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

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

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. 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 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

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

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

Using our Point Weight Function Method in engineering applications 1.Software for fracture design of the complex turbine engine component (Southwest Research Institute, San Antonio, USA, 2004) Our approach is used completely

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 Check of the PWFM accuracy for semi-elliptic cracks 0 90

IPS NASU

Dependence SIF from ratio a/l

IPS NASU Dependence SIF from ratio a/l

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

IPS NASU where C 1, C 2, v 1, v 2, - material constants t, - time, N – loading cycles, H – wall thickness T – unit time, k – number of cycles in unit of time where C 1, C 2, v 1, v 2, - material constants t, - time, N – loading cycles, H – wall thickness T – unit time, k – number of cycles in unit of time Complex damage

IPS NASU Using stable form crack growth

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

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

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

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

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

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

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 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. 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 welding seam --//-- for heat-affected area SIF for base material --//-- for welding seam Critical SIF for base material --//-- for welding seam --//-- for heat-affected area

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

IPS NASU fields for chosen history points minimal margin margin for time points fields for chosen history points minimal margin margin for time points c) Table of the calculated temperature margin for all points of crack front and time points c) Table of the calculated temperature margin for all points of crack front and time points

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

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

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

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

IPS NASU 1. Failure probability calculation for structural element 2. Failure probability calculation for crack 3. Calculation parameters 4. In addition К min, K 0 (Т), В 0, b - arbitrarily P f = 63,2% К min = 20 В 0 = 25 мм b = 4 Implementation MASTER CURVE Conception Implementation MASTER CURVE Conception

For time  T =0 failure probability equal 1.07* IPS NASU Time point t 4 = 3000 sec - the most dangerous time step Axial crack half length l - 40 мм., depth a - 50 мм. Time point t 4 = 3000 sec - the most dangerous time step Axial crack half length l - 40 мм., depth a - 50 мм. SIF dependences on angle Result for main scenario

Dependences of logarithm probability on  T IPS NASU

Probability density for  T = 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. 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.