بررسی رشد دو ترک پادمتقارن در ورق براثر کشش لبه ها با سرعت های مختلف با استفاده از تئوری پری داینامیک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی هوافضا، دانشگاه سمنان، سمنان ، ایران

2 دانشکده مهندسی مکانیک، دانشگاه گیلان، رشت، ایران

چکیده

با وجود توسعه مدل‌های پیش بینی شروع و رشد ترک، این موضوع هنوز یکی از چالش‌های عمده در مکانیک محیط‌های پیوسته است. مشکل اصلی در فرمول‌بندی ریاضی این موضوع به این علت به وجود می‌آید که فرض می‌شود جسم پس از تغییر شکل هنوز محیط پیوسته باقی می‌ماند. بنابراین، ساختار ریاضیاتی مساله با به وجود آمدن یک ناپیوستگی )مانند ترک و شکست( دچار مشکل می‌شود. این اتفاق بدین دلیل رخ می‌دهد که تئوری کلاسیک از معادلات دیفرانسیل با مشتقات جزئی برای تشریح فضای مادی استفاده می‌کند و این مشتقات جزئی در محل ناپیوستگی تعریف نشده است. برای غلبه بر این محدودیت، روش پری داینامیک برای مدل سازی مسائل شامل ناپیوستگی معرفی شده که در آن ناپیوستگی هایی مانند ترک و شکست در سازه به عنوان نوعی دیگر از تغییر شکل در نظر گرفته می‌شود. در این مقاله مساله رشد ترک در ورقی با دو ترک پادمتقارن تحت کشش بررسی شده و پس از صحه گذاری نتایج با مطالعات موجود، اثر سرعت اعمال بار کششی بر نحوه رشد ترک مورد بررسی قرار گرفته است. نتایج این تحقیق نشان می‌دهد که روش پری داینامیک توانایی بالایی در شبیه‌سازی رفتار سازه با هر سرعت بارگذاری را دارد و سرعت اعمال بار تاثیر مستقیمی بر نحوه رشد ترک و ایجاد پدیده چند شاخه شدن ترک دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A Peridynamic Study on Crack Growth in Plates with Two Anti-symmetric Cracks under Various Tensile Velocities

نویسندگان [English]

  • M. Shakouri 1
  • S. R. Kazemi 2
1 Department of Aerospace Engineering, Semnan University, Semnan, Iran
2 Department of Mechanical Engineering, University of Guilan, Guilan, Iran
چکیده [English]

 Despite the development of some advanced concepts in fracture mechanics during recent decades, the prediction of crack initiation and its growth in materials is still a major challenge. The main difficulty is because of the continuum based mathematical formulation, which assumes that a body remains continuous as it deforms. In fact, the classical theory is formulated using spatial partial differential equations. This presents a characteristic limitation to the classical theory, as the spatial derivatives in the governing equations lose their meaning due to the presence of a discontinuity, such as a crack. To overcome this problem, Peridynamic theory could be used to improve the analysis of cracked structures. Basically, the peridynamic theory is a reformulation of the equation of motion in solid mechanics that is better suited for modeling bodies with discontinuities, such as cracks. The theory uses spatial integral equations that can be applied to a discontinuity. The present study uses this approach to study the effects of applying tensile loads on crack paths in a plate with two parallel initial cracks located in an anti-symmetric manner. The results are compared with other investigations and it is shown that the velocity of applying load has significant effect on crack path and branching.

کلیدواژه‌ها [English]

  • Peridynamic Theory
  • crack growth
  • Branching
  • Loading rate
[1] A.A. Griffith, The phenomena of rupture and flow in solids, Philosophical transactions of the royal society of london. Series A, containing papers of a mathematical or physical character, (1921) 163-198.
[2] A.C. Eringen, C. Speziale, B. Kim, Crack-tip problem in non-local elasticity, Journal of the Mechanics and Physics of Solids, 25(5) (1977) 339-355.
[3] A.C. Eringen, Nonlocal polar elastic continua, International journal of engineering science, 10(1) (1972) 1-16.
[4] S.A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids, 48(1) (2000) 175-209.
[5] S.A. Silling, E. Askari, A meshfree method based on the peridynamic model of solid mechanics, Computers & Structures, 83(17-18) (2005) 1526-1535.
[6] E. Madenci, E. Oterkus, Peridynamic theory and its applications, Springer, 2014.
[7] C. Hao, L. Wijerathne, T. ICHIMURA, Stability of dynamic growth of two anti-symmetric cracks using PDS-FEM, Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)), 68(1) (2012) 10-17.
[8] O. Weckner, R. Abeyaratne, The effect of long-range forces on the dynamics of a bar, Journal of the Mechanics and Physics of Solids, 53(3) (2005) 705-728.
[9] S.A. Silling, M. Zimmermann, R. Abeyaratne, Deformation of a peridynamic bar, Journal of Elasticity, 73(1-3) (2003) 173-190.
[10] S.A. Silling, F. Bobaru, Peridynamic modeling of membranes and fibers, International Journal of Non-Linear Mechanics, 40(2-3) (2005) 395-409.
[11] W. Gerstle, N. Sau, S. Silling, Peridynamic modeling of concrete structures, Nuclear Engineering and Design, 237(12-13) (2007) 1250-1258.
[12] S.A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari, Peridynamic States and Constitutive Modeling, Journal of Elasticity, 88(2) (2007) 151-184.
[13] S.A. Silling, Linearized Theory of Peridynamic States, Journal of Elasticity, 99(1) (2010) 85-111.
[14] R.B. Lehoucq, M.P. Sears, Statistical mechanical foundation of the peridynamic nonlocal continuum theory: Energy and momentum conservation laws, Physical Review E, 84(3) (2011) 031112.
[15] S.A. Silling, A coarsening method for linear peridynamics, International Journal for Multiscale Computational Engineering, 9(6) (2011).
[16] R. Lehoucq, S. Silling, Force flux and the peridynamic stress tensor, Journal of the Mechanics and Physics of Solids, 56(4) (2008) 1566-1577.
[17] J.A. Mitchell, A nonlocal, ordinary, state-based plasticity model for peridynamics, SAND Report, 7597 (2011).
[18] J.A. Mitchell, A non-local, ordinary-state-based viscoelasticity model for peridynamics, Sandia National Lab Report, 8064 (2011) 1-28.
[19] B. Kilic, A. Agwai, E. Madenci, Damage prediction in notched composites using peridynamic theory, (2008).
[20] M.J. Taylor, Numerical simulation of thermo-elasticity, inelasticity and rupture in membrane theory, University of California, Berkeley, 2008.
[21] J.T. Foster, S.A. Silling, W.W. Chen, Viscoplasticity using peridynamics, International journal for numerical methods in engineering, 81(10) (2010) 1242-1258.
[22] K. Dayal, K. Bhattacharya, Kinetics of phase transformations in the peridynamic formulation of continuum mechanics, Journal of the Mechanics and Physics of Solids, 54(9) (2006) 1811-1842.
[23] S.A. Silling, O. Weckner, E. Askari, F. Bobaru, Crack nucleation in a peridynamic solid, International Journal of Fracture, 162(1-2) (2010) 219-227.
[24] T.L. Warren, S.A. Silling, A. Askari, O. Weckner, M.A. Epton, J. Xu, A non-ordinary state-based peridynamic method to model solid material deformation and fracture, International Journal of Solids and Structures, 46(5) (2009) 1186-1195.
[25] J.T. Foster, S.A. Silling, W. Chen, An energy based failure criterion for use with peridynamic states, International Journal for Multiscale Computational Engineering, 9(6) (2011).
[26] S. Silling, Dynamic fracture modeling with a meshfree peridynamic code, Computational fluid and solid mechanics, (2003) 641-644.
[27] S.A. Silling, E. Askari, Peridynamic modeling of impact damage, in: ASME/JSME 2004 Pressure Vessels and Piping Conference, American Society of Mechanical Engineers, 2004, pp. 197-205.
[28] Y.D. Ha, F. Bobaru, Characteristics of dynamic brittle fracture captured with peridynamics, Engineering Fracture Mechanics, 78(6) (2011) 1156-1168.
[29] M.S. Breitenfeld, P.H. Geubelle, O. Weckner, S.A. Silling, Non-ordinary state-based peridynamic analysis of stationary crack problems, Computer Methods in Applied Mechanics and Engineering, 272 (2014) 233-250.
[30] J. O’Grady, J. Foster, Peridynamic beams: A non-ordinary, state-based model, International Journal of Solids and Structures, 51(18) (2014) 3177-3183.
[31] J. O’Grady, J. Foster, Peridynamic plates and flat shells: A non-ordinary, state-based model, International Journal of Solids and Structures, 51(25-26) (2014) 4572-4579.
[32] C.T. Wu, B. Ren, A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process, Computer Methods in Applied Mechanics and Engineering, 291 (2015) 197-215.
[33] J. Amani, E. Oterkus, P. Areias, G. Zi, T. Nguyen-Thoi, T. Rabczuk, A non-ordinary state-based peridynamics formulation for thermoplastic fracture, International Journal of Impact Engineering, 87 (2016) 83-94.
[34] E. Madenci, S. Oterkus, Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening, Journal of the Mechanics and Physics of Solids, 86 (2016) 192-219.
[35] K. Oguni, M.L.L. Wijerathne, T. Okinaka, M. Hori, Crack propagation analysis using PDS-FEM and comparison with fracture experiment, Mechanics of Materials, 41 (2009) 1242-1252.
[36] G. Sarego, Q. Le, F. Bobaru, M. Zaccariotto, U. Galvanetto, Linearized State‐based Peridynamics for 2D problems, International Journal for Numerical Methods in Engineering, (2016).