Determination The Stress Intensity Factor in The Un-Central Edge Cracks With The concentrated Load
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک
فرزاد فریبا
1
(هیئت علمی)
سید مهران زحلی
2
(خصوصی)
کلید واژه: Stress intensity factor, Stress distribution, Concentrate load, Edge crack,
چکیده مقاله :
The stress distribution on the tip of the cracks and the stress intensity factor on them are the main courses in the fracture mechanic. The stress intensity factor of the cracks with the different load exited and the different geometry are listed in the tables of the standard books. In all of them, the cracks are located in the central point of the plates. In the uniform edge loaded case, the crack position is not effect on the stress intensity factor of the crack but in the case that the load is concentrated the stress distribution different from point to another point and therefore the stress intensity factor of the crack, is changed with the crack displacement from the point of the exited load. In this paper, the stress intensity factor changes with the distance of it from the edge of the semi-infinite plate with the edge crack is investigated. A new relation is introduced from the simulation solution with the Abaqus. Then, similar relation from analytical solution from the theory of the linear fracture mechanic was proposed. This relation was determined from the stress distribution calculation in the plate with the pointed load with the analytical solution from the elasticity theory. This two relations were compared with another and finally the more accurate relation was introduced as the relation of the stress intensity factor with the distance from the edge of the plate.
تعیین توزیع تنش در نوک ترک و تعیین ضریب شدت تنش در آن، یکی از مباحث مطرحه و مهم در مکانیک شکست می باشد. مقدار ضریب شدت تنش برای حالت های محتلف بار گذاری و هندسه های مختلف نمونه و ترک در استاندارد ها ارائه شده است. اما در تمامی این حالت ها ترک در وسط ورق واقع شده است. هنگامی که توزیع تنش یکنواخت در لبه های ورق وجود دارد، موقعیت ترک چندان تاثیری در مقدار ضریب شدت تنش نخواهد داشت، اما در بار گذاری های متمرکز با دور شدن از محل اعمال بار توزیع تنش تغییر نموده و مقدار ضریب شدت تنش نیز تغییر می کند. بنابراین تغییرات ضریب شدت تنش در ترک های واقع شده در نقاط غیر مرکزی یکی از مواردی است که باید مورد بررسی قرار گیرد. در این تحقیق، رابطه ای برای تعیین ضریب شدت تنش در ترک لبه ای در بار گزاری متمرکز بر حسب فاصله از لبه بار گذاری ارائه شده است. این رابطه با استفاده از شبیه سازی از طریق نرم افزار آباکوس به دست آمده و سپس با استفاده از روابط تحلیلی موجود، و با تعیین توزیع تنش در ورق مورد بررسی و استفاده از روابط موجود در نظریه شکست خطی و در محدوده الاستیک نیز تغییرات ضریب شدت تنش استخراج شده است. این دو رابطه با هم مقایسه شده و در نهایت یک رابطه برای این منظور ارائه شده است.
[1] Da Vincil. L., Fracture Mechanic, Bibilioteca Ambrosiana, 1894, Vol. 54.
[2]Galilei G., Dialogues concerning two new sciences, Evanston, University of Illinois Press, pp. 35-78.
[3]Griffith A.A., The phenomena of Ruture and Flow In Solid, Phil Trans. Royal Soc., 221, 1921, pp. 163-167.
[4] Anderson T.L, Fracture Mechanics, CRC Press 1994.
[5] Inglis C.E., Stresses In A Plate Due To The Presence Of Cracks And Sharp Corners, Transactions of The Institute of Naval-Architects, Vol. 55, 1913, pp. 219-241.
[6] Irwin G.R., Fracture Dynamics, fracture of metals, American society for metals, Cleveland, 1948, pp. 147-166.
[7] Orowan E., Fracture of solids, reports on progress in physics, Vol. 7, 1948, pp.185-232.
[8] Mott N.F., Fracture of Metals: Theoretical Considerations, Engineering, Vol. 165, 1948, pp.16-18.
[9] Irwin G.E., Onset of fast crack propagation in high strength steel and aluminum alloys, sagamore research conference proceeding, Vol. 2, 1956, pp. 289-305.
[10] Westergaard H.M., Bearing pressures and cracks, journal of applied mechanics, Vol. 6,1939, pp. 49-53.
[11] Irwin G.R., Fracture Dynamics, fracture of metals, American society for metals, 1948, pp.147-166.
[12] Williams M.L., on the stress distribution at the base of a stationary crack, journal of applied mechanics, 24, 1957, pp.109-114.
[13] Wells A.A., The condition of fast fracture in aluminul alloys wiyh particular reference to comet failures, British welding research association report, April 1955, pp. 76.
[14] Winne D.H., Wundt B.M. Application of the Griffith-Irwin theory of crack propagation to the bursting behavior of disks, including analytical and experimental studies, Transactions of the American society of mechanical engineers, Vol. 80, 1958, pp. 1643-1655.
[15] Paris P.C., A rational analytic theory of fatigue”, the trend in engineering, Vol. 13, 1961, pp. 9-14.
[16] Wells A.A., Unstable crack propagation in metals: cleavage and fast fracture. Proc Crack Propagation Symposium, Vol. 1, 1961, pp. 84.
[17] Rice JR, Rosengren GF, Plane strain deformation near a crack tip in a power law hardening materials. Journal of Mechanical Physic Solids, Vol. 16, 1968, pp. 1–12.
[18]Oliver J., Continuum Modeling of Strong Discontinuities in Mechanics, International journal for numerical methods in engineering Vol. 17, 1995, pp. 49-61.
[19] Rashid MM., The Arbitrary local mesh refinement method, An computer method in applied Mechanics and Engineering, Vol. 5, 1995, pp.45-58.
[20] Moes N., Dolbow J., Belytschko T., A finite element method for crack growth without re-meshing, International journal for numerical methods in engineering, Vol. 46, 1999, pp.131-150.
[21] Hang N., Sukumar N., Prevosl J.H.,, Modeling quasi-static crack growth with the extended finite element method Part II: Numerical application, International Journal of Solid And Structure, Vol. 40, 2003, pp.7539-7552.
[22] Retore J., Gravoult A., Morestin F., Combescure A., Estimation of mixed-mode stree intensity factors using digital image correlation and an interaction integral, International Journal of Fracture, Vol. 132, pp. 65-79.
[23] Perez N., Fracture Mechanic, Kluwer Academic Publishers, 2004.
[24] Sadd H.R., Theory of Elastisity, Kingstone, 2005.
