Utilization of splitting strips in fracture mechanics tests of quasi-brittle materials

Abstract

In this study, utilizing the boundary collocation approach based on the generalized Westergaard formulation developed by Sanford, alternative splitting strips with various ratios of length/depth, L/h = 0.5, 0.75, 1.25, and 1.5, were first discussed for fracture mechanics of quasi-brittle materials for different load-distributed widths. By modifying Sanford's approach, some formulae calculating the tensile capacity of materials were subsequently proposed for strips without notches. To determine the simulating capacity of the split-tension strips on the fracture behavior of quasi-brittle materials, the formulas derived in this study were also applied to a popular fracture approach, the two-parameter model (TPM) in concrete fracture. As a result of the stress analysis based on this application, a square prismatic specimen type with edge crack was proposed to determine the fracture parameters of quasi-brittle materials. Subsequently, an experimental investigation on splitting cubes with edge cracks (L/h = 0.5) was performed. The analysis of this specimen based on TPM yielded viable and promising results.

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References

  1. 1.

    Tang, T., Shah, S.P., Ouyang, C.: Fracture mechanics and size effect of concrete in tension. ASCE J. Struct. Eng. 118, 3169–3185 (1992)

    Article  Google Scholar 

  2. 2.

    Sanford, R.J.: Principles of Fracture Mechanics. Prentice-Hall, New Jersey, USA (2003)

    Google Scholar 

  3. 3.

    Kundu, T.: Fundamentals of Fracture Mechanics. CRC Press, Boca Raton (2008)

    Google Scholar 

  4. 4.

    Popov, V.Z., Morozov, E.M.: Elastic-Plastic Fracture Mechanics. Mir Publishers, Moscow (1978)

    Google Scholar 

  5. 5.

    Ukadgaonker, V.G.: Theory of elasticity and fracture mechanics. PHI Learning, Delhi (2015)

    Google Scholar 

  6. 6.

    Tang, T.: Effect of load-distributed width on split tension of unnotched and notched cylindrical specimens. J. Test Eva. 22, 401–409 (1994)

    Article  Google Scholar 

  7. 7.

    Rocco, C., Guinea, G.V., Planas, J., Elices, M.: Size effect and boundary condition in the Brazilian tests: theoretical analysis. Mater. Struct. 32, 437–444 (1999)

    Article  Google Scholar 

  8. 8.

    Ince, R.: Determination of concrete fracture parameters based on two-parameter and size effect models using split-tension cubes. Eng. Fract. Mech. 77, 2233–2250 (2010)

    Article  Google Scholar 

  9. 9.

    Ince, R.: Determination of concrete fracture parameters based on peak-load method with diagonal split-tension cubes. Eng. Fract. Mech. 82, 100–114 (2012)

    Article  Google Scholar 

  10. 10.

    Ince, R.: Determination of the fracture parameters of the double-K model using weight functions of split-tension specimens. Eng. Fract. Mech. 96, 416–432 (2012)

    Article  Google Scholar 

  11. 11.

    Ince, R., Çetin, S.Y.: Effect of grading type of aggregate on fracture parameters of concrete. Mag. Conc. Res. 71(16), 860–868 (2019)

    Article  Google Scholar 

  12. 12.

    Ince, R.: The fracture mechanics formulas for split-tension strips. J. Theor. Appl. Mech. 55, 607–619 (2017)

    Article  Google Scholar 

  13. 13.

    Filon, L.N.G.: On the approximate solution of the bending of a beam of rectangular section. Trans. R. Soc. Lond. Ser. (A) 201, 63–155 (1903)

    MATH  Google Scholar 

  14. 14.

    Davies, J.D., Bose, D.K.: Stress distribution in splitting tests. ACI J. 65, 662–669 (1968)

    Google Scholar 

  15. 15.

    Schleeh, W.S.: Determination of the tensile strength of concrete. Beton 28(2), 57–62 (1978) (in German)

  16. 16.

    Neville, A.M.: Properties of Concrete, 4th edn. Longman, London (1995)

    Google Scholar 

  17. 17.

    Timoshenko, S.P., Godier, J.N.: Theory of Elasticity, 3rd edn. McGraw Hill, New York (1970)

    Google Scholar 

  18. 18.

    Tweed, J., Das, S.C., Rooke, D.P.: The stress intensity factor of a radial crack in a finite elastic disc. Int. J. Eng. Sci. 10, 323–335 (1972)

    Article  Google Scholar 

  19. 19.

    Tada, H., Paris, P.C., Irwin, G.R.: Stress Analysis of Cracks Handbook, 3rd edn. ASME Press, New York (2000)

    Google Scholar 

  20. 20.

    Westergaard, H.M.: Bearing pressures and cracks. J. Appl. Mech. 61, A49-59 (1939)

    Google Scholar 

  21. 21.

    Williams, M.L.: On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 109–114 (1957)

    MathSciNet  MATH  Google Scholar 

  22. 22.

    Gross, B., Roberts, E., Srawley, J.E.: Elastic displacements for various edge-cracked plate specimens. Int. J. Fract. 4(3), 267–276 (1968)

    Article  Google Scholar 

  23. 23.

    Fett, T.: Stress Intensity Factors: T-Stresses—Weight Functions. KIT Scientific Publishing, Berlin (2008)

    Google Scholar 

  24. 24.

    Sanford, R.J.: A critical re-examination of the Westergaard method for solving opening-mode crack problems. Mech. Res. Com. 6(5), 289–294 (1979)

    Article  Google Scholar 

  25. 25.

    Beardin, K., Dally, J.W., Sanford, R.J.: Experimental determination of KI for short internal cracks. J. App. Mech. 68, 937–943 (2001)

    Article  Google Scholar 

  26. 26.

    Hills, D.A., Kelly, P.A., Dai, D.N., Korsunsky, A.M.: Solution of Crack Problems: The Distributed Dislocation Technique. Springer, Berlin (1996)

    Google Scholar 

  27. 27.

    Smith, R.N.L.: Basic Fracture Mechanics: Including an Introduction to Fatigue. Butterworth-Heinemann, Oxford (1991)

    Google Scholar 

  28. 28.

    Gdoutos, E.E.: Fracture Mechanics Criteria and Applications. Kluwer Academic Publishers, London (1990)

    Google Scholar 

  29. 29.

    Wu, X.R.: A review and verification of analytical weight function methods in fracture mechanics. Fatigue Fract. Eng. Mater. Struct. 42, 2017–2042 (2019)

    Article  Google Scholar 

  30. 30.

    Ince, R.: Usage of compact compression specimens to determine non-linear fracture parameters of concrete. Fatigue Fract. Eng. Mater. Struct. 44, 410–426 (2021)

    Article  Google Scholar 

  31. 31.

    Isida, M.: Effect of width and length on stress intensity factor of internally cracked plates under various boundary conditions. Int. J. Fract. 7(3), 301–316 (1971)

    Article  Google Scholar 

  32. 32.

    Wu, X.R., Carlsson, A.J.: Weight Functions and Stress Intensity Factor Solutions. Pergamon Press, Oxford (1991)

    Google Scholar 

  33. 33.

    Kuliyev, S.A.: Conformal mapping function of a complex domain and its application. Arch. Appl. Mech. 90, 993–1003 (2020)

    Article  Google Scholar 

  34. 34.

    Tan, F., Zhang, Y., Li, Y.: An improved hybrid boundary node method for 2D crack problems. Arch. Appl. Mech. 85, 101–116 (2015)

    Article  Google Scholar 

  35. 35.

    Moaveni, S.: Finite Element Analysis Theory and Application with ANSYS. Pearson Education, London (2014)

    Google Scholar 

  36. 36.

    Collatz, L.: The Numerical Treatment of Differential Equations. Springer, New York (1966)

    Google Scholar 

  37. 37.

    Simon, K.M., Kishen, J.M.C.: A multiscale model for post-peak softening response of concrete and the role of microcracks in the interfacial transition zone. Arch. Appl. Mech. 88, 1105–1119 (2018)

    Article  Google Scholar 

  38. 38.

    Bazant, Z.P.: Size effect on structural strength: a review. Arch. Appl. Mech. 69, 703–725 (1999)

    Article  Google Scholar 

  39. 39.

    Weiβgrager, P., Leguillon, D., Becker, W.: A review of finite fracture mechanics: crack initiation at singular and non-singular stress raisers. Arch. Appl. Mech. 86, 375–401 (2016)

    Article  Google Scholar 

  40. 40.

    Jenq, Y.S., Shah, S.P.: Two-parameter fracture model for concrete. ASCE J. Eng. Mech. 111(10), 1227–1241 (1985)

    Article  Google Scholar 

  41. 41.

    ACI 318–11: Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute, Farmington Hills (2011)

  42. 42.

    Yang, S., Tang, T., Zollinger, D.G., Gurjar, A.: Splitting tension tests to determine concrete fracture parameters by peak-load method. Adv. Cem. Based Mater. 5, 18–28 (1997)

    Article  Google Scholar 

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Correspondence to Ragip Ince.

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Ince, R. Utilization of splitting strips in fracture mechanics tests of quasi-brittle materials. Arch Appl Mech (2021). https://doi.org/10.1007/s00419-021-01913-5

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Keywords

  • Boundary collocation method
  • Fracture mechanics
  • Green’s function
  • Quasi-brittle materials
  • Splitting test