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Batura A . S . , Orynyak I.V.

IPS NASU. ENGINEERING METHODS FOR STRESS INTENSITY FACTOR CALCULATION FOR 2-D AND 3-D BODIES WITH CRACKS. Batura A . S . , Orynyak I.V. Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine. IPS NASU. Weight Function Method for plane bodies.

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Batura A . S . , Orynyak I.V.

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  1. IPSNASU ENGINEERING METHODS FOR STRESS INTENSITY FACTOR CALCULATION FOR 2-D AND 3-D BODIES WITH CRACKS BaturaA.S., Orynyak I.V. Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine

  2. IPSNASU Weight Function Method for plane bodies - weight function, - the law of stress distribution, G – geometry parameters. - asymptotical (singular) part of WF, - correction (regular) part of WF. Then for any specified stress law (for example ) obtain where and doesn’t depend upon geometry.

  3. IPSNASU Weight Function Method for plane bodies In particular, for a plane body with an edge crack The main idea of Weight Function Methods: If we have the SIF solution for one particular loading we can obtain the SIF solution for any other law of loading.

  4. IPSNASU Application of WFM for a pipes Crack compliance method (modification of Cheng & Finnie approach) In the circular pipe additional force N and moment M appear. Angle and displacement discontinuity can be expressed in the next form: where YN, YM – are the dimensionless SIF, induced by M and N as in the plane body,

  5. IPSNASU Application of WFM for a pipes Crack compliance method (modification of Cheng & Finnie approach) - caused by loading, - caused by force, - caused by moment. Obtain result SIF : SIF is smaller than in the case of straight plane ! Using equilibrium equations for a ring and initial parameter method, get the expression for a dimensionless SIF decrease from the case of straight plane (Y0): where - dimensionless pressure.

  6. IPSNASU Application of WFM for a pipes Crack compliance method (modification of Cheng & Finnie approach) Result plots Conclusion: Advanced SIF formula for pipes was obtained. The feature of the SIF decreasing at rising of the pressure was found.

  7. IPSNASU Weight Function Method for 3-D bodies (1) (2) - elliptical crack, - for semi- elliptical crack, - for quarter-elliptical crack -correction part - asymptotical part for elliptical crack.

  8. IPSNASU loading dependent geometry dependent If is known we obtain and can calculate for any law of loading. where - is a known SIF for any law of loading. Weight Function Method for 3-D bodies Similarly to the 2-D case, So

  9. IPSNASU Check of the PWFM accuracy for semi-elliptic cracks SIF along crack front (angle), homogeneous loading 90 0

  10. IPSNASU

  11. IPSNASU

  12. IPSNASU Dependence SIF from ratio a/l

  13. IPSNASU Dependence SIF from ratio a/l

  14. IPSNASU The solution: approximation of the stress law with function of the next type: , calculation of the SIF array for each stress function . Approximate SIF function can be build as linear combination of precalculated . Weight Function Method for 3-D bodies. Simplified (speed up) approach. The problem: triple integral (square and contour) with singularity at the edge high computation cost (especially for repeating – fatigue, stress-corrosion,… – calculations) !!!

  15. IPSNASU Weight Function Method for 3-D bodies. Simplified (speed up) approach. Polynomial example The expression for dimensionless SIF functions :

  16. Weight Function Method for 3-D bodies. Simplified (speed up) approach. IPSNASU Polynomial example For simple expressions for IijA,C(α) were obtained : Semi-elliptical crack on the inner surface of the cylinder.

  17. Application of the peveloped methods: Software “ReactorA” IPSNASU • This program is intended for calculation of reactor pressure vessel residual life and safety margin with respect to brittle fracture. • User sets loading and temperature fields in the different moments of time. Then material fracture toughness, embrittlement parameters are also set by user. • Residual life is calculated deterministically and probabilistically (MASTER CURVE approach) for various points of crack front

  18. IPSNASU ReactorAadvantages • The sizes of stress and temperature fields' aren't bounded • Number of time moments is bounded only by the memory size • Cladding is taken into account • Welding seam and heat-affected area are taken into account • Deterioration is taken into account not only as shift of the material fracture toughness function but also as its inclination • Original feature of the software is using of the author variant of the weight function method. It allows to set loading on the crack surface in the form of table.

  19. IPSNASU 3. Residual Life calculation of the NPP pressure vessel using fracture mechanics methods Input Data 1) Stress field for time Table arbitrary size

  20. IPSNASU Input Data 2) Temperature field for time Table arbitrary size

  21. IPSNASU weld seam heat-affected zone basematerial cladding crack base material cladding crack Input Data 3) Crack types a)Axialwith weld seam b)circumferential

  22. IPSNASU 4) The basic material characteristics 1. Arctangents 2. Exponent 3. User (pointed) function Common shape of the crack growth resistance function is for user function Atakes from coordinates of first point

  23. IPSNASU 5) Shift and inclination conceptions 1.Shift 2.Inclination

  24. IPSNASU 6) Dependence of shift on radiation a)Analytical form b)Table form

  25. IPSNASU Results Scenario – Break of the Steam Generator Collector WWER-1000 operated at full power It is given: - stress field, - temperature field, = 1000, 2000, 2800, 3000, 3160, 3600, 4000 sec - time points Axial crack. Half-lengthl -40 мм., depth a - 50 мм.

  26. IPSNASU a)Dependences of the calculated and critical SIF from temperature for time = 3000 sec SIFfor base material --//-- forweld seam Critical SIFfor base material --//-- for weld seam --//-- forheat-affected area

  27. IPSNASU b)History of the dependences calculated SIF fromtemperature forsome points and all times intervals andcritical SIF T historyforbasic material --//-- for weld seam criticalSIFforbasic material --//-- forweld seam --//-- forheat-affected area

  28. IPSNASU c)Table of the calculated temperature margin for all points of crack front and time points fields for chosen history points minimal margin margin for time points

  29. IPSNASU d) Figure of the calculated margin calculated temperature margin shift of the temperature by user table shift of the temperature by analytical model

  30. IPSNASU Calculated temperature margin Results for other crack geometries New geometry for axial crack Half lengthl - 60мм Depth a - 40 мм

  31. IPSNASU Calculated temperature margin New geometry for axial crack Half lengthl - 40мм Depth a - 60 мм

  32. IPSNASU calculated temperature margin New geometry for circumferential crack Half lengthl - 60мм Depth a - 30 мм

  33. IPSNASU Implementation MASTER CURVE Conception 1. Failure probability calculation for structural element 2. Failure probability calculation forcrack 3. Calculation parameters Pf = 63,2% Кmin = 20 В0 = 25 мм b = 4 4. In addition Кmin, K0(Т), В0, b - arbitrarily

  34. IPSNASU Result for main scenario Time point t4= 3000 sec Axial crack half lengthl -40 мм., depth a - 50 мм. For timeDT =0 failure probability equal 1.07*10-05 SIF dependences on angle

  35. IPSNASU Dependences of logarithm probability on DT

  36. IPSNASU Probability density forDT = 50

  37. Application of the developed methods: Software “WFM” IPSNASU • This program is intended for SIFcalculation for different (1-D and 2-D) types of cracks and for endurance estimation with using different fatigue and stress-corrosion laws. • User sets “maximum”, “minimum” and “corrosion” loading fields. • SIF, grow of the crack dimensions in time and endurance are calculated. “Until specified depth” or “until specified count of cycles” modes are presented.

  38. IPSNASU 1. Damages 2. Cracks WFM: implemented types of damages and cracks

  39. IPSNASU WFM: example of result window • Input and output data can be exchanged with clipboard.

  40. IPSNASU CONCLUSION 1. Efficient methods of stress intensity factor (SIF) calculation are developed. 2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created.

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