviour for aluminium alloy plates during CAF, and to obtain the effective scaling criteria for the CAFed plates after springback. The method was demonstrated by scaling down CAF manufacturing of both singly curved and doubly curved large plates under both proportional and non-proportional geometrical scaling conditions. The analytical results of the scaling method and numerical results obtained by CAF FE modelling were found to be in good agreement. Scaling diagrams linking the key deformation (springback) and structural (flexural rigidity) variables to scaling ratios under both proportional and non-proportional conditions were generated, and the developed scaling diagrams have been validated by corresponding CAF experiments. The scaling method developed in this study provides guidance on the design of scaled-down CAF experimental trials and will be used in the practical CAF process of large/extra-large panels.


  1. 1.

    Zhan L, Lin J, Dean T (2011) A review of the development of creep age forming: experimentation, modelling and applications. Int J Mach Tools Manuf 51(1):1–17

    Article  Google Scholar 

  2. 2.

    Yang Y, Zhan L, Shen R, Liu J, Li X, Huang M, He D, Chang Z, Ma Y, Wan L (2018) Investigation on the creep-age forming of an integrally-stiffened AA2219 alloy plate: experiment and modeling. Int J Adv Manuf Technol 95(5–8):2015–2025

    Article  Google Scholar 

  3. 3.

    Holman MC (1989) Autoclave age forming large aluminum aircraft panels. J Mech Work Technol 20:477–488

    Article  Google Scholar 

  4. 4.

    Brandão F, Delijaicov S, Bortolussi R (2017) CAF—a simplified approach to calculate springback in Al 7050 alloys. Int J Adv Manuf Technol 91(9–12):3273–3284

    Article  Google Scholar 

  5. 5.

    Zhang J, Deng Y, Zhang X (2013) Constitutive modeling for creep age forming of heat-treatable strengthening aluminum alloys containing plate or rod shaped precipitates. Mater Sci Eng A 563:8–15

    Article  Google Scholar 

  6. 6.

    Li Y, Shi Z, Lin J, Yang Y-L, Rong Q, Huang B-M, Chung T-F, Tsao C-S, Yang J-R, Balint DS (2017) A unified constitutive model for asymmetric tension and compression creep-ageing behaviour of naturally aged Al-Cu-Li alloy. Int J Plast 89:130–149

    Article  Google Scholar 

  7. 7.

    Rong Q, Shi Z, Li X, Sun X, Li Y, Yang Y-L, Meng L, Lin J (2017) Experimental studies and constitutive modelling of AA6082 in stress-relaxation age forming conditions. Procedia Eng 207:293–298

    Article  Google Scholar 

  8. 8.

    Lam AC, Shi Z, Lin J, Huang X (2015) Influences of residual stresses and initial distortion on springback prediction of 7B04-T651 aluminium plates in creep-age forming. Int J Mech Sci 103:115–126

    Article  Google Scholar 

  9. 9.

    Lin J, Ho K, Dean T (2006) An integrated process for modelling of precipitation hardening and springback in creep age-forming. Int J Mach Tools Manuf 46(11):1266–1270

    Article  Google Scholar 

  10. 10.

    Bonnafé J, Destandau C, Fougeras J (1996) Age creep forming process modeling and experimentation in aluminium alloys—validation on Ariane 5 main tank bulkhead segments. Proceedings of the 4th European Conference on Residual Stresses (ECRS4), Cluny France

  11. 11.

    Levers A (2003) Jumbo processes. Manuf Eng 82(3):42–45

    Article  Google Scholar 

  12. 12.

    Marcon A, Melkote SN, Yoda M (2018) Effect of nozzle size scaling in co-flow water cavitation jet peening. J Manuf Process 31:372–381

    Article  Google Scholar 

  13. 13.

    Zohuri B (2015) Dimensional analysis and self-similarity methods for engineers and scientists. Springer, Switzerland

    Google Scholar 

  14. 14.

    Yarin L (2012) The Pi-theorem: applications to fluid mechanics and heat and mass transfer, vol 1. Springer Science & Business Media, Berlin

    Google Scholar 

  15. 15.

    Vollertsen F, Hu Z, Niehoff HS, Theiler C (2004) State of the art in micro forming and investigations into micro deep drawing. J Mater Process Technol 151(1):70–79

    Article  Google Scholar 

  16. 16.

    Pertence A, Cetlin P (2000) Similarity of ductility between model and real materials. J Mater Process Technol 103(3):434–438

    Article  Google Scholar 

  17. 17.

    García-Rodríguez S, Alba-Baena N, Rudolph N, Wellekoetter J, Li X, Osswald T (2012) Dimensional analysis and scaling in mechanical mixing for fabrication of metal matrix nanocomposites. J Manuf Process 14(3):388–392

    Article  Google Scholar 

  18. 18.

    García-Rodríguez S, Puentes J, Li X, Osswald T (2014) Prediction of vortex height from mechanical mixing in metal matrix nanocomposite processing by means of dimensional analysis and scaling. J Manuf Process 16(2):212–217

    Article  Google Scholar 

  19. 19.

    Storåkers B, Biwa S, Larsson P-L (1997) Similarity analysis of inelastic contact. Int J Solids Struct 34(24):3061–3083

    MathSciNet  Article  MATH  Google Scholar 

  20. 20.

    Pawelski O (1992) Ways and limits of the theory of similarity in application to problems of physics and metal forming. J Mater Process Technol 34(1–4):19–30

    Article  Google Scholar 

  21. 21.

    Jeswiet J, Geiger M, Engel U, Kleiner M, Schikorra M, Duflou J, Neugebauer R, Bariani P, Bruschi S (2008) Metal forming progress since 2000. CIRP J Manuf Sci Technol 1(1):2–17

    Article  Google Scholar 

  22. 22.

    Shahri HRF, Mahdavinejad R (2018) A novel method towards approximation of the temperature distribution in electric discharge machining of Ti-6Al-4V by up-scaling approach. Int J Adv Manuf Technol 96(1–4):503–520

    Article  Google Scholar 

  23. 23.

    Davey K, Darvizeh R, Al-Tamimi A (2017) Scaled metal forming experiments: a transport equation approach. Int J Solids Struct 125:184–205

    Article  Google Scholar 

  24. 24.

    Moghaddam M, Darvizeh R, Davey K, Darvizeh A (2018) Scaling of the powder compaction process. Int J Solids Struct 144-145:192–212

    Article  Google Scholar 

  25. 25.

    Guines D, Gavrus A, Ragneau E (2008) Numerical modeling of integrally stiffened structures forming from creep age forming technique. Int J Mater Form 1(1):1071–1074

    Article  Google Scholar 

  26. 26.

    Zhan L, Lin J, Dean TA, Huang M (2011) Experimental studies and constitutive modelling of the hardening of aluminium alloy 7055 under creep age forming conditions. Int J Mech Sci 53(8):595–605

    Article  Google Scholar 

  27. 27.

    Barenblatt GI (2003) Scaling, vol 34. Cambridge University Press, Cambridge

    Google Scholar 

  28. 28.

    Tan Q-M (2011) Dimensional analysis: with case studies in mechanics. Springer Science & Business Media, Berlin

    Google Scholar 

  29. 29.

    Anders D, Münker T, Artel J, Weinberg K (2012) A dimensional analysis of front-end bending in plate rolling applications. J Mater Process Technol 212(6):1387–1398

    Article  Google Scholar 

  30. 30.

    Landau L, Lifshitz E (1986) Theory of elasticity, 3rd edn. Pergamon Press, Oxford

    Google Scholar 

  31. 31.

    Li Y, Shi Z, Lin J, Yang Y-L, Saillard P, Said R (2018) FE simulation of asymmetric creep-ageing behaviour of AA2050 and its application to creep age forming. Int J Mech Sci 140:228–240

    Article  Google Scholar 

  32. 32.

    Lifshitz EM, Kosevich AM, Pitaevskii LP (1986) Chapter II—the equilibrium of rods and plates. In: Theory of elasticity, 3rd edn. Butterworth-Heinemann, Oxford, pp 38–86

    Google Scholar 

  33. 33.

    Jeunechamps P-P, Ho K, Lin J, Ponthot J-P, Dean T (2006) A closed form technique to predict springback in creep age-forming. Int J Mech Sci 48(6):621–629

    Article  MATH  Google Scholar 

  34. 34.

    Timoshenko SP, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-hill, New York

    Google Scholar 

  35. 35.

    Lam AC, Shi Z, Lin J, Huang X, Zeng Y, Dean TA (2015) A method for designing lightweight and flexible creep-age forming tools using mechanical splines and sparse controlling points. Int J Adv Manuf Technol 80(1–4):361–372

    Article  Google Scholar 

  36. 36.

    Xu Y, Zhan L, Huang M, Shen R, Ma Z, Xu L, Wang K, Wang X (2018) Deformation behavior of Al-cu-mg alloy during non-isothermal creep age forming process. J Mater Process Technol 255:26–34

    Article  Google Scholar 

Download references


Much appreciated is the strong support received from CRRC Qingdao Sifang Co., Ltd. The research was performed at the CRRC Sifang-Imperial Centre for Rail Transportation Manufacturing Technologies at Imperial College London.

Author information



Corresponding author

Correspondence to Zhutao Shao.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Shao, Z., Rong, Q. et al. Development of similarity-based scaling criteria for creep age forming of large/extra-large panels. Int J Adv Manuf Technol 101, 1537–1551 (2019).

Download citation


  • Sheet metal forming
  • Creep age forming
  • Similarity theory
  • Scaling criteria
  • Extra-large panel
  • Dimensional analysis