تحلیل شکست دینامیکی مود ترکیبی ورق مدرج تابعی با روش بدون مش

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه شیراز

2 پژوهشکده هوا دریا

چکیده

در این مقاله تحلیل ترک مود ترکیبی ورق مدرج تابعی با استفاده از روش MLPG انجام شده است و تأثیر تغییرات مقدار و زاویه‌ی گرادیان خواص بر ضرایب شدت تنش دینامیکی مود اول، دوم و مؤثر دینامیکی بررسی شده است. برای حل معادلات وابسته به زمان که توسط MLPG شکسته شده اند روش های تفاضل مرکزی و نیومارک استفاده شده است. اگر چه روش انتگرال J یکی از روش های مرسوم در محاسبه‌ی ضریب شدت تنش است اما به‌طور کلی این روش برای مواد مدرج تابعی قابل استفاده نیست. بنابراین در این مقاله برای محاسبه‌ی ضریب شدت تنش از انتگرال مستقل از مسیر J* که برای مواد ناهمگن فرمول بندی شده، استفاده گردیده است. نتایج نشان می-دهد که روش حاضر تطابق خوبی با حل دقیق و سایر حل های موجود دارد. هم‌چنین نتایج نشان می دهد، که حداکثر و حداقل مقدار ضریب شدت تنش مؤثر برای E2/E1>1 به‌ترتیب در زاویه‌ی گرادیان خواص 0 و 90 درجه رخ می دهد و برای E2/E1

کلیدواژه‌ها


عنوان مقاله [English]

Mixed-Mode Dynamic Fracture Analysis of FGM Plate by MFree Method

نویسندگان [English]

  • A. Abdollahifar 1
  • M.R. Nami 1
  • B. Saranjam 2
چکیده [English]

In this paper, the mixed-Mode dynamic fracture analysis of a FGM plate is performed using MLPG method also the effect of changes in value and angle of material gradation on the dynamic Stress Intensity Fctor(SIF) of Mode I, II, and effective are investigated. To solve time dependent equations that discretized by MLPG method, the Central Difference Method (CDM) and the Newmark method are used. Although the J integral is one of the most common methods to calculate the SIF, but in general, it is not applicable for FGMs. So, in this paper the path independent integral, J*, which is formulated for the non-homogeneous material is used to calculate stress intensity factor. Results show that the present method has good agreement with the exact and other existent solutions. Results also, show the maximum and minimum values of effective stress intensity factor for E2/E1>1 are occurred at material gradation angle equal to 0 and 90 respectively, and for E2/E1

کلیدواژه‌ها [English]

  • Mixed-Mode dynamic fracture analysis
  • Meshless local Petrov-Galerkin (MLPG) method
  • Material gradation angle
  • Functionally graded material (FGM)
  • Newmark method
  • Central difference method (CDM))
1. Broek, D., "The Practical Use of Fracture Mechanics", Kluwer Academic Publishers, Southamptom, U.K., (1989).
2. Freund, L.B., "Energy flux into the tip of an extended crack in an elastic solid," J. Elasticity, Vol. 21, pp. 345-356, (1996).
3. Baker, B.R., "Dynamic Stresses Created by a Moving Crack." J. Appl. Mech., Vol. 29, pp. 449-545, (1962).
4. Chen, Y.M. and Wilkens, M.L., "Numerical Analysis of Dynamic Crack Problems, In Elastodynamic Crack Problems", Noordhoff Inter. Publng, the Netherlands, pp. 317–325, (1977).
5. Hua, Z.F., Tian-You, S.N. and Lan-Quao, T., "Composite materials dynamic fracture studies by generalized Shmuely difference algorithm." Eng. Fract. Mech., Vol. 54, pp. 869–77, (1996).
6. Nishioka, T., Atluri, S.N., "Numerical Modeling of Dynamic Crack Propagation in Finite Bodies by Moving Singular Elements", Part II. J. Appl. Mech., Vol. 47, pp. 577-582, (1980).
7. Nishioka, T., "Recent Developments in Computational Dynamic Fracture Mechanics, In Dynamic Fracture Mechanics", Comput. Mech. Publ., Southampton, UK, pp. 1–58, (1995)
8. Aberson, J.A., Anderson, J.M. and King, W.W., "Dynamic analysis of cracked structures using singularity finite elements", In: Sih GC, editor. Mech. of fract., Noordhoff Int Pub, Vol. 4, pp.
249–94, (1977).
9. Song, S.H. and Paulino, G.H., "Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method", Int. J. Solids and Struct., Vol. 43, pp. 4830–4866, (2006).
10. Nicholson, J.W., "Computation of dynamic stress intensity factors by the time domain boundary integral equation method", Analysis. Engng. Fract. Mech., Vol. 31, pp. 759-767, (1988).
11. Mettu, S.R. and Kim, K.S., "An application of the time domain boundary integral equation method to dynamic crack propagation", Engng Fract. mech, Vol. 39, pp. 769-782, (1991).
12. Dominguez, J., "Time domain boundary element method for dynamic stress intensity factor computations", Int. J. Num. Meth. Engng., Vol. 33, pp. 635-647, (1992).
13. Aliabadi, M.H. and Portela, A., "The dual boundary elemnt method", Int. J. Num. Meth. Engng,
Vol. 33, pp. 1269-1287, (1992).
14. Fedelinski, P., Aliabadi, M.H. and Rooke, D.P., "The dual boundary method: J-integral for dynamic stress intensity factors.", Int. J F., Vol. 65, pp. 369-381, (1994).
15. Wen, P.H., Aliabadi, M.H. and Rooke, D.P., "Cracks in Three Dimensions: A Dynamic Dual Boundary Element Analysis", Comput. Methods Appl. Mech.Engrg, Vol. 167, pp. 139–151, (1998).
16. Fedelenski, P. and Aliabadi, M.H., "The dual boundary element in dynamic fracture mechanics," Engng Anal. Bound. Elem., Vol. 12, pp. 203-210, (1993).
17. Albuquerque, E.L., Sollero, P. and Fedelinski, P., "Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems", Comp. and Struct., Vol. 81,
pp. 1703–1713, (2003).
18. Aliabadi, M.H., "Boundary element method in fracture mechanics", Appl. Mech. Rev., Vol.50,
pp. 83-96, (1997).
19. Zhang, C.H. and Savaidis, A., "Time-domain BEM for dynamic crack analysis", Math. and Comp. in Simul., Vol. 35, pp. 17-40, (1999).
20. Zhang, C.H., "A 2D hypersingular time-domain traction BEM for transient elastodynamic crack analysis," Engng Anal. in BEM, Vol. 35, pp. 17-40, (2002).
21. Fedelinski, P., "Boundary element method in dynamic analysis of structures with cracks", Engng Anal. in BEM, Vol. 28, pp. 1135-1147, (2004).
22. Zhang, C.H. and sladek, V., "A frequency-domain BEM for 3D non-synchronous crack interaction analysis in elastic solids", Enging anal in BEM, Vol. 30,pp. 167-175, (2006).
23. Ferretti, E., "Crack Propagation Modeling by Remeshing Using the Cell Method (CM)" CMES,
Vol. 4, pp. 51–72, (2003).
24. GUO, Y.J. and NAIRN, J.A. "Three-Dimensional Dynamic Fracture Analysis Using the Material Point Method", CMES, Vol. 1, No. 1, pp. 11-25, (2006).
25. Guo, Y.; Nairn, J.A., "Calculation of J integral and stress intensity factors using the material point method", CMES, Vol. 6, pp. 295–308, (2004).
26. Batra, R.C. and Ching, H.K. "Analysis of Elastodynamic Deformations near a Crack/Notch Tip by the meshless local Petrov- Galerkin (MLPG) method", CMES, Vol. 3, pp. 717–730, (2002).
27. Sladek, J., Sladek V. and Zhang, C., "The MLPG method for crack analysis in anisotropic functionally graded mmaterials", SID, Vol. 1, pp. 131– 144, (2005).
28. Niino, M., Hirai, T. and Watanabe, R., "Functionally gradient material as barrier for space plane" J. Jpn. Son. Com. Mater., Vol. 13, pp. 257-264, (1987)
29. Banks-sills, L., Eliasi, R. and Berlin, Y. "Modeling of functionally graded materials in dynamic analysis", comp part B Enging: Part B, Vol. 33, pp. 7-15., (2002)
30. Jin, Z.H., Noda, N., "Crack tip singular fields in nonhomogeneous materials", J Appl Mech, Vol. 61, pp. 738-740, (1994).
31. Marur, P.R. and Tippur, H.h V., "Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient", Int J Solids and Struct, Vol. 37, pp.
5353-5370, (2000).
32. Tohgo, K., Sakaguchi, M. and Ishii, H., "Applicability of fracture mechanics in strength evaluation of functionally graded materials", JSME Int. J. Series A, Vol. 39(4), pp. 479-488, (1996).
33. Gu, P., Dao, M. and Asaro, R.J., "A simplified method for calculating the crack tip field of functionally graded materials using the domain integral", J Appl Mech, Vol. 66, pp. 101-108, (1999).
34. Chen, J., Wu, L. and Du, S., "A Modified J Integral for Functionally Graded Materials", Mech. Res. Commun., Vol. 27(3), pp. 301-306, (2000).
35. Liu, G.R. and Gu, Y.T, "An introduction to meshfree methods and their programming", Springer, (2005).
36. Atluri, S.N. and Zhu, T., "A new Meshless Local Petrov Galerkin (MLPG) approach in computational mechanics", Comp. Mech, Vol. 22, pp. 117-127, (1998).
37. Liu, K., Long, Sh. and Li, G., "A simple and less-costly meshless local Petrov-Galerkin (MLPG) method for dynamic fracture problem", Engng Anal. with Bound. Elem, Vol. 30 , pp. 72-76, (2006).
38. Qian, L.F. and Ching, H.K., "Static and dynamic analysis of 2-D functionally graded elasticity by using meshless local Petrov-Galerkin method", Journal of the Chinese Institute of Engineers,
Vol. 27(4), pp. 491-503, (2004).
39. Sladek, J., Sladek, V., Zhang, Ch. and Tan, CH.-L., "Evaluation of fracture parameters for crack problems in FGM by a meshless method", Theo. Appl. mech., Vol. 44(3), pp. 603-636, (2006).
40. Abdollahifar, A. and Nami, M.R., "Investigating the effect of angle between the material gradation direction and crack on mixed-mode stress intensity factor of FGM plates using MLPG method". Modares Mech. Enging, in persian, Vol. 13(1), pp. 138-150, (2013).
41. Fleming, M., Chu, Y., Moran, B. and Belytschko, T., "Enriched element-free Galerkin methods for crack tip fields", Int. J. Num. Meth. in Engng, Vol. 40, pp. 1483-1504, (1997).
42. Belytschko, T., Lu, Y.Y. and Gu L., "Crack propagation by Element-free Galerkin methods" Engineering Fracture Mechanics, Vol. 51, No. 2, pp. 295-315, (1995).
43. Abdollahifar, A. and Nami, M.R., "Determination of dynamic stress intensity factor in FGM plates by MLPG method", IJST, Trans. of Mech. Engng, Vol. 38(M1+), pp. 181-194, (2014).
44. Eischen, J.W., "Fracture of nonhomogeneous materials", Int. J. Fract., Vol. 34(1), pp. 3-22, (1987).
45. Lucht, T., "Finite element analysis of three-dimensional crack growth by the use of a boundary element sub model", Eng. Fract. Mech., Vol. 76, pp. 2148-2162, (2009).
46. Shukla, A., "Dynamic Fracture Mechanics", World Scientific Publishing Co., (2006).
CAPTCHA Image