نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکترا، مهندسی مکانیک، دانشگاه آزاد اسلامی. واحد دماوند.تهران

2 استادیار، مهندسی مکانیک، دانشگاه آزاد اسلامی واحد دماوند. تهران

چکیده

با توجه به حساسیت نتایج در ناحیه تورق و جدایش بین لایه‌ها در لمینیت‌های کامپوزیتی، لازم است تا از تئوری‌های دقیق که تمام مولفه‌های تنش را در بر گیرند برای بررسی این ناحیه استفاده شود. به این منظور در مطالعه حاضر، روش بسته شدن مجازی ترک بر اساس تئوری لایه گون، برای تحلیل گسترش تورق و جدایش بین لایه‌ها در یک تیر کامپوزیتی توسعه داده شده است. نرخ آزادسازی انرژی کرنشی در مود یک، بر اساس خواص ماده تعیین شده و یک الگوریتم برای پیاده سازی روش ارائه شده است. روش مذکور بر روی تیر کامپوزیتی یکسر گیردار دو لبه متقارن در دو حالت دو و سه بعدی به صورت عددی در نرم افزار متلب اجرا شده و به منظور صحت سنجی روش، با نتایج کارهای گذشته مبتنی بر المان محدود مقایسه شده است. همچنین حل تحلیلی مسئله نیز ارائه شده و با نتایج کار حاضر مورد مقایسه قرار گرفته است. رفتار نیرو-جابجایی یک تیرکامپوزیتی تحلیل شده که نشان دهنده قابلیت مناسب این روش در تحلیل تورق و گسترش جدایش بین لایه‌ها بوده و در عین حال حجم محاسبات به نسبت المان محدود سه بعدی کاهش یافته است.

کلیدواژه‌ها

عنوان مقاله [English]

Development of the Virtual Crack Closure Technique using Layer Wise theory for Delamination Propagation of a Composite Beam in Mode I

نویسندگان [English]

  • Sayed Ali Mousavi Tarsi 1
  • Mehdi Afshin 2

1 Department of Mechanical Engineering, Damavand Branch, Islamic Azad University, Damavand, Iran.

2 Department of Mechanical Engineering, Damavand Branch, Islamic Azad University, Damavand, Iran.

چکیده [English]

Due to the sensitivity of the results in the delamination area of composite laminates, it is necessary to use accurate theories that include all components of stress to study this area. For this purpose, in the present study, the virtual crack closure technique based on layer wise theory has been developed to analyze the propagation of delamination in a composite beam. The strain energy release rate in mode I is determined based on the properties of the material and an algorithm is proposed to implement the method. The present method has been implemented numerically in MATLAB software on a 2D and 3D Double Cantilever Beam (DCB). In order to validate the method, it has been compared with the results of previous works based on Finite Element method. An analytical solution to the problem is also presented and compared with the results of the present work. The force-displacement behavior of a DCB composite beam is analyzed, which indicates the suitable capability of this method in the analysis of propagation of delamination, and the computations are reduced relative to the three-dimensional Finite Element.

کلیدواژه‌ها [English]

  • Composite Beam
  • Delamination
  • Layer Wise
  • VCCT
[1]  Orifici, A. C., Herszberg, I., and Thomson, R. S., “Review of methodologies for composite material modelling incorporating failure,” Composite Structures, Vol. 86, No. 1–3, pp. 194–210, 2008.
[2]  Carraro, P. A., Novello, E., Quaresimin, M., and Zappalorto, M., “Delamination onset in symmetric cross-ply laminates under static loads: Theory, numerics and experiments,” Composite Structures, Vol. 176, pp. 420–432, 2017.
[3]  Turon, A., Camanho, P. P., Costa, J., and Renart, J., “Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: Definition of interlaminar strengths and elastic stiffness,” Composite Structures, Vol. 92, No. 8, pp. 1857–1864, 2010.
[4]  Feng, D. and Aymerich, F., “Finite element modelling of damage induced by low-velocity impact on composite laminates,” Composite Structures, Vol. 108, No. 1, pp. 161–171, 2014.
[5]  Bak, L. V., Turon, A., Lindgaard, E., and Lund, E., “A simulation method for high-cycle fatigue-driven delamination using a cohesive zone model,” International Journal for numerical methods in engineerin, Vol. 106, No. February, pp. 1102–1119, 2012.
[6]  Fan, X. L., Sun, Q. and Kikuchi, M., “Review of Damage Tolerant Analysis of Laminated Composites,” Journal of Solid Mechanics, Vol. 2, No. 3, pp. 275–289, 2010.
[7]  Heidari-Rarani, M. and Sayedain, M., “Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches,” Theoretical and Applied Fracture Mechanics, Vol. 103, No. January, pp. 1–10, 2019.
 [8] Soroush, M., MalekzadehFard, k. and Sharavi M., “Experimental Measurement of Parameters for High Velocity Impact Simulation on Composite Plate Based On PDM and CZM,” In Persian, Modares Mechanical Engineering, Vol. 19, No. 9, pp. 2215–2226, 2019.
[9]  Krueger, R., “An approach to assess delamination propagation simulation capabilities in commercial finite element codes,” National Aeronautics and Space Administration, Hampton, VA, Report No. NASA TM/2008-215123, 2008.
[10] Barbero, E. J. and Reddy, J. N., “Modeling of delamination in composite laminates using a layer-wise plate theory,” International Journal of Solids and Structures, Vol. 28, No. 3, pp. 373–388, 1991.
[11] Reddy, J. N., “An evaluation of equivalent-single-layer and layerwise theories of composite laminates,” Composite Structures, Vol. 25, No. 4, pp. 21–35, 1993
[12] Tabiei, A. and Zhang, W., “Composite laminate delamination simulation and experiment: A review of recent development,” Applied Mechanics Reviews, Vol. 70, No. 3, 2018.
[13] Xie, D., Sherrill, B. and Biggers, J., “Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: Formulation and validation,” Engineering Fracture Mechanics, Vol. 73, No. 6, pp. 771–785, 2006.
[14] Reeder, J.R., “3D Mixed-Mode Delamination Fracture Criteria–An Experimentalist’s Perspective James R. Reeder,” 21st Anual Technical Conference, pp. 1–19, 2006.
[15] Shokrieh, M. M, and Zeinedini, A., “Modeling of delamination fracture toughness of I and II mixed mode of a laminated composite asymmetric double cantilever beam,” In Persian, Journal of Modeling in Engineering, Vol. 13, No. 41, pp. 1–11, 2015.
[16] Ahmadi-Najafabadi, M., Sedighi, M., Salehi, M. and Hossini-Toudeshky, H, “Investigation and monitoring of delamination in FMLs under mode I and II loading with FEM and AE,” In Persian, Modares Mechanical Engineering, Vol. 15, No. 9, pp. 78–86, 2015.
[17] R. Mohammadi, M. Saeedifar, M. A. Najafabadi, and H. H. Toudeshky, “Acoustic Emission Based Methodology to Evaluate the Fracture Toughness in Carbon / Epoxy Composites,” Amirkabir J. Mech. Eng., vol. 49, no. 2, pp. 137–138, 2017, doi: 10.22060/mej.2016.668.
[18] ASTM Standard D5528, “Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites,” Annu. B. ASTM Stand., vol. 15.03, no. American Society for Testing and Materials, 2000.
[19] Azimi, M., Mirjavadi, S. S., Asli, S. A. and Hamouda, A. M. S., “Fracture Analysis of a Special Cracked Lap Shear (CLS) Specimen with Utilization of Virtual Crack Closure Technique (VCCT) by Finite Element Methods,” Journal of Failure Analysis and Prevention, Vol. 17, No. 2, pp. 304–314, 2017.
[20] Aymerich, F., Lecca, G. and Priolo, P., “Modelling of delamination growth in composite laminates by the virtual internal bond method,” Composites Part A: Applied Science and Manufacturing, Vol. 39, No. 2, pp. 145–153, 2007.
[21] Rybicki, E. F. and Kanninen, M. F., “A finite element calculation of stress intensity factors by a modified crack closure integral,” Engineering Fracture Mechanics, Vol. 9, No. 4, pp. 931–938, 1977.
[22] Shivakumar, K. N., Tan, P. W. and Newman, J. C., “A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies,” International Journal of Fracture, Vol. 36, No. 3, pp. 43–50, 1988.
[23] Watwood, V. B., “The finite element method for prediction of crack behavior,” Nuclear Engineering and Design., Vol. 11, No. 2, pp. 323–332, 1970.
[24] Krueger, R., “Virtual crack closure technique: History, approach, and applications,” Applied Mechanics Reviews, Vol. 57, No. 1–6, pp. 109–143, 2004.
[25] Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites, Annual Book of ASTM Standard, ASTM D6671-01, 2000.
[26] Liu, P. F., Hou, S. J, Chu, J. K, Hu, X. Y., Zhou, C. L., and Yan, L, “Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique,” Composite Structures, Vol. 93, No. 6, pp. 1549–1560, 2011.
[27] Whitcomb, J. D., “Analysis of Instability-Related Growth of a Through- Width Delamination,” National Aeronautics and Space Administration, Langley Research Center, Hampton,VA, Report No. NASA TM-86301, 1984..
[28] Camanho, P. P., Davila, C. G. and Pinho, S. T., “Fracture analysis of composite co-cured structural joints using decohesion elements,” Fatigue and Fracture of Engineering Materials and Structures, Vol. 27, No. 9, pp. 745–757, 2004.
[29] Benzeggagh, M. L. and Kenane, M., “Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus,” Composites Science and Technology, Vol. 56, No. 4, pp. 439–449, 1996.
[30] Camanho, P. P., Da´vila, C. G. and De Moura, M.F, “Numerical Simulation of Mixed-mode Progressive Delamination in Composite Materials,” Journal of Composite Materials, Vol. 37, No. 16, pp. 1415–1439, 2007.
[31] Camanho, P. P. and Davila, C.G., “Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials,” National Aeronautics and Space Administration, Langley Research Center, Hampton, VA, Report No. NASA/TM-2002-211737, 2002.
[32] Reddy, J. N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis,” Second ed., CRC Press, 2004.
[33] Tahani, M. and Nosier, A., “Edge effects of uniformly loaded cross-ply composite laminates,” Materials and Design, Vol. 24, No. 8, pp. 647–658, 2003.
[34] Afshin, M. and Taheri-Behrooz, F., “Interlaminar stresses of laminated composite beams resting on elastic foundation subjected to transverse loading,” Computational Materials Science, Vol. 96, pp. 439–447, 2015.
[35] Marjanović, M., Meschke, G. and Vuksanović, D., “A finite element model for propagating delamination in laminated composite plates based on the Virtual Crack Closure method,” Composite Structures, Vol. 150, pp. 8–19, 2016.
[36] G. R. Babu and B. Santhosh, “Experimental and Analytical Investigation on Delamination of Composites,” vol. 4, no. 12, pp. 41–45, 2015.
[37] Orifici, A. C., Thomson, R. S., Degenhardt, R., Bisagni, C. and Bayando, J., “Development of a finite-element analysis methodology for the propagation of delamination in composite structures,” Mechanics ofComposite Materials, Vol. 43, No. 1, pp. 9–28, 2007.
[38] Balzani, C. and Wagner, W., “An interface element for the simulation of delamination in unidirectional fiber-reinforced composite laminates,” Engineering Fracture Mechanics, Vol. 75, No. 9, pp. 2597–2615, 2008.
[39] Chen, J, Crisfield, M., Kinloch, A. J., Busso, E. P., Matthews, F. L. and Qiu, Y., “Mechanics of Composite Materials and Structures Predicting Progressive Delamination of Composite Material Specimens via Interface Elements,” Mechanics of Composite Materials, No. 11, pp. 37–41, 2010.
[40] Tenchev, R. T. and Falzon, B. G., “A pseudo-transient solution strategy for the analysis of delamination by means of interface elements,” Finite Elements in Analysis and Design, Vol. 42, No. 9, pp. 698–708, 2006.