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202 Ilare Bordeasu et al. (5) [ ] 1 1 m n K ⋅ ( 1− R) da = C1 ⋅ dN max − for R ≥ 0, [ ] 1 1 da −m n = C1 ⋅ K max ⋅ ( 1− R) for R < 0 dN are C1 = 1,447 x 10 -12 ; n1 = 3,6; m = 1; the values for the breaking tenacity corresponding to a plane state of stresses are KC = 110 MPa m 1/2 , respectively for a plane state of deformation KIC = 77 MPa m 1/2 , the yielding point σC = 262 MPa, the elastic modulus E = 206843 MPa and Poisson’s ratio ν = 0.3, the limit value of the stress intensity factor under which the crack does not propagate ΔK = 1,5 MPa m 1/2 . In Fig. 6 is presented the crack evolution for some time intervals under a load having a symmetric alternative bending cycle. a) a = 1mm, c = 2mm b) a = 16 mm, c = 32 mm N = 80370 hours (initiation) N = 153243 hours (propagation) c) a=150 mm and 2c= 320 mm N = 159737 hours (fracture, breakdown) Fig. 6 – Propagation of circumferential crack in the hollow shaft. The simulation begun with the following initial value of the crack a = 1 mm and c = 2 mm, values which are reached after 80370 running hours. The number
Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 203 of hours, for the crack propagation is added to the initial time (80370). The obtained results show that after 15937 running hours the crack penetrates completely the annular wall of the shaft. 3. Conclusions The studies of the fatigue crack propagation lead to the following results: 1. In the joint zone between the flange and the shaft body, the crack occurs after approximately 80370 running hours. 2. The propagation of the fatigue cracks were obtained using the Paris law with the completion of Walker, and show that the crack reach the dimensions a = 16 mm (depth) şi 2c = 64 mm (length) after 153243 running hours. After that the propagation speed increases to a high degree and after only 159737 running hours the breakdown occur (a=150 mm and 2c= 320 mm). 3. The obtained results can be used by the supervising staff in order to prescribe the intervals of periodical inspections and to avoid major damages. Acknowledgements. The present work has been supported from the Contract No. RU 177/10.10.2008, BC 146/13.10.2008 (Analiză privind soluţia de fiabilizare a arborelui turbinelor aplicată cu ocazia retehnologizării hidroagregatelor din CHE Porţile de Fier II. Propuneri de metodologie de urmărire în timp a stării arborilor turbinelor din CHE Porţile de Fier II şi CHE Gogosu) Received:March 15, 2010 1 Politehnica” University of Timisoara, e-mail: ilarica59@gmail.com 2 Hidroelectrica Iron Gates, Dr.Tr. Severin e-mail: dragos.novac@hidroelectrica.ro R E F E R E N C E S 1. B o r d e a ș u I., P o p o v i c i u M.O., N o v a c D., Fatigue Studies Upon Horizontal Hydraulic Turbines Shaft and Estimation of Crack Initiation Machine Design, University of Novi Sad, Faculty of Technical Sciences, 2009, pp 183- 186. 2. F o r m a n R.G., H e a r n e y V.E., E n g l e R.M., Numerical analysis of crack propagation in cyclic-loaded structures, Journal of Basic Engineering, Trans. ASME, Vol. 89, (1967). 3. H a r t n e r J. A., AFGROW Users Guide and Technical Manual, Wright-Patterson Air Force BASE, Ohio, 2008.
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