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Virtual Field Characterization for Ratcheting Effect Under Cyclic Loading

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Abstract

Background

Ratcheting is an important mechanical behavior of metals and alloys, which is caused by the repeated accumulations of tensile and compressive strain in circle load. However, the current characterization methods of ratcheting effect are mostly based on standardized testing and uniform data, and more comprehensive field measurement data cannot be used.

Objective

This paper focuses on how to make full use of field measurement data to characterize ratcheting effect and identify the corresponding kinematic constitutive.

Methods

A nonlinear virtual field method that can invert the parameters of Chaboche constitutive from strain field data is proposed. And a return mapping strategy driven by iteration of internal variables is used to reconstruct the stress field, which ensures the convergence speed and global convergence in the black box search of the nonlinear virtual field method.

Results

By using the finite-element model to generate the strain field data, the numerical experiment shows that the ratchet path identified by the nonlinear virtual field algorithm is basically consistent with the prior ratchet path generated by the finite-element simulation. The adaptability of the algorithm to data density and noise amplitude was also verified: under lower data noise interference, more strain field training data makes the inversion results more accurate; but in the case of high sound amplitude, it is necessary to reduce the data size to obtain accurate fitting results of the ratchet path.

Conclusions

By training the measured field data from 3D-digital image correlation, it is shown that the algorithm can also run effectively under the complex working conditions of non-uniform deformation.

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References

  1. Prager W (1956) A new method of analyzing stresses and strains in work-hardening plastic solids. ASME J Appl Mech 23:493–496

    Article  MathSciNet  Google Scholar 

  2. Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plas 2(2):149–188

    Article  Google Scholar 

  3. Kullig E, Wippler S (2006) Numerical integration and FEM-implementation of a viscoplastic Chaboche-model with static recovery. Comput Mech 38(6):1–13

    Article  Google Scholar 

  4. Gallerneau F, Chaboche JL (1999) Fatigue life prediction of single crystals for turbine blade applications. Int J Damage Mech 8(4):404–427

    Article  Google Scholar 

  5. Hopperstad OS, Remseth S (2010) A return mapping algorithm for a class of cyclic plasticity models. Int J Numer Meth Eng 38(4):549–564

    Article  Google Scholar 

  6. Taherizadeh A, Green DE, Yoon JW (2013) Anisotropic hardening model based on non-associated flow rule and combined nonlinear kinematic hardening for sheet materials. Numisheet: the International Conference and Workshop on Numerical Simulation of 3d Sheet Metal Forming Processes. Am Inst Phys 496–499

  7. Meng C, Tang Z, Chen M et al (2018) Return mapping algorithm in principal space for general isotropic elastoplasticity involving multi-surface plasticity and combined isotropic-kinematic hardening within finite deformation framework. Finite Elem Anal Des 150:1–19

    Article  MathSciNet  Google Scholar 

  8. Badnava H, Pezeshki SM, Fallah NK et al (2012) Determination of combined hardening material parameters under strain controlled cyclic loading by using the genetic algorithm method. J Mech Sci Technol 26(10):3067–3072

    Article  Google Scholar 

  9. Mancini E, Isidori D, Sasso M et al (2017) Characterization of the cyclic-plastic behaviour of flexible structures by applying the Chaboche model. Arch Civ Mech Eng 17(4):761–775

    Article  Google Scholar 

  10. Jiang JP, Chen T, Jin P et al (2014) Parameter determination of Chaboche kinematic hardening models and ratcheting simulation. J Beijing Univ Aeronaut Astronaut 40(10):1430–1435

    Google Scholar 

  11. Savic V Jr, LGH, Fekete JR. (2010) Digital image correlation study of plastic deformation and fracture in fully martensitic steels. Exp Mech 50(1):99–110

    Article  Google Scholar 

  12. Gioacchino FD, Fonseca JQD (2013) Plastic strain mapping with sub-micron resolution using digital image correlation. Exp Mech 53(5):743–754

    Article  Google Scholar 

  13. Gao LL, Qin XY, Zhang CQ et al (2015) Ratcheting behavior of articular cartilage under cyclic unconfined compression. Mater Sci Eng C 57:371–377

    Article  Google Scholar 

  14. Tang J, Chen X, Dai F, Wei F (2020) Experimental investigation of fracture damage of notched granite beams under cyclic loading using DIC and AE techniques. Fatigue Fract Eng Mater Struct. https://doi.org/10.1111/ffe.13253

    Article  Google Scholar 

  15. Venkatachalam S, Mohiddin SMK, Murthy H (2018) Determination of damage evolution in CFRP subjected to cyclic loading using DIC. Fatigue Fract Eng Mater Struct 41(6):1412–1425

    Article  Google Scholar 

  16. Tong J, Lina B, Lu YW (2015) Near-tip strain evolution under cyclic loading: In situ experimental observation and numerical modelling. Int J Fatigue 71:45–52

    Article  Google Scholar 

  17. Eric B, Besel M (2017) Energy based analysis of crack tip plastic zone of AA2024-T3 under cyclic loading. Int J Fatigue 100(PT. 1):263–273

    Google Scholar 

  18. Broggiato G, Campana F, Cortese L et al (2012) Comparison between two experimental procedures for cyclic plastic characterization of high strength steel sheets. J Eng Mater Technol 134:255–263

    Article  Google Scholar 

  19. Campana F, Cortese L, Placidi F (2005) FEM evaluation of spring back after sheet metal forming: application to high strength steels of a combined isotropic-kinematic hardening model. 1st International Conference on Super High Strength Steels

  20. Grédiac M (1989) Principe Des Travaux Virtuels et Identification. Comptes Rendus de l'Académie des Sciences 309(1):1–5

  21. Avril S, Pierron F, Pannier Y, Rotinat R (2008) Stress reconstruction and constitutive parameter identification in plane-stress elasto-plastic problems using surface measurements of deformation fields. Exp Mech 48(4):403–419

    Article  Google Scholar 

  22. Pierron F, Grédiac M (2012) The Virtual Fields Method. Berlin: Springer 59(10):107–120

    MATH  Google Scholar 

  23. Pierron F, Avril S, Tran VT (2010) Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening. Int J Solids Struct 47(22–23):2993–3010

    Article  Google Scholar 

  24. Bai RX, Jiang H, Lei ZK et al (2018) Virtual field method for identifying elastic-plastic constitutive parameters of aluminum alloy laser welding considering kinematic hardening. Opt Lasers Eng 110:122–131

    Article  Google Scholar 

  25. Notta-Cuvier D, Langrand B, Lauro F et al (2015) An innovative procedure for characterising a coupled elastoplastic damage model of behaviour using the virtual fields method. Int J Solids Struct 69–70:415–427

    Article  Google Scholar 

  26. Jiang H, Lei ZK, Bai RX et al (2020) Identifying elasto-plastic damage coupling model of laser-welded aluminum alloy by virtual field method and digital image correlation. Opt Laser Technol 129:106268

  27. Simo JC, Hughes TJR (2008) Computational Inelasticity. Springer, New York, pp 126–132

    MATH  Google Scholar 

  28. Yuan YX, Sun WY (1997) Optimization theory and methods. Science Press, Beijing

    Google Scholar 

  29. Feng Z, Rowlands RE (1991) Smoothing finite-element and experimental hybrid technique for stress analyzing composites. Comput Struct 6:631–639

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank the National Natural Science Foundation of China (Nos. 12002078, 11772081, 11972106).

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Correspondence to Z. Lei or R. Bai.

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Jiang, H., Lei, Z., Bai, R. et al. Virtual Field Characterization for Ratcheting Effect Under Cyclic Loading. Exp Mech 61, 867–883 (2021). https://doi.org/10.1007/s11340-021-00709-6

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  • DOI: https://doi.org/10.1007/s11340-021-00709-6

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