Fragmentation Of Containers Due To Explosive Pressure
Analytical Service Pty Ltd
TECHNICAL NOTE 70

TECHNICAL NOTE 70

This review is limited to an investigation of a disintegrating ring, which should be thought of as a segment of a cylindrical container. Examples of such containers are artillery shells, pressure vessels in general and airplane fuselages in particular. Pressure is applied by an internal explosion in a container. Depending on the amount and placement of the detonating material various outcomes are possible: No shell failure, some break-up or a total disintegration with the shell flying off in pieces. A good understanding of the fragmentation process provides important clues for investigation of aircraft accidents.

Our main interest lies with the thin-wall shells. Yet, the artillery pieces deserve a mention, as their bursting process was thoroughly investigated and quantified.

STATIC BREAK-UP

In a typical configuration of those members, hoop stress predominates. The pressure grows slowly until the shell begins to yield and then breaks. If pressure then suddenly drops, because of the loss of fluid, for example, a single break is the only effect, as in Fig.1b. On the other hand, pressure may persist sufficiently long for a fracture to also take place at the diametrically opposite side, as shown in Fig.1c. This is the effect of primarily bending at this second location and one expect it mostly when dealing with brittle materials. (Such materials are not typical of pressure vessels.)

It should be remembered that even though the pressure grows slowly , the loss of integrity is a sudden phenomenon.

Fig. 1 Pressurized ring is shown in (a), quasi-static breaking at a single point in (b) and, on some occasions, at two points (c).

MECHANISM OF MULTIPLE FRACTURING

When the pressure growth is rapid, the container may break into a number of pieces. To explain this we assume that the strength of the ring material varies randomly along its circumference between an upper and the lower limit or between the weakest and the strongest spot.

The ring in Fig. 2 is subjected to an explosive pressure p, which stretches it, thereby inducing hoop stress and strain. The ring begins to swell and, at some point in time, the first rupture takes place. The increase in pressure continues and subsequent breaks eventuate until disintegration comes to an end and the pieces of the ring fly off. The breakup time, between the first and the last rupture, is measured in microseconds for relatively small objects, like artillery shells, but may take milliseconds for an aircraft fuselage.

In explaining the mechanism, it is sufficient to discuss only two points of the ring, where a disintegration can take place: the weakest point A with the allowable tensile strain e1 and an additional point B with e₂, while e₁ < e₂. When the hoop strain level becomes as large as e₁, the fracture takes place at A. But the strain still grows and if it reaches e2, the failure will also take place at B.

However, this may not necessarily happen because there is another phenomenon, namely a relieving stress wave, as illustrated in Fig. 2.b. This wave emanates from every new crack and it reduces the stress in the material to an insignificant value. If the pressure and therefore strain growth is not sufficiently fast, then the wave reaches point B sooner than the strain attains the value of e₂ and the fracture at B does not happen. The multiple breaking effect is therefore the net result of two competing processes; strain growth and spreading of the relieving wave. This "race" and additional breaking continues until the relief wave expands over the whole perimeter of the ring.

Fig. 2 Left: A ring with only two weak spots (a) and a ring fragment showing the unloading wave spreading from a fracture point (b).

The quicker the energy release from the explosive, the faster the pressure growth and more broken pieces result, as numerous experiments tell us.

As in many applications of structural dynamics, the terms “fast” and “slow” should be understood as explained in Details.

The stress waves in materials spread with a so-called sonic speed. For steel and commonly used aluminium alloys this is close to 5000 m/s. The stress-relieving wave mentioned above spreads with the same speed.

Fig. 3 Left: Statically broken ring is in (a), one affected by mild explosion is in (b) and one after strong explosion in (c).

The quicker the energy release from the explosive, the faster the pressure growth and more broken pieces result, as numerous experiments tell us. As in many applications of structural dynamics, the terms “fast” and “slow” should be understood as explained in Details.

The stress waves in materials spread with a so-called sonic speed. For steel and commonly used aluminium alloys this is close to 5000 m/s. The stress-relieving wave mentioned above spreads with the same speed.

SPECIAL FEATURES OF EXPLOSION IN A FUSELAGE

What was discussed so far was related to a somewhat idealized case of a cylindrical container under radial pressure with that pressure being uniformly applied to a circumference. In a large fuselage, such a uniformity is impossible to attain. First, there are some structural deviation from a tubular shape, namely the floor structure. Secondly, the volume taken by passengers in their chairs provides shadowing for a localized explosive action.

Considering the size of a commercial airliner, a solid explosive will have more than one type of effect. First, it may destroy nearby objects and only push other objects at some distance. One can expect a varying pattern of destruction when moving away from the epicenter. Part of the fuselage may be shattered close to it, but at some distance the pressure impulse may be capable of only splitting the fuselage tube along a line parallel to the aircraft axis.

A more uniform explosive action happens when the air-fuel mix detonates. Pressures are typically smaller, but they are applied over a longer time duration.

A typical fuselage has densely spaced stringers and frames. Apart from increasing strength, those additional elements do not influence the breaking pattern very much, except by keeping the crack lines straight. (This is because it is more difficult for a crack to cross those stiffening elements thereby moving sideways.)

CONCLUSIONS FOR AIRCRAFT ACCIDENT INVESTIGATION

When an aircraft is found in many pieces, a natural question occurs: Did an explosion take place in addition to the mechanical impact against the ground?

Here are some other questions, which must be answered before the above is addressed:

1. Is there any reason to think that the aircraft fell from a great height?
2. Was the cruising speed prior to ground contact much greater than expected?
3. Did the ship have a chance to collide with serious ground obstacles like brick or concrete walls and steel structures?
4. Did it fall on a concrete surface or rocky ground?

In the absence of the affirmative answers, the structure-ground impact must be regarded as mild and certainly not capable of causing the fragmentation of the body of the fuselage in the manner described previously. The most likely damage would be the break-off of the protruding parts.

If the answer to all of the above items is NO, and tens of airframe pieces are found then an explosion becomes a possibility. If hundreds of fragments can be seen, then it is a certainty.

DETAILS

(This section is rather technical and it is meant for engineers working in structures.)

Static or quasi-static loading means that pressure is applied slowly. On the other hand, dynamic or shock loading implies fast or abrupt application. Those adjectives relate to the natural period of a structural element under consideration. When pressure increases to its maximum value over 5 or 6 natural periods, it is a quasi-static load. When it does so over a fraction of the period, it is a rapid loading or a shock loading. During an explosive loading the main part of the impulse typically lasts only a small fraction of the natural period.

The hoop or the circumferential stress and strain is the main factor governing rupture. The longitudinal stress plays a lesser role and, depending on the construction, the longitudinal stress may not even exist.

The growth of stress/strain was described in a simplified way, by emphasizing the hoop stress only. When a strong explosive action takes place, pressure is applied to surface as a compressive stress. Due to its large magnitude and short duration the shell acquires an outward radial velocity, which then induces the increasing hoop stress.

What was previously explained in terms of strain in Fig.2 may also, for many materials, be expressed in terms of stress. The weakest point is A with the tensile strength F₁ and then point B with F₂, while F₁<F₂. When the hoop stress σh becomes as large as F₁, the fracture takes place at A and afterwards, when σh reaches F₂, point B breaks.

Typical pressure vessels or boilers can also fail due to a sudden steam overpressure. This usually produces only a few pieces, but they can travel quite far. (Sometimes it involves so- called rocketing effect, with known cases of the end cap travelling about a kilometer in distance.)

The formula below shows a simple way of estimating the number of fragments in a ring when break-up duration is known.

		βl
	n=
		ctb
	n is the resulting number of fragments l is the length of circumference tbis breakup duration c is the unloading wave speed (sonic speed) 1 < β < 2, often β ≈ 1.5

Note: t_b counts from the initiation of the first crack to the completion of the last one. A separate calculation is needed to find t_b