Critical crack calculations

It was assumed that the fuselage rupture and associated star-burst petalling process was driven by an expanding 'bubble' of high pressure gas, produced by the conversion of solid explosive material into gas products. As the explosive gas pressures reduced due to dissipation through the structure and external venting, the service differential pressure loading would have taken over from the explosive pressures as the principal force driving the skin fractures.

The high temperature gas would initially have been confined within the container where, because of the low volume, the pressure would have been extremely high (too high for containment) and the gas bubble would have expanded violently into the cavities of the fuselage between the outer skin and the container. This gas bubble would have continued to expand, with an accompanying fall in pressure due to the increasing volume combined with a corresponding drop in temperature.

The precise nature of the gas expansion process could not be determined directly from the evidence and it was therefore necessary to make a number of assumptions about its behaviour, based on the geometry of the hull and the area of fuselage skin which the high pressure bubble would have ruptured. Essentially, it was assumed that the gas bubble would expand freely in the circumferential direction, into the cavity between the fuselage skin and the container. In contrast, the freedom for the bubble to expand longitudinally would have been restricted by the presence of the fuselage frames, which would have partially blocked the passage of gas in the fore and aft directions. However, the pressures acting on the frames would have been such that they would have buckled and failed, allowing the gas to vent into the next 'bay', producing failure of the next frame. This sequential frame-failure process would have continued until the pressure had fallen to a level which the frames could withstand. During the period of frame failure and the associated longitudinal expansion of the gas bubble, this expansion rate was assumed to be half that of the circumferential rate.

It was assumed that venting would have taken place through the ruptured skin and that the boundary of the petalled hole followed behind the expanding gas bubble, just inside its outer boundary, i.e. the expanding gas bubble would have stretched and 'unzipped' the skins as it expanded. This process would have continued until the gas bubble had expanded/vented to a level where the pressure was no longer able to drive the petalling mechanism because the skin stresses had reduced to below the natural strength of the material.

The following structural model was assumed:

The critical crack calculations were based upon the generalised model of a plate under biaxial loading in which there was an elliptical hole with sharp cracks emanating from it. This is a good approximation of the initial condition, i.e.. the shattered hole, and an adequate representation of the subsequent phase, when the hole was enlarging in its star-burst, petalling, mode.

The analyses of critical crack dimensions in the circumferential and longitudinal directions were based on established Fracture Resistance techniques. The method utilises fracture resistance data for the material in question to establish the critical condition at which the rate of energy released by the crack just balances the rate of energy absorbed by the material in the cracking process, i.e. the instantaneous value of the parameter Kr, commonly referred to as the fracture toughness Kc. From this, the relationship between critical stress and crack length can be determined.

Using conventional Linear Elastic Fracture Mechanics (LEFM) with fracture toughness data from RAE experimental work and published geometric factors relating to cracks emanating from elliptical holes, the stress levels required to drive cracks of increasing lengths in both circumferential and longitudinal directions were calculated. The skin stresses at sequential stages of the expanding gas bubble/skin petalling process were then calculated and compared with these data.

The results of the analysis indicated that, once the large petalled hole had been produced by explosive gas overpressure, the hoop stresses generated by fuselage pressurisation loads acting alone would have been sufficient to drive cracks longitudinally for large distances beyond the boundaries of the petalled hole. Thus, with residual gas overpressure acting as well, the 43 feet (total length) longitudinal fractures observed in the wreckage are entirely understandable. The calculations also suggested that the hoop fractures, due to longitudinal stresses in the skins, would have extended beyond the boundary of the petalled hole, though the excess stress driving the fractures in this direction would have been much smaller than for the longitudinal fractures, and the level of uncertainty was greater due to the difficulty of producing an accurate model reflecting the diffusion of longitudinal loads into the skins. Nevertheless, the results suggested that the circumferential cracks would extend downwards just beyond the keel, and upwards as far as the window belt - conclusions which accord reasonably well with the wreckage evidence.