zldmЗаводская лаборатория. Диагностика материаловIndustrial laboratory. Diagnostics of materials1028-68612588-0187ООО «Издательство «ТЕСТ-ЗЛ»10.26896/1028-6861-2025-91-11-77-84zldm-2660Research ArticleИССЛЕДОВАНИЕ СТРУКТУРЫ И СВОЙСТВ. МЕХАНИКА МАТЕРИАЛОВ: ПРОЧНОСТЬ, РЕСУРС, БЕЗОПАСНОСТЬTESTING OF STRUCTURE AND PARAMETERS. MECHANICAL TESTING METHODSМетод определения сопротивления расслоению композитов, армированных непрерывными волокнами, при изгибе балок с боковым поперечным надрезомMethod for determination of continuous fibers reinforced composite delamination resistance in bending of beams with lateral transverse notchПолиловА. Н.PolilovA. N.

Александр Николаевич Полилов 

101000, Москва, Малый Харитоньевский переулок, д. 4

Alexander N. Polilov

4, Malyi Kharitonyevsky per., Moscow, 101000

polilovan@mail.ruВласовД. Д.VlasovD. D.

Данила Денисович Власов 

101000, Москва, Малый Харитоньевский переулок, д. 4

Danila D. Vlasov

4, Malyi Kharitonyevsky per., Moscow, 101000

Институт машиноведения им. А. А. Благонравова РАНРоссияMechanical Engineering Research Institute of the Russian Academy of SciencesRussian Federation20252611202591117784Copyright © Полилов А.Н., Власов Д.Д., 20252025Полилов А.Н., Власов Д.Д.Polilov A.N., Vlasov D.D.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.zldm.ru/jour/article/view/2660

К важным прочностным характеристикам волокнистых композитов с полимерной матрицей относится их сопротивление расслоению и расщеплению, которое традиционно определяют при изгибе коротких балок (в терминах межслойной сдвиговой прочности) или образцов с искусственными расслоениями (в терминах критической скорости высвобождения энергии, или удельной работы расслоения). Реализация этих методик сопряжена с известными сложностями интерпретации и сопоставления результатов. В данной работе предложен метод определения критического значения коэффициента интенсивности напряжений при возникновении трещины расслоения около вершины поперечного слоям надреза, который позволяет: сравнить трещиностойкость различных композитов и металлов; оценить потенциальную прочность однонаправленных волокнистых композитов при разрушении по механизму множественного расщепления; сформулировать требования «равнопрочности» по условию одновременного возникновения разных видов разрушения. Приведены экспериментальные результаты по сопротивлению расслоению композитов с различными схемами армирования в терминах критического коэффициента интенсивности напряжений при повороте трещины. Полученные результаты сопоставлены с межслойной прочностью материала.

Important strength characteristics of fiber-reinforced composites with polymer matrix include their resistance to delamination and splitting, which is traditionally determined in bending of short beams (in terms of interlayer shear strength) or specimens with artificial delaminations (in terms of critical energy release rate, i.e., specific work of delamination). The implementation of these techniques is associated with known difficulties in interpretation and comparison of results. The method of determining the critical value of the stress intensity factor at the occurrence of delamination crack near the apex of the transverse layer notch is proposed in this paper. It allows: to compare the crack resistance of various composites and metals, to estimate the potential strength of unidirectional fiber-reinforced composites at fracture by the mechanism of multiple splitting, to formulate the requirements of «equal strength» under the condition of simultaneous occurrence of different types of fracture. Experimental results on the resistance to delamination of composites with different reinforcement schemes in terms of the critical stress intensity factor at crack rotation and their comparison with the interlayer strength of the material are presented.

композит полимерныйстеклопластикуглепластикпрочностьрасслоениерасщеплениемеханика разрушенияизгибтрещинакоэффициент интенсивности напряженийскорость высвобождения упругой энергииpolymer composite materialCFPRGFRPstrengthdelaminationsplittingfracture mechanicsbendingcrackstress intensity factorelastic energy release rateРабота выполнена при финансовой поддержке Минобрнауки России, соглашение № 075-15-2025-646.ReferencesWalsh P. H. Linear Fracture mechanics in orthotropic materials / Eng. Fracture Mech. 1972. Vol. 4. No. 3. P. 533 – 541. DOI: 10.1016/0013-7944(72)90064-1Walsh P. H. Linear Fracture mechanics in orthotropic materials / Eng. Fracture Mech. 1972. Vol. 4. No. 3. P. 533 – 541. DOI: 10.1016/0013-7944(72)90064-1Khaji Z., Fakoor M. Examining the effect of crack initiation angle on fracture behavior of orthotropic materials under mixed- mode I/II loading / Int. J. Solids Struct. 2022. Vol. 256. 111952. DOI: 10.1016/j.ijsolstr.2022.111952Khaji Z., Fakoor M. Examining the effect of crack initiation angle on fracture behavior of orthotropic materials under mixed- mode I/II loading / Int. J. Solids Struct. 2022. Vol. 256. 111952. DOI: 10.1016/j.ijsolstr.2022.111952Esmaeili A., Mohammadi B., Yousefi A. fracture parameters and crack initiation assessment employing mixed-mode I/II fracture criterion in laminate composites using digital image correlation method / Theor. Appl. Fracture Mech. 2023. Vol. 127. 104095. DOI: 10.1016/j.tafmec.2023.104095Esmaeili A., Mohammadi B., Yousefi A. fracture parameters and crack initiation assessment employing mixed-mode I/II fracture criterion in laminate composites using digital image correlation method / Theor. Appl. Fracture Mech. 2023. Vol. 127. 104095. DOI: 10.1016/j.tafmec.2023.104095Biswal S., Singh G. Determination of fracture toughness and traction-separation relation in mode I/II of a natural quasi-brittle orthotropic composite using multi-specimen approach / Eng. Fracture Mech. 2023. Vol. 282. 109163. DOI: 10.1016/j.engfracmech.2023.109163Biswal S., Singh G. Determination of fracture toughness and traction-separation relation in mode I/II of a natural quasi-brittle orthotropic composite using multi-specimen approach / Eng. Fracture Mech. 2023. Vol. 282. 109163. DOI: 10.1016/j.engfracmech.2023.109163Sako R., Aoki R., Higuchi R., et al. Experiments on the mode II fracture toughness in ENF tests of CFRP curved beams / Composite Struct. 2022. Vol. 292. 115692. DOI: 10.1016/j.compstruct.2022.115692Sako R., Aoki R., Higuchi R., et al. Experiments on the mode II fracture toughness in ENF tests of CFRP curved beams / Composite Struct. 2022. Vol. 292. 115692. DOI: 10.1016/j.compstruct.2022.115692Sanford R. L., Stonesifer F. R. Fracture toughness measurements in unidirectional glass-reinforced plastics / J. Compos. Mater. 1971. Vol. 5. No. 2. P. 241 – 245. DOI: 10.1177/002199837100500208Sanford R. L., Stonesifer F. R. Fracture toughness measurements in unidirectional glass-reinforced plastics / J. Compos. Mater. 1971. Vol. 5. No. 2. P. 241 – 245. DOI: 10.1177/002199837100500208Raimondo A., Urcelay Oca I., Bisagni C. Influence of interface ply orientation on delamination growth in composite laminates / J. Compos. Mater. 2021. Vol. 55. No. 27. P. 3955 – 3972. DOI: 10.1177/00219983211031636Raimondo A., Urcelay Oca I., Bisagni C. Influence of interface ply orientation on delamination growth in composite laminates / J. Compos. Mater. 2021. Vol. 55. No. 27. P. 3955 – 3972. DOI: 10.1177/00219983211031636Pankov A. V., Tokar V. L., Petronyuk Y. S., et al. Determination of crack resistance characteristics of layered carbon plastics on specimens without a crack initiator using the method of acoustic microscopy / Industr. Lab. Mater. Diagn. 2020. Vol. 86. No. 8. P. 58 – 65 [in Russian]. DOI: 10.26896/1028-6861-2020-86-8-58-65Pankov A. V., Tokar V. L., Petronyuk Y. S., et al. Determination of crack resistance characteristics of layered carbon plastics on specimens without a crack initiator using the method of acoustic microscopy / Industr. Lab. Mater. Diagn. 2020. Vol. 86. No. 8. P. 58 – 65 [in Russian]. DOI: 10.26896/1028-6861-2020-86-8-58-65Fakoor 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. 2022. Vol. 56. P. 1261 – 1291. DOI: 10.1007/s00226-022-01392-zFakoor 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. 2022. Vol. 56. P. 1261 – 1291. DOI: 10.1007/s00226-022-01392-zLiu W., Feng P., Huang J. Bilinear softening model and double K fracture criterion for quasi-brittle fracture of pultruded FRP composites / Composite Struct. 2017. Vol. 160. P. 1119 – 1125. DOI: 10.1016/j.compstruct.2016.10.134Liu W., Feng P., Huang J. Bilinear softening model and double K fracture criterion for quasi-brittle fracture of pultruded FRP composites / Composite Struct. 2017. Vol. 160. P. 1119 – 1125. DOI: 10.1016/j.compstruct.2016.10.134Zobnin A. I., Lomakin E. V. Central transverse crack in an orthotropic elastic strip / Izv. AN SSSR. MTT. 1974. No. 1. P. 44 – 52 [in Russian].Zobnin A. I., Lomakin E. V. Central transverse crack in an orthotropic elastic strip / Izv. AN SSSR. MTT. 1974. No. 1. P. 44 – 52 [in Russian].Garpelli F. P., Gonzalez R. F. M., Sales R. C. M., et al. Experimental characterization of Mode II fatigue delamination growth onset in composite joints / J. Compos. Mater. 2022. Vol. 56. No. 1. P. 115 – 132. DOI: 10.1177/00219983211056736Garpelli F. P., Gonzalez R. F. M., Sales R. C. M., et al. Experimental characterization of Mode II fatigue delamination growth onset in composite joints / J. Compos. Mater. 2022. Vol. 56. No. 1. P. 115 – 132. DOI: 10.1177/00219983211056736Bokhoeva L. A., Baldanov A. B., Rogov V. E., et al. Influence of nanopowders addition on strength of multilayer composite materials / Industr. Lab. Mater. Diagn. 2021. Vol. 87. No. 8. P. 42 – 50 [in Russian]. DOI: 10.26896/1028-6861-2020-86-8-58-65Bokhoeva L. A., Baldanov A. B., Rogov V. E., et al. Influence of nanopowders addition on strength of multilayer composite materials / Industr. Lab. Mater. Diagn. 2021. Vol. 87. No. 8. P. 42 – 50 [in Russian]. DOI: 10.26896/1028-6861-2020-86-8-58-65Polilov A. N., Khokhlov V. K. Calculated criterion of composite beams strength at bending / Mech. Eng. 1979. N. 2. P. 53 – 57 [in Russian].Polilov A. N., Khokhlov V. K. Calculated criterion of composite beams strength at bending / Mech. Eng. 1979. N. 2. P. 53 – 57 [in Russian].Polilov A. N., Vlasov D. D., Tatus N. A. Refined criterion of delamination at bending of a composite beam / Industr. Lab. Mater. Diagn. 2023. Vol. 89. No. 10. P. 63 – 73 [in Russian]. DOI: 10.26896/1028-6861-2023-89-10-63-73Polilov A. N., Vlasov D. D., Tatus N. A. Refined criterion of delamination at bending of a composite beam / Industr. Lab. Mater. Diagn. 2023. Vol. 89. No. 10. P. 63 – 73 [in Russian]. DOI: 10.26896/1028-6861-2023-89-10-63-73Ostapska K., Malo R. A. Wedge splitting test of wood for fracture parameters estimation of Norway Spruce / Eng. Fracture Mech. 2020. Vol. 232. 107024. DOI: 10.1016/j.engfracmech.2020.107024Ostapska K., Malo R. A. Wedge splitting test of wood for fracture parameters estimation of Norway Spruce / Eng. Fracture Mech. 2020. Vol. 232. 107024. DOI: 10.1016/j.engfracmech.2020.107024Yoshihara H. Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen / Eng. Fracture Mech. 2008. Vol. 75. No. 16. P. 4727 – 4739. DOI: 10.1016/j.engfracmech.2008.06.010Yoshihara H. Mode II fracture mechanics properties of wood measured by the asymmetric four-point bending test using a single-edge-notched specimen / Eng. Fracture Mech. 2008. Vol. 75. No. 16. P. 4727 – 4739. DOI: 10.1016/j.engfracmech.2008.06.010Khaji 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. Fracture Mech. 2021. Vol. 113. 102962. DOI: 10.1016/j.tafmec.2021.102962Khaji 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. Fracture Mech. 2021. Vol. 113. 102962. DOI: 10.1016/j.tafmec.2021.102962Moustaphaoui A. E., Chouaf A., Kimakh R. Experimental and numerical study of the delamination of Ceiba plywood under mode I, mode II and mixed-mode (I + II) loading using the DCB, ELS and MMF tests / Int. J. Fracture. 2021. Vol. 231. No. 6. P. 1 – 20. DOI: 10.1007/s10704-021-00557-4Moustaphaoui A. E., Chouaf A., Kimakh R. Experimental and numerical study of the delamination of Ceiba plywood under mode I, mode II and mixed-mode (I + II) loading using the DCB, ELS and MMF tests / Int. J. Fracture. 2021. Vol. 231. No. 6. P. 1 – 20. DOI: 10.1007/s10704-021-00557-4Polilov A. N. Resistance to delamination of unidirectional composites / Mech. Eng. 1978. No. 5. P. 74 – 78 [in Russian].Polilov A. N. Resistance to delamination of unidirectional composites / Mech. Eng. 1978. No. 5. P. 74 – 78 [in Russian].Buznikov Yu. N., Polilov A. N., Khokhlov V. K., Finogenov G. N. Determination of resistance of carbon plastics to interlayer fracture near notches / Mech. Eng. 1980. No. 1. P. 114 – 118 [in Russian].Buznikov Yu. N., Polilov A. N., Khokhlov V. K., Finogenov G. N. Determination of resistance of carbon plastics to interlayer fracture near notches / Mech. Eng. 1980. No. 1. P. 114 – 118 [in Russian].Rabotnov Yu. N. Mechanics of deformable solid. Textbook for students of mechanical, mathematical and physical specialties of universities. — Moscow: Nauka, 1988. — 712 p. [in Russian].Rabotnov Yu. N. Mechanics of deformable solid. Textbook for students of mechanical, mathematical and physical specialties of universities. — Moscow: Nauka, 1988. — 712 p. [in Russian].Aniskovich E. V., Lepikhin A. M., Moskvichev V. V. Estimation of static crack resistance of thin-walled vessels working under pressure / Industr. Lab. Mater. Diagn. 2018. Vol. 84. No. 9. P. 55 – 63 [in Russian]. DOI: 10.26896/1028-6861-2018-84-9-55-63Aniskovich E. V., Lepikhin A. M., Moskvichev V. V. Estimation of static crack resistance of thin-walled vessels working under pressure / Industr. Lab. Mater. Diagn. 2018. Vol. 84. No. 9. P. 55 – 63 [in Russian]. DOI: 10.26896/1028-6861-2018-84-9-55-63Harrison N. L. Strain energy release rates for turning cracks / Fibre Sci. Technol. 1972. Vol. 5. No. 3. P. 197 – 212. DOI: 10.1016/0015-0568(72)90015-2Harrison N. L. Strain energy release rates for turning cracks / Fibre Sci. Technol. 1972. Vol. 5. No. 3. P. 197 – 212. DOI: 10.1016/0015-0568(72)90015-2Harrison N. L. Splitting of fiber-reinforced materials / Fibre Sci. Technol. 1973. Vol. 6. No. 1. P. 25 – 38. DOI: 10.1016/0015-0568(73)90014-6Harrison N. L. Splitting of fiber-reinforced materials / Fibre Sci. Technol. 1973. Vol. 6. No. 1. P. 25 – 38. DOI: 10.1016/0015-0568(73)90014-6Polilov A. N., Tatus N. A. Principles of improving the structure of composite products based on the study of biotechnology and biomaterials / MSCU Bull. 2021. Vol. 16. No. 9. P. 1191 – 1216 [in Russian]. DOI: 10.22227/1997-0935.2021.9.1191-1216Polilov A. N., Tatus N. A. Principles of improving the structure of composite products based on the study of biotechnology and biomaterials / MSCU Bull. 2021. Vol. 16. No. 9. P. 1191 – 1216 [in Russian]. DOI: 10.22227/1997-0935.2021.9.1191-1216

The authors declare that there are no conflicts of interest present.