High-Temperature Fracture Mechanics Parameter Measurement and Yielding Zone Analysis of Superalloy GH4169 Based on Single-Lens 3D Digital Image Correlation


Fracture mechanics parameters are crucial for evaluating the failure of a material; furthermore, the yielding zone near the crack tip is closely related to the ultimate bearing capacity. How to characterize these parameters has drawn a lot of attention from mechanics researchers. Currently, the digital image correlation (DIC) method, due to its advantage of being able to perform full-field, non-contact measurements, has great potential for application in the measurement of the mentioned parameters. In this paper, a bi-prism-based single lens (BSL) 3D DIC technique was utilized to determine the fracture mechanics parameters and the yielding zone size of the Ni-based superalloy GH4169 at room temperature and 650 °C. In the measurement, the displacement fields of single-edge cracked specimens under a uniaxial tensile load were measured using the BSL 3D DIC system. And then, the J integral and stress intensity factor K at room and high temperature were calculated from the displacement fields. Finally, the J integral calculated using the path integral method (J _ 1) and the J integral converted from the stress intensity factor K (J _ 2) were used to evaluate the yielding condition near the crack tip Yoneyama et al. (Strain 50(2):147–160, 2014), while a specific value was also determined as the critical small-scale yielding load from the variations of J _ 1 and J _ 2. Additionally, the relationship between the yielding zone size rp, calculated from K and the value ∆J = J _ 2 − J _ 1 was established, which was found to be linear. On the rp − ∆J curve, the intercept on the rp axis could be regarded as the critical size of small-scale yielding zone.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Jafarian F, Umbrello D et al (2014) Finite element simulation of machining Inconel 718 alloy including microstructure changes[J]. Int J Mech Sci 88:110–121

    Article  Google Scholar 

  2. 2.

    Yoneyama S, Arikawa S, Kusayanagi S (2014) Evaluating J-integral from displacement fields measured by digital image correlation[J]. Strain 50(2):147–160

    Article  Google Scholar 

  3. 3.

    Abshirini M, Dehnavi MY, Beni MA, Soltani N (2014) Interaction of two parallel U-notches with tip cracks in PMMA plates under tension using digital image correlation[J]. Theor Appl Fract Mech 70:75–82

    Article  Google Scholar 

  4. 4.

    Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks[J]. J Appl Mech 35(2):379–386

    Article  Google Scholar 

  5. 5.

    Becker TH, Mostafavi M, Tait RB et al (2012) An approach to calculate the J -integral by digital image correlation displacement field measurement[J]. Fatigue Fract Eng Mater Struct 35(10):971–984

    Article  Google Scholar 

  6. 6.

    Mcneill SR, Peters WH, Sutton MA (1987) Estimation of stress intensity factor by digital image correlation[J]. Eng Fract Mech 28(1):101–112

    Article  Google Scholar 

  7. 7.

    Peters WH, Ranson WF (1982) Digital imaging techniques in experimental stress analysis[M]. Environmental jurisprudence in India. Kluwer Law International, pp 427–431

  8. 8.

    Pan B, Qian KM, Xie HM, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001

    Article  Google Scholar 

  9. 9.

    Luo PF, Chao YJ, Sutton MA, Peters WH III (1993) Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision[J]. Exp Mech 33(2):123–132

    Article  Google Scholar 

  10. 10.

    Sutton MA (2008) Digital image correlation for shape and deformation measurements[M]. Springer US, pp 565–600

  11. 11.

    Yoneyama S, Morimoto Y, Takashi M (2006) Automatic evaluation of mixed-mode stress intensity factors utilizing digital image correlation[J]. Strain 42(1):21–29

    Article  Google Scholar 

  12. 12.

    Rabbolini S, Pataky GJ, Sehitoglu H, Beretta S (2015) Fatigue crack growth in Haynes 230 single crystals: an analysis with digital image correlation[J]. Fatigue Fract Eng Mater Struct 38(5):583–596

    Article  Google Scholar 

  13. 13.

    Gonzáles GLG, González JAO, Castro JTP, Freire JLF (2017) A J-integral approach using digital image correlation for evaluating stress intensity factors in fatigue cracks with closure effects[J]. Theor Appl Fract Mech 90:14–21

    Article  Google Scholar 

  14. 14.

    Breitbarth E, Besel M (2017) Energy based analysis of crack tip plastic zone of AA2024-T3 under cyclic loading[J]. Int J Fatigue 100:263–273

    Article  Google Scholar 

  15. 15.

    Wu L, Zhu J, Xie H, Zhou M (2016) Single-lens 3D digital image correlation system based on a bilateral telecentric lens and a bi-prism: systematic error analysis and correction[J]. Opt Lasers Eng 87:129–138

    Article  Google Scholar 

  16. 16.

    Wu LF, Zhu JG, Xie HM et al (2016) An accurate method for shape retrieval and displacement measurement using bi-prism-based single Lens 3D digital image correlation[J]. Exp Mech 56(9):1–14

    Article  Google Scholar 

  17. 17.

    Xie H, Zhu J, Wu L (2015) Single-lens 3D digital image correlation system based on a bilateral telecentric lens and a bi-prism: validation and application[J]. Appl Opt 54(26):7842–7850

    Article  Google Scholar 

  18. 18.

    Wu L, Zhu J, Xie H (2014) A modified virtual point model of the 3D DIC technique using a single camera and a bi-prism[J]. Meas Sci Technol 25(11):115008

    Article  Google Scholar 

  19. 19.

    Wu LF, Yin YJ, Zhang Q et al (2017) Bi-prism-based single-lens three dimensional digital image correlation system with a long working distance: methodology and application in extreme high temperature deformation test[J]. SCIENCE CHINA Technol Sci:1–14

  20. 20.

    Abanto-Bueno J, Lambros J (2002) Investigation of crack growth in functionally graded materials using digital image correlation[J]. Eng Fract Mech 69(14–16):1695–1711

    Article  Google Scholar 

  21. 21.

    Yates JR, Zanganeh M, Tai YH (2010) Quantifying crack tip displacement fields with DIC[J]. Eng Fract Mech 77(11):2063–2076

    Article  Google Scholar 

  22. 22.

    Irwin G (1960) Plastic zone near a crack tip and fracture toughness. In: Proceedings of the seventh Sagamore ordnance material conference, pp 63–78

  23. 23.

    Kujawski D (2010) Estimations of stress intensity factors for small cracks at notches[J]. Fatigue Fract Eng Mater Struct 14(10):953–965

    Article  Google Scholar 

Download references


This research as financially supported the National Natural Science Foundation of China (Grant Nos. 11672153, 11232008).

Author information



Corresponding author

Correspondence to H. Xie.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yin, Y., Wu, L., Li, J. et al. High-Temperature Fracture Mechanics Parameter Measurement and Yielding Zone Analysis of Superalloy GH4169 Based on Single-Lens 3D Digital Image Correlation. Exp Mech 59, 953–962 (2019). https://doi.org/10.1007/s11340-019-00490-7

Download citation


  • Single-lens 3D digital image correlation
  • J integral
  • Stress intensity factor
  • Yielding zone