Meccanica DO1 IO.l007/s11012-011-9500-7

Stress intensity factors for surface cracks in round bar under single and combined loadings

A.E. Ismail . A.K. AriBn . S. Ahdullah . M.J. Ghazali

Received: 27 September 2010 / Acnpted: 10 October 201 1 F, Springer Science+Business Media B.V. 201 1

Abstract This paper numerically discusses stress in- tensity factor (SIE) calculations for surface cracks in round bars subjected to single and combined loadings. Different crack aspect ratios, a/b, ranging from 0.0 to 1.2 and the relative crack depth, a j D , in the range of 0.1 to 0.6 are considered. Since the torsion loading is non-symmetrical, the whole finite element model has been constructed, and the loadings have been remotely applied to the model. The equivalent SIE F& is then used to cnmbiue the individual SIF from the bending or tension with torsion loadings. Then, it is compared with the combined SIF, FgE obtained numerically us- ing the finite element analysis under similar loadings. It is found that the equivalent SIF method success- fully predicts the combined S E F i Q for Mode I when compared with F;E. However, some discrepancies be- tween the results, determined from the two different

a ~ c h e s , ~ it is also noted that the F$E is higher than the FgQ

A.E. Ismail (€3) Depatrncnt Engineering Mechanics, Faculty of Mechanical & Manufachning Enaeering, University Tun Hussein Om Malaysia, 86400 Barn Pahat, Johor, Malaysia e-mail: cmran@uthm.cdu.my

A.K. Ariffin - S. Ahdullah - M.I. Ghazali D e p m e n t Mechanical &Materials Engineering, Faculty of Engineering & Built Environment, University Kehangsaan Malaysia, 43600 UKhf Bangi, Selangor, Malaysia

due to the difference in crack face interactions and de- formations.

Keywords Combined stress intensity factors . Finite element analysis . Surface crack. Crack face interactions

1 Introdnetion

Mechanical power transmission is successfully con- ducted by the application of the cylindrical-shaped bar. This transmission is not only subjected by sin- gle loading, hut it is frequently occurred in combined loadings. Such structural components are subjected to cyclic stresses which can cause mechanical damages and premature failure. In services, a rotating shaft can generally be subjected to combined loading due to its

s e 1 f w g i w U U d i n g moment, and sometime it is combined with bending andlor axial stresses. Many factors have been contributed for sur- face cracks to initiate such as notches [I-?], corrosion [4] and metallurgical [5] defects. In fact, any arbitrary shapes of crack initiation may grow and take a semi- elliptical shape 161. Then, linear elastic fracture me- chanics (LEFM) has been used to analyse stress inten- sity factors (SIFs) along the crack front

The solution of SIFs for a wide range of geame- tries under Mode I loadings has been reported else- where in the literature [7-91. However, the SIFs un- der Mode IlI [lo] and under combined loadings such

Published online: 08 November 201 1

Meccanica

3. Benedetti M, Beghini M, be^ L, Fontanari V (2008) Experimental investigation on the pmoazation of fa- - - - tigue cracks emanating from sharp notches. Meccanica 43(2):201-210

4. Mahmoud KM (2007) Fracbln strength for a high strength steel bridge cable wire with a surface mck. Theor Appl Ract Mech 48(2):152-160

5. Gray GT, ~ h o ~ & s o u AW, Wiuiam JC (1985) Influence of microstructure on fatigue c m k initiation in fully pearlitic steels. Metall Trans 16(5):75&760

6. Lin XB, RA Smith (1997) Shape growth simulation of sur- face cracks in tension fatigue round bars. Int J Farigue 19(6):461469

7. Raju IS, Newman JC (1986) Shess intensity factors for cir- cumferential surface m c h in pipes and rods undcr ten- sion and bending loads. Fracture Mechanics: ASTM Spe- cial Technical Publication 905, No 17, pp 789405

8. Murakami Y, T s m H (1987) Shess intensity factor hand- book. Pergamon, New York

9. Caminteri A (1992) Elli~tical-arc surface cracks in mund . . . hi. Fxt~gw l.r3c1 lir.; ?.ljler SIWCI 15(1 I ) . ! 111-1 15.;

10. Chur (:H. Yeh CN 1201 I , hlnde I l l fraclurcpr.,hlsmi~itvc~ xb~lrmly urlcnld cc~cks ,,,olr.u within rw, bonJcd fun-- tlonally rrdrlcd m~lcnnl \trips .\lcc;anc~ 4h(L)C17- -169

Fig. 16 Model deformations under bending moment

11. Fonte MD, Ereitas MD (1499) Stress intensity factor for semi-elliptical s d c e cracks in round h a s under bending and torsion. Int JFatigue 21(5):45743

12. Shin CS, Cai CQ (2004) Experimental and finite element analyses an stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending. Int J Fract 129(31:23%264

Fiz. 17 Model deformations under combined bending and tor sion loadings

closed under the pure torsion, and vice versa under the combined loadings. The opening of the crack faces un- der combined loadings increases the relative node dis-

BNSYS then uses these relative distances to calculate the SIFs. A; a result, higher F:B is ob- tained with respect to the F g Q , due to the different mechanisms of crack deformations and interactions.

References

1. Ismail AE, AriFfin AK, Abdullah S, GhazaliMJ (2011) Off- set crack propagation analysis under mixed-mode loadings. h t J Automot Techno1 12(2):225-232

2. Yan X, Liu B (2011) A numerical analysis of cracks ema- nating from a s&ce elliptical hole in infinite body in ten- sion. Meccanica 46(2):26&278

- - . . 13. Cqinteri A, Brighenti R, Vantadori S (2006) Surface crack

in notched round bars under cvdic tension and bending. Int - J Fatigue 28(3):251-260

14. Caminteri A. Vantadori S (2009) Sidde-shaped cracks in m<lalll: round b:irs unJcrcycli; eccentnc i\ral lo:~.l~n;. lnr I l'a1i:ue 3 1,47551-765

15. ~ h a h i i A R ~ a b i b i SE (2007) Stress intensiw factors in a hollow cylinder containing a circumferential semi- elliptical cracksubjected to combined loading. Int JFatigue 29(1):12&140

16. Toribio J, Matos JC, Ganzalez B, Escuadra J (2009) Nn- merical modeling of crack shape evolution for suriace flaws in round bars under tensile load in^. Ene Fad Anal

model of fatigue crack propagation under mixed modecon- ditians. Meccanica 44(1):189-195

18. Guinea GV, Planas I, Elices M (2000) Kr evaluation by the disolacement extrapolation technique. Eng Fract Mech 66(3):i43-255

19. Aslantas K (2003) A different appmach for calculation of . . shess intensity factors in contini&s fiber reinforced metal matrix composites. h t J Solids Struct 40(26):7475-7481

20. Aslantas K, Ergun E, Tasgetiren S (2006) A numerical model far calculation of stress intensityfactors in pmide- reinforced metal-matrix composites. Int J Mech Mater Des 3(2):201-208

21. Rice JR (1968) A path independent integral and the ap- proximate analysis of sirain concentration by notches and crachs. J Appl Mech 35:379-386

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Meccanica

22. Kim YJ, Kim 1.5, Shim DJ, Kim YJ (2004) Applicability of 24. ANSYS 11.0 Documentation (2010). ANSYS Company reference stress based J estimates to semi-elliptical surface 25. Ismail .&, Ariifin AK, Abdullah S, Ghazali MJ. Daud R crack problems. J Shain Anal 39245-260 (2011) Mode III stress intensity factor of surface crack in

23. Kim YJ, Shim DJ, Choi JB, Kim YJ (2002) Approximate J round bars. Adu Mate1 Res 214:192-196 estimates far tension-loaded plates with serm-elliptical sur- 26. Qian J, Fatemi A (1996) Mixed mode fatigue crack growth: face cmcks. Eng F ~ a c t Mech 69:1447-1463 A literature survey. Eng Fract Mech 55(6):969-990

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