How to cite this paper
Zeleke, M., Dintwa, E & Nwaigwe, K. (2021). Stress intensity factor computation of inclined cracked tension plate using XFEM.Engineering Solid Mechanics, 9(4), 363-376.
Refrences
Aliha, M.R., Bahmani, A., & Akhondi, S. (2016). Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. European Journal of Mechanics-A/Solids, 58, 148-162.
Ameri, B., Taheri-Behrooz, F., & Aliha, M. R. M. (2021). Evaluation of the Geometrical Discontinuity effect on Mixed-Mode I/II Fracture Load of FDM 3D-Printed Parts. Theoretical and Applied Fracture Mechanics, 113, 102953.
Anderson, T. L. (2017). Fracture mechanics: fundamentals and applications. CRC press.
Barsoum, R. S. (1974). Application of Quadratic Isoparametric Finite Elements in Linear Fracture Mechanics. International Journal of Fracture, 10(4), 603-605.
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45, 601–620.
Belytschko, T., Gu, L., & Lu, Y. Y. (1994). Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Materials Science and Engineering, 2(3A), 519.
Belytschko, T., Liu, W. K., Moran, B., & Elkhodary, K. I. (2014 ). Nonlinear Finite Elements for Continua and Structures. 2nd ed . Chichester: Wiley.
Belytschko, T., Lu, Y. Y., & Gu, L. (1994). Elementfree Galerkin methods. International Journal for Numerical Methods in Engineering, 37(2), 229-256.
Bhadauria, S. S., Pathak, K. K., & Hora, M. S. (2010). Finite element modeling of crack initiation angle under mixed mode (I/II) fracture. Journal of Solid Mechanics, 2, 231-247.
Bouhala, L., Shao, Q., Koutsawa, Y., Younes, A., Núñez, P., Makradi, A., et al. (2013). An XFEM crack-tip enrichment for a crack terminating at a bi-material interface. Engngineering Fracture Mechanics, 102, 51–64.
Ching, H. K., & Yen, S. C. (2005, ). Meshless local petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites Part B: Engineering, 36(3), 223–40.
El Fakkoussi, S., Moustabchir, H., Elkhalfi, A., & Pruncu, C. I. (2019). Computation of the stress intensity factor KI for external longitudinal semi-elliptic cracks in the pipelines by FEM and XFEM methods. International Journal of Interaction Design Manufacturing, 13, 545–555.
Fayed, A. S. (2017). Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates. Engineering Solid Mechanics, 5(1), 61-70.
Gonzalez, M., Teixeira, P., Wrobel, L. C., & Martinez, M. (2015). A new Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method. Latin American Journal of Solids and Structures, 12(9), 1677-1697.
Griffith, A. (1920). The Phenomena of Rupture and Flow in Solids. Philosophical Transactions, Series A, 221, 163-198.
Gu, Y., Wang, W., Zhang, L. C., & Feng, X. Q. (2011). An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. Engineering Fracture Mechanics, 78(1), 175–90.
Han, Q., Wang, Y., Yin, Y., & Wang, D. (2015). Determination of stress intensity factor for mode I fatigue crack based on finite element analysis. Engineering Fracture Mechanics , 138, 118-126 .
Hedayati, E., & Vahedi, M. (2014). Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum. World Journal of Mechanics, 4, 24-30.
Hellen, T. K. (1975). On the Method of Virtual Crack Extension. International Journal for Numerical Methods in Engineering, 9(1), 187-207.
Henshell, R. D., & Shaw, K. G. (1975). Crack Tip Finite Elements Are Unnecessary. International Journal for Numerical Methods in Engineering, 9(3), 495-507.
Irwin, G. (1957). Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate. Journal of Applied Mechanics, 24, 361-364.
Laftah, R. M. (2016). Study of Stress Intensity Factor in Corrugated Plate Using Extended Finite Element Method (XFEM). Engineering & Technical Journal, Part (A), 34(15), 2982-2992.
Lee, S. H., Kim, K. H., & Yoon, Y. C. (2016). Particle difference method for dynamic crack propagation. International Journal of Impact Engineering, 87, 132–145.
Leung, A. Y., Zhou, Z., & Xu, X. (2014)). Determination of stress intensity factors by the finite element discretized symplectic method. International Journal of Solids and Structures, 51(5), 1115-1122 .
Lins, R., Ferreira, M., & Proença, S. e. (2015). An a-posteriori error estimator for linear elastic fracture mechanics using the stable generalized/extended finite element method. Computer Mechanics, 56, 947-965.
Liu, W. K., Jun, S., & Zhang, Y. F. (1995). Reproducing kernel particle methods. International Journal of Numerical Methods Fluids, 20(8–9), 1081–11066.
Lu, Y. Y., Belytschko, T., & Gu, L. (1994). A new implementation of the element free Galerkin method. Computational Methods in Applied Mechanical Engineering, 113(3-4), 397–414.
Menk, A., & Bordas, S. P. (2011). Crack growth calculations in solder joints based on microstructural phenomena with x-fem. Computational Materials Science, 50(3), 1145–1156.
Mirmohammad, S. H., Safarabadi, M., Karimpour, M., Aliha, M. R. M., & Berto, F. (2018). Study of composite fiber reinforcement of cracked thin-walled pressure vessels utilizing multi-scaling technique based on extended finite element method. Strength of Materials, 50(6), 925-936.
Moes, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46, 131-150.
Moran, B., & Shih, C. F. (1987). Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics, 27(6), 615-642.
Murakami, Y., & Keer, L. M. (1993). Stress Intensity Factors Handbook (Vol. 3).
Ortiz, J. E., & Cisilino, A. P. (2006). Boundary element method for J-integral and stress intensity factor computations in three-dimensional interface cracks. International Journal of Fracture, 133(3), 197-222.
Pais, M. (2011). Variable Amplitude Fatigue Analysis Using Surrogate Models and Exact XFEM Reanalysis. University of Florida.
Paris, P., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic Engineering Transaction of ASME, 85, 528-534.
Parks, D. M. (1974). A Stiffness Derivative Finite Element Technique for Determination of Crack Tip Stress Intensity Factors. International Journal of Fracture, 10, 487-502.
Pommier, S., Gravouil, A., Combescure, A., & Moës, N. (2011). Extended finite element method for crack propagation. London, UK: ISTE.
Portela, A., Aliabadi, M. H., & Rooke, D. P. (1992). The dual boundary element method: effective implementation for crack problems. International Journal for Numerical Methods in Engineering, 33(6), 1269-1287.
Rabczuk, T., & Belytschko, T. (2004). Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 61(13), 2316-2343.
Rice, R. J. (1968). A Path Independent Integral and the Approximate Analysis of Strain Concentrations by Notches and Cracks. Journal of Applied Mechanics, 35, 379-386.
Rybicki, E. F., & Kanninen, M. F. (1977). A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral. Engineering Fracture Mechanics, 9(4), 931-938.
Shih, C. F., De Lorenzi, H. G., & German, M. D. (1976). Crack Extension Modeling with Singular Quadratic Isoparametric Element. International Journal of Fracture, 12(4), 647-651.
Singh, I. V., Mishra, B. K., Bhattacharya, S., & Patil, R. U. (2012). The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue, 36(1), 109-119.
Stern, M., Becker, E. B., & Dunham, R. S. (1976). A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture, 12, 359-68.
Sukumar, N., Chopp, D. L., Moës, N., & Belytschko, T. (2001). Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanical Engineering, 190(46-47), 6183–6200.
Sukumar, N., Moes, N., Moran, B., & Belytschko, T. (2000). Extended Finite element method for three-dimensional crack modelling. International Journal of Numerical Methods in Engineering, 48, 1549 -1570.
Szabo, B. A., & Babuška, I. (1988). Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners. In Fracture mechanics: nineteenth symposium (pp. 101-124). West Conshohocken: ASTM International.
Tada, H., Paris, P., & Irwin, G. (2000). The Stress Analysis of Cracks Handbook. 3rd ed., New York.
Ameri, B., Taheri-Behrooz, F., & Aliha, M. R. M. (2021). Evaluation of the Geometrical Discontinuity effect on Mixed-Mode I/II Fracture Load of FDM 3D-Printed Parts. Theoretical and Applied Fracture Mechanics, 113, 102953.
Anderson, T. L. (2017). Fracture mechanics: fundamentals and applications. CRC press.
Barsoum, R. S. (1974). Application of Quadratic Isoparametric Finite Elements in Linear Fracture Mechanics. International Journal of Fracture, 10(4), 603-605.
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45, 601–620.
Belytschko, T., Gu, L., & Lu, Y. Y. (1994). Fracture and crack growth by element free Galerkin methods. Modelling and Simulation in Materials Science and Engineering, 2(3A), 519.
Belytschko, T., Liu, W. K., Moran, B., & Elkhodary, K. I. (2014 ). Nonlinear Finite Elements for Continua and Structures. 2nd ed . Chichester: Wiley.
Belytschko, T., Lu, Y. Y., & Gu, L. (1994). Elementfree Galerkin methods. International Journal for Numerical Methods in Engineering, 37(2), 229-256.
Bhadauria, S. S., Pathak, K. K., & Hora, M. S. (2010). Finite element modeling of crack initiation angle under mixed mode (I/II) fracture. Journal of Solid Mechanics, 2, 231-247.
Bouhala, L., Shao, Q., Koutsawa, Y., Younes, A., Núñez, P., Makradi, A., et al. (2013). An XFEM crack-tip enrichment for a crack terminating at a bi-material interface. Engngineering Fracture Mechanics, 102, 51–64.
Ching, H. K., & Yen, S. C. (2005, ). Meshless local petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads. Composites Part B: Engineering, 36(3), 223–40.
El Fakkoussi, S., Moustabchir, H., Elkhalfi, A., & Pruncu, C. I. (2019). Computation of the stress intensity factor KI for external longitudinal semi-elliptic cracks in the pipelines by FEM and XFEM methods. International Journal of Interaction Design Manufacturing, 13, 545–555.
Fayed, A. S. (2017). Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates. Engineering Solid Mechanics, 5(1), 61-70.
Gonzalez, M., Teixeira, P., Wrobel, L. C., & Martinez, M. (2015). A new Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method. Latin American Journal of Solids and Structures, 12(9), 1677-1697.
Griffith, A. (1920). The Phenomena of Rupture and Flow in Solids. Philosophical Transactions, Series A, 221, 163-198.
Gu, Y., Wang, W., Zhang, L. C., & Feng, X. Q. (2011). An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. Engineering Fracture Mechanics, 78(1), 175–90.
Han, Q., Wang, Y., Yin, Y., & Wang, D. (2015). Determination of stress intensity factor for mode I fatigue crack based on finite element analysis. Engineering Fracture Mechanics , 138, 118-126 .
Hedayati, E., & Vahedi, M. (2014). Using Extended Finite Element Method for Computation of the Stress Intensity Factor, Crack Growth Simulation and Predicting Fatigue Crack Growth in a Slant-Cracked Plate of 6061-T651 Aluminum. World Journal of Mechanics, 4, 24-30.
Hellen, T. K. (1975). On the Method of Virtual Crack Extension. International Journal for Numerical Methods in Engineering, 9(1), 187-207.
Henshell, R. D., & Shaw, K. G. (1975). Crack Tip Finite Elements Are Unnecessary. International Journal for Numerical Methods in Engineering, 9(3), 495-507.
Irwin, G. (1957). Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate. Journal of Applied Mechanics, 24, 361-364.
Laftah, R. M. (2016). Study of Stress Intensity Factor in Corrugated Plate Using Extended Finite Element Method (XFEM). Engineering & Technical Journal, Part (A), 34(15), 2982-2992.
Lee, S. H., Kim, K. H., & Yoon, Y. C. (2016). Particle difference method for dynamic crack propagation. International Journal of Impact Engineering, 87, 132–145.
Leung, A. Y., Zhou, Z., & Xu, X. (2014)). Determination of stress intensity factors by the finite element discretized symplectic method. International Journal of Solids and Structures, 51(5), 1115-1122 .
Lins, R., Ferreira, M., & Proença, S. e. (2015). An a-posteriori error estimator for linear elastic fracture mechanics using the stable generalized/extended finite element method. Computer Mechanics, 56, 947-965.
Liu, W. K., Jun, S., & Zhang, Y. F. (1995). Reproducing kernel particle methods. International Journal of Numerical Methods Fluids, 20(8–9), 1081–11066.
Lu, Y. Y., Belytschko, T., & Gu, L. (1994). A new implementation of the element free Galerkin method. Computational Methods in Applied Mechanical Engineering, 113(3-4), 397–414.
Menk, A., & Bordas, S. P. (2011). Crack growth calculations in solder joints based on microstructural phenomena with x-fem. Computational Materials Science, 50(3), 1145–1156.
Mirmohammad, S. H., Safarabadi, M., Karimpour, M., Aliha, M. R. M., & Berto, F. (2018). Study of composite fiber reinforcement of cracked thin-walled pressure vessels utilizing multi-scaling technique based on extended finite element method. Strength of Materials, 50(6), 925-936.
Moes, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46, 131-150.
Moran, B., & Shih, C. F. (1987). Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics, 27(6), 615-642.
Murakami, Y., & Keer, L. M. (1993). Stress Intensity Factors Handbook (Vol. 3).
Ortiz, J. E., & Cisilino, A. P. (2006). Boundary element method for J-integral and stress intensity factor computations in three-dimensional interface cracks. International Journal of Fracture, 133(3), 197-222.
Pais, M. (2011). Variable Amplitude Fatigue Analysis Using Surrogate Models and Exact XFEM Reanalysis. University of Florida.
Paris, P., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic Engineering Transaction of ASME, 85, 528-534.
Parks, D. M. (1974). A Stiffness Derivative Finite Element Technique for Determination of Crack Tip Stress Intensity Factors. International Journal of Fracture, 10, 487-502.
Pommier, S., Gravouil, A., Combescure, A., & Moës, N. (2011). Extended finite element method for crack propagation. London, UK: ISTE.
Portela, A., Aliabadi, M. H., & Rooke, D. P. (1992). The dual boundary element method: effective implementation for crack problems. International Journal for Numerical Methods in Engineering, 33(6), 1269-1287.
Rabczuk, T., & Belytschko, T. (2004). Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 61(13), 2316-2343.
Rice, R. J. (1968). A Path Independent Integral and the Approximate Analysis of Strain Concentrations by Notches and Cracks. Journal of Applied Mechanics, 35, 379-386.
Rybicki, E. F., & Kanninen, M. F. (1977). A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral. Engineering Fracture Mechanics, 9(4), 931-938.
Shih, C. F., De Lorenzi, H. G., & German, M. D. (1976). Crack Extension Modeling with Singular Quadratic Isoparametric Element. International Journal of Fracture, 12(4), 647-651.
Singh, I. V., Mishra, B. K., Bhattacharya, S., & Patil, R. U. (2012). The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue, 36(1), 109-119.
Stern, M., Becker, E. B., & Dunham, R. S. (1976). A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture, 12, 359-68.
Sukumar, N., Chopp, D. L., Moës, N., & Belytschko, T. (2001). Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanical Engineering, 190(46-47), 6183–6200.
Sukumar, N., Moes, N., Moran, B., & Belytschko, T. (2000). Extended Finite element method for three-dimensional crack modelling. International Journal of Numerical Methods in Engineering, 48, 1549 -1570.
Szabo, B. A., & Babuška, I. (1988). Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners. In Fracture mechanics: nineteenth symposium (pp. 101-124). West Conshohocken: ASTM International.
Tada, H., Paris, P., & Irwin, G. (2000). The Stress Analysis of Cracks Handbook. 3rd ed., New York.