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In the ability to extend Hashin criterion for mixed mode I/II fracture assessment of cracked orthotropic materials

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Abstract

The problem of fracture assessment of orthotropic materials under mixed mode I/II loading is investigated in this study. The Hashin criterion, which is widely used to study the failure of composite materials, is extended to cracked orthotropic materials. The crack is assumed to grow along the fibers and in the isotropic matrix media. Hashin criterion as a well-known formulation for failure investigation of composites is extended to cracked orthotropic materials with two different approaches. As a first approach, the orthotropic stress field around the crack tip is considered for extraction of the extended Hashin criterion (EHC). In the next one, Hashin criterion is considered in conjunction with the reinforcement isotropic solid (RIS) concept as a superior material model named here as HC-RIS. Accuracy of the results is evaluated by comparing the fracture limit curves extracted from EHC and HC-RIS with the available experimental data which have been extracted from double cantilever beam (DCB) and single edge notched tension (SENT) test specimens on Scots pine, Eastern red spruce and Norway spruce.

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References

  1. Golewski, G.L.: Determination of fracture toughness in concretes containing siliceous fly ash during mode III loading. Struct. Eng. Mech. 62(1), 1–9 (2017)

    Google Scholar 

  2. Wang, B.L., Han, J.C.: Transverse cracking of orthotropic composite laminates: a fracture mechanics approach. Arch. Appl. Mech. 80, 1301–1316 (2010)

    MATH  Google Scholar 

  3. Golewski, G.L.: Fracture performance of cementitious composites based on quaternary blended cements. Materials 15(17), 6023 (2022)

    Google Scholar 

  4. Golewski, G.L.: Evaluation of fracture processes under shear with the use of DIC technique in fly ash concrete and accurate measurement of crack path lengths with the use of a new crack tip tracking method. Measurement 181, 109632 (2021)

    Google Scholar 

  5. Chabchoub, M., Vieille, B., Moutou Pitti, R.: Numerical estimation of the mode I strain energy release rate in woven-ply thermoplastic-based composites at high temperature based on Gθ method. Theor. Appl. Fract. Mech. 101, 169–177 (2019)

    Google Scholar 

  6. Golewski, G.L.: The phenomenon of cracking in cement concretes and reinforced concrete structures: The mechanism of cracks formation, causes of their initiation, types and places of occurrence, and methods of detection—A review. Buildings 13(3), 765 (2023)

    Google Scholar 

  7. Golewski, G.L.: Comparative measurements of fracture toughgness combined with visual analysis of cracks propagation using the DIC technique of concretes based on cement matrix with a highly diversified composition. Theor. Appl. Fract. Mech. 121, 103553 (2022)

    Google Scholar 

  8. Golewski, G.L.: An extensive investigations on fracture parameters of concretes based on quaternary binders (QBC) by means of the DIC technique. Constr. Build. Mater. 351, 128823 (2022)

    Google Scholar 

  9. Kiss, B., Szekrényes, A.: Fracture and mode mixity analysis of shear deformable composite beams. Arch. Appl. Mech. 89, 2485–2506 (2019)

    Google Scholar 

  10. Odounga, B., Moutou Pitti, R., Toussaint, E., Grédiac, M.: Mode I fracture of tropical woods using grid method. Theor. Appl. Fract. Mech. 95, 1–17 (2018)

    Google Scholar 

  11. Khaji, Z., Fakoor, M.: Fracture study of wood considering the effect of T-stress term based on matrix reinforcement coefficients model. Arch. Appl. Mech. 93(5), 1963–1983 (2023)

  12. Jernkvist, L.O.: Fracture of wood under mixed mode loading: I. Derivation of fracture criteria. Eng. Fract. Mech. 68(5), 549–563 (2001)

  13. Jernkvist, L.O.: Fracture of wood under mode loading, II: Experimental investigation of picea abies. Eng. Fract. Mech. 68, 565–576 (2001)

    Google Scholar 

  14. Mall, S., Murphy, J.F., Shottafer, J.E.: Criterion for mixed mode fracture in wood. J. Eng. Mech. 109(3), 680–690 (1983)

    Google Scholar 

  15. Romanowicz, M., Seweryn, A.: Verification of a non-local stress criterion for mixed mode fracture in wood. Eng. Fract. Mech. 75(10), 3141–3160 (2008)

    Google Scholar 

  16. Khaji, Z., Fakoor, M.: A Semi-theoretical criterion based on the combination of strain energy release rate and strain energy density concepts (STSERSED): Establishment of a new approach to predict the fracture behavior of orthotropic materials. Theor. Appl. Fract. Mech. 118, 103290 (2022)

    Google Scholar 

  17. Fakoor, M., Shahsavar, S.: The effect of T-stress on mixed mode I/II fracture of composite materials: Reinforcement isotropic solid model in combination with maximum shear stress theory. Int. J. Sol. Struct. 229, 111145 (2021)

    Google Scholar 

  18. Saouma, V.E., Ayari, M.L., Leavell, D.A.: Mixed mode crack propagation in homogeneous anisotropic solids. Eng. Fract. Mech. 27(2), 171–184 (1987)

    Google Scholar 

  19. Fakoor, M., Rafiee, R., Zare, S.: Equivalent reinforcement isotropic model for fracture investigation of orthotropic materials. Steel Compos. Struct. 30(1), 1–12 (2019)

    Google Scholar 

  20. Fakoor, M., Khansari, N.M.: Mixed mode I/II fracture criterion for orthotropic materials based on damage zone properties. Eng. Fract. Mech. 153, 407–420 (2016)

    Google Scholar 

  21. Fakoor, M., Manafi Farid, H.: Mixed-mode I/II fracture criterion for crack initiation assessment of composite materials. Acta Mech. 230, 281–301 (2019)

    MathSciNet  Google Scholar 

  22. Manafi Farid, H., Fakoor, M.: Mixed mode I/II fracture criterion for arbitrary cracks in orthotropic materials considering T-stress effects. Theor. Appl. Fract. Mech. 99, 147–160 (2019)

    Google Scholar 

  23. Wu, E.M.: Application of fracture mechanics to anisotropic plates. J. Appl. Mech. 34(4), 967–974 (1967)

    Google Scholar 

  24. Woo, C.W., Chow, C.L.: Mixed mode fracture in orthotropic media. In: Sih, G.C., Valluri, S.R. (eds.) Fracture Mechanics in Engineering Application, pp. 387–96. Sijthoff and Noordhoff, Rockville (1979)

  25. Hunt, D.G., Croager, W.P.: Mode II fracture toughness of wood measured by a mixed-mode test method. J. Mater. Sci. Lett. 1, 77–79 (1982)

    Google Scholar 

  26. Buczek, M.B., Herakovich, C.T.: A normal stress criterion for crack extension direction in orthotropic composite materials. J. Compos. Mater. 19(6), 544–553 (1985)

    Google Scholar 

  27. Leicester, R.H.: Application of linear fracture mechanics to notched timber elements. Prog. Struct. Mat. Eng. 8(1), 29–37 (2006)

    Google Scholar 

  28. de Morais, A.B.: Double cantilever beam testing of multidirectional laminates. Compos. A: Appl. Sci. Manuf. 34, 1135–1142 (2003)

    Google Scholar 

  29. de Morais, A.B., de Moura, M.F., Gonçalves, J.P.M., Camanho, P.P.: Analysis of crack propagation in double cantilever beam tests of multidirectional laminates. Mech. Mater. 35(7), 641–652 (2003)

    Google Scholar 

  30. Williams, J.G., Ewing, P.D.: Fracture under complex stress—the angled crack problem. Int. J. Fract. 26, 346–351 (1984)

    Google Scholar 

  31. Larsson, S.G., Carlsson, A.J.: Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials. J. Mech. Phys. Solids 21(4), 263–277 (1973)

    Google Scholar 

  32. Smith, D.J., Ayatollahi, M.R., Pavier, M.J.: The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading. Fatigue Fract. Eng. Mater. Struct. 24(2), 137–150 (2001)

    Google Scholar 

  33. Gdoutos, E.E., Zacharopoulos, D.A., Meletis, E.I.: Mixed-mode crack growth in anisotropic media. Eng. Fract. Mech. 34(2), 337–346 (1989)

    Google Scholar 

  34. Carloni, C., Nobile, L.: Maximum circumferential stress criterion applied to orthotropic materials. Fatigue Fract. Eng. Mater. Struct. 28(9), 825–833 (2005)

    Google Scholar 

  35. Nobile, L., Piva, A., Viola, E.: On the inclined crack problem in an orthotropic medium under biaxial loading. Eng. Fract. Mech. 71(4–6), 529–546 (2004)

    Google Scholar 

  36. Nobile, L., Carloni, C.: Fracture analysis for orthotropic cracked plates. Compos. Struct. 68(3), 285–293 (2005)

    Google Scholar 

  37. Anaraki, A.G., Fakoor, M.: General mixed mode I/II fracture criterion for wood considering T-stress effects. Mater. Des. 31(9), 4461–4469 (2010)

    Google Scholar 

  38. Anaraki, A.G., Fakoor, M.: Mixed mode fracture criterion for wood based on a reinforcement microcrack damage model. Mater. Sci. Eng. A 527(27), 7184–7191 (2010)

    Google Scholar 

  39. Anaraki, A.G., Fakoor, M.: A new mixed-mode fracture criterion for orthotropic materials, based on strength properties. J. Strain Anal. Eng. 46(1), 33–44 (2011)

    Google Scholar 

  40. Fakoor, M., Shahsavar, S., Berto, F.: Mixed-mode fracture assessment of wooden structures with cracks initiated along and across the fibers considering non-singular T-stress term. Wood Sci. Technol. 56, 1261–1291 (2022)

    Google Scholar 

  41. Fakoor, M., Rafiee, R., Sheikhansari, M.: The influence of fiber-crack angle on the crack tip parameters in orthotropic materials. Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 231(3), 418–431 (2017)

    Google Scholar 

  42. Tsai, S.W., Hahn, H.T.: Introduction to composite materials, Technomic Publishing Co, Inc.; 1st edition (1980)

  43. Sih, G.C., Paris, P.C., Irwin, G.R.: On cracks in rectilinearly anisotropic bodies. Int. J. Fract. Mech. 1(3), 189–203 (1965)

    Google Scholar 

  44. Wood Handbook—Wood as an Engineering Material, Forest Products Laboratory; United States Department of Agriculture Forest Service, Madison, WI (2010)

  45. Yang, S., Yuan, F.-G.: Kinked crack in anisotropic bodies. Int. J. Solids Struct. 37(45), 6635–6682 (2000)

    MATH  Google Scholar 

  46. Tzu-Chiang, W., Shih, C.F., Zhigang, S.: Crack extension and kinking in laminates and bicrystals. Int. J. Solids Struct. 29(3), 327–344 (1992)

    MATH  Google Scholar 

  47. He, M.Y., Hutchinson, J.W.: Kinking of a crack out of an interface. J. Appl. Mech. 56(2), 270–278 (1989)

    Google Scholar 

  48. van der Put, T.A.C.M.: A new fracture mechanics theory for orthotropic materials like wood. Eng. Fract. Mech. 74(5), 771–781 (2007)

    Google Scholar 

  49. Fakoor, M.: Augmented strain energy release rate (ASER): A novel approach for investigation of mixed-mode I/II fracture of composite materials. Eng. Fract. Mech. 179, 177–189 (2017)

    Google Scholar 

  50. Khaji, Z., Fakoor, M.: Strain energy release rate in combination with reinforcement isotropic solid model (SERIS): A new Mixed-mode I/II criterion to investigate fracture behavior of orthotropic materials. Theor. Appl. Fract. Mech. 113, 102962 (2021)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

    Mahdi Fakoor & Alireza Vazirinejad

  2. Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran

    Zahra Daneshjoo

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  1. Mahdi Fakoor
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  2. Alireza Vazirinejad
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  3. Zahra Daneshjoo
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Correspondence to Mahdi Fakoor.

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Fakoor, M., Vazirinejad, A. & Daneshjoo, Z. In the ability to extend Hashin criterion for mixed mode I/II fracture assessment of cracked orthotropic materials. Arch Appl Mech 93, 3851–3862 (2023). https://doi.org/10.1007/s00419-023-02465-6

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