نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، دانشگاه علم و صنعت ایران، دانشکده مهندسی مکانیک، تهران، ایران

2 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران، ایران

چکیده

در این پژوهش از یک مدل‌ مایکرومکانیکی جهت پیش‌بینی انتقال تنش از لایه میانی کامپوزیت سه فازی تقویت‌شده استفاده‌شده است. مدل متقارن شامل الیاف، زمینه و لایه میان آن‌ها است. در این مطالعه رفتار مکانیکی اجزا تشکیل دهنده کامپوزیت به‌صورت الاستیک خطی فرض شده‌اند. همچنین، زمینه به‌صورت یک ماده‌ی همسانگرد و الیاف و لایه‌ی میانی به‌صورت مواد همسانگرد عرضی فرض شده‌اند. تحلیل تنش سه بعدی در دو حالت الف) لایه میانی کاملاً متصل و سالم و ب) لایه میانی تا حدی جداشده انجام شده است. از مدل‌سازی تحلیلی، یک جفت معادلات دیفرانسیل جزئی مستقل برحسب مؤلفه‌های نامعین جابجایی‌ به‌دست‌آمده‌ است. سپس به‌منظور حل دقیق معادلات دیفرانسیل از روش جداسازی متغیرها و بسط توابع ویژه استفاده شد. حل‌های تحلیلی برای شرایط مرزی آزاد در سطح خارجی ماتریس جهت مدل کردن آزمون بیرون کشی به‌دست‌آمده‌اند. در هر دو حالت نتایج حاصل از روش تحلیلی همخوانی خوبی با نتایج به دست آماده از روش عددی دارند. با مقایسه مؤلفه‌های تنش برشی، شعاعی و محوری مشخص می‌شود که کامپوزیت سه فازی به‌مراتب مقادیر کمتری نسبت به کامپوزیت دوفازی اتخاذ می‌کند، همچنین میدان تنش به‌دست‌آمده در حالت تا حدی جداشده، مقادیر کوچک‌تری نسبت به حالت سالم اتخاذ می‌کند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Micromechanics of stress transfer through the interphase in pull out test of fiber through the resin

نویسندگان [English]

  • Fathollah Taheri-Behrooz 1
  • Seyyed Mohammad Javad Mahdavizade 2
  • Mohammad Javad Gholami 2

1 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

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

چکیده [English]

In the current paper, a micromechanical based model is presented to estimate the stress transfer in interphase of three-phase reinforced composites. The symmetric model consists of fiber, matrix and a layer in between them. In this study, composite constituents were considered as linear elastic materials. Also, the matrix was treated as isotropic material while the fiber and the interphase were considered as transversely isotropic materials. The stress distribution solutions for an intact model and partially debonded model are obtained. A pair of uncoupled partial differentiation equations were obtained in terms of unknown displacement components. The separation of variable with Eigenfunction expansion methods were used to derive the exact solution of the PDE’s. Analytical solutions for the free boundary conditions on the external surface of the matrix are obtained to simulate the pullout test. In both cases, numerical findings revealed a good correlation with the analytical results. By comparing the shear, radial and axial stress components become clear that three- phase composite adopts smaller amounts than of two- phase composites. Also, it was shown that the stress field in the partially debonded model has small quantities in comparison to the intact model.

کلیدواژه‌ها [English]

  • Micromechanics
  • Interphase
  • Stress transfer
  • Intact
  • Partially debonded
 
[1] Wu, Q. Li, M. Gu, Y. Li, Y. And Zhang, Z., “Nano-Analysis On The Structure And Chemical Composition Of The Interphase Region In Carbon Fiber Composite“, Composites Part A: Applied Science And Manufacturing, Vol. 56, Pp. 143-149, 2014.
[2] Drzal, L. T., “The Interphase In Epoxy Composites“, In: Epoxy Resins And Composites II ,Springer, Vol. 2, No. 3, Pp. 1-32, 1986.
[3] Sottos, N. Mccullough, R. And Scott, W., “The Influence Of Interphase Regions On Local Thermal Displacements In Composites“, Composites Science And Technology, Vol. 44, No. 4, Pp. 319-332, 1992.
[4] Atkins, A. G., “Intermittent Bonding For High Toughness/High Strength Composites“, Journal Of Materials Science, Vol. 10, No. 5, Pp. 819-832, 1975.
[5] Gao, S.-L. And Mäder, E., “Characterisation Of Interphase Nanoscale Property Variations In Glass Fibre Reinforced Polypropylene And Epoxy Resin Composites“, Composites Part A: Applied Science And Manufacturing, Vol. 33, No. 4, Pp. 559-576, 2002.
[6] Huang, Y. And Young, R. J., “Interfacial Micromechanics In Thermoplastic And Thermosetting Matrix Carbon Fibre Composites“, Composites Part A: Applied Science And Manufacturing, Vol. 27, No. 10, Pp. 973-980, 1996.
[7] Liu, L. Song, Y. Fu, H. Jiang, Z. Zhang, X. Wu, L. And Huang, Y., “The Effect Of Interphase Modification On Carbon Fiber/Polyarylacetylene Resin Composites“, Applied Surface Science, Vol. 254, No. 17, Pp. 5342-5347, 2008.
[8] Naslain, R. R., “The Design Of The Fibre-Matrix Interfacial Zone In Ceramic Matrix Composites“, Composites Part A: Applied Science And Manufacturing, Vol. 29, No. 9, Pp. 1145-1155, 1998.
[9] Kim, J.-K. And Mai, Y.-W., “Engineered Interfaces In Fiber Reinforced Composites“, Elsevier, A, Vol. 978, No. 1, Pp. 08-042695-2,1998.
[10] Cox, H., “The Elasticity And Strength Of Paper And Other Fibrous Materials“, British Journal Of Applied Physics, Vol. 3, No. 3, Pp. 72, 1952.
[11] Hsueh, C.-H., “Interfacial Debonding And Fiber Pull-Out Stresses Of Fiber-Reinforced Composites“, Materials Science And Engineering: A, Vol. 123, No. 1, Pp. 1-11, 1990.
[12] Hsueh, C.-H., “Interfacial Debonding And Fiber Pull-Out Stresses Of Fiber-Reinforced Composites III: With Residual Radial And Axial Stresses“, Materials Science And Engineering: A, Vol. 145, No. 2, Pp. 135-142, 1991.
[13] Hsueh, C.-H., “Interfacial Debonding And Fiber Pull-Out Stresses Of Fiber-Reinforced Composites IV: Sliding Due To Residual Stresses“, Materials Science And Engineering: A, Vol. 145, No. 2, Pp. 143-150, 1991.
[14] Hsueh, C.-H., “Interfacial Debonding And Fiber Pull-Out Stresses Of Fiber-Reinforced Composites Part V. With A Viscous Interface“, Materials Science And Engineering: A, Vol. 149, No. 1, Pp. 1-9, 1991.
[15] Hsueh, C.-H., “Interfacial Debonding And Fiber Pull-Out Stresses Of Fiber-Reinforced Composites VII: Improved Analyses For Bonded Interfaces“, Materials Science And Engineering: A, Vol. 154, No. 2, Pp. 125-132, 1992.
[16] Aveston, J., Kelly, A., “Theory Of Multiple Fracture Of Fibrous Composites“, Journal Of Materials Science, Vol. 8, No. 3, Pp. 352-362, 1973.
[17] Nairn, J. A., “On The Use Of Shear-Lag Methods For Analysis Of Stress Transfer In Unidirectional Composites“, Mechanics Of Materials, Vol. 26, No. 2, Pp. 63-80, 1997.
[18] Nairn, J. A., “A Variational Mechanics Analysis Of The Stresses Around Breaks In Embedded Fibers“, Mechanics Of Materials, Vol. 13, No. 2, Pp. 131-154, 1992.
[19] Kovalev, S. P. Miranzo, P. And Osendi, M. I., “Finite Element Simulation Of Thermal Residual Stresses In Joining Ceramics With Thin Metal Interlayers“, Journal Of The American Ceramic Society, Vol. 81, No. 9, Pp. 2342-2348, 1998.
[20] Christensen, R. And Lo, K., “Solutions For Effective Shear Properties In Three Phase Sphere And Cylinder Models“, Journal Of The Mechanics And Physics Of Solids, Vol. 27, No. 4, Pp. 315-330, 1979.
[21] Needleman, A. Borders, T. Brinson, L. Flores, V. And Schadler, L., “Effect Of An Interphase Region On Debonding Of A CNT Reinforced Polymer Composite“, Composites Science And Technology, Vol. 70, No. 15, Pp. 2207-2215, 2010.
[22] Qing, H., “A New Theoretical Model Of The Quasistatic Single-Fiber Pullout Problem: Analysis Of Stress Field“, Mechanics Of Materials, Vol. 60, Pp. 66-79, 2013.
[23] Hashin, Z., “Thermoelastic Properties Of Fiber Composites With Imperfect Interface“, Mechanics Of Materials, Vol. 8, No. 4, Pp. 333-348, 1990.
[24] Hayes, S. Lane, R. And Jones, F., “Fibre/Matrix Stress Transfer Through A Discrete Interphase. Part 1: Single-Fibre Model Composites“, Composites Part A: Applied Science And Manufacturing, Vol. 32, No. 3, Pp. 379-389, 2001.
[25] Jiang, Y. Guo, W. And Yang, H., “Numerical Studies On The Effective Shear Modulus Of Particle Reinforced Composites With An Inhomogeneous Inter-Phase“, Computational Materials Science, Vol. 43, No. 4, Pp. 724-731, 2008.
[26] Qiu, Y. And Weng, G., “Elastic Moduli Of Thickly Coated Particle And Fiber-Reinforced Composites“, Journal Of Application Mechanics, Vol. 58, No. 2, Pp. 388-398, 1991.
[27] Rjafiallah, S. Guessasma, S. And Bizot, H., “Effect Of Surface Etching On Interphase And Elastic Properties Of A Biocomposite Reinforced Using Glass–Silica Particles“, Composites Science And Technology, Vol. 70, No. 8, Pp. 1272-1279, 2010.
[28] Tsai, H. C., Arocho, A. M., Gause, L. W., “Prediction Of Fiber-Matrix Interphase Properties And Their Influence On Interface Stress, Displacement And Fracture Toughness Of Composite Material“, Materials Science And Engineering: A, Vol. 126, No. 1-2, Pp. 295-304, 1990.
[29] Mogilevskaya, S. And Crouch, S., “A Galerkin Boundary Integral Method For Multiple Circular Elastic Inclusions With M Homogeneously Imperfect Interfaces“, International Journal Of Solids And Structures, Vol. 39, No. 18, Pp. 4723-4746, 2002.
[30] Shen, L. And Li, J., “Homogenization Of A Fibre/Sphere With An Inhomogeneous Interphase For The Effective Elastic Moduli Of Composites“, In Proceeding Of, The Royal Society,Vol. 461, No. 3, Pp. 1475-1504, 2005.
[31] Wang, J. Crouch, S. L. And Mogilevskaya, S. G., “Numerical Modeling Of The Elastic Behavior Of Fiber-Reinforced Composites With Inhomogeneous Interphases“, Composites Science And Technology, Vol. 66, No. 1, Pp. 1-18, 2006.
[32] Shen, L. And Li, J., “Effective Elastic Moduli Of Composites Reinforced By Particle Or Fiber With An Inhomogeneous Interphase“, International Journal Of Solids And Structures, Vol. 40, No. 6, Pp. 1393-1409, 2003.
[33] Wu, Z. Ye, J. And Cabrera, J., “3D Analysis Of Stress Transfer In The Micromechanics Of Fiber Reinforced Composites By Using An Eigen-Function Expansion Method“, Journal Of The Mechanics And Physics Of Solids, Vol. 48, No. 5, Pp. 1037-1063, 2000.
[34] Upadhyaya, P. And Kumar, S., “Micromechanics Of Stress Transfer Through The Interphase In Fiber-Reinforced Composites“, Mechanics Of Materials, Vol. 89, Pp. 190-201, 2015.
[35] Zhou, L.-M. Kim, J.-K. And Mai, Y.-W., “Interfacial Debonding And Fibre Pull-Out Stresses“, Journal of Materials Science, Vol. 27, No. 12, pp. 3155-3166, 1992.