Orynyak I.V., Borodii M.V., Batura A.S. IPS NASU SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY Orynyak I.V., Borodii M.V., Batura A.S. Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine 

IPS NASU Software “REACTOR” This program is intended for calculation of reactor pressure vessel residual life and safety margin with respect to brittle fracture. Residual life is calculated deterministically and probabilistically (MASTER CURVE approach) for various points of crack front

IPS NASU Software advantages The sizes of stress and temperature fields' aren't bounded Number of time moments is bounded only by the computer 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.

IPS NASU Report sections Theoretical background and verification of the SIF calculation methods. Kinetics of the crack growth by fatigue or stress-corrosion mechanism. Software description and residual life calculation of the NPP pressure vessel using fracture mechanics methods

SIF calculation by Point Weight Function Method IPS NASU SIF calculation by Point Weight Function Method s x Q’ !!! The contribution in SIF 1/800 area nearby Q’ point correspondent to 1/4 value of SIF Q’- point on the front; - value SIF; -weight function; - loading; - crack surface; Q – load application point

IPS NASU We search weight function in the form - asymptotic WF (elliptic crack in infinite body) - correction coefficient, basic solution is used

Using our Point Weight Function Method in engineering applications IPS NASU Using our Point Weight Function Method in engineering applications Software for fracture design of the complex turbine engine component (Southwest Research Institute, San Antonio, USA, 2004) Our approach is used completely

Using our Point Weight Function Method in engineering applications IPS NASU Using our Point Weight Function Method in engineering applications 2. Modeling of elliptical crack in a infinite body and in a pressured cylinder by a hybrid weight function approach (France, Int. J. Pressure Vessel and Piping. 2005) Our approach to take for a basis

SIF along crack front (angle), homogeneous loading IPS NASU Check of the PWFM accuracy for semi-elliptic cracks  SIF along crack front (angle), homogeneous loading 90

IPS NASU

IPS NASU

Dependence SIF from ratio a/l IPS NASU Dependence SIF from ratio a/l

Dependence SIF from ratio a/l IPS NASU Dependence SIF from ratio a/l

2. Kinetics of the crack growth by fatigue or IPS NASU 2. Kinetics of the crack growth by fatigue or stress-corrosion mechanism 1. Fatigue   2. Stress-corrosion

Complex damage IPS NASU where C1, C2 , v1 , v2 , - material constants t, - time, N – loading cycles, H – wall thickness T – unit time, k – number of cycles in unit of time    

Using stable form crack growth IPS NASU Using stable form crack growth

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

IPS NASU Input Data 2) Temperature field for time Table arbitrary size

Input Data IPS NASU 3) Crack types a) Axial with weld seam weld seam heat-affected zone base material cladding crack b) circumferential base material cladding crack

4) The basic material characteristics IPS NASU 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 A takes from coordinates of first point

IPS NASU 5) Shift and inclination conceptions 1. Shift 2. Shift + Inclination

6) Dependence of shift on radiation IPS NASU 6) Dependence of shift on radiation a)Analytical form b)Table form

IPS NASU 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-length l - 40 мм., depth a - 50 мм.

IPS NASU a) Dependences of the calculated and critical SIF from temperature for time = 3000 sec SIF for base material --//-- for welding seam Critical SIF for base material --//-- for heat-affected area

IPS NASU b) History of the dependences calculated SIF from temperature for some points and all times intervals and critical SIF T history for base material --//-- for welding seam critical SIF for base material --//-- for heat-affected area

c) Table of the calculated temperature margin IPS NASU 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

d) Figure of the calculated margin IPS NASU d) Figure of the calculated margin calculated temperature margin shift of the temperature by user table shift of the temperature by analytical model

Results for other crack geometries IPS NASU Results for other crack geometries New geometry for axial crack Calculated temperature margin Half length l - 60мм Depth a - 40 мм

IPS NASU New geometry for axial crack Half length l - 40мм Calculated temperature margin Half length l - 40мм Depth a - 60 мм

IPS NASU New geometry for circumferential crack Half length l - 60мм calculated temperature margin Half length l - 60мм Depth a - 30 мм

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

Result for main scenario IPS NASU Result for main scenario Time point t4 = 3000 sec - the most dangerous time step Axial crack half length l - 40 мм., depth a - 50 мм. For time DT =0 failure probability equal 1.07*10-05 SIF dependences on angle

IPS NASU Dependences of logarithm probability on DT

IPS NASU Probability density for DT = 50

IPS NASU CONCLUSION 1. Efficient method of stress intensity factor (SIF) calculation is developed. 2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created. 3. The program application were demonstrated by prediction residual life and temperature margins under modeling of the incident scenario.