Theoretical stress concentration

In an infinite area of thin sheet of infinitely strong homogeneous, perfectly elastic material, stressed in tension in one direction uniformly; the introduction of an infinitely thin straight crack of length 2a centimetres perpendicular to the direction of the stress field, disturbs the distribution of stress in its vicinity. Mathematical analysis of this idealised case enables the stress at any point to be determined. Along the line of the crack, within the uncracked material, the tension stress perpendicular to the direction of the crack is inversely proportional to the square root of the distance from the crack tip. Thus it can be seen that the stress at the crack tip in this theoretical example is infinite, and the stress raising effect of cracks in real materials is explained qualitatively. For this case the 'constant' of proportionality is denoted by a quantity K1 divided by the square root of 2pi. In other cases the value of K1 depends upon the arrangement of the material, the stresses, the cracks, and the properties of the material. K1 is called the 'stress intensity factor'. In reality stressed steel fails progressively near to the tip of a sharp crack. In A533B steel the crack is observed to widen a little at the tip before tearing begins, a process called 'blunting'. In some tests the crack opens a little, and measurements are made of the angle of opening near to the crack tip, (Crack Opening Angle) or the width of the crack at a small standard distance from the crack tip (Crack Opening Displacement). The value of K1 for a given arrangement, at the point where stable tearing commences is called the critical value, denoted by K1c, and safety is said to be assured if this value is not exceeded. However, in the reality of crack growth in service, there would be no physical sign that this was so except for detection of the crack by periodic inspection and the subsequent withdrawal of the vessel from service. Repairs of such defects are an unknown quantity. Provision of new replacement vessels is a possibility. The more worrisome possibility is that operation with a 'stably' growing crack, if it continues for more than two millimetres, will eventually reach the stage at which the vessel wall starts to become weakened by the crack and no longer able to support the pressure load.

The Sizewell 'B' proof pressure test

Historically, pressure vessels have been over pressure tested, cold, at the start of operation at a test pressure greater than the maximum pressure anticipated in service. It has been demonstrated that for pressure vessels which survive such a test, the procedure confers a positive margin of safety between the maximum size of defect which could be present during the successful test without causing failure, and the size of defect which would cause failure during normal service.

The nature and significance of the proof pressure testing of the Sizewell 'B' reactor pressure vessel is explained at page 143 in reference 26, as follows:

ASME III REQUIRES A TEST PRESSURE OF 1.25 X DESIGN PRESSURE. TEST CONDITIONS ARE TO BE SUCH THAT 2 MILLIMETRES OF STABLE CRACK GROWTH ARE ASSURED.

"IF THE COLD HYDROTEST IS ASSUMED TO BE AT A TEMPERATURE WHERE ALL MATERIALS ARE AT UPPER SHELF CONDITIONS, FAILURE WOULD NOT OCCUR WHEN SEMI-ELLIPTICAL CRACKS OF 175MM X 1050MM WERE PRESENT. EVEN IF LOWER BOUND TOUGHNESS IS ASSUMED THE CORRESPONDING SIZE IS 155M X 930MM. FOR SOMEWHAT SMALLER CRACKS, I.E. THOSE DEFECTS LARGER THAN THE INITIATION DEFECT SIZE BUT LESS THAN THE SIZE NECESSARY TO CAUSE FAILURE, SOME STABLE CRACK GROWTH MAY OCCUR DURING THE HYDROTEST."

IT IS CONCLUDED THAT "THE HYDROTEST IN ITS PRESENT FORM WILL ONLY REVEAL VERY LARGE DEFECTS AND THAT THE TEST ITSELF MAY WELL CAUSE SOME DAMAGE TO SOMEWHAT LESSER DEFECTS NOT LARGE ENOUGH TO CAUSE FAILURE."

In the case of the Sizewell 'B' reactor pressure vessel the traditional cold over pressure test, which would have involved a definite risk of brittle failure, has, arbitrarily, been dispensed with and replaced by an ineffective procedure. The replacement test conditions used are insufficient to provide any significant degree of assurance that significant defects are not present either at the time of the test or subsequently. Furthermore the possibility exists that the conduct of the proof pressure test, far from conferring any future immunity, may in fact have increased the likelihood of subsequent catastrophic failure.

The severity of the proof pressure testing strategy of the Sizewell 'B' reactor pressure vessel seems to have been constrained by a fear of 'over-testing' by which the vessel might have been caused to fail unnecessarily at a proof pressure test when otherwise it might have survived without failure for the duration of its maximum lifetime. This fear can easily be understood when it is realized that large steam drums (e.g. Cockenzie) have been caused to break into pieces at cold proof tests, the failure having been initiated by the combination of a relatively tiny defect and brittleness of the steel in its vicinity. The choice of ensuring ductile behaviour throughout the pressure circuit, by raising its temperature everywhere above the brittle to ductile transition temperature would require a considerably higher test pressure in order to ensure that small defects will initiate failure at the time of the test, if they are present, which, after all, is the object of the exercise. The change in the conditions used for the initial overpressure proof test for the Sizewell 'B' reactor pressure vessel has been introduced without any conclusive statistical evidence of its effectiveness or otherwise. The risk of brittle failure initiated by a tiny defect is the price paid formerly in the traditional cold over pressure test for the assured immunity against failure in service which the test used to provide. The absence of this assurance means that instead, reliance is placed upon the greater understanding of the physical processes underlying steel pressure vessel reliability which fracture mechanics and periodic ultrasonic inspection may provide. Details of the results of such inspections are kept secret from public knowledge even against the freedom of information legislation.

A large ductile fragment

a massive fragment
Reference 25; "An illustration of the destructive potential of high pressure systems. This picture shows the 33,000 pound (15 tonne) fragment from a 140-ton (142 tonne) HIP (hot isostatic pressure) system, operating at 15,000 psi (718 kPa) and 1650 degrees fahrenheit (898 degrees centigrade) that failed catastrophically. The fragment travelled approximately 700 feet (213 metres) from the pressure vessel to beyond the plant boundary."

It might be thought that the very large size calculated for critical cracks in a ductile steel pressure vessel must mean that catastrophic failure is virtually impossible since such large defects would be certain to be found by periodic inspection, even if they did not cause serious leakage first. However, the occurrence of such catastrophic failures demonstrates that this is not the case.

In the case of the Sizewell 'B' reactor pressure vessel, there are not, as yet, any such examples, and a full scale tests to destruction of such a ductile vessel is not contemplated on the grounds of expense. It is possible that a clearer understanding of the onset of catastrophic failure of stressed ductile structures might be gained from the close study and analysis of other catastrophic failures which have occurred in service.

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