J. Chattopadhyay

A database to evaluate stress intensity factors of elbows with throughwall flaws under combined internal pressure and bending moment

Abstract The advent of the leak-before-break (LBB) concept has widely replaced the traditional design basis event of a double-ended guillotine break (DEGB) in the design of primary heat transport (PHT) piping. The use of the LBB concept requires postulation of the largest credible cracks at highly stressed locations and demonstration of their stability under the maximum credible loading conditions. Stress analysis of PHT piping in nuclear power plants shows that the highly stressed piping components are normally elbows and branch tees. This necessitates detailed fracture mechanics evaluation of such piping connections by computing their stress intensity factors (SIF) and/or J -integral. Simple analytical solutions for evaluation of the SIF and J -integral for cracks in straight pipes are readily available in the literature. However the same type of solution for elbows and tees is limited in the open literature. In the present work a database is generated to evaluate the SIF for throughwall circumferential and longitudinal cracks under combined internal pressure and bending moment. Different parameters used to characterise a cracked elbow are pipe factor ( h ), pipe bore radius to thickness ratio ( r t ) and crack length. Another parameter (ϱ) is used to consider the relative magnitude of stresses due to internal pressure and remote bending moment. This database has been used to derive closed-form expressions to evaluate the SIF for elbows with cracks in terms of the aforementioned parameters.

Limit load analysis and safety assessment of an elbow with a circumferential crack under a bending moment

The use of the leak-before-break concept in the design of a Primary Heat Transport (PHT) piping system for nuclear power plants requires postulation of the largest credible flaws at highly stressed points and demonstration of system stability under the most severe loading conditions. In the PHT piping system, the elbows and branch tees are normally found to be among the most highly stressed piping components. This necessitates detailed flaw evaluation of these components. In the present paper, safety assessment of a pump discharge elbow of 500 MWe Indian PHWR with a throughwall circumferential crack under a bending moment is carried out using the R6 approach. The stress intensity factors (SIF) have been computed by using a database of SIF for elbows with cracks which was generated in one of our recent studies. Limit loads at plastic collapse have been evaluated by carrying out non-linear finite element analysis. Finally, the safety assessment of the pump discharge elbow is performed by doing a sensitivity study on crack length, applied moment and material fracture toughness.

Deterministic assessment of reactor pressure vessel integrity under pressurised thermal shock

Abstract A deterministic fracture mechanics analysis does not address the uncertainties involved in material properties, magnitudes of loads, location and size of the flaws, etc. However, in a real life situations such uncertainties can affect significantly the conclusions drawn out of a deterministic analysis. The principles of probabilistic fracture mechanics may be used to ascertain the effects of such uncertainties. A computer code PARISH (Probabilistic Assessment of Reactor Integrity under pressurised thermal SHock) has been developed based on principles of PFM for analysing a reactor vessel subjected to pressurised thermal shock. The code assumes a crack in the reactor vessel of random dimension depending upon Marshall flaw depth cumulative distribution function. The applied SIF at the tip of this crack is computed either using closed form solution or a precomputed data base. The material K IC is then calculated using the crack tip temperature and RT NDT . The value of RT NDT depends on the initial value of RT NDT and the increase in the value of RT NDT depending upon the fluence, copper content and nickel content. A Gaussian distribution is assumed for these parameters. If the applied SIF is more than the material K IC , the crack is assumed to propagate. The crack can be arrested only if the applied SIF is less than the material K Ia at that location. The material K Ia again depends upon the RT NDT, which in turn depends upon the fluence, copper content and nickel content of the material at that location. The vessel failure is assumed if the crack propagates by the 75% of the thickness. Such procedure is repeated for large number of cracks (of the order of one million). Using Monte-Carlo simulation, probabilities of no crack initiation, crack initiation and vessel failure are calculated. The present probabilities are conditional in the sense that the transient is assumed to occur. The case studies are presented involving a nuclear reactor vessel subjected to two different kinds of pressurised thermal shocks.