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Linear Least Square Approach for the Estimation of Crack Tip Fracture Parameters Using Isopachic Data from Thermoelastic Stress Analysis


Thermoelastic stress analysis (TSA) is a nondestructive evaluation tool used for obtaining the stress fields in the vicinity of critical region of the structure. In this work, TSA was used to determine the stress fields around discontinuities like hole and crack in metallic structure and the stress results were post-processed to obtain the stress concentration/stress intensity factor. Initially, experiments were conducted on a mild steel specimen with a hole under tensile cyclic loading and an infrared thermography camera was used to capture the temperature distribution on the surface of the specimen. The stress fields around the hole obtained using TSA were then used to evaluate the stress concentration factor (SCF) and compared with analytical and finite element results. Subsequently, experiments were extended to analyze mild steel specimens with straight and inclined cracks to obtain near-crack-tip stress fields using TSA. A linear least square approach was then used to determine the stress intensity factor (SIF) from the TSA stress results. Finite element modeling of the straight and inclined cracks were done to compute the SIFs. The stress intensity factors calculated from TSA results were then compared with analytical and numerical results. The procedure outlined here establishes an experimental approach based on TSA technique for the accurate determination of SCF/SIF.

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  1. Biot M, J Appl Phys 27 (1956) 240.

    Article  Google Scholar 

  2. Rocca M B R, Trans MME 188 (1950) 327.

    Google Scholar 

  3. Pitarresi G, and Patterson E, J Strain Anal Eng Design 38 (2003) 405.

    Article  Google Scholar 

  4. Dulieu-Barton J M, Quinn S, Eyre C, and Cunningham P, in Applied Mechanics and Materials, Vol. 1, Trans Tech Publication (2004), p 197.

  5. Dulieu-Barton J, Emery T, Quinn S, and Cunningham P, Meas Sci Technol 17 (2006) 1627.

    CAS  Article  Google Scholar 

  6. Fruehmann R, Dulieu-Barton J, Quinn S, Peton-Walter J, and Mousty P, in Journal of Physics: Conference Series, vol. 382, IOP Publishing, (2012), p 012058.

  7. Sathon N, and Dulieu-Barton J, in Fracture of Nano and Engineering Materials and Structures, Springer (2006), p 577.

  8. Quinn S, Dulieu-Barton J, Strain 38 (2002) 105.

    Article  Google Scholar 

  9. Vieira R B, Philip S K, Gonzáles G L G, Freire J L F, Yang B, Rowlands R E, J Mech Eng Autom 6 (2016) 66.

    Google Scholar 

  10. Choi M, Park J, Kim W, Lee S, Kim K, and Kang K, in 9th International Conference on Quantitative Infrared Thermography (2008), p 2.

  11. Howell G, Dulieu-Barton J M, Achintha M, and Robinson A F, in International Conference on Experimental Mechanics 2014, Vol. 9302, International Society for Optics and Photonics (2015), p 93021W.

  12. Tomlinson R, and Olden E, Strain 35 (1999) 49.

    Article  Google Scholar 

  13. Diaz F, Yates J, and Patterson E, Int J Fatigue 26 (2004) 365.

    Article  Google Scholar 

  14. Diaz F A, Francisco A, Patterson, E A and Yates J R, Frattura ed Integrità Strutturale 7 (2013) 109.

    Article  Google Scholar 

  15. Zou L L, in Applied Mechanics and Materials, Vol. 405, Trans Tech Publication (2013), p 3143.

    Article  Google Scholar 

  16. Farahani B V, Tavares P J, Moreira P, Procedia Struct Integrity 2 (2016) 2148.

    Article  Google Scholar 

  17. Atluri S, and Kobayashi A, in Handbook on experimental mechanics, p 1.

  18. Ramesh K, Gupta S, and Kelkar A A, Eng Fract Mech 56 (1997) 25.

    Article  Google Scholar 

  19. Harilal R, Vyasarayani C, and Ramji M, Opt Lasers Eng 75 (2015) 95.

    Article  Google Scholar 

  20. Patil P, Vyasarayani C, and Ramji M, Opt Lasers Eng 93 (2017) 182.

    Article  Google Scholar 

  21. FLIR Systems Inc., Infrared Imaging Software: Altair LI,

  22. Pilkey W D, Pilkey W D, Formulas for stress, strain, and structural matrices, Vol. 107, J. Wiley New York (1994).

    Google Scholar 

  23. Murakami Y, Stress intensity factors handbook, Pergamon Press, U.K (1987).

    Google Scholar 

Download references


This research work was supported by the Ministry of Human Resource Development (MHRD), Government of India.

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Correspondence to Gangadharan Raju.

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Kolanu, N.R., Tripathy, S.K., Raju, G. et al. Linear Least Square Approach for the Estimation of Crack Tip Fracture Parameters Using Isopachic Data from Thermoelastic Stress Analysis. Trans Indian Inst Met 72, 2933–2945 (2019).

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  • Thermoelastic stress analysis
  • Thermography
  • Stress concentration factor
  • Stress intensity factor