Theories and experiments on effects of acoustic energy field in micro-square cup drawing

  • Chang-Li ZhaEmail author
  • Wei Chen


A vibration-assisted uniaxial tension experimental setup was designed to study the stress-strain relationship induced by ultrasonic excitation, and an acoustic-plastic constitutive model was developed and calibrated based on dislocation density evolution under experimental data. Also a prediction model for the drawing height of micro-square cups in vibration-assisted plastic deformation was investigated based on the dangerous section stress theory and the acoustic-plastic constitutive model. The prediction model was validated by designing a finite element model and an experimental deep drawing system under various working conditions, in which 200-μm-thick stainless steel 304 was excited by ultrasonic vibration at frequency 19.891 kHz and different amplitudes. It was found the predicted drawing height of micro-square cups agreed well with the experimental results, indicating the prediction model was able to accurately predict the drawing height of micro-square cups during vibration-assisted metal micro-forming.


Ultrasonic vibration Acoustic softening and stress superposition Micro-square cup Prediction model 


Funding information

This work was financially supported by the National Science Foundation of China (Grant No.51875263) and the Natural Science Foundation of Educational Commission of Anhui Province of China (Grant No. KJ2019A0576).


  1. 1.
    Blaha F, Langenecker B (1955) Tensile deformation of zinc crystal under ultrasonic vibration. Sci Nat 42(20):556CrossRefGoogle Scholar
  2. 2.
    Langenecker B (1966) Effects of ultrasound on deformation characteristics of metals. IEEE Trans Sonics Ultrasonics 13(1):1–8CrossRefGoogle Scholar
  3. 3.
    Dawson GR, Winsper CE, Sansome DH (1970) Application of high-frequency and low frequency oscillations to plastic deformation of metals: part 2 - a complete appraisal of the development and potential. Met Form 37:254–261Google Scholar
  4. 4.
    Huang Y, Wu Y, Huang J (2014) The influence of ultrasonic vibration-assisted micro-deep drawing process. Int J Adv Manuf Technol 71(5–8):1455–1461CrossRefGoogle Scholar
  5. 5.
    Mostafapur A, Ahangar S, Dadkhah R (2013) Numerical and experimental investigation of pulsating blankholder effect on drawing of cylindrical part of aluminum alloy in deep drawing process. Int J Adv Manuf Technol 69(5–8):1113–1121CrossRefGoogle Scholar
  6. 6.
    Bai Y, Yang M (2013) Investigation on mechanism of metal foil surface finishing with vibration-assisted micro-forging. J Mater Process Technol 213(3):330–336CrossRefGoogle Scholar
  7. 7.
    Kim GD, Loh BG (2010) Machining of micro-channels and pyramid patterns using elliptical vibration cutting. Int J Adv Manuf Technol 49(9–12):961–968CrossRefGoogle Scholar
  8. 8.
    Liu K, Li XP, Rahman M, Liu XD (2004) Study of ductile mode cutting in grooving of tungsten carbide with and without ultrasonic vibration assistance. Int J Adv Manuf Technol 24(5–6):389–394CrossRefGoogle Scholar
  9. 9.
    Bagherzadeh S, Abrinia K (2015) Effect of ultrasonic vibration on compression behavior and microstructural characteristics of commercially pure aluminum[J]. J Mater Eng Perform 24(11):4364–4376CrossRefGoogle Scholar
  10. 10.
    Lou Y, Liu X, He J (2017) Ultrasonic-assisted extrusion of ZK60Mg alloy micropins at room temperature. Ultrasonics 83:194–202CrossRefGoogle Scholar
  11. 11.
    Izumi O, Oyama K, Suzuki Y (1966) Effects of superimposed ultrasonic vibration on compressive deformation of metals. Trans Jpn Inst Metals 7(3):162–167CrossRefGoogle Scholar
  12. 12.
    Ohgaku T, Takeuchi N (1987) The Blaha effect of alkali halide crystals. Phys Status Solidi A 102(1):293–299CrossRefGoogle Scholar
  13. 13.
    Malygin GA (2000) Acoustoplastic effect and the stress superimposition mechanism. Phys Solid State 42(1):72–78CrossRefGoogle Scholar
  14. 14.
    Daud Y, Lucas M, Huang Z (2007) Modelling the effects of superimposed ultrasonic vibrations on tension and compression tests of aluminium. J Mater Process Technol 186(1):179–190CrossRefGoogle Scholar
  15. 15.
    Liu Y, Suslov S, Han Q (2012) Microstructure of the pure copper produced by upsetting with ultrasonic vibration. Mater Lett 67(1):52–55CrossRefGoogle Scholar
  16. 16.
    Ahmadi F, Farzin M, Mandegari M (2015) Effect of grain size on ultrasonic softening of pure aluminum. Ultrasonics 63:111–117CrossRefGoogle Scholar
  17. 17.
    Yao Z, Kima GY, Faidley LA (2012) Acoustic softening and residual hardening in aluminum: modeling and experiments. Int J Plast 39(39):75–87CrossRefGoogle Scholar
  18. 18.
    Yao Z, Mei D, Chen Z (2016) Modeling of metallic surface topography modification by high-frequency vibration. J Sound Vib 363:258–271CrossRefGoogle Scholar
  19. 19.
    Bunget C, Ngaile G (2011) Influence of ultrasonic vibration on micro-extrusion. Ultrasonics 51(5):606–616CrossRefGoogle Scholar
  20. 20.
    Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324Google Scholar
  21. 21.
    Frost HJ, Ashby MF (1982) Deformation-mechanism maps : the plasticity and creep of metals and ceramics. Pergamon, OxfordGoogle Scholar
  22. 22.
    Wang CJ, Liu Y, Guo B (2016) Acoustic softening and stress superposition in ultrasonic vibration assisted uniaxial tension of copper foil: experiments and modeling. Mater Des 112:246–253CrossRefGoogle Scholar
  23. 23.
    Barlat F, Glazov MV, Brem JC, Lege DJ (2002) A simple model for dislocation behavior, strain and strain rate hardening evolution in deforming aluminum alloys. Int J Plast 18(7):919–939CrossRefGoogle Scholar
  24. 24.
    Kocks UF (1987) Constitutive behavior based on crystal plasticity. Springer, NetherlandsCrossRefGoogle Scholar
  25. 25.
    Palmer BS (1972) Ultrasonics: methods and applications. Phys Bull 23(4):223–223CrossRefGoogle Scholar
  26. 26.
    Jiang KH, Yang YG (2011) Stamping technology and die design, BeijingGoogle Scholar
  27. 27.
    Ledbetter HM (1981) Stainless-steel elastic constants at low temperatures. J Appl Phys 52(3):1587–1589CrossRefGoogle Scholar
  28. 28.
    Siddiq A, Sayed TE (2012) A thermomechanical crystal plasticity constitutive model for ultrasonic consolidation. Comput Mater Sci 51(1):241–251CrossRefGoogle Scholar
  29. 29.
    Yao Z, Kim GY, Faidley LA, Zou Q, Mei D, Chen Z (2012) Effects of superimposed high-frequency vibration on deformation of aluminum in micro/meso-scale upsetting. J Mater Process Technol 212(3):640–646CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringJiangsu UniversityZhenjiangChina
  2. 2.School of Physics and Electronic EngineeringAnqing Normal UniversityAnqingChina

Personalised recommendations