Volume 3 nr 1 / 2011 - Academia Oamenilor de Stiinta din Romania

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56 Mircea O. Popoviciu, Ilare Bordeasu, Liviu Marsavina7. Fatigue computationsa. Estimation of the crack initiation time through fatigueThe fatigue computation was done for the z stress component, produced throughthe superposition of the bending and tension. The characteristics of the loadingcycle in the connection zone, resulted from the strength computations [1], using theASNYS program are: σ max = 88.86 MPa, σ min = - 6.52 MPa and R = σ min /σ max = -0.07.Fig. 12. Cycles number until crack initiation.After using the fatigue module (FATIGUE TOOL) of the ANSYS v.11 program[2] resulted a minimum duration, until the fissures initiation, of N i = 3.013910 8cycles, equalling 80370 running hours.b. Number of cycles estimation for the propagation of a crack for variablestresses with constant amplitudeIt must be underlined, that the final break zone is characterized through high velocitiesof the crack propagation. The service life, expressed through the number of cyclesneeded for the extension of a fissure, can be obtained from:Nfacrda dN N f NNd Nr da(6)d f ( K, R)The relation (6) was used to calculate the number of cycles N r needed for theextension of a fissure from the detectable length a d corresponding to N d cycles tothe critical length a cr which is reached after N f cycles. The computation can beCopyright © Editura Academiei Oamenilor de Știință din România, 2011Watermark Protected
Analytical Evaluation of Crack Propagation for Bulb Hydraulic Turbines Shafts 57done graphically, analytically or numerically. The analytical method is suited fora limited number of situations in which the intensity factor can be correlated withthe crack length and the geometrical factors remain unchanged in the integral limits.In present, there are specialized programs for computing automatically the lifeduration. One of these programs is AFGROW developed by Hartner at WRIGHT-PATTERSON AIR FORCE BASE for estimating the durability of attack aircraftscomponents. For the fracture line propagation it was considered a piece having ringcross- section with an elliptical crack disposed on circle, Figure 8. For such geometry,Raju and Newman (1984) proposed for the stress intensity factor a solution, underthe form [3]:dKI t Hb F d, c, Di , De, (7)Qwhere:- σ t represent the tension stress applied to the shaft;- σ b is the bending stress;- H and F are functions depending on the crack geometry (the crack depth andlength), the thickness of the shaft wall and the frontal position of the fissure whileQ is obtained from (8):1.65d dQ 11,1464 for 1c cThe simulation was done with AFGROW [4]. The initial crack depth d = 1 mmand crack length c = 2 mm are reached after 80370 hours in conformity with thestudy of fissure initiation. For the study of crack propagation, it was taken intoconsideration a composite loading bending plus tension, with the condition that thestatic load is superposed over bending resulting a pulsating cycle with σ max = 88,9MPa, σ min = - 6,5 MPa , R = - 0,07; the loading amplitude remaining constant. Thematerial constants are those of the American steel AISI 1020 comprised in thedata base of the AFGROW program (C= 1.447x10 -12 , n = 3.6, m = 1; the breakingtenacity corresponding for the plane state of tension K C =110 MPa m 1/2 , respectivefor the plane state of deformation K IC 77 MPa m 1/2 , yield strength σ C = 262 MPa,elastic modulus E = 206843 MPa, the Poisson’s number ν = 0.3, the limit value ofthe intensity factor variation under which the fissure does not propagate ΔK=1,5MPa m 1/2 ).The number of hours for the fracture line propagation was added to the initiationnumber of hours. With the previous conditions, the crack increase until d = 16mm, 2c = 64 mm is obtained after 153,243 hours. It is important to know that afteronly 159,737 service hours the crack pierces completely the shaft wall (the curved= 300 in Figure 8 is reached).(8)Copyright © Editura Academiei Oamenilor de Știință din România, 2011Watermark Protected
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3FOREWORDBased on a rich scientific
Page 7 and 8: Annals of the Academy of Romanian S
Page 11 and 12: The remanufacturing of an articulat
Page 19 and 20: Influence of Vibrations and Dynamic
Page 27 and 28: Products recovery opportunities at
Page 29 and 30: Products recovery opportunities at
Page 33 and 34: Recycling and Remanufacturing -Two
Page 35 and 36: Recycling and Remanufacturing -Two
Page 39 and 40: The Study of Heavy Metal from Envir
Page 45 and 46: mg/kg d.wThe Study of Heavy Metal f
Page 47 and 48: ConclusionsThe Study of Heavy Metal
Page 51 and 52: Analytical Evaluation of Crack Prop
Page 53 and 54: Analytical Evaluation of Crack Prop
Page 55 and 56: Y d Notations:Analytical Evaluation
Page 57: Analytical Evaluation of Crack Prop
Page 63 and 64: General Considerations Regardingthe
Page 71 and 72: Intelligent Networks, Smart Grids C
Page 81 and 82: Two-dimensional Modelling of Accide
Page 97 and 98: Project Indicators -Essential Facto
Page 103 and 104: ConclusionsProject Indicators -Esse
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Critical Infrastructures Protection
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Annals of the Academy of Romanian S
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Disturbances in The Power Supply Ne
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