2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Authors

  • Mohammed Bentahar
  • Moulai Arbi Youcef
  • Noureddine Mahmoudi
  • Habib Benzaama

DOI:

https://doi.org/10.54021/seesv5n1-165

Keywords:

stress intensity factors, contour integral (J), SFEMD, crack, ASTM A36 steel material

Abstract

Numerical methods today play a useful and important role in solving various problems related to fracture mechanics including modeling crack propagation, fretting fatigue and cohesion... Furthermore, these methods have been widely used to solve problems in linear and nonlinear fracture mechanics in cases of elastic, plastic fracture problems. The evaluation of stress intensity factor in 2D and 3D geometries, thus these techniques widely used for non-standard crack configurations. The objective of this work is study the effects of the crack length and the number of structural elements on the two crack parameters such as the stress intensity factor KI and KII and the contour integral (J). As well as presenting a numerical modeling of crack propagation, for a LEHIM (Linear Elastic Homogeneous Isotopic Material) with mechanical characteristics by the method SFEMD (Stretching Finite Element Method Developed), the model chosen with quadratic elements with 4 nodes (CPE4). However, this method is based on the effect of the number of contours and the number of elements around the crack tip on the variation of the stress intensity factors. In addition, the crack propagation criterion (MCSC) was used, a computer program was created in FORTRAN language to develop and evaluate the stress intensity factors and the contour integral (J). Several examples of crack lengths a = 0.7, 1.4, 2.1, 2.8 and 3.5 mm were used. Additionally, the number of items has been changed several times. The stress intensity factors of modes I and II and direction angles (α) are calculated to solve the problem using the ABAQUS finite element code. The results obtained by the SFEMD method and the results of the analytical method are very close.

References

ACHCHHE, L.; MANOJ, B. V.; KUNDAN, M. Numerical Analysis of an Edge Crack Isotropic Plate with Void/Inclusions under Different Loading by Implementing XFEM. Journal of Applied and Computational Mechanics, v. 7, n. 3, p. 1362-1382, 2021. 10.22055/JACM.2019.31268.1848.

ALDERLIESTEN, R. Fatigue crack propagation and delamination growth in glare. Delft: DUP Science, 2005.

ALIABADI, M. H. The Boundary Element method. Applications in Solids and Structures, New York, v. 2, 2002. ISBN: 978-0-470-84298-0.

ALSHOAIBI, A. M.; FAGEEHI, Y. A. A Computational Framework for 2D Crack Growth Based on the Adaptive Finite. Element Method, Appl. Sci, v. 13, n. 1, 2023. 284, https:// doi.org/10.3390/app13010284.

ANINDITO, P.; MAKABE, C. The crack growth behavior after overloading on rotating bending fatigue. Engineering Failure Analysis, v. 16, n. 7, p. 2245–2254, 2009.

ANLAS, G.; SANTARE, M. H.; LAMBROS, J. Numerical calculation of stress intensity factors in functionally graded materials. International Journal of Fracture, v. 104, n. 2, p. 131-143, 2000.

BENTAHAR, M.; BENZAAMA, H. Numerical Simulation of 2D Crack Propagation using SFEM Method by Abaqus. Tribology and Materials, v. 1, n. 4, p. 145-149, 2022. https://doi.org/10.46793/tribomat.2022.018.

BENTAHAR, M. Numerical study of a centred crack on an elastoplastic material by the FEM method. Tribology and Materials, v. 2, n. 3, p. 108-113, 2023. https://doi.org/10.46793/tribomat.2023.011.

BENTAHAR, M.; BENZAAMA, H. Application of SFEM Method to Analyse Crack Parameters of Ultra High Molecular Weight Polyethylene Material. International Journal of Applied and Structural Mechanics, v. 3, n. 6, p. 25-33, 2023. DOI: https://doi.org/10.55529/ijasm.36.25.33.

BENTAHAR, M.; BENZAAMA, H. Numerical simulation of the synthetic strain energy and crack characterization. Selcuk University Journal of Engineering Sciences, v. 22, n. 03, p. 100-109, 2023.

BENTAHAR, M. Numerical modeling of the crack propagation parameters of two different elements by the FEM method. Advanced Engineering Letters, v. 3, n. 1, p. 36-41, 2024. https://doi.org/10.46793/adeletters.2024.3.1.5.

BENTAHAR, M.; BENZAAMA, H.; BENTOUMI, M.; MOUKTARI, M. A New automated stretching finite element method for 2D crack propagation. Journal of Theoritical and Applied Mechanics (JTAM), v. 55, n. 3, p. 869-881, 2017. https://doi.org/10.15632/jtam-pl.55.3.869.

BENTAHAR, M.; BENZAAMA, H.; MAHMOUDI, N. Numerical modeling of the contact effect on the parameters of cracking in a 2D Fatigue Fretting Model. Frattura ed Integrità Strutturale, v. 57, p. 182-194, 2021. https://doi.org/10.3221/

IGF-ESIS.57.15.

BREITBARTH, E.; STROHMANN, T.; BESEL, M.; REH, S. Determination of Stress Intensity Factors and J integral based on Digital Image Correlation. Frattura ed Integrità Strutturale, v. 49, p. 12-25, 2019. https://doi.org/10.3221/IGF-ESIS.49.02.

CHANG, J.; XU, J.; MUTOH, Y. A general mixed-mode brittle fracture criterion for cracked materials. Engineering Fracture Mechanics, v. 73, n. 9, p. 1249-1263, 2006.

CHEN, F. M.; CHAO, C. K.; CHIU, C. C.; NODA, N. A. Stress intensity factors for cusp-type crack problem under mechanical and thermal loading. Journal of Mechanics, v. 37, p. 327–332, 2021. https://doi.org/10.1093/jom/ufaa028.

CHO, J. R. Computation of 2-D mixed-mode stress intensity factors by Petrov-Galerkin natural element method. Structural Engineering and Mechanics, v. 56, n. 4, p. 589-603, 2015. https://doi: 10.12989/sem.2015.56.4.589.

CHRISTER, S.; KJELL, E. The J-area integral applied in peridynamics. Int J Fract, v. 228, p. 127–142, 2021. https://doi.org/10.1007/s10704-020-00505-8.

COURTIN, S.; GARDIN, C.; BEZINE, G.; HAMOUDA, H. B. H. Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS. Eng. Fract. Mech, v. 72, p. 2174–2185, 2005, DOI:10.1016/j.engfracmech.2005.02.003.

DE MORAIS, A. B. Calculation of stress intensity factors by the force method. Engineering Fracture Mechanics, v. 74, n. 5, p. 739-750, 2007.

DESTUYNDER, P. H.; DJAOUA, M. Sur une interprétation mathématique de l’intégrale de Rice en théorie de la rupture fragile. Math. Meth. In the Appl. Sci, v. 3, p. 70–87, 1981.

ERDOGAN, F.; CIVELEK, M. B. Crack problems for a rectangular sheet and infinite stripe. International Journal of Fracture, v. 19, p. 139–159, 1982.

EWALDS, H.; WANHILL, R. Fracture Mechanics. New York: Edward Arnold, 1989.

FAGEEHI, Y. A. Prediction of Fatigue Crack Growth Rate and Stress Intensity Factors Using the Finite Element Method. Advances in Materials Science and Engineering, 2022. ID 2705240, https://doi.org/10.1155/2022/2705240.

FAGEEHI, Y. A.; ALSHOAIBI, A. M. Numerical simulation of mixed-mode fatigue crack growth for compact tension shear specimen. Adv, Mater. Sci. Eng, p. 5426831, 2020. https://doi.org/10.1155/2020/5426831.

FARROKH, S.; JON, O. Stress Intensity Factor Determination for Three-Dimensional Crack Using the Displacement Discontinuity Method with Applications to Hydraulic Fracture Height Growth and Non- Planar Propagation Paths. 2nd ISRM International Conference for Effective and Sustainable Hydraulic Fracturing At: Brisbane, Australia. November, 2012. DOI: 10.5772/56308.

FAYED, A. S. Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates. Engineering Solid Mechanics, v. 5, n. 1, 61-70, 2017. DOI: 10.5267/j.esm.2016.8.001.

GAJJAR, M.; PATHAK, H. Fracture analysis of plastically graded material with thermo-mechanical J-integral. Proceedings of the Institution of Mechanical Engineers, v. 235, n. 5, 2021. https://doi.org/10.1177/1464420721991583.

GAJJAR, M.; PATHAK, H. Fracture analysis of plastically graded material with thermo-mechanical J-integral. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials Design and Applications, v. 235, n. 5, p. 1128-1145, 2021. doi:10.1177/1464420721991583.

GOZIN, M. H.; AGHAIE-KHAFRI, M. 2D and 3D finite element analysis of crack growth under compressive residual stress field. International Journal of Solids and Structures, v. 49, n. 23–24, p. 3316-3322, 2012. https://doi.org/10.

/j.ijsolstr.2012.07.014.

GUINEA, G. V.; PLANAS, J.; ELICES, M. KI evaluation by the displacement extrapolation technique. Eng. Fract. Mech, v. 66, p. 243–255, 2000. DOI: 10.1016/S0013-7944(00)00016-3.

ISMAIL, A. E.; ARIFFIN, A. K.; ABDULLAH, S.; GHAZALI, M. J. Off-set crack propagation analysis under mixed mode loadings. Int Journal of Automotive Technology, v. 12, n. 2, p. 225–232, 2011.

ISMAIL, A. E.; ARIFFIN, A. K.; ABDULLAH, S.; GHAZALI, M. J. Ungkapan kamiran-J retak permukaan pada bar silinder padu kenaan beban ragam I. Jurnal Teknologi Sciences and Engineering, v. 68, n. 1, p. 7–17, 2014.

LEPRETRE, E.; CHATAIGNER, S.; DIENG, L.; GAILLET, L. Stress Intensity Factor Assessment for the Reinforcement of Cracked Steel Plates Using Prestressed or Non-Prestressed Adhesively Bonded CFRP. Materials, v. 14, n. 7, p. 1625, 2021. https://doi.org/ 10.3390/ma14071625.

LUO, H.; YANG, R.; WANG, Y.; YANG, G.; LI, C.; AN, C.; ZHANG, Y. Experimental Study on the Caustics of Moving Cracks and Elliptical Curvature under Impact Loading. Advances in Civil Engineering, 2021. ID 5524635, https://doi.org/10.1155/2021/5524635.

MONTASSIR, S.; MOUSTABCHIR, H.; ELKHALFI, A. Application of NURBS in the Fracture Mechanics Framework to Study the Stress Intensity Factor. Statistics, Optimization and Information Computing, v. 11, n. 1): 106–115, 2023. https://doi.org/10.19139/soic-2310-5070-1553.

MURAT, Y. The investigation crack problem through numerical analysis. Structural Engineering and Mechanics, v. 57, n. 6, p. 1143 -1156, 2016. https://doi: 10.12989/sem.2016.57.6.1143.

NGUYEN, Q. S. Méthodes énergétiques en mécanique de la rupture. J. de Méca, v. 19, n. 2, p. 363-386, 1980.

NGUYEN, T. T.; PHAM, V. S.; TRAN, H. A.; NGUYEN, D. H.; NGUYEN, T. H.; DINH, H. B. Effect of Residual Stress on Mode-I Stress Intensity Factor: A Quantitative Evaluation and a Suggestion of an Estimating Equation. Metals, v. 13, p. 1132, 2023. https://doi.org/10.3390/met13061132.

NIKFAM, M. R.; ZEINODDINI, M.; AGHEBATI, F.; ARGHAEI, A. A. Experimental and XFEM modelling of high cycle fatigue crack growth in steel welded T-joints. International Journal of Mechanical Sciences, v. 153-154, p. 178–193, 2019. https://doi.org/10.1016/j.ijmecsci.2019.01.040.

NIU, Y.; FAN, J.; SHI, X.; WEI, J.; JIAO, C.; HU, J. Application of the J-Integral and Digital Image Correlation (DIC) to Determination of Multiple Crack Propagation Law of UHPC under Flexural Cyclic Loading. Materials, v. 6, p. 1296, 2023. https://doi.org/10.3390/ ma16010296.

RAO, B. N.; RAHMAN, S. An efficient meshless method for fracture analysis of cracks. Computational Mechanics, v. 26, p. 398-408, 2000. DOI: 10.1007/s00

RICE, J. R. A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J. of Appl. Mech, v. 35, p. 379-386, 1968. https://doi.org/10.1115/1.3601206.

SAVERIO, F. Modélisation tridimensionnelle de la fermeture induite par plasticité lors de la propagation d’une fissure de fatigue dans l’acier 304L. Thèse (Doctorat) – L’Ecole Nationale Supérieure de Mécanique et D’Aérotechnique. Soutenue le 24/11/2014. https://theses.hal.science/tel-01129079.

SHUAI, H.; ZHIHAI, C.; YOULI, Z.; QIZHI, Z.; YONG, C.; HAN, G.; HONGBO, W.; JING, L. Elasto-Plastic Fracture Mechanics Analysis of the Effect of Shot Peening on 300M Steel. Materials, v. 14, p. 3538, 2021. https://doi.org/ 10.3390/ma

SIH, G. C.; ERDOGAN, F. On crack extension in plants (plates) under plane loading and transverse shear. ASME Meeting WA-163, New York, v. 3, 1962.

SUTTHISAK, P.; KOBSAK, P.; PRAMOTE, D. J-integral calculation by domain integral technique using adaptive finite element method. Structural Engineering and Mechanics, v. 28, n. 4, p. 461-477, 2008. DOI: https://doi.org/10.12989/

sem.2008.28.4.461.

TADA, H. P.; PARIS, P. C.; IRWIN, G. R. The Stress Analysis of Cracks Handbook. American Society of Mechanical Engineering, 2000.

TORIBIO, J.; GONZÁLEZ, B.; MATOS, J. C.; MULAS, Ó. Stress Intensity Factors for Embedded, Surface, and Corner Cracks in Finite-Thickness Plates Subjected to Tensile Loading. Materials, v. 14, p. 2807, 2021. https://doi.org/10.3390/ ma14112807.

WANG, H. T.; WU, G.; PANG, Y. Y. Theoretical and Numerical Study on Stress Intensity Factors for FRP-Strengthened Steel Plates with Double-Edged Cracks. Sensors, v. 18, p. 2356, 2018. https://doi.org/10.3390/s18072356.

ZHU, W.; SMITH, D. On the use of displacement extrapolation to obtain crack tip singular stresses and stress intensity factors. Eng. Fract. Mech, v. 51, p. 391–400, 1995. DOI:10.1016/0013-7944(94)00319-D.

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Published

2024-06-24

How to Cite

Bentahar, M., Youcef, M. A., Mahmoudi, N., & Benzaama, H. (2024). 2D numerical modeling of crack propagation using SFEMD method of a LEHI material. STUDIES IN ENGINEERING AND EXACT SCIENCES, 5(1), 3329–3350. https://doi.org/10.54021/seesv5n1-165