Vol. 7 � 4, 2017 p 35-43| Science & Technologies: Oil and Oil Products Pipeline Transportation

Pages	Article name, authors, abstract and keyword
35-43	Numerical modeling of crack propagation under mixed-mode loading �. Boulenouar ^a, N. Benamara ^a, M. Merzoug ^a ^a Laboratory of Materials and Reactive Systems, Mechanical Engineering Department, University of Sidi-Bel-Abbes. BP 89. Larbi Ben Mhidi, Sidi Bel Abbes 22000, Algeria https://doi.org/10.28999/2541-9595-2017-7-4-35-43 Abstract: Finite element analysis (FEA) combined with the concepts of Linear Elastic fracture me-chanics (LEFM) provides a practical and convenient means to study the fracture and crack growth of materials. In this paper, a numerical modeling of automatic crack propagation under mode I and mixed-mode loading is presented. The onset criterion of crack propagation is based on the stress intensity factor, which is the most important parameter that must be accurately estimated and facilitated by the singular element. Using the Ansys Parametric Design Language (APDL), the displacement extrapolation technique (DET) and the maximum circumferential stress (MCS) theory are employed, to obtain the stress intensity factors (SIFs) at crack tip and the crack direction at each step of propagation. The predicted results showed excellent agreement with numerical and analytical results obtained by other researchers. Thus, it is concluded that the automatic crack propagation method developed allows efficient and accurate simulation of mixed mode crack propagation problems. Keywords: crack propagation, stress intensity factors, mixed-mode loading, displacement extrapolation Reference for citing: Boulenouar �., Benamara N., Merzoug M. Numerical modeling of crack propagation under mixed-mode loading. Naukatekhnol. truboprov. transp. neftiinefteprod. = Science & Technologies: Oil and Oil Products Pipeline Transportation. 2017;7(4):35�43. References: [1] De Araújo T., Bittencourt T., Roehl D., Martha L. Numerical estimation of fracture parameters in elastic and elastic-plastic analysis. Paper presented at: European congress on computational methods in applied sciences and engineering; 2000 Sep 11�14; Barcelona, Spain. [2] Erdogan F., Sih G. C. On the crack extension in plane loading and transverse shear. J Basic Engng. 1963;85:519�27. [3] Nuismer R. J. An energy release rate criterion for mixed mode fracture. Int J Fract 1975;11:245�50. [4] Wu C. H. Fracture under combined loads by maximum energy release rate criterion. J App Mech. 1978;45:553�8. [5] Sih G. C. Strain-energy-density factor applied to mixed mode crack problems. Int J Fract. 1974;10:305�21. [6] Ma F., Deng X., Sutton M. A., Newman J. J. A CTOD-based mixed-mode fracture criterion mixed-mode crack behavior. ASTM STP 1359. 1999; p. 86�110. [7] Sutton M. A., Deng X., Ma F., Newman J. J., James M. Development and application of a crack tip opening displacement- ased mixed mode fracture criterion. Int J Solids Struct. 2000;37:3591�618. [8] ANSYS, Inc. Programmer�s Manual for Mechnical APDL, Release 12.1 November 2009. [9] Shih C. F, Asaro R. J. Elastic�plastic analysis of cracks on bimaterial interfaces. Part I, Small scale yielding. J Appl Mech 1988;55:299�316. [10] Rybicki E. F, Kanninen M. F. Finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech. 1977;(9):931�8. [11] Parks D. M. A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract. 1974;10:487�502. [12] Chan S. K., Tuba I. S., Wilson W. K. On the finite element method in linear fracture mechanics. Eng Fract Mech. 1970;(2):1�17. [13] Bittencourt T. N., Wawrzynek P. A., Ingraffea A.R. Quasi-automatic simulation of crack propaga-tion for 2D LEFM problems. Eng Fract Mech. 1996;55:321�334. [14] Phongthanapanich S., Dechaumphai P. Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis, Finite Elem. Anal. Des. 2004;40:1753�1771. [15] Alshoaibi A. M., Ariffin A. K., Almaghrabi M. N. Development of Efficient Finite Element Software of Crack Propagation Simulation using Adaptive Mesh Strategy. Am J Appl Sci. 2009;6(4):661�666. [16] Barsoum R. S. Triangular quarter-point elements as elastic and perfectly-plastic crack tip ele-ments. Int J Numer. Methods Eng. 1977;(11):85�98. [17] Andersen M. R. Fatigue crack initiation and growth in ship structures [dissertation PhD]. Technical University of Denmark; 1998. [18] Boulenouar A., Benseddiq N., Mazari M. Two-dimensional numerical estimation of stress in-tensity factors and crack propagation in linear elastic analysis. ETASR. 2003;(3):506�510. [19] Boulenouar A., Benseddiq N., Mazari M. FE Model for linear-elastic mixed mode loading: esti-mation of SIFs and crack propagation. Journal of Theoretical and Applied Mechanics. 2014;52:373�383. [20] Boulenouar A., Benseddiq N., Mazari M. Strain energy density prediction of crack propagation for 2D linear elastic materials. Theor. Appl. Fract. Mech. 2013;67�68:29�37. [21] Ayhan Ali O. Simulation of three-dimensional fatigue crack propagation using enriched finite elements. Computers and Structures. 2011;89:801�812. [22] Prieto L. L. Modelling and analysis of crack turning on aeronautical structures [dissertation PhD]. Uni-versitat Politcnica de Catalunya, EADS; 2007. [23] Yan X. Rectangular tensile sheet with single edge crack or edge half-circular-hole crack. J. Eng. Failure Anal. 2007;14:1406�1410. [24] Souiyah M., Alshoaibi A., Muchtar A., Ariffin A. K. Two-dimensional finite element method for stress intensity factor using adaptive mesh strategy. Acta Mech. 2009;204:99�108. [25] Bouchard P. O., Bay F., Chastel Y. Numerical modelling of crack propagation: automatic remesh-ing and comparison of different criteria. Comput Methods in Appl Mech and Engrg. 2003;192:3887�3908. [26] Abdulnaser M. Alshoaibi. Effect of Holes under Quasi-Static Loading on Crack Propagation Tra-jectory. www.jazanu.edu.sa/Administrations/sfc/.../eng/.../2.pd... [27] Rashid M. M. The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis. Comput. Methods Appl. Mech. Engrg. 1998;154:133�150. [28] Legrain G. Extension de l�approche X-FEM aux grandes transformations pour la fissuration des milieux hyperélastiques [dissertation]. Ecole Centrale Nantes � Université de Nantes; 2006.

Pages

Article name, authors, abstract and keyword

35-43

Numerical modeling of crack propagation under mixed-mode loading

�. Boulenouar ^a, N. Benamara ^a, M. Merzoug ^a

^a Laboratory of Materials and Reactive Systems, Mechanical Engineering Department, University of Sidi-Bel-Abbes. BP 89. Larbi Ben Mhidi, Sidi Bel Abbes 22000, Algeria

https://doi.org/10.28999/2541-9595-2017-7-4-35-43

Abstract: Finite element analysis (FEA) combined with the concepts of Linear Elastic fracture me-chanics (LEFM) provides a practical and convenient means to study the fracture and crack growth of materials. In this paper, a numerical modeling of automatic crack propagation under mode I and mixed-mode loading is presented. The onset criterion of crack propagation is based on the stress intensity factor, which is the most important parameter that must be accurately estimated and facilitated by the singular element. Using the Ansys Parametric Design Language (APDL), the displacement extrapolation technique (DET) and the maximum circumferential stress (MCS) theory are employed, to obtain the stress intensity factors (SIFs) at crack tip and the crack direction at each step of propagation. The predicted results showed excellent agreement with numerical and analytical results obtained by other researchers. Thus, it is concluded that the automatic crack propagation method developed allows efficient and accurate simulation of mixed mode crack propagation problems.

Keywords: crack propagation, stress intensity factors, mixed-mode loading, displacement extrapolation

Reference for citing:
Boulenouar �., Benamara N., Merzoug M. Numerical modeling of crack propagation under mixed-mode loading. Naukatekhnol. truboprov. transp. neftiinefteprod. = Science & Technologies: Oil and Oil Products Pipeline Transportation. 2017;7(4):35�43.

References:
[1] De Araújo T., Bittencourt T., Roehl D., Martha L. Numerical estimation of fracture parameters in elastic and elastic-plastic analysis. Paper presented at: European congress on computational methods in applied sciences and engineering; 2000 Sep 11�14; Barcelona, Spain.
[2] Erdogan F., Sih G. C. On the crack extension in plane loading and transverse shear. J Basic Engng. 1963;85:519�27.
[3] Nuismer R. J. An energy release rate criterion for mixed mode fracture. Int J Fract 1975;11:245�50.
[4] Wu C. H. Fracture under combined loads by maximum energy release rate criterion. J App Mech. 1978;45:553�8.
[5] Sih G. C. Strain-energy-density factor applied to mixed mode crack problems. Int J Fract. 1974;10:305�21.
[6] Ma F., Deng X., Sutton M. A., Newman J. J. A CTOD-based mixed-mode fracture criterion mixed-mode crack behavior. ASTM STP 1359. 1999; p. 86�110.
[7] Sutton M. A., Deng X., Ma F., Newman J. J., James M. Development and application of a crack tip opening displacement- ased mixed mode fracture criterion. Int J Solids Struct. 2000;37:3591�618.
[8] ANSYS, Inc. Programmer�s Manual for Mechnical APDL, Release 12.1 November 2009.
[9] Shih C. F, Asaro R. J. Elastic�plastic analysis of cracks on bimaterial interfaces. Part I, Small scale yielding. J Appl Mech 1988;55:299�316.
[10] Rybicki E. F, Kanninen M. F. Finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech. 1977;(9):931�8.
[11] Parks D. M. A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Fract. 1974;10:487�502.
[12] Chan S. K., Tuba I. S., Wilson W. K. On the finite element method in linear fracture mechanics. Eng Fract Mech. 1970;(2):1�17.
[13] Bittencourt T. N., Wawrzynek P. A., Ingraffea A.R. Quasi-automatic simulation of crack propaga-tion for 2D LEFM problems. Eng Fract Mech. 1996;55:321�334.
[14] Phongthanapanich S., Dechaumphai P. Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis, Finite Elem. Anal. Des. 2004;40:1753�1771.
[15] Alshoaibi A. M., Ariffin A. K., Almaghrabi M. N. Development of Efficient Finite Element Software of Crack Propagation Simulation using Adaptive Mesh Strategy. Am J Appl Sci. 2009;6(4):661�666.
[16] Barsoum R. S. Triangular quarter-point elements as elastic and perfectly-plastic crack tip ele-ments. Int J Numer. Methods Eng. 1977;(11):85�98.
[17] Andersen M. R. Fatigue crack initiation and growth in ship structures [dissertation PhD]. Technical University of Denmark; 1998.
[18] Boulenouar A., Benseddiq N., Mazari M. Two-dimensional numerical estimation of stress in-tensity factors and crack propagation in linear elastic analysis. ETASR. 2003;(3):506�510.
[19] Boulenouar A., Benseddiq N., Mazari M. FE Model for linear-elastic mixed mode loading: esti-mation of SIFs and crack propagation. Journal of Theoretical and Applied Mechanics. 2014;52:373�383.
[20] Boulenouar A., Benseddiq N., Mazari M. Strain energy density prediction of crack propagation for 2D linear elastic materials. Theor. Appl. Fract. Mech. 2013;67�68:29�37.
[21] Ayhan Ali O. Simulation of three-dimensional fatigue crack propagation using enriched finite elements. Computers and Structures. 2011;89:801�812.
[22] Prieto L. L. Modelling and analysis of crack turning on aeronautical structures [dissertation PhD]. Uni-versitat Politcnica de Catalunya, EADS; 2007.
[23] Yan X. Rectangular tensile sheet with single edge crack or edge half-circular-hole crack. J. Eng. Failure Anal. 2007;14:1406�1410.
[24] Souiyah M., Alshoaibi A., Muchtar A., Ariffin A. K. Two-dimensional finite element method for stress intensity factor using adaptive mesh strategy. Acta Mech. 2009;204:99�108.
[25] Bouchard P. O., Bay F., Chastel Y. Numerical modelling of crack propagation: automatic remesh-ing and comparison of different criteria. Comput Methods in Appl Mech and Engrg. 2003;192:3887�3908.
[26] Abdulnaser M. Alshoaibi. Effect of Holes under Quasi-Static Loading on Crack Propagation Tra-jectory. www.jazanu.edu.sa/Administrations/sfc/.../eng/.../2.pd...
[27] Rashid M. M. The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis. Comput. Methods Appl. Mech. Engrg. 1998;154:133�150.
[28] Legrain G. Extension de l�approche X-FEM aux grandes transformations pour la fissuration des milieux hyperélastiques [dissertation]. Ecole Centrale Nantes � Université de Nantes; 2006.