If the surface exposed to the fluctuating temperatures is smooth and free from defects — for example, a rolled steel section that has not been subject to damage during manufacture or site assembly — it may be possible to show that no cracks will be formed. Experimental data on high-cycle fatigue damage indicate that for 316 stainless steel strain fluctuations with an amplitude of less than about 0.0008 do not initi­ate surface cracks even up to 109 cycles. This corresponds to surface temperature fluctuations of 45 K. This indicates that the above-core structure is not likely to be at risk if the differences between the coolant outlet temperatures from adjacent core or breeder subassemblies do not exceed this value.

In the case of a welded structure however it is very difficult to demonstrate freedom from surface defects 0.1-0.5 mm deep and it has to be recognised that temperature fluctuations may well make such cracks grow. In most cases they start to grow quickly, but the rate of growth soon declines. This is because high-frequency temperature fluctuations at the surface are attenuated rapidly as they penetrate into the material, and a growing crack soon reaches a depth at which it is too small to cause further growth. The crack growth is said to “arrest” at this depth.

It is usually the case that shallow cracks have no significant effect on the strength of reactor structures. Thus damage due to high-cycle fatigue can be taken to be acceptable if the crack arrest depth is 1 mm or less or, equivalently, if a crack of this depth will not grow. A crack grows if the variation of the stress intensity factor at its tip AK exceeds a critical value AKth, the growth threshold. AKth depends on the stress ratio R of the fluctuations. R is the ratio of maximum stress to minimum in the cycle, so that if the mean stress is zero R = -1,

whereas R = 0 if the stress is zero at one extreme of the cycle. For 316 stainless steel at 550 °C AKth is about 12 MPam1/2 for R = -1 and 8 MPam1/2 for R = 0.

A sinusoidal temperature fluctuation attenuates with depth x below the surface as exp(—x(nf/X)1/2) where X is the thermal diffusivity and f is the frequency, so at the tip of a crack of depth h the strain range Ає is given by

Ae(h) = aAT0 exp(—hy/n f/X). (4.2)

The condition for crack arrest is then h = hc, where

ЕАє. )yfnhc/(1 — v) = AKth. (4.3)

Here E is Young’s modulus (= 2 x 1011 Pa) and v is Poisson’s ratio (= 0.3). Figure 4.5 shows the variation of hc with AT0 for f = 1 Hz, a = 18 x 10—6 K-1 and X = 6 x 10—5 m2 s-1. For surface temperature fluctuations of AT0 = 50 K the crack arrest depth hc is about 1.4 mm.