Experimental and theoretical characterization of mixed mode brittle failure from square holes

Abstract

Mixed mode crack initiation in PMMA specimens containing square holes is investigated experimentally by uniaxial tensile tests. The crack deflection with respect to the V-notch bisector and the failure load both increase for decreasing hole sizes, to which correspond higher mode mixities. In order to catch this behavior from a theoretical point of view, Finite Fracture Mechanics (FFM) approach is employed numerically through a full finite element analysis. The FFM implementation requires only two material parameters, namely the strength and the fracture toughness. They are identified through the comparison between failure load predictions and experimental measurements on circular holes with different diameters. The resulting FFM blind predictions on square holes are in good agreement with recorded data. Finally, FFM is implemented through an asymptotic matching expansion procedure and an excellent matching with the previous simulations is found.

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References

  1. Ayatollahi MR, Aliha MRM (2009) Analysis of a new specimen for mixed mode fracture tests on brittle materials. Eng Fract Mech 76:1563–1573

    Article  Google Scholar 

  2. Ayatollahi MR, Torabi AR, Bahrami B (2016) On the necessity of using critical distance model in mixed mode brittle fracture prediction of V-notched Brazilian disk specimens under negative mode I conditions. Theor Appl Fract Mech 84:38–48

    Article  Google Scholar 

  3. Carrère N, Martin E, Leguillon D (2015) Comparison between models based on a coupled criterion for the prediction of the failure of adhesively bonded joints. Eng Fract Mech 138:185–201

    Article  Google Scholar 

  4. Carpinteri A, Cornetti P, Pugno N, Sapora A, Taylor D (2008) A finite fracture mechanics approach to structures with sharp V-notches. Eng Fract Mech 75:1736–1752

    Article  Google Scholar 

  5. Cornetti P, Sapora A, Carpinteri A (2013) Mode mixity and size effect in V-notched structures. Int J Sol Struct 50(10):1562–1582

    Article  Google Scholar 

  6. Doitrand A, Leguillon D (2018a) 3D application of the coupled criterion to crack initiation prediction in epoxy/aluminum bimaterial specimens under four point bending. Int J Sol Struct 143:175–182

    CAS  Article  Google Scholar 

  7. Doitrand A, Leguillon D (2018b) Numerical modeling of the nucleation of facets ahead of a primary crack under mode I+III loading. Int J Fract 213:37–50

    CAS  Article  Google Scholar 

  8. Doitrand A, Fagiano C, Carrère N, Chiaruttini V, Hirsekorn M (2017) Damage onset modeling in woven composites based on a coupled stress and energy criterion. Eng Fract Mech 169:189–200

    Article  Google Scholar 

  9. Doitrand A, Estevez R, Leguillon D (2019) Experimental characterization and numerical modeling of crack initiation in rhombus hole PMMA specimens under compression. Eur J Mech A Solid 76:290–299

    Article  Google Scholar 

  10. Doitrand A, Martin E, Leguillon D (2020a) Numerical implementation of the coupled criterion: matched asymptotic and full finite element approaches. Finite Elem Anal Des 168:103344

    Article  Google Scholar 

  11. Doitrand A, Leguillon D, Estevez R (2020b) Experimental determination of generalized stress intensity factors from full-field measurements. Eng Fract Mech 206:106980

    Article  Google Scholar 

  12. Felger J, Rosendahl PL, Leguillon D, Becker W (2019) Predicting crack patterns at bi-material junctions: a coupled stress and energy approach. Int J Sol Struct 164:191–201

    CAS  Article  Google Scholar 

  13. Gómez FJ, Elices M, Berto F, Lazzarin P (2009) Fracture of V-notched specimens under mixed mode (I + II) loading in brittle materials. Int J Fract 159:121–135

    Article  Google Scholar 

  14. Hashin Z (1996) Finite thermoelastic fracture criterion with application to laminate cracking analysis. J Mech Phys Solids 44(7):1129–1145

    CAS  Article  Google Scholar 

  15. Hills DA, Dini D (2011) Characteristics of the process zone at sharp notch roots. Int J Solids Struct 48:2177–2183

    Article  Google Scholar 

  16. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A Solids 21:61–72

    Article  Google Scholar 

  17. Leguillon D, Sanchez-Palencia E (1987) Computation of singular solutions in elliptic problems and elasticity. Wiley, New York

    Google Scholar 

  18. Martin E, Poitou B, Leguillon D, Gatt JM (2008) Competition between deflection and penetration at an interface in the vicinity of a main crack. Int J Fract 151(2):247–268

    Article  Google Scholar 

  19. Nairn JA (2000) Exact and variational theorems for fracture mechanics of composites with residual stresses, traction-loaded cracks and imperfect interfaces. Int J Fract 105:243–271

    Article  Google Scholar 

  20. Priel E, Bussiba A, Gilad I, Yosibash Z (2007) Mixed mode failure criteria for brittle elastic V-notched structure. Int J Fract 144:247–265

    CAS  Article  Google Scholar 

  21. Priel E, Yosibash Z, Leguillon D (2008) Failure initiation at a blunt V-notch tip under mixed mode loading. Int J Fract 149:143–173

    CAS  Article  Google Scholar 

  22. Sapora A, Cornetti P, Carpinteri A (2013) A finite fracture mechanics approach to V-notched elements subjected to mixed-mode loading. Eng Fract Mech 97:216–226

    Article  Google Scholar 

  23. Sapora A, Cornetti P, Campagnolo A, Meneghetti G (2020) Fatigue limit: crack and notch sensitivity by finite fracture mechanics. Theor Appl Fract Mech 105:102407

    Article  Google Scholar 

  24. Seweryn A, Lukaszewicz A (2002) Verification of brittle fracture criteria for elements with V-shaped notches. Eng Fract Mech 69:1487–1510

    Article  Google Scholar 

  25. Yosibash Z, Priel E, Leguillon D (2006) A failure criterion for brittle elastic materials under mixed-mode loading. Int J Fract 141:291–312

    CAS  Article  Google Scholar 

Download references

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Correspondence to Aurélien Doitrand.

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Doitrand, A., Cornetti, P., Sapora, A. et al. Experimental and theoretical characterization of mixed mode brittle failure from square holes. Int J Fract (2021). https://doi.org/10.1007/s10704-020-00512-9

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Keywords

  • Square hole
  • PMMA
  • Uniaxial test
  • Mixed mode failure
  • Finite fracture mechanics
  • Circular hole