Numerical simulation of the synthetic strain energy and crack characterization parameters using the FEM method of a two-dimensional multi-position model

Bentahar Mohammed, Habib Benzaama


Fracture mechanics is a science that studies the growth and propagation of cracks, as well as the ability to absorb cracks of a component or material under service conditions (operation, service life, etc.). This paper deals with the numerical modeling of the strain energy evolution (ALLAE), the J-integral and stress intensity factors, of a multi-position initial crack of length a = 1mm. The first part is based on the study of the positions of the cracks of the upper face which contain positive values, and the second part of the study is based on the study of the positions of the cracks of the lower face which contain negative values. The finite element method was used on a two-dimensional model in the first mode I. Additionally, elasto-plastics material was applied. Thus, the CPS8, 8-node biquadratic plane stress quadrilateral elements were used. The crack is then modeled numerically using the ABAQUS finite element calculation code. In addition, the results obtained concerning the numerical modeling were compared, and discussed between the different positions either higher dimensions y=8, 6.4, 4.8, 3.2 and 1.6mm or lower dimensions y= -6.4, -4.8, -3.2 and 1.6mm. A good correspondence was obtained between the different comparison results in all the modeling cases of our work. When there is a crack on the upper face, the real KI varies between 50 and 92 (Mpa√m), the KII varies between -8 and 8.8 (Mpa√m). Thus, the integral J varies between 3 × 10-8 and 1.2 × 10-7 (KJ/m2) and the dissipation energy ALLAE varies between 0 and 3 × 10-11 (J). In addition, when there is a crack on the lower side, the varied KI factor between 45 and 85 (Mpa√m), KII varies between -0.5 and 7 (Mpa√m) Thus, the integral-J varies between 3×10-8 and 1×10-7(KJ/m2) and the dissipation energy ALLAE varies between 0 and 2×10-11(J).

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M.H. Gozin and M. Aghaie-Khafri, 2012, “2D and 3D finite element analysis of crack growth under compressive residual stress field”, International Journal of Solids and Structures, Vol. 49, (23–24), 15 November, pp. 3316-3322,

L. Yazhe, X. Nengxiong , T. Jinzhi and M. Gang, 2019, “Comparative modelling of crack propagation in elastic– plastic materials using the meshfree local radial basis point interpolation method and eXtended finite-element method”, 6(11)

Z. Sun, X. Zhuang and Y, Zhang, 2019, “Cracking Elements Method for Simulating Complex Crack Growth”, J. Appl. Comput. Mech, 5(3) pp. 552-562 DOI: 10.22055/JACM.2018.27589.1418.

P.O. Bouchard, F. Bay and Y. Chastel, 2003, “Numerical modelling of crack propagation automatic remeshing and comparison of different criteria, Computer Methods Applied Mechanics Engineering, 192 (35/36), pp.3887-3908.

J. Réthoré, A. Gravouil and A. Combescure, 2005, “An energy-conserving scheme for dynamic crack growth using the extended finite element method”, International Journal for Numerical Methods in Engineering, 63(5). pp. 631-659.

A.C.O. Miranda, M.A. Meggiolaro J.T.P. Castro, L.F. Martha and T.N. Bittencourt 2003, “Fatigue life and crack predictions in generic 2D structural components”, Engineering Fracture Mechanics, 70 (10). pp.1259-1279.

A.R. Khoei, H. Azadia, and H. Moslemia, 2008, “Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery technique”, Engineering Fracture Mechanics, 75, pp.2921-2945.

D. Azocar, M. Elgueta, and M.C. Rivara, 2010, “Automatic LEFM crack propagation method based on local Lepp-Delaunay mesh refinement”, Advances in Engineering Software, 41, pp. 111-119.

M. Bentahar, H. Benzaama, M. Bentoumi and M. Mouktari, A new automated stretching finite element method for 2D crack propagation, Journal of Theoritical and Applied Mechanics (JTAM), Vol. 55,No. 3, pp. 869-881, 2017, https://DOI:10.15632/jtam-pl.55.3.869.

M. Bentahar, H. Benzaama, Numerical Simulation of 2D Crack Propagation using SFEM Method by Abaqus, Tribology and Materials, vol. 1, No. 4, 2022, pp. 145-149;

T.W. Kim, H.Y. Jeon, and J.H. Choe, 2005, “Prediction of The Fatigue Life of Tires Using CED and VCCT”. Key Eng. Mater. 297–300,102–107.

S.M.Barhli,L.Saucedo- Mora,M.S.L.Jordan, A.F.Cinar, C.Reinhard,M.Mostafavi andT.J.Marrow, 2017, “Synchrotron X-ray characterization of crack strain fields in polygranular graphite, CarbonV 124”, November, pp. 357-371.

M. Bentahar, H. Benzaama and N. Mahmoudi, 2021, “Numerical Modeling of the Evolution of the Strain energy ALLSE of the Crack Propagation by The X-FEM Method”, Revue des Matériaux et Energies Renouvelable, l5 (2).pp.24-31.

F. Saverio, 2014, “Modélisation tridimensionnelle de la fermeture induite par plasticité lors de la propagation d’une fissure de fatigue dans l’acier 304L thèse de doctorat”, l’école nationale supérieure de mécanique et d’aérotechnique.

J.R. Rice, (1968). “A path independent integral and the approximate analysis of strain concentrations by notches and cracks”. J. of Appl. Mech, 35, pp.379-386.

H.D. Bui, 1973, “Dualité entre les intégrales de contour”. Compte Rendu Acad. Sciences, T. 276, Paris.

Nguyen, Q.S.,1980, Méthodes énergétiques en mécanique de la rupture. J. de Méca,19(2). pp. 363-386.

Ph. Destuynder, and M. Djaoua, 1981, “Sur une interprétation mathématique de l’intégrale de Rice en théorie de la rupture fragile”, Math. Meth. In the Appl. Sci, 3. pp. 70-87.

H.P. Tada, P.C. Paris, and G.R. Irwin, 2000, “The Stress Analysis of Cracks Handbook”, American Society of Mechanical Engineering.

M. Bentahar, 2023, “ALLDMD Dissipation Energy Analysis by the Method Extended Finite Elements of a 2D Cracked Structure of an Elastic Linear Isotropic Homogeneous Material”, Journal of Electronics, Computer Networking and Applied Mathematics, Vol. 03, No. 02, pp 1-8,DOI:

M. Bentahar, 2023, “Fatigue Analysis of an Inclined Crack Propagation Problem by the X-FEM Method”, International Journal of Applied and Structural mechanics, Vol. 03 , No. 04 , June-July, pp 23-31,

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