Work at the Naval Ordnance Laboratory produced a correlation to relate the strain in a vessel wall to the chemical explosive charge (22, 23).

The correlation of Eq. (5.10) expresses a relation between the shock energy W and the strain є in terms of the dimensions of the vessel and material properties of the vessel wall

1.407o-t££°-85(3.41 + 0.117 Rilh0)(Re2 — Rf)1*5
10s(l.47 + 0.0373 /?i/A0)°-15 R°-u

where

0*t (Ту — f — (£/£ц)[(Тц(1 £u) (Ту] (5.11)

and (Ту is the yield stress (psi), є is the strain, £u is the ultimate strain, eru is the ultimate stress (psi), q is the density (lb/ft3), 7?e is the external radius (ft), Rt is the internal radius (ft), h0 equals Re — Ru IF is the blast energy (lb TNT). Use of the correlation assumes that the vessel absorbs the strain energy radially and uniformly in the cylindrical wall, that the internal structure in the vessel has no effect, and that the classic stress-strain curve applies. The correlation applies only to radial sections of the vessel and another method must be used to assess damage to the bottom head. The top head is assumed not to see shock damage due to the large attenuation of shock pressures before arrival.

The Proctor correlation has been applied to an analysis of the SL-1 accident vessel damage to determine which observed radial damage strains could be attributed to shock and which could be attributed to blast and water hammer effects. The application provided a good representation of the observed facts and provides therefore some confirmation for the use of the correlation (23).

Figure 5.9 provides a plot of the SL-1 circumferential residual strain as a

function of the vessel length showing the shadowing effect of the thermal shield.

From this measured strain, the strain energy of each of the 24 rings, into which the vessel was divided, was determined by integrating the classical stress up to the strain value for each ring according to

SE — inRmth (ode (5.12)

J о

where SE is the strain energy (ft-lb), Rm is the initial radius to the center of the ring (in.), t is the thickness of ring (in.), h is the height of ring (in.), a is the classical stress in ring (psi), and e is the strain in the ring (in./in.). This strain energy was then summed for different regions of the vessel on the assumption that different mechanisms for damage existed in each region.

It was assumed that the water coolant was cold at 300°K and that the energy release was 50 MW-sec. This energy release was equivalent to that part of the energy produced in the inner fuel elements that could be rapidly transferred to the water. The 50 MW-sec was assumed to be equivalent to

26.2 lb of pentolite producing about 459 moles of detonation gases with a pressure of 21,230 psi, calculated from the ideal gas law and a charge volume of 0.276 ft3.

Now calculating the reduction of this pressure due to the expansion of the vessel, the figure of 1780 psia was obtained and a value for the work expansion was calculated from a P dv integration. The study assumed that the gas bubble accelerated the water above the core until it hit the vessel head, and calculated the work done in this expansion by another P dv integration for the increase in gas volume due to the fact that it has moved the water upward. This expansion then left a residual pressure of 133 psia, and produced a hammer velocity of 147 ft/sec.

Table 5.11 shows a comparison of the damage estimates for the SL-1 and the Proctor calculations. The correlation of Eq. (5.10) was used to predict a maximum strain from the initial charge weight, on the assumption that the damage expected for a slow energy release would be similar to that from a pentolite explosion of one-eighth of the prompt nuclear energy release. The correlation predicted a strain of 0.028 in./in. against the meas­ured maximum of 0.023 in./in.

It is recognized that using the Proctor correlation for the prediction of shock damage to the vessel wall is pessimistic in view of the different char­acteristics of nuclear and chemical explosions. However, Proctor (22, Ta­ble 3) does give recommended reductions in effective charge weight for slower releases.