How to cite this paper
Barrinaya, M., Alfiyuranda, M., Ramezani, M., Putra, I., Ramesh, S., Kadarno, P., Hastuty, S & Purbolaksono, J. (2022). Modes I-II-III stress intensity factors of a semi-elliptical surface crack at a round bar under torsion loading by FEM and DBEM.Engineering Solid Mechanics, 10(4), 399-406.
Refrences
Abd-Elhady, A. (2013). Mixed mode I/II stress intensity factors through the thickness of disc type specimens. Engineering Solid Mechanics, 1(4), 119-128.
Aliabadi, M.H. & Rooke, D.P. (1991). Numerical Fracture Mechanics (Solid Mechanics and Its Applications (8)) 1991st Ed. Springer.
Aliabadi, M.H. (1997). Boundary element methods in fracture mechanics. Applied Mechanics Review, 50, 83-96.
Alshoaibi, A. (2020). Finite element-based model for crack propagation in linear elastic materials. Engineering Solid Mechanics, 8(2), 131-142.
Aliha, M.R.M., & Ayatollahi, M.R. (2008). On mixed-mode I/II crack growth in dental resin materials. Scripta Materialia, 59(2), 258-261.
Aliha, M.R.M., Ayatollahi, M.R., Smith, D.J. & Pavier, M. J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Engineering Fracture Mechanics, 77(11), 2200-2212.
Aliha, M.R.M. & Ayatollahi, M. R. (2012). Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion. International Journal of Solids and Structures, 49(13), 1877-1883.
Aliha, M.R.M., Shaker, S. & Keymanesh, M.R. (2019). Low temperature fracture toughness study for bitumen under mixed mode I + II loading condition. Engineering Fracture Mechanics, 206, 297-309.
Athanassiadis, A., Boissenot, J. M., Brevet, P., Francois, D., & Raharinaivo, A. (1981). Linear elastic fracture mechanics computations of cracked cylindrical tensioned bodies. International Journal of Fracture, 17(6), 553-566.
Bahmani, A., Aliha, M. R. M., Sarbijan, M. J., & Mousavi, S. S. (2020). An extended edge-notched disc bend (ENDB) specimen for mixed-mode I+ II fracture assessments. International Journal of Solids and Structures, 193, 239-250.
Bažant, Z. P., & Estenssoro, L. F. (1979). Surface singularity and crack propagation. International Journal of Solids and Structures, 15(5), 405-426.
Benthem, J. (1977). State of stress at the vertex of a quarter-infinite crack in a half-space. International Journal of Solids and Structures, 13(5), 479-492.
Benthem, J. P. (1980). The quarter-infinite crack in a half space; alternative and additional solutions. International Journal of Solids and Structures, 16(2), 119-130.
Carpinteri, A. (1992). Elliptical-arc surface cracks in round bars. Fatigue & Fracture of Engineering Materials and Structures, 15(11), 1141–1153.
Carpinteri, A. (1993). Shape change of surface cracks in round bars under cyclic axial loading. International Journal of Fatigue, 15(1), 21-26.
Carpinteri, A., & Brighenti, R. (1996). Part-through cracks in round bars under cyclic combined axial and bending loading. International journal of fatigue, 18(1), 33-39.
Carpinteri, A., & Brighenti, R. (1996). Fatigue propagation of surface flaws in round bars: a three‐parameter theoretical model. Fatigue & Fracture of Engineering Materials & Structures, 19(12), 1471-1480.
Carpinteri, A., Brighenti, R. & Vantadori, S. (2006). Surface crack in notched round bars under cyclic tension and bending. International Journal of Fatigue, 28(3), 251–260.
Caspers, M., & Mattheck C. (1987), Weighted averaged stress intensity factors of circular-fronted cracks in cylindrical bars, Fatigue & Fracture of Engineering Materials and Structures, 9, 329-341.
Chandra, D., Purbolaksono, J., Nukman, Y., Ramesh, S., Liew, H.L. & Hassan, M.A. (2014). Fatigue growth of a surface crack in a V-shaped notched round bar under cyclic tension. Journal of Zhejiang University Science A, 15(11), 873-882.
Chandra D., Putra I.S., Ariffin A.K., Nukman Y., Mardi N.A. & Purbolaksono J. (2016). Fatigue growth analysis of a surface crack in a solid cylinder under combined cyclic axial-torsion loading, Experimental Techniques, 40(5), 1397-1407.
Cisilino, A.P., & Aliabadi, M.H. (1999). Three-dimensional boundary element analysis of fatigue crack growth in linear and non-linear fracture problems. Engineering Fracture Mechanics, 63(6), 713-733.
Citarella, R., Lepore, M., Shlyannikov, V. & Yarullin, R. (2014). Fatigue surface crack growth in cylindrical specimen under combined loading. Engineering Fracture Mechanics, 131, 439-453.
Dixon, J.R., & Pook, L.P. (1969). Stress intensity factors calculated generally by the finite element technique, Nature, 224, 166-167.
De Matos, P., & Nowell, D. (2008). The influence of the poisson’s ratio and corner point singularities in three-dimensional plasticity-induced fatigue crack closure: A numerical study. International Journal of Fatigue, 30, 1930–1943.
Fonte, M., & Freitas, M. (1997). Semi-elliptical crack growth under rotating or reversed bending combined with steady torsion. Fatigue & Fracture of Engineering Materials and Structures, 20(6), 895-906.
Fonte, M., & Freitas, M. (1999). Stress intensity factor for semi-elliptical surface cracks in round bars under bending and torsion. International Journal of Fatigue, 21(5), 457–463.
Forman, R.G., & Shivakumar, V. (1986), Growth behavior of surface cracks in the circumferential plane of solid and hollow cylinders. Fracture Mechanics, 17, ASTM STP 905, 59-74.
Gray, L. J., Martha, L. F., & Ingraffea, A. R. (1990). Hypersingular integrals in boundary element fracture analysis. International journal for numerical methods in engineering, 29(6), 1135-1158.
Guo, W., Shen, H., & Li, H. (2003). Stress intensity factors for elliptical surface cracks in round bars with different stress concentration coefficient. International journal of fatigue, 25(8), 733-741.
Højfeldt, E., & Østervig, C. B. (1986). Fatigue crack propagation in shafts with shoulder fillets. Engineering fracture mechanics, 25(4), 421-427.
Ismail, A.E., Ariffin, A.K., Abdullah, S., & Ghazali, M.J. (2012). Stress intensity factors for surface cracks in round bar under single and combined loadings. Meccanica, 47(5), 1141-1156.
Joseph, R.P., Purbolaksono, J., Liew, H.L., Ramesh, S., & Hamdi M. (2014). Stress intensity factors of a corner crack emanating from a pinhole of a solid cylinder. Engineering Fracture Mechanics, 128, 1-7.
Joseph, R.P., Putra, I.S., Darmawan, A.S., Liew, H.L., Ramesh, S., Kadarno, P., Mohammad, M.A., & Purbolaksono, J. (2020). Fracture analysis of a corner crack in a pinhole of a solid cylinder under torsion loading. Engineering Solid Mechanics, 8(4), 353-364.
Kuna, M. (2013). Finite Elements in Fracture Mechanics: Theory – Numerics - Applications (Solid Mechanics and Its Applications (201)) 2013th Ed. Springer.
Kotousov, A. (2010). Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates. International Journal of Solids and Structures, 47, 1916–1923.
Kotousov, A., Lazzarin, P., Berto, F. & Pook, L.P. (2013). Three-dimensional stress states at crack tip induced by shear and anti-plane loading. Engineering Fracture Mechanics,108, 65-74
Kotousov, A., Berto, F., Lazzarin, P., & Pegorin, F. (2012). Three dimensional finite element mixed fracture mode under anti-plane loading of a crack. Theoretical and Applied Fracture Mechanics, 62, 6226-6233.
Lazzarin, P., & Zappalorto, M. (2012). A three‐dimensional stress field solution for pointed and sharply radiused V‐notches in plates of finite thickness. Fatigue & Fracture of Engineering Materials & Structures, 35(12), 1105-1119.
Lin, X. B., & Smith, R. A. (1997). Shape growth simulation of surface cracks in tension fatigued round bars. International Journal of Fatigue, 19(6), 461-469.
Lin, X. B., & Smith, R. A. (1998). Fatigue growth simulation for cracks in notched and unnotched round bars. International Journal of Mechanical Sciences, 40(5), 405-419.
Lorentzen, T., Kjaer, N. E., & Henriksen, T. K. (1986). The application of fracture mechanics to surface cracks in shafts. Engineering fracture mechanics, 23(6), 1005-1014.
Mackay, T. L., & Alperin, B. J. (1985). Stress intensity factors for fatigue cracking in high-strength bolts. Engineering Fracture Mechanics, 21(2), 391-397.
Mi, Y., & Aliabadi, M.H. (1992). Dual boundary element method for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements, 10(2), 161-171.
Predan, J., Močilnik, V., & Gubeljak, N. (2013). Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion. Engineering Fracture Mechanics, 105, 152-168.
Pook, L.P. (1994). Some implications of corner point singularities. Engineering Fracture Mechanics, 48(3), 367-378.
Pook, L. P. (2013). A 50‐year retrospective review of three‐dimensional effects at cracks and sharp notches. Fatigue & Fracture of Engineering Materials & Structures, 36(8), 699-723.
Pook, L. P., Berto, F., Campagnolo, A., & Lazzarin, P. (2014). Coupled fracture mode of a cracked disc under anti-plane loading. Engineering Fracture Mechanics, 128, 22-36.
Pook, L. P., Campagnolo, A., Berto, F., & Lazzarin, P. (2015). Coupled fracture mode of a cracked plate under anti-plane loading. Engineering Fracture Mechanics, 134, 391-403.
Pook, L. P., Campagnolo, A., & Berto, F. (2016). Coupled fracture modes of discs and plates under anti‐plane loading and a disc under in‐plane shear loading. Fatigue & Fracture of Engineering Materials & Structures, 39(8), 924-938.
Pook, L. P., Berto, F., & Campagnolo, A. (2017). State of the art of corner point singularities under in-plane and out-of-plane loading. Engineering Fracture Mechanics, 174, 2-9.
Portela, A., Aliabadi, M. H., & Rooke, D. (1992). The dual boundary element method: effective implementation for crack problems. International journal for numerical methods in engineering, 33(6), 1269-1287.
Raju, I. S., & Newman Jr, J. C. (1985). Stress-intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads (No. NASA-TM-87594).
Ramezani, M. K., Purbolaksono, J., Andriyana, A., Ramesh, S., & Putra, I. S. (2018). Empirical solutions for stress intensity factors of a surface crack in a solid cylinder under pure torsion. Engineering Fracture Mechanics, 193, 122-136.
Ramezani, M. K., Purbolaksono, J., Andriyana, A., Ramesh, S., & Mardi, N. A. (2018). Analysis of surface cracks in round bars using dual boundary element method. Engineering Analysis with Boundary Elements, 93, 112-123.
Shin, C. S., & Cai, C. Q. (2004). Experimental and finite element analyses on stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending. International Journal of fracture, 129(3), 239-264.
Shivakumar, K. N., & Raju, I. S. (1990). Treatment of singularities in cracked bodies. International journal of fracture, 45(3), 159-178.
Teh, S., Andriyana, A., Ramesh, S., Putra, I. S., Kadarno, P., & Purbolaksono, J. (2021). Tetrahedral meshing for a slanted semi-elliptical surface crack at a solid cylinder. Engineering Fracture Mechanics, 241, 107400.
Toribio, J., Matos, J. C., González, B., & Escuadra, J. (2009). Numerical modelling of crack shape evolution for surface flaws in round bars under tensile loading. Engineering Failure Analysis, 16(2), 618-630.
Toribio, J., Álvarez, N., González, B., & Matos, J. C. (2009). A critical review of stress intensity factor solutions for surface cracks in round bars subjected to tension loading. Engineering Failure Analysis, 16(3), 794-809.
Toribio, J., Matos, J. C., González, B., & Escuadra, J. (2014). Numerical modelling of cracking path in round bars subjected to cyclic tension and bending. International Journal of Fatigue, 58, 20-27.
Watson, J.O. (1986). Hermitian cubic and singular elements for plain strain, in Development in Boundary Element Methods 4, ed. P.K. Banerjee & J.O. Watson, Elsevier Applied Science Publishers, Barking, UK.
Wawrzynek, P.A., & Ingraffea, A.R. (2003). 3.01 - Finite Element Methods for Linear Elastic Fracture Mechanics. Comprehensive Structural Integrity, 3, 1-88.
Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics, 24, 109-114.
Zakavi, B., Kotousov, A., Khanna, A., & Branco, R. (2019). A new method for analysis of part-elliptical surface cracks in structures subjected to fatigue loading. Theoretical and Applied Fracture Mechanics, 103, 102258.
Aliabadi, M.H. & Rooke, D.P. (1991). Numerical Fracture Mechanics (Solid Mechanics and Its Applications (8)) 1991st Ed. Springer.
Aliabadi, M.H. (1997). Boundary element methods in fracture mechanics. Applied Mechanics Review, 50, 83-96.
Alshoaibi, A. (2020). Finite element-based model for crack propagation in linear elastic materials. Engineering Solid Mechanics, 8(2), 131-142.
Aliha, M.R.M., & Ayatollahi, M.R. (2008). On mixed-mode I/II crack growth in dental resin materials. Scripta Materialia, 59(2), 258-261.
Aliha, M.R.M., Ayatollahi, M.R., Smith, D.J. & Pavier, M. J. (2010). Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Engineering Fracture Mechanics, 77(11), 2200-2212.
Aliha, M.R.M. & Ayatollahi, M. R. (2012). Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion. International Journal of Solids and Structures, 49(13), 1877-1883.
Aliha, M.R.M., Shaker, S. & Keymanesh, M.R. (2019). Low temperature fracture toughness study for bitumen under mixed mode I + II loading condition. Engineering Fracture Mechanics, 206, 297-309.
Athanassiadis, A., Boissenot, J. M., Brevet, P., Francois, D., & Raharinaivo, A. (1981). Linear elastic fracture mechanics computations of cracked cylindrical tensioned bodies. International Journal of Fracture, 17(6), 553-566.
Bahmani, A., Aliha, M. R. M., Sarbijan, M. J., & Mousavi, S. S. (2020). An extended edge-notched disc bend (ENDB) specimen for mixed-mode I+ II fracture assessments. International Journal of Solids and Structures, 193, 239-250.
Bažant, Z. P., & Estenssoro, L. F. (1979). Surface singularity and crack propagation. International Journal of Solids and Structures, 15(5), 405-426.
Benthem, J. (1977). State of stress at the vertex of a quarter-infinite crack in a half-space. International Journal of Solids and Structures, 13(5), 479-492.
Benthem, J. P. (1980). The quarter-infinite crack in a half space; alternative and additional solutions. International Journal of Solids and Structures, 16(2), 119-130.
Carpinteri, A. (1992). Elliptical-arc surface cracks in round bars. Fatigue & Fracture of Engineering Materials and Structures, 15(11), 1141–1153.
Carpinteri, A. (1993). Shape change of surface cracks in round bars under cyclic axial loading. International Journal of Fatigue, 15(1), 21-26.
Carpinteri, A., & Brighenti, R. (1996). Part-through cracks in round bars under cyclic combined axial and bending loading. International journal of fatigue, 18(1), 33-39.
Carpinteri, A., & Brighenti, R. (1996). Fatigue propagation of surface flaws in round bars: a three‐parameter theoretical model. Fatigue & Fracture of Engineering Materials & Structures, 19(12), 1471-1480.
Carpinteri, A., Brighenti, R. & Vantadori, S. (2006). Surface crack in notched round bars under cyclic tension and bending. International Journal of Fatigue, 28(3), 251–260.
Caspers, M., & Mattheck C. (1987), Weighted averaged stress intensity factors of circular-fronted cracks in cylindrical bars, Fatigue & Fracture of Engineering Materials and Structures, 9, 329-341.
Chandra, D., Purbolaksono, J., Nukman, Y., Ramesh, S., Liew, H.L. & Hassan, M.A. (2014). Fatigue growth of a surface crack in a V-shaped notched round bar under cyclic tension. Journal of Zhejiang University Science A, 15(11), 873-882.
Chandra D., Putra I.S., Ariffin A.K., Nukman Y., Mardi N.A. & Purbolaksono J. (2016). Fatigue growth analysis of a surface crack in a solid cylinder under combined cyclic axial-torsion loading, Experimental Techniques, 40(5), 1397-1407.
Cisilino, A.P., & Aliabadi, M.H. (1999). Three-dimensional boundary element analysis of fatigue crack growth in linear and non-linear fracture problems. Engineering Fracture Mechanics, 63(6), 713-733.
Citarella, R., Lepore, M., Shlyannikov, V. & Yarullin, R. (2014). Fatigue surface crack growth in cylindrical specimen under combined loading. Engineering Fracture Mechanics, 131, 439-453.
Dixon, J.R., & Pook, L.P. (1969). Stress intensity factors calculated generally by the finite element technique, Nature, 224, 166-167.
De Matos, P., & Nowell, D. (2008). The influence of the poisson’s ratio and corner point singularities in three-dimensional plasticity-induced fatigue crack closure: A numerical study. International Journal of Fatigue, 30, 1930–1943.
Fonte, M., & Freitas, M. (1997). Semi-elliptical crack growth under rotating or reversed bending combined with steady torsion. Fatigue & Fracture of Engineering Materials and Structures, 20(6), 895-906.
Fonte, M., & Freitas, M. (1999). Stress intensity factor for semi-elliptical surface cracks in round bars under bending and torsion. International Journal of Fatigue, 21(5), 457–463.
Forman, R.G., & Shivakumar, V. (1986), Growth behavior of surface cracks in the circumferential plane of solid and hollow cylinders. Fracture Mechanics, 17, ASTM STP 905, 59-74.
Gray, L. J., Martha, L. F., & Ingraffea, A. R. (1990). Hypersingular integrals in boundary element fracture analysis. International journal for numerical methods in engineering, 29(6), 1135-1158.
Guo, W., Shen, H., & Li, H. (2003). Stress intensity factors for elliptical surface cracks in round bars with different stress concentration coefficient. International journal of fatigue, 25(8), 733-741.
Højfeldt, E., & Østervig, C. B. (1986). Fatigue crack propagation in shafts with shoulder fillets. Engineering fracture mechanics, 25(4), 421-427.
Ismail, A.E., Ariffin, A.K., Abdullah, S., & Ghazali, M.J. (2012). Stress intensity factors for surface cracks in round bar under single and combined loadings. Meccanica, 47(5), 1141-1156.
Joseph, R.P., Purbolaksono, J., Liew, H.L., Ramesh, S., & Hamdi M. (2014). Stress intensity factors of a corner crack emanating from a pinhole of a solid cylinder. Engineering Fracture Mechanics, 128, 1-7.
Joseph, R.P., Putra, I.S., Darmawan, A.S., Liew, H.L., Ramesh, S., Kadarno, P., Mohammad, M.A., & Purbolaksono, J. (2020). Fracture analysis of a corner crack in a pinhole of a solid cylinder under torsion loading. Engineering Solid Mechanics, 8(4), 353-364.
Kuna, M. (2013). Finite Elements in Fracture Mechanics: Theory – Numerics - Applications (Solid Mechanics and Its Applications (201)) 2013th Ed. Springer.
Kotousov, A. (2010). Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates. International Journal of Solids and Structures, 47, 1916–1923.
Kotousov, A., Lazzarin, P., Berto, F. & Pook, L.P. (2013). Three-dimensional stress states at crack tip induced by shear and anti-plane loading. Engineering Fracture Mechanics,108, 65-74
Kotousov, A., Berto, F., Lazzarin, P., & Pegorin, F. (2012). Three dimensional finite element mixed fracture mode under anti-plane loading of a crack. Theoretical and Applied Fracture Mechanics, 62, 6226-6233.
Lazzarin, P., & Zappalorto, M. (2012). A three‐dimensional stress field solution for pointed and sharply radiused V‐notches in plates of finite thickness. Fatigue & Fracture of Engineering Materials & Structures, 35(12), 1105-1119.
Lin, X. B., & Smith, R. A. (1997). Shape growth simulation of surface cracks in tension fatigued round bars. International Journal of Fatigue, 19(6), 461-469.
Lin, X. B., & Smith, R. A. (1998). Fatigue growth simulation for cracks in notched and unnotched round bars. International Journal of Mechanical Sciences, 40(5), 405-419.
Lorentzen, T., Kjaer, N. E., & Henriksen, T. K. (1986). The application of fracture mechanics to surface cracks in shafts. Engineering fracture mechanics, 23(6), 1005-1014.
Mackay, T. L., & Alperin, B. J. (1985). Stress intensity factors for fatigue cracking in high-strength bolts. Engineering Fracture Mechanics, 21(2), 391-397.
Mi, Y., & Aliabadi, M.H. (1992). Dual boundary element method for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements, 10(2), 161-171.
Predan, J., Močilnik, V., & Gubeljak, N. (2013). Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion. Engineering Fracture Mechanics, 105, 152-168.
Pook, L.P. (1994). Some implications of corner point singularities. Engineering Fracture Mechanics, 48(3), 367-378.
Pook, L. P. (2013). A 50‐year retrospective review of three‐dimensional effects at cracks and sharp notches. Fatigue & Fracture of Engineering Materials & Structures, 36(8), 699-723.
Pook, L. P., Berto, F., Campagnolo, A., & Lazzarin, P. (2014). Coupled fracture mode of a cracked disc under anti-plane loading. Engineering Fracture Mechanics, 128, 22-36.
Pook, L. P., Campagnolo, A., Berto, F., & Lazzarin, P. (2015). Coupled fracture mode of a cracked plate under anti-plane loading. Engineering Fracture Mechanics, 134, 391-403.
Pook, L. P., Campagnolo, A., & Berto, F. (2016). Coupled fracture modes of discs and plates under anti‐plane loading and a disc under in‐plane shear loading. Fatigue & Fracture of Engineering Materials & Structures, 39(8), 924-938.
Pook, L. P., Berto, F., & Campagnolo, A. (2017). State of the art of corner point singularities under in-plane and out-of-plane loading. Engineering Fracture Mechanics, 174, 2-9.
Portela, A., Aliabadi, M. H., & Rooke, D. (1992). The dual boundary element method: effective implementation for crack problems. International journal for numerical methods in engineering, 33(6), 1269-1287.
Raju, I. S., & Newman Jr, J. C. (1985). Stress-intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads (No. NASA-TM-87594).
Ramezani, M. K., Purbolaksono, J., Andriyana, A., Ramesh, S., & Putra, I. S. (2018). Empirical solutions for stress intensity factors of a surface crack in a solid cylinder under pure torsion. Engineering Fracture Mechanics, 193, 122-136.
Ramezani, M. K., Purbolaksono, J., Andriyana, A., Ramesh, S., & Mardi, N. A. (2018). Analysis of surface cracks in round bars using dual boundary element method. Engineering Analysis with Boundary Elements, 93, 112-123.
Shin, C. S., & Cai, C. Q. (2004). Experimental and finite element analyses on stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending. International Journal of fracture, 129(3), 239-264.
Shivakumar, K. N., & Raju, I. S. (1990). Treatment of singularities in cracked bodies. International journal of fracture, 45(3), 159-178.
Teh, S., Andriyana, A., Ramesh, S., Putra, I. S., Kadarno, P., & Purbolaksono, J. (2021). Tetrahedral meshing for a slanted semi-elliptical surface crack at a solid cylinder. Engineering Fracture Mechanics, 241, 107400.
Toribio, J., Matos, J. C., González, B., & Escuadra, J. (2009). Numerical modelling of crack shape evolution for surface flaws in round bars under tensile loading. Engineering Failure Analysis, 16(2), 618-630.
Toribio, J., Álvarez, N., González, B., & Matos, J. C. (2009). A critical review of stress intensity factor solutions for surface cracks in round bars subjected to tension loading. Engineering Failure Analysis, 16(3), 794-809.
Toribio, J., Matos, J. C., González, B., & Escuadra, J. (2014). Numerical modelling of cracking path in round bars subjected to cyclic tension and bending. International Journal of Fatigue, 58, 20-27.
Watson, J.O. (1986). Hermitian cubic and singular elements for plain strain, in Development in Boundary Element Methods 4, ed. P.K. Banerjee & J.O. Watson, Elsevier Applied Science Publishers, Barking, UK.
Wawrzynek, P.A., & Ingraffea, A.R. (2003). 3.01 - Finite Element Methods for Linear Elastic Fracture Mechanics. Comprehensive Structural Integrity, 3, 1-88.
Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics, 24, 109-114.
Zakavi, B., Kotousov, A., Khanna, A., & Branco, R. (2019). A new method for analysis of part-elliptical surface cracks in structures subjected to fatigue loading. Theoretical and Applied Fracture Mechanics, 103, 102258.