نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار، مهندسی مکانیک، دانشگاه تهران، تهران، ایران

2 دانشجوی دکترا ، مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران، ایران

3 استاد، دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران، ایران

چکیده

مسیر رشد ترک از شیارهای V شکل نوک گرد در نمونه‌ی ‌دیسک برزیلی ساخته شده از پلیمر پلکسی گلاس تحت بارگذاری برشی-‌ فشاری به دو صورت تجربی و تئوری مورد بررسی قرار گرفته است. در ابتدا با انجام 18 آزمایش شکست، مسیر تجربی رشد ترک بر روی نمونه‌ی دیسک برزیلی دارای شیار V شکل (RV-BD) برای زوایای دهانه‌‌ی شیار مختلف و شعاع نوک شیار 5/0 میلی‌متر به دست آمده است. سپس با استفاده از دو روش المان محدود توسعه یافته بر مبنای مدل ناحیه‌ی چسبناک و روش گام به گام بر مبنای معیار حداکثر تنش محیطی، مسیر رشد ترک پیش‌بینی شده است. پیش‌بینی‌های حاصل از هر دو روش المان محدود توسعه یافته و روش گام به گام و همچنین نتایج آزمایشگاهی نشان می‌دهند که اگرچه شیار V شکل تحت بارگذاری برشی- فشاری قرار دارد، اما شکست آن در اثر تنش‌های کششی موجود در لبه‌ی شیار آغاز شده و تا مرز خارجی قطعه رشد می‌کند. تطابق کیفی مسیرهای پیش‌بینی شده توسط هر دو معیار با مسیر به دست آمده از مشاهدات آزمایشگاهی نشان دهنده‌ی توانایی هر دو روش در پیش‌بینی مسیر رشد ترک، برای شیارهای V شکل تحت بارگذاری برشی- فشاری می‌باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Crack growth trajectory prediction in V-notched polymeric specimen under combined compressive-shear loading conditions

نویسندگان [English]

  • Ali Reza Torabi 1
  • Bahador Bahrami 2
  • Majid Reza Ayatollahi 3

1 - Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran

2 - School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

3 Professor, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

چکیده [English]

Crack growth trajectory in V-notched specimens is investigated by polymeric round-tip V-notched Brazilian disk (RV-BD) under combined compressive-shear loading conditions both experimentally and theoretically. First, the experimental fracture trajectory of RV-BD specimens is obtained by means of 18 fracture tests for various notch opening angles and 0.5 mm notch tip radius. Then, by utilizing two methods, namely the extended finite element method (XFEM) based on the cohesive zone model and the incremental method on the basis of the maximum tangential stress (MTS criterion), the fracture trajectory is predicted. Predictions of both the methods and also the experimental observations show that although the V-notch is under compressive-shear loading conditions, fracture initiates due to the tensile stresses at the notch border and propagates to the external boundary of the specimen. The graphical agreement of the two predicted trajectories with the experimental one demonstrates the ability of both methods in predicting the fracture trajectory for V-notches under compressive-shear loading conditions.

کلیدواژه‌ها [English]

  • Crack growth trajectory
  • V-notch
  • Extended finite element
  • Incremental method
1-   
[1] Williams, M. L., “Stress Singularities Resulting From Various Boundary Conditions” Journal of Applied Mechanics, Vol. 19, No. 4, pp. 526–528, 1952.
[2]  Lazzarin, P. and Tovo, R., “A Unified Approach To The Evaluation Of Linear Elastic Stress Fields In The Neighborhood Of Cracks And Notches” International Journal of Fracture, Vol. 78, No. 1, pp. 3–19, 1996.
[3] Filippi, S. Lazzarin, P. and Tovo, R., “Developments of Some Explicit Formulas Useful To Describe Elastic Stress Fields Ahead of Notches In Plates” International Journal of Solids and Structures, Vol. 39, No. 17, pp. 4543–4565, 2002.
[4] Strandberg, M., “A Numerical Study of The Elastic Stress Field Arising From Sharp And Blunt V-notches In A SENT-Specimen” International Journal of Fracture, Vol. 100, pp. 329–342, 2000.
[5] Saporta, A. A. Brik, C. and Song, C., “Computation of Three-dimensional Fracture Parameters at Interface Cracks and Notches by the Scaled Boundary Finite Element Method” Engineering Fracture Mechanics, Vol. 148, pp. 213–242, 2015.
[6]  Ayatollahi, M. R. Torabi, A. R. and Bahrami, B., “Comprehensive Notch Shape Factors For V-notched Brazilian Disk Specimens Loaded Under Mixed Mode I/II From Pure Opening Mode To Pure Closing Mode” Archive of Applied Mechanics, pp. 1–15, 2016.
[7] Ayatollahi, M. R. and Nejati, M., “Determination of NSIFs And Coefficients of Higher Order Terms For Sharp Notches Using Finite Element Method” International Journal of Mechanical Sciences, Vol. 53, No. 3, pp. 164–177, 2011.
[8] Yu, T. and Shi, L., “Determination of Sharp V-notch Stress Intensity Factors Using The Extended Finite Element Method” The Jouranl of Strain Analysis for Engineering Design, Vol. 47, No. 2, pp. 95–103, 2012.
[9]  Seweryn, A. and Łukaszewicz, A., “Verification of Brittle Fracture Criteria For Elements With V-shaped Notches” Engineering Fracture Mechanics, Vol. 69, pp. 1487–1510, 2002.
[10] Treifi, M. Olutunde Oyadiji, S., “Strain Energy Approach to Compute Stress Intensity Factors For Isotropic Homogeneous and Bi-Material V-Notches” International Journal of Solids and Structures, Vol. 50, No. 14-15, pp. 2196–2212, 2013.
[11] Ayatollahi, M. R. and Nejati, M., “Experimental Evaluation of Stress Field Around The Sharp Notches Using Photoelasticity” Materials & Design, Vol. 32, No. 2, pp. 561–569, 2011.
[12] Yadegari Dehnavi, M. R. Eshraghi, I. and Soltani, N., “Investigation of Fracture Parameters of Edge V-notches in A Polymer Material Using Digital Image Correlation” Polymer Testing, Vol. 32, No. 4, pp. 778–784, 2013.
[13] Yao, X. F. Yeh, H. Y. and Xu, W., “Fracture Investigation At V-notch Tip Using Coherent Gradient Sensing (CGS)” International Journal of Solids and Structures, Vol. 43, No. 5, pp. 1189–1200, 2006.
[14] Dunn, M. L. Suwito, W. and Cunningham, S. J., “Fracture Initiation At Sharp Notches: Correlation Using Critical Stress Intensities” International Journal of Solids and Structures, Vol. 34, No. 29, pp. 3873–3883, 1997.
[15] Lazzarin, P. and Zambardi, R., “A Finite-volume-energy Based Approach To Predict The Static and Fatigue Behavior of Components With Sharp V-shaped Notches” International Journal of Fracture, Vol. 112, pp. 275–298, 2001.
[16] Ayatollahi, M. R. and Torabi, A. R., “Tensile Fracture In Notched Polycrystalline Graphite Specimens” Carbon, Vol. 48, No. 8, pp. 2255–2265, 2010.
[17] Cendon, D. A. Torabi, A. R. and Elices, M., “Fracture Assessment of Graphite V-notched and U-notched Specimens
by Using the Cohesive Crack Model” Fatigue & Fracture of Engineering Materials & Structures, Vol. 38, No. 5, pp. 563–573, 2015.
[18] Dunn, M. L. and Suwito, W., “Fracture Initiation At Sharp Notches Under Mode I, Mode II, and Mild Mixed Mode Loading” International Journal of Fracture, Vol. 84, pp. 367–381, 1997.
[19] Priel, E. Yosibash, Z. and Leguillon, D., “Failure Initiation At A Blunt V-notch Tip Under Mixed Mode Loading” International Journal of Fracture, Vol. 149, pp. 143–173, 2008.
[20] Yosibash, Z. Priel, E. and Leguillon, D., “A Failure Criterion For Brittle Elastic Materials Under Mixed-mode Loading” International Journal of Fracture, Vol. 141, No. 1, pp. 291–312, 2006.
[21] Ayatollahi, M. R. and Torabi, A. R., “Investigation of Mixed Mode Brittle Fracture In Rounded-tip V-notched Components” Engineering Fracture Mechanics, Vol. 77, No. 16, pp. 3087–3104, 2010.
[22] Torabi, A. R, and Amininejad, SH., “Experimental and Theoretical Fracture Analysis of Quasi-brittle Polymer Components Containing V-notches With End Holes Under Combined Tensile-shear loading” Journal of Science and Technology of Composites, Vol. 2, No. 2, pp. 41-54, 2015. (In Persian)
[23] Torabi, A. R. Bahrami, B. and Ayatollahi, M. R., “Mixed Mode I/II Brittle Fracture In V-notched Brazilian Disk Specimens Under Negative Mode I Conditions” Physical Mesomechanics, Vol. 19, No. 3, pp. 332–348, 2016.
[24] Ayatollahi, M. R. Torabi, A. R. and Bahrami, B., “On The Necessity Of Using Critical Distance Model In Mixed Mode Brittle Fracture Prediction of V-notched Brazilian Disk Specimens Under Negative Mode I Conditions” Theoretical and Applied Fracture Mechanics, Vol. 84, pp. 38–48, 2016.
[25] Akbardoost, J. Mohajerani,  S. M. H. and Torabi, A. R., “Investigation of Fracture Trajectory In Blunt V-notched Specimens Under Mixed Mode I/II Loading” Modares Mechanical Engineering, Vol. 16, No. 3, pp. 161–172, 2016. (In persian)
[26] Aliha, M. R. M. Ayatollah, M. R. Smith, D. J. and Pavier, M. J., “Geometry And Size Effects On Fracture Trajectory In A Limestone Rock Under Mixed Mode Loading” Engineering Fracture Mechanics, Vol. 77, No. 11, pp. 2200–2212, 2010.
[27] Belytschko, T. and Black, T., “Elastic Crack Growth In Finite Elements With Minimal Remeshing” International Journal of Numerical Methods in Engineering, Vol. 45, No. 5, pp. 601–620, 1998.
[28] Barenblatt, G. I., “The Mathematical Theory of Equilibrium Cracks In Brittle Fracture” Advances in Applied Mechanics, Vol. 7, pp. 55–129, 1962.
[29] Ayatollahi, M. R. and Torabi, A. R., “A Criterion For Brittle Fracture In U-notched Components Under Mixed Mode Loading” Engineering Fracture Mechanics, Vol. 76, No. 12, pp. 1883–1896, 2009.
[30] Ayatollahi, M. R. Torabi, A. R. and Azizi, P., “Experimental And Theoretical Assessment of Brittle Fracture In Engineering Components Containing A Sharp V-notch” Experimental mechanics, Vol. 51, No. 6, pp. 919–932, 2011.
[31] Ayatollahi, M. R. and Aliha, M. R. M., “Mixed Mode Fracture In Soda Lime Glass Analyzed By Using The Generalized MTS Criterion” International Journal of Solids and Structures, Vol. 46, No. 2, pp. 311–321, 2009.
[32] Irwin, G. R., “Analysis Of Stresses And Strains Near The End of A Crack Traversing A Plate.” Journal of Applied Mechanics, Vol. 24, pp. 361–364, 1957.
[33] Aliha, M. R. M. Ayatollahi, M. R. Smith, D. J. and Pavier, M. J., “Geometry and Size Effects on Fracture Trajectory in A Limestone Rock Under Mixed Mode Loading” Engineering Fracture Mechanics, Vol. 77, No. 11, pp. 2200–2212, 2010.