IJE TRANSACTIONS C: Aspects Vol. 29, No. 12 (December 2016) 1741-1746    Article in Press

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M. Najimi, F. Haji Aboutalebi and H. Beheshti
( Received: August 29, 2016 – Accepted in Revised Form: November 11, 2016 )

Abstract    In this paper, the plates made of functionally graded material (FGM) with and without a crack are numerically simulated, employing the finite element method (FEM). The material property variations are defined to be fully continuous; therefore, the elements can be as small as required. For this purpose, variations of the material properties are applied in both the integration points and in the nodes by implementing a subroutine in the ABAQUS software and hence, the stress field in the singular points such as crack tip is accurately achieved. First, the stresses in the plate without a crack are numerically determined and the accuracy of FGM behavior is validated. Then, the J-integral is investigated and the stress intensity factor (SIF) of the plate with a crack is calculated, using the strain energy release rate (SERR) and the J -integral. In the following, dependency of the J-integral on the path is studied and the results are compared with the contour independent J-integral. Finally, it is shown that if the selected path limits toward zero, the results of the J-integral, the SERR, and the contour independent J-integral are all the same. This is due to considering the continuously varying of material properties and the effect of fining the mesh at the crack tip.


Keywords    J-Integral, Stress Intensity Factor (SIF), Functionally Graded Material (FGM), Strain Energy Release Rate (SERR)


چکیده    در این مقاله با استفاده از روش اجزاءمحدود، صفحات از جنس مواد مدرج تابعی فاقد ترک و دارای ترک بهصورت عددی شبیهسازی میشوند. تغییرخواص ماده بهصورت کاملا پیوسته تعریف گردیده، بنابراین اندازه المانها میتواند تا حد مورد نیاز کوچک شود. بههمین منظور، تغییرخواص ماده در نقاط انتگرالگیری و گرهها توسط یک زیربرنامه در نرمافزار آباکوس اعمال گردیده و در نتیجه میدان تنش در نقاط تکین مانند نوک ترک بهدرستی حاصل میشود. ابتدا، تنشها در صفحه بدون ترک بهصورت عددی محاسبه گردیده و صحت رفتار ماده مدرج تابعی اعتبارسنجی میشود. سپس، انتگرال جی مورد بررسی قرار گرفته، ضرایب شدت تنش برای صفحه ترکدار با استفاده از نرخ رهایش انرژی کرنشی و انتگرال جی محاسبه میگردد. سپس، وابستگی انتگرال جی به مسیر مطالعه شده و نتایج با انتگرال جی مستقل از مسیر مقایسه میگردد. در آخر، نشان داده میشود که اگر مسیر انتخاب شده به سمت صفر میل کند، نتایج انتگرال جی، نرخ رهایش انرژی کرنشی و انتگرال جی مستقل از مسیر یکسان خواهد بود. این امر بهدلیل پیوسته در نظرگرفتن تغییرخواص ماده و تاثیر ریزکردن المانها در نوک ترک میباشد.


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