2
How to cite this paper
APA: Mantilla, J., Martínez, M., Villegas, D., Bohorquez, O & Díaz, J. (2024). Dual boundary element method for comparative studies on fatigue crack growth models. Engineering Solid Mechanics, 12(4), 409-422.
Chicago/Turabian: Mantilla, J., Martínez, M., Villegas, D., Bohorquez, O & Díaz, J. 2024. "Dual boundary element method for comparative studies on fatigue crack growth models." Engineering Solid Mechanics 12, no. 4 (2024): 409-422.
AMA: Mantilla, J., Martínez, M., Villegas, D., Bohorquez, O & Díaz, J. Dual boundary element method for comparative studies on fatigue crack growth models. Engineering Solid Mechanics. 2024;12(4):409-422.
References
Aliabadi, M. H. (1997). Boundary Element Formulations in Fracture Mechanics. Applied Mechanics Reviews, 50(2), 83–96. https://doi.org/10.1115/1.3101690
Amsterdam, E., Willem E. Wiegman, J., Nawijn, M., & De Hosson, J. T. M. (2023). On the strain energy release rate and fatigue crack growth rate in metallic alloys. Engineering Fracture Mechanics, 286, 109292. https://doi.org/10.1016/J.ENGFRACMECH.2023.109292
ASTM. (2023). Standard Test Method for Measurement of Fatigue Crack Growth Rates, E647 - 23. https://doi.org/10.1520/E0647-23A
Balderrama, R., Cisilino, A. P., & Martinez, M. (2006). Boundary Element Method Analysis of Three-Dimensional Thermoelastic Fracture Problems Using the Energy Domain Integral. Journal of Applied Mechanics, 73(6), 959–969. https://doi.org/10.1115/1.2173287
Bassindale, C., Wang, X., Tyson, W. R., & Xu, S. (2018). Numerical verification of stress intensity factor solution for clamped single edge notched tension (SENT) specimens. Fatigue & Fracture of Engineering Materials & Structures, 41(2), 494–499. https://doi.org/10.1111/FFE.12700
Boljanović, S., & Maksimović, S. (2011). Analysis of the crack growth propagation process under mixed-mode loading. Engineering Fracture Mechanics, 78(8), 1565–1576. https://doi.org/10.1016/J.ENGFRACMECH.2011.02.003
Cheng, A., & Chen, N. Z. (2017). Fatigue crack growth modelling for pipeline carbon steels under gaseous hydrogen conditions. International Journal of Fatigue, 96, 152–161. https://doi.org/10.1016/J.IJFATIGUE.2016.11.029
Citarella, R., Giannella, V., Vivo, E., & Mazzeo, M. (2016). FEM-DBEM approach for crack propagation in a low pressure aeroengine turbine vane segment. Theoretical and Applied Fracture Mechanics, 86, 143–152. https://doi.org/10.1016/J.TAFMEC.2016.05.004
Díaz, J. G., & Freire, J. L. de F. (2022). LEFM crack path models evaluation under proportional and non-proportional load in low carbon steels using digital image correlation data. International Journal of Fatigue, 156, 106687. https://doi.org/10.1016/J.IJFATIGUE.2021.106687
Forman, R. G., Kearney, V. E., & Engle, R. M. (1967). Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures. Journal of Basic Engineering, 89(3), 459–463. https://doi.org/10.1115/1.3609637
Gdoutos, E. E. (1990). Linear elastic stress field in cracked bodies. Fracture Mechanics Criteria and Applications, 15–75. https://doi.org/10.1007/978-94-009-1956-3_2
Gómez, E., Díaz, J., Mantilla, J., Bohorquez, O., & Martínez, M. (2024). Experimental and Numerical Evaluation of Equivalent Stress Intensity Factor Models under Mixed-Mode (I+II) Loading. Infrastructures 2024, Vol. 9, Page 45, 9(3), 45. https://doi.org/10.3390/INFRASTRUCTURES9030045
Kats, B. A., & Katz, D. B. (2019). Cauchy–Hadamard integral with applications. Monatshefte Für Mathematik 2019 189:4, 189(4), 683–689. https://doi.org/10.1007/S00605-019-01263-Z
Klesnil, M., & Lukáš, P. (1972). Influence of strength and stress history on growth and stabilisation of fatigue cracks. Engineering Fracture Mechanics, 4(1), 77–92. https://doi.org/10.1016/0013-7944(72)90078-1
Koko, A., Earp, P., Wigger, T., Tong, J., & Marrow, T. J. (2020). J-integral analysis: An EDXD and DIC comparative study for a fatigue crack. International Journal of Fatigue, 134, 105474. https://doi.org/10.1016/J.IJFATIGUE.2020.105474
Krscanski, S., & Brnic, J. (2020). Prediction of fatigue crack growth in metallic specimens under constant amplitude loading using virtual crack closure and forman model. Metals, 10(7), 1–14. https://doi.org/10.3390/MET10070977
Lardner, R. W. (1968). A dislocation model for fatigue crack growth in metals. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, 17(145), 71–82. https://doi.org/10.1080/14786436808218181
Leite, P. G. P., & Gomes, G. (2019). Numerical simulation of fatigue crack propagation in mixed-mode (I+II) using the program BemCracker2D. International Journal of Structural Integrity, 10(4), 497–514. https://doi.org/10.1108/IJSI-04-2018-0022
Liu, C., Li, B., Cai, Y., & Chen, X. (2020). Fatigue crack propagation behaviour of pressurised elbow pipes under cyclic bending. Thin-Walled Structures, 154, 106882. https://doi.org/10.1016/J.TWS.2020.106882
Machniewicz, T. (2013). Fatigue crack growth prediction models for metallic materials. Fatigue & Fracture of Engineering Materials & Structures, 36(4), 293–307. https://doi.org/10.1111/J.1460-2695.2012.01721.X
Malíková, L., Veselý, V., & Seitl, S. (2016). Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria. International Journal of Fatigue, 89, 99–107. https://doi.org/10.1016/J.IJFATIGUE.2016.01.010
Mantilla, J., Poveda, D., & Martínez, M. (2021). Estimation of the Stress Intensity Factor in a Wedge Splitting Test Under Static Load Using the Finite Elements Method. Respuestas, 26(1), 53–61. https://doi.org/10.22463/0122820X.1934
Moore, P., & Pisarski, H. (2017). SENT testing standard BS 8571 and its ongoing development. International Journal of Pressure Vessels and Piping, 156, 2–7. https://doi.org/10.1016/J.IJPVP.2017.05.011
Mukherjee, A., Ghosh, M., Mondal, K., Venkitanarayanan, P., Moon, A. P., & Varshney, A. (2015). Study of mechanical properties, microstructures and corrosion behavior of al 7075 t651 alloy with varying strain rate. IOP Conference Series: Materials Science and Engineering, 75(1), 012031. https://doi.org/10.1088/1757-899X/75/1/012031
Newman, J. C., Anagnostou, E. L., & Rusk, D. (2014). Fatigue and crack-growth analyses on 7075-T651 aluminum alloy coupons under constant- and variable-amplitude loading. International Journal of Fatigue, 62, 133–143. https://doi.org/10.1016/J.IJFATIGUE.2013.04.020
Paris, P., & Erdogan, F. (1963). A Critical Analysis of Crack Propagation Laws. Journal of Basic Engineering, 85(4), 528–533. https://doi.org/10.1115/1.3656900
Peixoto, R. G., Borges, B., Fonseca, F., & Guerra Peixoto, R. (2023). Direct evaluation of J-Integrals by Gauss-Legendre quadrature in the Dual Boundary Element Method. https://doi.org/10.21203/RS.3.RS-3168091/V1
Portela, A., Aliabadi, M. H., & Rooke, D. P. (1993). Dual boundary element incremental analysis of crack propagation. Computers & Structures, 46(2), 237–247. https://doi.org/10.1016/0045-7949(93)90189-K
Price, R. J., & Trevelyan, J. (2014a). Boundary element simulation of fatigue crack growth in multi-site damage. Engineering Analysis with Boundary Elements, 43, 67–75. https://doi.org/10.1016/J.ENGANABOUND.2014.03.002
Price, R. J., & Trevelyan, J. (2014b). Boundary element simulation of fatigue crack growth in multi-site damage. Engineering Analysis with Boundary Elements, 43, 67–75. https://doi.org/10.1016/J.ENGANABOUND.2014.03.002
Rice, J. R. (1968). A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35(2), 379–386. https://doi.org/10.1115/1.3601206
Sajith, S., Murthy, K. S. R. K., & Robi, P. S. (2019). Mixed mode fatigue crack growth studies of crack emanating from circular hole. AIP Conference Proceedings, 2200(1), 020041. https://doi.org/10.1063/1.5141211
Sajith, S., Shukla, S. S., Murthy, K. S. R. K., & Robi, P. S. (2020). Mixed mode fatigue crack growth studies in AISI 316 stainless steel. European Journal of Mechanics - A/Solids, 80, 103898. https://doi.org/10.1016/J.EUROMECHSOL.2019.103898
Sajuri, Z., Alang, N. A., Razak, N. A., & Aziman, M. A. (2011). Fracture Toughness and Fatigue Crack Growth Behavior of Rail Track Material. Key Engineering Materials, 462–463, 1109–1114. https://doi.org/10.4028/WWW.SCIENTIFIC.NET/KEM.462-463.1109
Santana, E., & Portela, A. (2016a). Dual boundary element analysis of fatigue crack growth, interaction and linkup. Engineering Analysis with Boundary Elements, 64, 176–195. https://doi.org/10.1016/J.ENGANABOUND.2015.12.002
Santana, E., & Portela, A. (2016b). Dual boundary element analysis of fatigue crack growth, interaction and linkup. Engineering Analysis with Boundary Elements, 64, 176–195. https://doi.org/10.1016/J.ENGANABOUND.2015.12.002
Sedmak, A. (2018). Computational fracture mechanics: An overview from early efforts to recent achievements. Fatigue & Fracture of Engineering Materials & Structures, 41(12), 2438–2474. https://doi.org/10.1111/FFE.12912
Shen, G., Gianetto, J., & Tyson, W. (2009). Measurement of J-R Curves Using Single-Specimen Technique On Clamped SE(T) Specimens. The Nineteenth International Offshore and Polar Engineering Conference.
Shlyannikov, V., Yarullin, R., Yakovlev, M., Giannella, V., & Citarella, R. (2021). Mixed-mode crack growth simulation in aviation engine compressor disk. Engineering Fracture Mechanics, 246, 107617. https://doi.org/10.1016/J.ENGFRACMECH.2021.107617
Shukla, S. S., & Murthy, K. S. R. K. (2023). A study on the effect of different Paris constants in mixed mode (I/II) fatigue life prediction in Al 7075-T6 alloy. International Journal of Fatigue, 176, 107895. https://doi.org/10.1016/J.IJFATIGUE.2023.107895
Singh, A., Tang, L., Dao, M., Lu, L., & Suresh, S. (2011). Fracture toughness and fatigue crack growth characteristics of nanotwinned copper. Acta Materialia, 59(6), 2437–2446. https://doi.org/10.1016/J.ACTAMAT.2010.12.043
Tanaka, K. (1974). Fatigue crack propagation from a crack inclined to the cyclic tensile axis. Engineering Fracture Mechanics, 6(3), 493–507. https://doi.org/10.1016/0013-7944(74)90007-1
Tanaka, K. (1983). The cyclic J-integral as a criterion for fatigue crack growth. International Journal of Fracture, 22(2), 91–104. https://doi.org/10.1007/BF00942715/METRICS
Vaidya, W. V., Horstmann, M., Angamuthu, K., & Koçak, M. (2010). Utilising CODmax as an indirect fatigue crack length measurement parameter for M(T) specimens of an airframe aluminium alloy AA6056. Materialpruefung/Materials Testing, 52(11–12), 771–777. https://doi.org/10.3139/120.110185
Wang, C., Pereira, K., Wang, D., Zinovev, A., Terentyev, D., & Abdel Wahab, M. (2023). Fretting fatigue crack propagation under out-of-phase loading conditions using extended maximum tangential stress criterion. Tribology International, 187, 108738. https://doi.org/10.1016/J.TRIBOINT.2023.108738
Wen, P., & Aliabadi, M. (2012). Dual Boundary Element Method for Modelling Curved Crack Paths. International Journal of Fracture , 176, 127–133. https://doi.org/10.1007/s10704-012-9719-x
Xu, M., Liu, Y., & Yuan, H. (2022). Characterization of crack-tip fields for elastoplastic fatigue crack growth Part I: Analysis of the ΔJ-integral. Engineering Fracture Mechanics, 275, 108847. https://doi.org/10.1016/J.ENGFRACMECH.2022.108847
Zhao, T., Zhang, J., & Jiang, Y. (2008). A study of fatigue crack growth of 7075-T651 aluminum alloy. International Journal of Fatigue, 30(7), 1169–1180. https://doi.org/10.1016/J.IJFATIGUE.2007.09.006
Zhu, X. K. (2017). Full-range stress intensity factor solutions for clamped SENT specimens. International Journal of Pressure Vessels and Piping, 149, 1–13. https://doi.org/10.1016/J.IJPVP.2016.11.004
Amsterdam, E., Willem E. Wiegman, J., Nawijn, M., & De Hosson, J. T. M. (2023). On the strain energy release rate and fatigue crack growth rate in metallic alloys. Engineering Fracture Mechanics, 286, 109292. https://doi.org/10.1016/J.ENGFRACMECH.2023.109292
ASTM. (2023). Standard Test Method for Measurement of Fatigue Crack Growth Rates, E647 - 23. https://doi.org/10.1520/E0647-23A
Balderrama, R., Cisilino, A. P., & Martinez, M. (2006). Boundary Element Method Analysis of Three-Dimensional Thermoelastic Fracture Problems Using the Energy Domain Integral. Journal of Applied Mechanics, 73(6), 959–969. https://doi.org/10.1115/1.2173287
Bassindale, C., Wang, X., Tyson, W. R., & Xu, S. (2018). Numerical verification of stress intensity factor solution for clamped single edge notched tension (SENT) specimens. Fatigue & Fracture of Engineering Materials & Structures, 41(2), 494–499. https://doi.org/10.1111/FFE.12700
Boljanović, S., & Maksimović, S. (2011). Analysis of the crack growth propagation process under mixed-mode loading. Engineering Fracture Mechanics, 78(8), 1565–1576. https://doi.org/10.1016/J.ENGFRACMECH.2011.02.003
Cheng, A., & Chen, N. Z. (2017). Fatigue crack growth modelling for pipeline carbon steels under gaseous hydrogen conditions. International Journal of Fatigue, 96, 152–161. https://doi.org/10.1016/J.IJFATIGUE.2016.11.029
Citarella, R., Giannella, V., Vivo, E., & Mazzeo, M. (2016). FEM-DBEM approach for crack propagation in a low pressure aeroengine turbine vane segment. Theoretical and Applied Fracture Mechanics, 86, 143–152. https://doi.org/10.1016/J.TAFMEC.2016.05.004
Díaz, J. G., & Freire, J. L. de F. (2022). LEFM crack path models evaluation under proportional and non-proportional load in low carbon steels using digital image correlation data. International Journal of Fatigue, 156, 106687. https://doi.org/10.1016/J.IJFATIGUE.2021.106687
Forman, R. G., Kearney, V. E., & Engle, R. M. (1967). Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures. Journal of Basic Engineering, 89(3), 459–463. https://doi.org/10.1115/1.3609637
Gdoutos, E. E. (1990). Linear elastic stress field in cracked bodies. Fracture Mechanics Criteria and Applications, 15–75. https://doi.org/10.1007/978-94-009-1956-3_2
Gómez, E., Díaz, J., Mantilla, J., Bohorquez, O., & Martínez, M. (2024). Experimental and Numerical Evaluation of Equivalent Stress Intensity Factor Models under Mixed-Mode (I+II) Loading. Infrastructures 2024, Vol. 9, Page 45, 9(3), 45. https://doi.org/10.3390/INFRASTRUCTURES9030045
Kats, B. A., & Katz, D. B. (2019). Cauchy–Hadamard integral with applications. Monatshefte Für Mathematik 2019 189:4, 189(4), 683–689. https://doi.org/10.1007/S00605-019-01263-Z
Klesnil, M., & Lukáš, P. (1972). Influence of strength and stress history on growth and stabilisation of fatigue cracks. Engineering Fracture Mechanics, 4(1), 77–92. https://doi.org/10.1016/0013-7944(72)90078-1
Koko, A., Earp, P., Wigger, T., Tong, J., & Marrow, T. J. (2020). J-integral analysis: An EDXD and DIC comparative study for a fatigue crack. International Journal of Fatigue, 134, 105474. https://doi.org/10.1016/J.IJFATIGUE.2020.105474
Krscanski, S., & Brnic, J. (2020). Prediction of fatigue crack growth in metallic specimens under constant amplitude loading using virtual crack closure and forman model. Metals, 10(7), 1–14. https://doi.org/10.3390/MET10070977
Lardner, R. W. (1968). A dislocation model for fatigue crack growth in metals. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, 17(145), 71–82. https://doi.org/10.1080/14786436808218181
Leite, P. G. P., & Gomes, G. (2019). Numerical simulation of fatigue crack propagation in mixed-mode (I+II) using the program BemCracker2D. International Journal of Structural Integrity, 10(4), 497–514. https://doi.org/10.1108/IJSI-04-2018-0022
Liu, C., Li, B., Cai, Y., & Chen, X. (2020). Fatigue crack propagation behaviour of pressurised elbow pipes under cyclic bending. Thin-Walled Structures, 154, 106882. https://doi.org/10.1016/J.TWS.2020.106882
Machniewicz, T. (2013). Fatigue crack growth prediction models for metallic materials. Fatigue & Fracture of Engineering Materials & Structures, 36(4), 293–307. https://doi.org/10.1111/J.1460-2695.2012.01721.X
Malíková, L., Veselý, V., & Seitl, S. (2016). Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria. International Journal of Fatigue, 89, 99–107. https://doi.org/10.1016/J.IJFATIGUE.2016.01.010
Mantilla, J., Poveda, D., & Martínez, M. (2021). Estimation of the Stress Intensity Factor in a Wedge Splitting Test Under Static Load Using the Finite Elements Method. Respuestas, 26(1), 53–61. https://doi.org/10.22463/0122820X.1934
Moore, P., & Pisarski, H. (2017). SENT testing standard BS 8571 and its ongoing development. International Journal of Pressure Vessels and Piping, 156, 2–7. https://doi.org/10.1016/J.IJPVP.2017.05.011
Mukherjee, A., Ghosh, M., Mondal, K., Venkitanarayanan, P., Moon, A. P., & Varshney, A. (2015). Study of mechanical properties, microstructures and corrosion behavior of al 7075 t651 alloy with varying strain rate. IOP Conference Series: Materials Science and Engineering, 75(1), 012031. https://doi.org/10.1088/1757-899X/75/1/012031
Newman, J. C., Anagnostou, E. L., & Rusk, D. (2014). Fatigue and crack-growth analyses on 7075-T651 aluminum alloy coupons under constant- and variable-amplitude loading. International Journal of Fatigue, 62, 133–143. https://doi.org/10.1016/J.IJFATIGUE.2013.04.020
Paris, P., & Erdogan, F. (1963). A Critical Analysis of Crack Propagation Laws. Journal of Basic Engineering, 85(4), 528–533. https://doi.org/10.1115/1.3656900
Peixoto, R. G., Borges, B., Fonseca, F., & Guerra Peixoto, R. (2023). Direct evaluation of J-Integrals by Gauss-Legendre quadrature in the Dual Boundary Element Method. https://doi.org/10.21203/RS.3.RS-3168091/V1
Portela, A., Aliabadi, M. H., & Rooke, D. P. (1993). Dual boundary element incremental analysis of crack propagation. Computers & Structures, 46(2), 237–247. https://doi.org/10.1016/0045-7949(93)90189-K
Price, R. J., & Trevelyan, J. (2014a). Boundary element simulation of fatigue crack growth in multi-site damage. Engineering Analysis with Boundary Elements, 43, 67–75. https://doi.org/10.1016/J.ENGANABOUND.2014.03.002
Price, R. J., & Trevelyan, J. (2014b). Boundary element simulation of fatigue crack growth in multi-site damage. Engineering Analysis with Boundary Elements, 43, 67–75. https://doi.org/10.1016/J.ENGANABOUND.2014.03.002
Rice, J. R. (1968). A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35(2), 379–386. https://doi.org/10.1115/1.3601206
Sajith, S., Murthy, K. S. R. K., & Robi, P. S. (2019). Mixed mode fatigue crack growth studies of crack emanating from circular hole. AIP Conference Proceedings, 2200(1), 020041. https://doi.org/10.1063/1.5141211
Sajith, S., Shukla, S. S., Murthy, K. S. R. K., & Robi, P. S. (2020). Mixed mode fatigue crack growth studies in AISI 316 stainless steel. European Journal of Mechanics - A/Solids, 80, 103898. https://doi.org/10.1016/J.EUROMECHSOL.2019.103898
Sajuri, Z., Alang, N. A., Razak, N. A., & Aziman, M. A. (2011). Fracture Toughness and Fatigue Crack Growth Behavior of Rail Track Material. Key Engineering Materials, 462–463, 1109–1114. https://doi.org/10.4028/WWW.SCIENTIFIC.NET/KEM.462-463.1109
Santana, E., & Portela, A. (2016a). Dual boundary element analysis of fatigue crack growth, interaction and linkup. Engineering Analysis with Boundary Elements, 64, 176–195. https://doi.org/10.1016/J.ENGANABOUND.2015.12.002
Santana, E., & Portela, A. (2016b). Dual boundary element analysis of fatigue crack growth, interaction and linkup. Engineering Analysis with Boundary Elements, 64, 176–195. https://doi.org/10.1016/J.ENGANABOUND.2015.12.002
Sedmak, A. (2018). Computational fracture mechanics: An overview from early efforts to recent achievements. Fatigue & Fracture of Engineering Materials & Structures, 41(12), 2438–2474. https://doi.org/10.1111/FFE.12912
Shen, G., Gianetto, J., & Tyson, W. (2009). Measurement of J-R Curves Using Single-Specimen Technique On Clamped SE(T) Specimens. The Nineteenth International Offshore and Polar Engineering Conference.
Shlyannikov, V., Yarullin, R., Yakovlev, M., Giannella, V., & Citarella, R. (2021). Mixed-mode crack growth simulation in aviation engine compressor disk. Engineering Fracture Mechanics, 246, 107617. https://doi.org/10.1016/J.ENGFRACMECH.2021.107617
Shukla, S. S., & Murthy, K. S. R. K. (2023). A study on the effect of different Paris constants in mixed mode (I/II) fatigue life prediction in Al 7075-T6 alloy. International Journal of Fatigue, 176, 107895. https://doi.org/10.1016/J.IJFATIGUE.2023.107895
Singh, A., Tang, L., Dao, M., Lu, L., & Suresh, S. (2011). Fracture toughness and fatigue crack growth characteristics of nanotwinned copper. Acta Materialia, 59(6), 2437–2446. https://doi.org/10.1016/J.ACTAMAT.2010.12.043
Tanaka, K. (1974). Fatigue crack propagation from a crack inclined to the cyclic tensile axis. Engineering Fracture Mechanics, 6(3), 493–507. https://doi.org/10.1016/0013-7944(74)90007-1
Tanaka, K. (1983). The cyclic J-integral as a criterion for fatigue crack growth. International Journal of Fracture, 22(2), 91–104. https://doi.org/10.1007/BF00942715/METRICS
Vaidya, W. V., Horstmann, M., Angamuthu, K., & Koçak, M. (2010). Utilising CODmax as an indirect fatigue crack length measurement parameter for M(T) specimens of an airframe aluminium alloy AA6056. Materialpruefung/Materials Testing, 52(11–12), 771–777. https://doi.org/10.3139/120.110185
Wang, C., Pereira, K., Wang, D., Zinovev, A., Terentyev, D., & Abdel Wahab, M. (2023). Fretting fatigue crack propagation under out-of-phase loading conditions using extended maximum tangential stress criterion. Tribology International, 187, 108738. https://doi.org/10.1016/J.TRIBOINT.2023.108738
Wen, P., & Aliabadi, M. (2012). Dual Boundary Element Method for Modelling Curved Crack Paths. International Journal of Fracture , 176, 127–133. https://doi.org/10.1007/s10704-012-9719-x
Xu, M., Liu, Y., & Yuan, H. (2022). Characterization of crack-tip fields for elastoplastic fatigue crack growth Part I: Analysis of the ΔJ-integral. Engineering Fracture Mechanics, 275, 108847. https://doi.org/10.1016/J.ENGFRACMECH.2022.108847
Zhao, T., Zhang, J., & Jiang, Y. (2008). A study of fatigue crack growth of 7075-T651 aluminum alloy. International Journal of Fatigue, 30(7), 1169–1180. https://doi.org/10.1016/J.IJFATIGUE.2007.09.006
Zhu, X. K. (2017). Full-range stress intensity factor solutions for clamped SENT specimens. International Journal of Pressure Vessels and Piping, 149, 1–13. https://doi.org/10.1016/J.IJPVP.2016.11.004