تعیین ضرایب شدت تنش در صفحات تابعی ارتوتروپیک با روش بدون المان گلرکین

نوع مقاله: مقاله پژوهشی

نویسندگان

1 عضو هیات علمی / دانشکدة مهندسی مکانیک، دانشگاه فردوسی مشهد

2 عضو هیات علمی/ دانشکدة مهندسی مکانیک، دانشگاه صنعتی شاهرود

3 عضو هیات علمی / گروه مهندسی رباتیک، دانشگاه صنعتی شاهرود

چکیده

روش‌های تولید مواد تابعی سبب می‌شود رفتار این مواد غیر ایزوتروپ باشد. در این مقاله از روش بدون ­المان گلرکین برای مطالعة شکست مواد تابعی ارتوتروپیک استفاده شده است. در این روش محاسبة عددی مشتق میدان­های اصلی و کمکی کرنش به‌سادگی انجام می­شود، حال آنکه روش المان محدود و فرم توسعه­یافتة آن با مشکلاتی همراه است. به‌علاوه در این مقاله یک انتگرال پایستار جدید برای محاسبة پارامترهای شکست در مواد غیرهمگن ارائه شده است که فرم یکسانی برای بارگذاری مکانیکی و حرارتی دارد. این شکل جدید از انتگرال برهم­کنش دارای ترم­هایی با تعبیر فیزیکی مشخص بوده و برای برهم­کنش میدان‌های خطی بر میدان الاستیک دارای ترم­های ثابت است و به‌طور سیستماتیک قابل تعمیم می­باشد. در این مقاله، ضرایب شدت تنش در مواد تابعی ارتوتروپیک با به‌کارگیری این انتگرال برهم‌کنش محاسبه شده است. برای گسسته­سازی معادلات حاکم از روش بدون المان گلرکین استفاده شده است. در چند مثال اثر تغییر خصوصیات مواد بر ضرایب شدت تنش بررسی شده است. مقایسة نتایج با مقادیر گزارش­شده در مقالات موجود بیانگر دقت قابل قبول رابطة ارائه‌شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Stress intensity factor calculation in orthotropic functionally graded layers using element-free Galerkin method

نویسندگان [English]

  • Mahmoud Shariati 1
  • Mohammad Bagher Nazari 2
  • Masoud Mahdizadeh Rokhi 3
چکیده [English]

Production methods of functionally graded materials cause anisotropic behavior. In this paper, the element-free Galerkin method is used to study of fracture behavior of orthotropic functionally graded materials. In this method, numerical calculation of the main and auxiliary strain fields is simply done while, in finite element and extended finite element methods, it is associated with difficulties. In addition to in this paper, a path-independent integral is presented to compute the fracture parameters in heterogeneous materials which has a unique form for mechanical and thermal loading. This new form of interaction integral includes terms with the certain physical interpretation. Also, the presented form of interaction integral has fixed term for interaction of linear fields on elastic field and it is systematically extensible. In this paper, the stress intensity factors in orthotropic functionally graded materials are obtained by using this interaction integral formula. The element-free Galerkin method is implemented to discrete the governing equations. The effect of materials characteristics on the stress intensity factors is studied in several examples. The obtained results are in good agreement with reported ones in existence papers.

کلیدواژه‌ها [English]

  • path-independent integral
  • crack
  • stress intensity factor
  • orthotropic functionally graded materials
  • element-free Galerkin method

[1] P. Gu, R. J. Asaro, Cracks in functionally graded materials, International Journal of solids and structures, Vol. 34, No. 1, pp. 1–17, 1997.

[2] M. Ozturk, F. Erdogan, Mode I crack problem in an inhomogeneous orthotropic medium, International Journal of Engineering Sciences, Vol. 35, No. 9, pp. 869–883, 1997.

[3] M. Ozturk, F. Erdogan, The mixed mode crack problem in an inhomogeneous orthotropic medium, International Journal of Fracture, Vol. 98, No. 3–4, pp. 243–261, 1999.

[4] B. N. Rao, S. Rahman, An interaction integral method for analysis of cracks in orthotropic functionally graded materials, Computational Mechanics, Vol. 32, No, 40–51, 2003.

[5] J-H. Kim, G. H. Paulino, The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors, International Journal of solids and structures, Vol. 40, No. 15, pp. 3967– 4001, 2003.

[6] J-H. Kim, G. H. Paulino, Mixed-mode J-integral formulation and implementation using graded finite elements for fracture analysis of nonhomogeneous orthotropic materials, Mechanics of Materials, Vol. 35, No. 1–2, pp. 107–128, 2003.

[7] J-H. Kim, G. H. Paulino, Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method, Engineering Fracture Mechanics, Vol. 69, No. 14–16, pp.1557–1586, 2002.

[8] J. Chen, Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure, International Journal of Fracture, Vol. 133, No. 4, pp. 303–328, 2005.

[9] S. Dag, Mixed-mode fracture analysis of functionally graded materials under thermal stresses: a new approach using Jk-integral, Journal of Thermal Stresses, Vol. 30, pp. 269-296, 2007.

[10] S. Dag, B. Yildirim, S. Topal, Computational Methods for Inclined Cracks in Orthotropic Functionally Graded Materials Under Thermal Stresses, Journal of Thermal Stresses, Vol. 36, No. 10, pp. 1001–1026, Oct. 2013.

[11] H. Bayesteh, S. Mohammadi, XFEM Fracture Analysis of Orthotropic Functionally Graded Materials, Compos. Part B Eng., Vol. 44, No. 1, pp. 8–25, 2013.

[12] E. Goli, M. T. Kazemi, XFEM Modeling of Fracture Mechanics in Transversely Isotropic FGMs via Interaction Integral Method, Proc. Mater. Sci., Vol. 3, pp. 1257–1262, 2014.

[13] H. Bayesteh, A. Afshar, S.Mohammdi, Thermo-Mechanical Fracture Study of Inhomogeneous Cracked Solids by the Extended Isogeometric Analysis Method, Eur. J. Mech.-A/Solids, Vol. 51, pp. 123–139, 2015.

[14] G. Bhardwaj, I. V. Singh, B. K. Mishra, T. Q. Bui, and Numerical Simulation of Functionally Graded Cracked Plates Using NURBS based XIGA under Different Loads and Boundary Conditions, Compos. Struct., Vol. 126, pp. 347–359, 2015.

[15] M. Shariati, M. Majidzadeh, M. B. Nazari, Determination of stress intensity factors in cracked FGM rectangular plates by element-free Galerkin method, Journal of Mechanical Engineering, Vol. 40, No. 1, pp. 55-66, 1389. (in Persianفارسی )

[16] M. B. Nazari, M. Shariati, M. R. Eslami, B. Hassani, Meshless Analysis of Cracked Functionally Graded Plates under Thermal Loading, Aerospace mechanics journal, Vol. 9, No. 4, pp. 1-16, 1392. (in Persianفارسی )

[17] M. Pant, I. V. Singh, B. K. Mishra, Numerical Simulation of Thermo-Elastic Fracture Problems Using Element Free Galerkin Method, Int. J. Mech. Sci., Vol. 52, No. 12, pp. 1745–1755, 2010.

[18] V. P. Nguyen, T. Rabczuk, S. Bordas, M. Duflot, Meshless Methods: A Review and Computer Implementation Aspects, Math. Comput. Simul., Vol. 79, No. 3, pp. 763–813, 2008.

[19] H. Koohkan, G. Baradaran, R. Vaghefi, A Completely Meshless Analysis of Cracks in Isotropic Functionally Graded Materials (Petrov–Galerki), Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., Vol. 224, pp. 581–590, 2009.

[20] S. Garg, M. Pant, Numerical simulation of adiabatic and isothermal cracks in functionally graded materials using optimized element-free Galerkin method, Journal of Thermal Stresses, Vol. 40, No. 5, pp 1-20, 2017.

[21] S. G. Lekhnitskii, Anisotropic plates, Gordon and Breach Science Publishers, New York, 1968.

[22] G. C. Sih, P. C. Paris, G. R. Irwin, On cracks in rectilinearly anisotropic bodies. International Journal of Fracture, Vol. 1, No. 2, pp. 189–203, 1965.

[23] T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl, Meshless methods: an overview and recent developments, Computer methods in applied mechanics and engineering, Vol. 139, No. 1-4, pp. 3–47, 1996.

[24] N. Konda, F. Erdogan, The mixed mode crack problem in a nonhomogeneous elastic medium, Engineering Fracture Mechanics, Vol. 47, pp. 533–45, 1994.

[25] S. Krenk, On the elastic constants of plane orthotropic elasticity, Journal of Composite Materials, Vol. 13, pp. 108–116, 1979.