امکان‌سنجی مدل‌سازی رشـد سه‌بعدی ترک در محیـط‌های متخلخـل با حفرات دایروی با استـفاده از مقاطع دوبعدی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشگاه زنجان

چکیده

با توجه به پیچیدگی‌های مطالعات آزمایشگاهی رشد ترک در مقیاس حفره، روش‌های عددی متعددی در تحلیل مسایل محیط‌های متخلخل استفاده شده است. این روش‌ها، در مورد نمونه‌های سه بعدی حجیم با هزینه‌های محاسباتی زیادی همراه است. بنابراین، ارائه روش‌هایی جهت کم نمودن هزینه‌های محاسباتی، اهمیت ویژه‌ای دارد. یکی از این راهکارها، شبیه‌سازی فرآیند رشد ترک و شکست به‌صورت دوبعدی و تعمیم آن به فضای سه‌بعدی است. در این پژوهش، امکان استفاده از این راهکار در تحلیل فرآیند تخریب مدل‌های سه‌بعدی و تخمین سریع‌تر رفتار ماده بررسی می‌شود. ابتدا، مدل‌های شامل یک ترک و یک حفره در نرم افزار آباکوس مدل‌سازی شده و در ادامه به مدل‌های پیچیده‌تر حاوی پنج حفره در آرایش‌های مختلف، تعمیم یافتند. مسیر رشد ترک و میزان مقاومت کششی مدل‌های سه‌بعدی و مقاطع دو‌بعدی به طور جداگانه محاسبه و مقایسه شدند. همچنین، مقاطع دوبعدی ابتدا در یک صفحه مختصات سه‌بعدی به یکدیگر الحاق شده و در نهایت در فضای سه‌بعدی نمایش داده شدند. نتایج نشان داد که مقاطع دوبعدی که شامل بیشترین تعداد حفرات مدل سه‌بعدی هستند، جواب‌های بهتری ارائه می‌دهند. از طرفی، صفحه نهایی شکستگی نمونه در مقاطع دوبعدی همانند مدل سه‌بعدی است. میانگین مقاومت کششی مقاطع دوبعدی تطابق قابل قبولی با مدل‌های سه‌بعدی دارند، به‌طوری که مقدار مقاومت محاسبه شده در بیشتر موارد، کمتر از 6% با نمونه سه‌بعدی اصلی اختلاف دارند. نزدیکی نتایج مقاطع دوبعدی با مدل سه‌بعدی و همچنین کاهش زمان پردازش مساله در حدود 85%، نشان از کارآیی روش پیشنهادی در این پژوهش است.

کلیدواژه‌ها

عنوان مقاله [English]

Feasibility Study of Three-Dimensional Crack Growth Modeling in Porous Media with Circular Pores Using Two-Dimensional Sections

نویسندگان [English]

  • Mohammad Besharati
  • Seyed Ahmad Lajevardi
  • Sadegh Karimpouli
  • Mohammad Rezanezhad
چکیده [English]

Due to the complexity of laboratory studies of crack growth in pore scale, several numerical methods have been used to analyze the porous media problems. These methods have high computational costs for large 3D samples. Therefore, it is important to provide bypath methods to reduce the computational costs. One of these methods is to simulate the crack growth and failure process in 2D, and generalize it to 3D space. In this research, the possibility of using this method  for failure analysis of 3D models and faster estimation of material behavior is investigated. First, models including one crack and one pore were modeled in ABAQUS software, and then generalized to more complex models containing five pores in different arrangements. Crack growth path and tensile strength of 3D models and 2D sections were calculated and compared separately. Also, the 2D sections were first merged into a 3D coordinate plane and finally displayed in 3D space. The results showed that the 2D sections which include the largest number of pores in the 3D model, provide better results. Moreover, the final fracture plane of the sample in 2D sections is the same as the 3D model. The average tensile strength of 2D sections is acceptable compared to 3D models and shows less than 6% difference from the original models in most cases. The close match between 2D and 3D models, as well as reducing the run time of processing to about 85%, is promising and indicates the efficiency of such methods.

کلیدواژه‌ها [English]

  • Porous media
  • Crack growth
  • Modeling
  • Abaqus
  • Two-dimensional sections

مراجع

  1. Dong, X., and Shin, Y. C., “Crack Formation Within Ceramics via Coupled Multiscale Genome and XFEM Predictions Under Various Loading Conditions”, Engineering Fracture Mechanics, Vol. 204, pp. 517-530, 2018.
  2. Khoei, A. R., Vahab, M., Haghighat, E., and Moallemi, S., “A Mesh-Independent Finite Element Formulation for Modeling Crack Growth in Saturated Porous Media Based on an Enriched-FEM Technique” , International Journal of Fracture, Vol. 188, pp. 79-108, 2014.
  3. Belytschko, T., and Black, T., “Elastic Crack Growth in Finite Elements” ,International Journal for Numerical Methods in Engineering, Vol. 45, pp. 601-620, 1999.
  4. Moës, N., Dolbow, J., and. Belytschko, T., “A Finite Element Method for Crack Growth Without Remeshing”, International Journal of Numerical Methods in Enginering, Vol. 46, No. 1, pp. 131-150, 1999.
  5. Shi, J., Chopp, D., Lua, J., Sukumar, N., and Belytschko, T., “Abaqus Implementation of Extended Finite Element Method Using A Level Set Representation for Three-Dimensional Fatigue Crack Growth and Life Predictions”, Engineering Fracture Mechanics, Vol. 77, No. 14, pp. 2840-2863, 2010.
  6. Sukumar, N., Chopp, D. L., and Moran, B., “Extended Finite Element Method and Fast Marching Method for Three-Dimensional Fatigue Crack Propagation”, Engineering Fracture Mechanics, Vol. 70, No. 1, pp. 29-48, 2003.
  7. Sedmak, A., Čolić, K., Grbović, A., Balać, I., and Burzić, M., “Numerical Analysis of Fatigue Crack Growth of Hip Implant”, Engineering Fracture Mechanics, Vol. 216, 2019.
  8. Fu, J. W., Chen, K., Zhu, W. S., Zhang, X. Z., and Li X. J., “Progressive Failure of New Modelling Material With A Single Internal Crack Under Biaxial Compression and the 3-D Numerical Simulation”, Engineering Fracture Mechanics, Vol. 165, pp. 140-152, 2016.
  9. Chandrupatla, T. R., and Belegundu, A. D., Introdction to Finite Elements in Engineering, 3rd ed., Vol. 10. 2002.
  10. Tang, C. A., Wong R. H. C., Chau, K. T., and Lin, P., “Modeling of Compression-Induced Splitting Failure in Heterogeneous Brittle Porous Solids”, Engineering Fracture Mechanics, Vol. 72, No. 4, pp. 597-615, 2005.
  11. Rezanezhad, M., Lajevardi, S. A., and Karimpouli, S., “Effects of Pore-Crack Relative Location on Crack Propagation in Porous Media Using XFEM Method”, Theoretical and Applied Fracture Mechanics, Vol. 103, 2019.
  12. Rezanezhad, M., Lajevardi, S. A., and Karimpouli, S., “Effects of Pore(S)-Crack Locations and Arrangements on Crack Growth Modeling in Porous Media”, Theoretical and Applied Fracture Mechanics, Vol. 107, 2020.
  13. Bohloli, B., and de Pater, C. J., “Experimental Study on Hydraulic Fracturing of Soft Rocks: Influence of Fluid Reology and Confining Stress”, Journal of Petroleum Science and Engineering 53, pp. 1-12, 2006.
  14. “Abaqus 6.14 Online Documentation,” Dassault Systèmes, 2014. http://130.149.89.49:2080/v6.14/.
  15. Rezanezhad, M., Lajevardi, S. A., and Karimpouli, S., “Crack Growth in Porous Media Using XFEM: Comparison of Modeling Strategies on the Abaqus”, Journal of Aalytical and Numerical Methods in Mining Engineering, Vol. 24, pp. 27-40, 2020 (in persian).
  16. Rezanezhad, M., Lajevardi, S. A., and Karimpouli, S., “Numerical Study of Crack Growth in Porous Media: Effect of Elliptical Porosity Parameters”, Journal of Aalytical and Numerical Methods in Mining Engineering, In press (in persian).
  17. Sharafisafa, M., and Nazem, M., “Application of the Distinct Element Method and the Extended Finite Element Method in Modelling Cracks and Coalescence in Brittle Materials”, Computational Materials Science, Vol. 91, pp. 102-121, 2014.
  18. Khitab, A., Anwar W., Mansouri, I., Tariq, M. K., and Mehmood, I., “Future of Civil Engineering Materials: A Review from Recent Developments”, Reviews on Advanced Materials Science, Vol. 42, No. 1, pp. 20-27, 2015.
  19. Mohammadi, S., Extended Finite Element Method: For Fracture Analysis of Structures, Blackwell Publishing Ltd, 2008.
  20. Elfakkoussi, S., Moustabchir, H., Elkhalfi, A., and Pruncu, C.I., “Computation of the Stress Intensity Factor KI for External Longitudinal Semi-Elliptic Cracks in the Pipelines by FEM and XFEM Methods”, International Journal on Interactive Design and Manufacturing, Vol. 13, No. 2, pp. 545-555, 2019.
  21. Moghaddam, H., Keyhanib, A., and Aghayan, I., “Modeling of Crack Propagation in Layered Structures Using Extended Finite Element Method”, Civil Engineering Journal, Vol. 2, No. 5, May, 2016
  22. Zhang, C., Cao, P., Cao, Y., and Li, J.,“ Using Finite Element Software to Simulation Fracture Behavior of Three-point Bending Beam with Initial Crack ”, Zhang, C., Cao, P., Cao, Y., and Li, J.,“ Using Finite Element Software to Simulation Fracture Behavior of Three-point Bending Beam with Initial Crack ”, Journal of Software, Vol. 8, No. 5, May, 2013.
  23. Abdellah, M. Y., “Delamination Modeling of Double Cantilever Beam of Unidirectional Composite Laminates”, Journal of Failure Analysis and Prevention,Vol. 17, pp. 1011-1018, 2017.
  24. Yang, W. H., “A Generalized Von Mises Criterion for Yield and Fracture”, Journal of Applied Mechanics, Vol. 47, No. 2, pp. 297-300, 1980. DOI: 10.1115/1.3153658.
  25. Zhu, X. K. and Leis, B. N., “Evaluation of Burst Pressure Prediction Models For Line Pipes”, International Journal of Pressure Vessels and Piping, vol. 89, pp. 85-97, 2012.
  26. Anderson, T. L., Fracture Mechanics Fundamentals and Applications, Taylor and Francis, CRC press, 2005.
  27. Rezanezhad, M., Lajevardi, S. A.,and Karimpouli, S., “Numerical Analysis of Effect of Different Shapes of Pore on Tensile Crack Growth”, Journal of Mineral Resources Engineering, 2021 (in Persian), doi 10.30479/JMRE.2021.14904.1481.
  28. Rezanezhad, M., Lajevardi, S. A., and Karimpouli, S., “Application of Equivalent Circle and Ellipse for Pore Shape Modeling in Crack Growth Problem: A Numerical Investigation in Microscale”, Engineering Fracture Mechanics, Vol. 253, 2021, 107882.
  29. Rezanezhad, M., Lajevardi, S. A., and Karimpouli, S., “An Investigation on Prevalent Strategies for XFEM-Based Numerical Modeling of Crack Growth in Porous Media”, Frontiers of Structural and Civil Engineering, https://doi.org/10.1007/s11709-021-0750-8. 

فایل ها

هم رسانی

ارجاع به این مقاله

آمار

تحت نظارت وف ایرانی