[1] Shih C F, Moran B, Nakamura T. Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture. 1986;30:79-102.
doi: 10.1007/BF00034019
[2] Chiarelli M, Frediani A. A computation of the three-dimensional J-integral for elastic materials with a view to applications in fracture mechanics. Engineering Fracture Mechanics. 1993;44(5):763-88.
doi: 10.1016/0013-7944(93)90205-7
[3] Rice J R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics. 1968;35:379–86.
doi: 10.1115/1.3601206
[4] Cherepanov G P. The propagation of cracks in a continuous medium. Journal of Applied Mathematics and Mechanics. 1967;31(3):503–12.
doi: 10.1016/0021-8928(67)90034-2
[5] Dag S, Arman E, Yildirim B. Computation of thermal fracture parameters for orthotropic functionally graded materials using J-Integral. International Journal of Solids and Structures. 2010;47:3480-88.
doi: 10.1016/j.ijsolstr.2010.08.023
[6] Eishcen J W. Fracture of nonhomogeneous materials. International Journal of Fracture.1987;34:3-22.
doi: 10.1007/BF00042121
[7] Kim J H, Paulino G H. Mixed mode J-Integral formulation and implementation using graded finite elements for fracture analysis of nonhomogeneous orthotropic materials. Mechanics of Matererials. 2003;35:107-28.
doi: 10.1016/S0167-6636(02)00159-X
[8] Raju I S, Shivalumar K N. An equivalent domain integral method in three-dimensional analysis of mixed mode crack problems. Engineering Fracture Mechanics.1992;42(6):935-59.
doi: 10.1016/0013-7944(92)90134-Z
[9] Okada H, Ishizaka T, Takahashi A, Arai K, Yusa Y. 3D J-integral evaluation for solids undergoing large elastic–plastic deformations with residual stresses and spatially varying mechanical properties of a material. 2020;236:107212.
doi: 10.1016/j.engfracmech.2020.107212
[10] Hein J, Kuna M. 3D J-integral for functionally graded and temperature dependent thermoelastic materials. Procedia Structural Integrity. 2016;2:2246-54.
doi: 10.1016/j.prostr.2016.06.281
[11] Amestoy M, Bui H D, Labbens R. On the definition of local path independent integrals in three-dimensional crack problems. Pergamon Press Ltd. 1981;8(4):231-36.
doi: 10.1016/0093-6413(81)90058-6
[12] Walters M C, Paulino G H, Dodds R H. Stress intensity factors for surface cracks in functionally graded materials under mode I thermomechanical loading. International Journal of Solids and Structures. 2004;41:1081-118.
doi: 10.1016/j.ijsolstr.2003.09.050
[13] Yue F, Wu Z. Fracture Mechanical Analysis of Thin-Walled Cylindrical Shells with Cracks. Metals. 2021;11:592.
doi: 10.3390/met11040592
[14] Hu J W. J-Integral Evaluation for Calculating Structural Intensity and Stress Intensity Factor Using Commercial Finite Element (FE) Solutions. Advanced Materials Research. 2013;650:379-84.
doi: 10.4028/www.scientific.net/AMR.650.379
[15] Courtin S, Gardin C, Be´zine G, Hadj Hamouda H B. Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS. 2005;72:2174-85.
doi: 10.1016/j.engfracmech.2005.02.003
[16] Olamide A, Bennecer A,Kaczmarczyk S. Finite Element Analysis of Fatigue in Offshore Pipelines with internal and external Circumferential Cracks. Applied Mechanics. 2020;1:193–223.
doi: 10.3390/applmech1040013
[17] Hoh H J, Pang J H L, Tsang K S. Stress intensity factors for fatigue analysis of weld toe cracks in a girth-welded pipe. International Journal of Fatigue. 2016;87:279-87.
doi: 10.1016/j.ijfatigue.2016.02.002
[18] Song H, Rahman S S. An extended J-integral for evaluating fluid-driven cracks in hydraulics Fracturing. Journal of Rock Mechanics and Geotechnical Engineering. 2018;10:832-43.
doi: 10.1016/j.jrmge.2018.04.009
[19] Vavrik D, Jandejsek I. Experimental evaluation of contour J integral and energy dissipated in the fracture process zone. Engineering Fracture Mechanics. 2014;129:14–25.
doi: 10.1016/j.engfracmech.2014.04.002
[20] Ghasemi H, Hamdia K.M. The J-Integral Method Compared to the API 579-1/ASME FFS-1 Standard to Calculate Stress Intensity Factor (SIF): Leak-Before-Break (LBB) Application with Uncertainty Quantification. Arabian Journal for Science and Engineering. 2023.
doi: 10.1007/s13369-023-08138-4
[21] Mohamed M A, Schroeder J. Stress intensity factor solution for crotch-corner cracks of tee-intersections of cylindrical shells. International Journal of Fracture. 1978;14(6):605-21.
doi: 10.1007/BF00115999
[22] WRC Bulletin 175, "PVRC Recommendations on Toughness Requirements for Ferritic Materials," Welding Research Council, 1972.