Steel and Composite Structures

  • 제50권2호
  • /
  • Pages.237-247
  • /
  • 2024
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Assessing interfacial fracture in orthotropic materials: Implementing the RIS concept with considering the T-stress term under mixed-mode I/II

  • Zahra Khaji (Faculty of New Sciences and Technologies, University of Tehran) ;
  • Mahdi Fakoor (Faculty of New Sciences and Technologies, University of Tehran)
  • 투고 : 2023.10.13
  • 심사 : 2023.12.28
  • 발행 : 2024.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

Research on interfacial crack formation in orthotropic bi-materials has experienced a notable increase in recent years, driven by growing concerns about structural integrity and reliability. The existence of a crack at the interface of bi-materials has a substantial impact on mechanical strength and can ultimately lead to fracture. The primary objective of this article is to introduce a comprehensive analytical model and establish stress relationships for investigating interfacial crack between two non-identical orthotropic materials with desired crack-fiber angles. In this paper, we present the application of the Interfacial Maximum Tangential Stress (IMTS) criterion, in combination with the Reinforcement Isotropic Solid (RIS) model, to investigate the behavior of interfacial cracks in orthotropic bi-materials under mixed-mode I/II loading conditions. We analytically characterize the stress state at the interfacial crack tip using both Stress Intensity Factors (SIFs) and the T-stress term. Orthotropic materials, due to their anisotropic nature, can exhibit complex crack tip stress fields, making it challenging to predict crack initiation behavior. The secondary objective of this study is to employ the IMTS criterion to predict the crack initiation angle and explore the notable impact of the T-stress term on fracture behavior. Furthermore, we validate the effectiveness of our approach in evaluating Fracture Limit Curves (FLCs) for interfacial cracks in orthotropic bi-materials by comparing our FLCs with relevant experimental data from existing literature.

키워드

참고문헌

  1. Aliha, M. and Ayatollahi, M. (2012), "Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion", Int. J. Solids Struct., 49(13), 1877-1883. https://doi.org/10.1109/IFEEA51475.2020.00046.
  2. Andrade, H., Trevelyan, J. and Leonel, E. (2023), "Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method", Theoretical Appl. Fract. Mech., 104091. https://doi.org/10.1016/j.tafmec.2023.104091.
  3. Ayatollahi, M. and Aliha, M. (2009), "Mixed mode fracture in soda lime glass analyzed by using the generalized MTS criterion", Int. J. Solids Struct., 46(2), 311-321. https://doi.org/10.1016/j.ijsolstr.2008.08.035.
  4. Braun, M. and Ariza, M. (2019), "New lattice models for dynamic fracture problems of anisotropic materials", Compos. Part B: Eng., 172, 760-768. https://doi.org/10.1016/j.compositesb.2019.05.082.
  5. Braun, M. and Ariza, M. (2020), "A progressive damage based lattice model for dynamic fracture of composite materials", Compos. Sci. Technol., 200, 108335. https://doi.org/10.1016/j.compscitech.2020.108335.
  6. Braun, M., Ivanez, I. and Ariza, M. (2021), "A numerical study of progressive damage in unidirectional composite materials using a 2D lattice model", Eng. Fract. Mech., 249, 107767. https://doi.org/10.1016/j.engfracmech.2021.107767.
  7. Charalambides, P., Lund, J., Evans, A. and McMeeking, R. (1989), "A test specimen for determining the fracture resistance of bimaterial interfaces", J. Appl. Mech., 56(1), 77-82. https://doi.org/10.1115/1.3176069.
  8. Chen, S., Shi, X. and Qiu, Z. (2011), "Shear bond failure in composite slabs-a detailed experimental study", Steel Compos. Struct., 11(3), 233-250. https://doi.org/10.12989/scs.2011.11.3.233.
  9. Chow, W. and Atluri, S. (1995), "Finite element calculation of stress intensity factors for interfacial crack using virtual crack closure integral", Comput. Mech., 16(6), 417-425. https://doi.org/10.1007/BF00370563.
  10. Chyanbin, H. (1993), "Fracture parameters for the orthotropic bimaterial interface cracks", Eng. Fract. Mech., 45(1), 89-97. https://doi.org/10.1016/0013-7944(93)90010-P.
  11. Dall'Asta, A., Dezi, L. and Leoni, G. (2002), "Failure mechanisms of externally prestressed composite beams with partial shear connection", Steel Compos. Struct., 2(5), 315-330. https://doi.org/10.12989/scs.2002.2.5.315.
  12. Daneshjoo, Z., Shokrieh, M., Fakoor, M. and Alderliesten, R. (2018), "A new mixed mode I/II failure criterion for laminated composites considering fracture process zone", Theoretical Appl. Fract. Mech., 98, 48-58. https://doi.org/10.1016/j.tafmec.2018.09.004.
  13. Erdogan, F. and Sih, G. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Fluids Mech., 85, 519-525. https://doi.org/10.1115/1.3656897.
  14. Esmaeili, A., Mohammadi, B. and Yousefi, A. (2023), "Fracture parameters and crack initiation assessment employing mixed-mode I/II fracture criterion in laminate composites using digital image correlation method", Theoretical Appl. Fract. Mech., 127, 104095. https://doi.org/10.1016/j.tafmec.2023.104095.
  15. Fakoor, M. and Khaji, Z. (2023), "A comprehensive study on the influence of T-stress term on crack initiation angle in orthotropic materials based on the modification of MTS, MSS, SER and SED criteria", Theoretical Appl. Fract. Mech., 124, 103751. https://doi.org/10.1016/j.tafmec.2023.103751.
  16. Fakoor, M. and Khansari, N.M. (2018), "General mixed mode I/II failure criterion for composite materials based on matrix fracture properties", Theoretical Appl. Fract. Mech., 96, 428-442. https://doi.org/10.1016/j.tafmec.2018.06.004.
  17. Fakoor, M. and Shahsavar, S. (2021), "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. Solids Struct., 229, 111145. https://doi.org/10.1016/j.ijsolstr.2021.111145.
  18. Fakoor, M., Rafiee, R. and Zare, S. (2019), "Equivalent reinforcement isotropic model for fracture investigation of orthotropic materials", Steel Compos. Struct., 30(1), 1-12. https://doi.org/10.12989/scs.2019.30.1.001.
  19. Farid, H.M. and Fakoor, M. (2020), "Mixed mode I/II fracture criterion to anticipate behavior of the orthotropic materials", Steel Compos. Struct., 34(5), 671-679. https://doi.org/10.12989/scs.2020.34.5.671.
  20. Golewski, G. and Sadowski, T. (2017), "The fracture toughness the KIIIc of concretes with F fly ash (FA) additive", Construct. Build. Mater., 143, 444-454. https://doi.org/10.1016/j.conbuildmat.2017.03.137.
  21. Golewski, G.L. (2017), "Improvement of fracture toughness of green concrete as a result of addition of coal fly ash Characterization of fly ash microstructure", Mater. Character., 134, 335-346. https://doi.org/10.1016/j.matchar.2017.11.008.
  22. Golewski, G.L. (2021), "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. https://doi.org/10.1016/j.measurement.2021.109632.
  23. Golewski, G.L. (2023a), "Concrete composites based on quaternary blended cements with a reduced width of initial microcracks", Appl. Sci., 13(12), 7338. https://doi.org/10.3390/app13127338.
  24. Golewski, G.L. (2023b), "Effect of coarse aggregate grading on mechanical parameters and fracture toughness of limestone concrete", Infrastructures, 8(8), 117. https://doi.org/10.3390/infrastructures8080117.
  25. Golewski, G.L. (2023c), "Mechanical properties and brittleness of concrete made by combined fly ash, silica fume and nanosilica with ordinary Portland cement", AIMS Mater. Sci, 10(3), 390-404. https://doi.org/10.3934/matersci.2023021.
  26. Golewski, G.L. (2023d), "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. https://doi.org/10.3390/buildings13030765.
  27. Golewski, G.L. (2023e), "Study of strength and microstructure of a new sustainable concrete incorporating pozzolanic materials", Struct. Eng. Mech., 86(4), 431-441. https://doi.org/10.12989/sem.2023.86.4.431.
  28. Hamdi, S.E., Pitti, R.M. and Dubois, F. (2017), "Temperature variation effect on crack growth in orthotropic medium: Finite element formulation for the viscoelastic behavior in thermal cracked wood-based materials", Int. J. Solids Struct., 115, 1-13. https://doi.org/10.1016/j.ijsolstr.2016.09.019.
  29. He, M.-Y. and Hutchinson, J.W. (1989), "Kinking of a crack out of an interface", J. Appl. Mech., 52(6), 270-278.https://doi.org/10.1115/1.3176078
  30. Hutchinson, J.W. and Suo, Z. (1991), "Mixed mode cracking in layered materials", Adv. Appl. Mech., 29, 63-191. https://doi.org/10.1016/S0065-2156(08)70164-9.
  31. Kaman, M.O. and Cetisli, F. (2012), "Numerical analysis of center cracked orthotropic fgm plate: Crack and material axes differ by θo", Steel Compos. Struct., 13(2), 187-206. https://doi.org/10.12989/scs.2012.13.2.187.
  32. Khaji, Z. and Fakoor, M. (2021), "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", Theoretical Appl. Fract. Mech., 113, 102962. https://doi.org/10.1016/j.tafmec.2021.102962.
  33. Khaji, Z. and Fakoor, M. (2022a), "Enhancing the ability of strain energy release rate criterion for fracture assessment of orthotropic materials under mixed-mode I/II loading considering the effect of crack tip damage zone", Steel Compos. Struct., 44(6), 803-814. https://doi.org/10.12989/scs.2022.44.6.817.
  34. Khaji, Z. and Fakoor, M. (2022b), "Examining the effect of crack initiation angle on fracture behavior of orthotropic materials under mixed-mode I/II loading", Int. J. Solids Struct., 256, 111952. https://doi.org/10.1016/j.ijsolstr.2022.111952.
  35. Khaji, Z., Fakoor, M., Farid, H.M. and Alderliesten, R. (2022), "Applying the new experimental midpoint concept on strain energy density for fracture assessment of composite materials", Theoretical Appl. Fract. Mech., 121, 103522. https://doi.org/10.1016/j.tafmec.2022.103522.
  36. Khansari, N.M., Fakoor, M. and Berto, F. (2019), "Probabilistic micromechanical damage model for mixed mode I/II fracture investigation of composite materials", Theoretical Appl. Fract. Mech., 99, 177-193. https://doi.org/10.1016/j.tafmec.2018.12.003.
  37. Lee, H. and Kim, Y.-J. (2001), "Interfacial crack-tip constraints and J-integrals in plastically mismatched bi-materials", Eng. Fract. Mech., 68(8), 1013-1031. https://doi.org/10.1016/S0013-7944(01)00007-8.
  38. Li, X.-F. and Xu, L. R. (2007), "T-stresses across static crack kinking", Journal of applied mechanics, 74(2), 181-190. https://doi.org/10.1115/1.2188016.
  39. Mulville, D., Mast, P. and Vaishnav, R. (1976), "Strain energy release rate for interfacial cracks between dissimilar media", Eng. Fract. Mech., 8(3), 555-565. https://doi.org/10.1016/0013-7944(76)90009-6.
  40. Muthu, N., Maiti, S., Falzon, B. and Yan, W. (2016), "Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant of EFG Method", Eng. Anal. Bound. Elements, 72, 11-26. https://doi.org/10.1016/j.enganabound.2016.07.017.
  41. Natarajan, S., Song, C. and Belouettar, S. (2014), "Numerical evaluation of stress intensity factors and T-stress for interfacial cracks and cracks terminating at the interface without asymptotic enrichment", Comput. Meth. Appl. Mech. Eng., 279, 86-112. https://doi.org/10.1016/j.cma.2014.06.024.
  42. Noda, N.-A., Miyazaki, T., Li, R., Uchikoba, T., Sano, Y. and Takase, Y. (2015), "Debonding strength evaluation in terms of the intensity of singular stress at the interface corner with and without fictitious crack", Int. J. Adhesion Adhesives, 61, 46-64. https://doi.org/10.1016/j.ijadhadh.2015.04.005.
  43. Pitti, R.M., Dubois, F., Petit, C. and Sauvat, N. (2007), "Mixed mode fracture separation in viscoelastic orthotropic media: numerical and analytical approach by the M θ v-integral", Int. J. Fract., 145, 181-193. https://doi.org/10.1007/s10704-007-9111-4.
  44. Pitti, R.M., Dubois, F., Pop, O. and Absi, J. (2009), "A finite element analysis for the mixed mode crack growth in a viscoelastic and orthotropic medium", Int. J. Solids Struct., 46(20), 3548-3555. https://doi.org/10.1016/j.ijsolstr.2009.05.020.
  45. Qian, W. and Sun, C. (1998), "Methods for calculating stress intensity factors for interfacial cracks between two orthotropic solids", Int. J. Solids Struct., 35(25), 3317-3330. https://doi.org/10.1016/S0020-7683(97)00181-9.
  46. Rafiee, R., Fakoor, M. and Hesamsadat, H. (2015), "The influence of production inconsistencies on the functional failure of GRP pipes", Steel Compos. Struct., 19(6), 1369-1379. https://doi.org/10.12989/scs.2015.19.6.1369.
  47. Raimondo, A., Urcelay Oca, I. and Bisagni, C. (2021), "Influence of interface ply orientation on delamination growth in composite laminates", J. Compos. Mater., 55(27), 3955-3972. https://doi.org/10.1177/00219983211031636.
  48. Rice, J. (1988), "Elastic fracture mechanics concepts for interfacial cracks", J. Appl. Mech., 55(1), 98-103. https://doi.org/10.1115/1.3173668.
  49. Rizov, V.I. (2017), "Non-linear study of mode II delamination fracture in functionally graded beams", Steel Comp. Struct, 23, 263-271. https://doi.org/10.12989/scs.2017.23.3.263.
  50. Ryoji, Y. and Jin-Quan, X. (1992), "Stress based criterion for an interface crack kinking out of the interface in dissimilar materials", Eng. Fract. Mech., 41(5), 635-644. https://doi.org/10.1016/0013-7944(92)90150-D.
  51. Shahsavar, S., Fakoor, M. and Berto, F. (2021), "Mixed mode I/II fracture criterion to anticipate cracked composite materials based on a reinforced kinked crack along maximum shear stress path", Steel Compos. Struct., 39(6), 765-779. https://doi.org/10.12989/scs.2021.39.6.765.
  52. Shokrieh, M., Daneshjoo, Z. and Fakoor, M. (2016), "A modified model for simulation of mode I delamination growth in laminated composite materials", Theoretical Appl. Fract. Mech., 82, 107-116. https://doi.org/10.1016/j.tafmec.2015.12.012.
  53. Smith, D., Ayatollahi, M. and Pavier, M. (2001), "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. https://doi.org/10.1046/j.1460-2695.2001.0037.x.
  54. Sun, C. and Manoharan, M. (1989), "Strain energy release rates of an interfacial crack between two orthotropic solids", J. Compos. Mater., 23(5), 460-478. https://doi.org/10.1177/002199838902300503.
  55. Sun, C.T. and Jih, C. (1987), "On strain energy release rates for interfacial cracks in bi-material media", Eng. Fract. Mech., 28(1), 13-20. https://doi.org/10.1016/0013-7944(87)90115-9.
  56. Toribio, J. and Ayaso, F. (2003), "A fracture criterion for high-strength steel structural members containing notch-shape defects", Steel Compos. Struct., 3(4), 231-242. https://doi.org/10.12989/scs.2003.3.4.231.
  57. Zhou, Z., Xu, X., Leung, A.Y. and Huang, Y. (2013), "Stress intensity factors and T-stress for an edge interface crack by symplectic expansion", Eng. Fract. Mech., 102, 334-347. https://doi.org/10.1016/j.engfracmech.2013.03.007.
  58. Zhu, D. and Du, W. (2022), "A criterion for a hydraulic fracture crossing a frictional interface considering T-stress", J. Petroleum Sci. Eng., 209, 109824. https://doi.org/10.1016/j.petrol.2021.109824.