تعیین ضرایب شدت تنش حرارتی پایدار در استوانه حاوی ترک نیم‌بیضوی محیطی

نوع مقاله : مقاله پژوهشی

نویسندگان

مجتمع دانشگاهی هوافضا، دانشگاه صنعتی مالک اشتر، تهران

چکیده

در این مقاله حل بسته‌ی ضرایب شدت تنش در نقطه‌ی عمقی ترک نیم‌بیضوی محیطی واقع در سطح داخلی استوانه بدست آمده است. استوانه تحت فشار (داخلی و خارجی) و انتقال حرارت از نوع جابجائی اجباری با سیال است. جهت تحلیل، ابتدا تابع وزن نقطه‌ی عمقی برای ترک نیم‌بیضوی محیطی با استفاده از دو بار مرجع ارائه شده است. انتخاب بار مرجع به صورت بارگذاری یکنواخت و خطی افزایشی روی سطح ترک در نظر گرفته شده و به هر کدام یک منحنی که تابع نسبت منظر ترک و عمق نسبی آن است برازش شده است. سپس مسأله حرارتی در حالت پایدار مورد بررسی قرار گرفته و ضرایب شدت تنش با استفاده از تابع وزن بدست آمده محاسبه شده است. اعتبارسنجی مدل ارائه شده در حالت خاص بارگذاری با نتایج سایر مقالات در حالات خاص بارگذاری مقایسه شده است که بیانگر دقت خوبی است. در ادامه اثرات نسبت منظر، عمق نسبی و نوع انتقال حرارت جابجایی روی ضرایب شدت تنش مورد بررسی قرار گرفته است. نتایج این تحقیق نشان می‌دهد که ترک‌های کم‌عمق در برخی حالات بارگذاری و اشکال ترک نسبت به ترک‌های عمیق‌تر بحرانی‌تر هستند و حل حالت اعمال دما در سطح داخلی استوانه نسبت به حالت جابجائی اجباری محافظه‌کارانه‌تر است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Determination of Steady State Thermal Stress Intensity Factors for Semi-Elliptical Circumferential Cracks in Cylinders

نویسندگان [English]

  • S. M. Nabavi
  • A. Zareei
Faculty of Aerospace Engineering, Malek-Ashtar University of Technology, Tehran, Iran
چکیده [English]

In this paper, the closed-form stress intensity factors are calculated at the deepest
point of a circumferential semi-elliptical crack located at the inner surface of a cylinder. The cylinder
is subjected to pressure (internal and external) and the inner surface of the cylinder is subjected to
convection cooling. To solve the problem, initially, a weight function is derived for the deepest point of
the circumferential semi-elliptical crack using two reference loads. Then, the steady state solution of the
thermoelasticity problem is derived and, finally, the stress intensity factors are extracted using the weight
function method. For some special cases of loading, the results of the present theory are compared with
available solutions in the literature indicating an acceptable agreement. Moreover, the effects of crack
relative depth and aspect ratio and heat transfer type on the thermal stress intensity factors are studied.
The extracted results demonstrate that for some cases of loading and crack geometry, shallow cracks are
more critical than deep ones and the solution of conduction heat transfer is more conservative than the
forced convection one.

کلیدواژه‌ها [English]

  • Circumferential semi-elliptical crack
  • Weight function method
  • Stress intensity factor
  • Cylinder
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