Introduction to forensic engineering
Introduction to forensic engineering

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Introduction to forensic engineering

6.3 Material evidence

On inspection, the evidence of failure was slight. The tank was intact, with only a small gap in the middle of a welded seam in the centre of the panel to show a serious accident had occurred (Figure 3, Paper 4). The crack had been opened up – deliberately by other investigators – so that it traversed almost the entire panel, when inspected several days after the accident. The crack was at the dead centre of the weld, where the panels had been joined together thermally.

SAQ 20

Draw an FTA diagram to show the possible causes of failure of the tank, starting, as usual, with the accident event itself. Include any other possible hypotheses in addition to those mentioned above. Indicate broadly what tests might be needed to clarify the problem of isolating the actual failure mechanism. What other information could prove useful in the investigation?


Figure 75 shows some of the main possible causes of the failure. As the failure occurred early in the product life, wear or other long-term mechanisms are not included. Weld quality is clearly an immediate candidate for inclusion in the diagram, but other failure mechanisms such as material attack, or choice of material, should be included.

The kind of analytical tests needed are:

  1. material quality checks using FTIR and DSC (check welds and check bulk material);

  2. mechanical testing of weld and bulk integrity;

  3. macroscopy and microscopy of the failed surface.

Other information that could be useful includes a material specification, and details of the way the tank was actually constructed. A specification for the tank itself is probably the most critical piece of information. Such a safety-critical product would almost certainly require detailed design calculations of wall strength and stiffness to ensure a given lifetime. Whether or not there are applicable standards would also need investigation, probably starting with the British Standards Institution and the American Society for Testing Materials.

Figure 75: Fault-tree analysis for the storage tank weld failure

It was clearly vital to examine the fracture surface, being apparently the only piece of forensic material evidence available about the incident. It had to be removed using a circular saw (a rather lengthy procedure with such a large tank, although cutting the soft polymer was like slicing cheese). The key fracture surface is shown in Figure 5, Paper 4. The fracture surface was simple, and showed:

  • four distinct zones;

  • a clear origin;

  • vertical flutes across all the surface.

It is easy to suggest the boundary to each zone represents a period of slow crack growth following each complete fill of the tank. Notice also, how the size of each zone increased with each fill, a feature to be expected from a growing crack. The origin (O1) appeared to be a small, elongated pit, or pin-hole, in the outer surface of the panel.

SAQ 21

Use Figure 76 to evaluate the magnitude of the stress concentration at the pin hole void at O1. Use information from Figures 5 and 7, Paper 4 to give you a basis for quantitative assessment of the severity of the defect. What can you say about the stress system acting on the tank? Use your ideas about the stress system to explain the shape of the cracks as they grew slowly under the load. There were other subcritical cracks (see Figure 6, Paper 4) that had grown from even larger pin-holes at other parts of the weld in the critical weld. Explain why they did not grow to criticality.

Figure 76 Standard reference for calculating stress concentration at an elliptical hole in an infinite panel in tension (Peterson, 1997)


Figure 5, Paper 4 shows the fracture surface at the origin of the critical crack that led directly to the leak in the tank. The dimensions of the original pinhole can be found from the photograph. The wall thickness is 12 mm, as stated in the caption to the figure. In the blown-up photograph, the wall is about 44 mm, therefore the photograph is about 3.7 (44/12) times bigger than life size. So all measured dimensions must be reduced by this factor to give actual sizes. The pinhole dimensions are:

  • depth from free surface is 1.62 mm (6/3.7)

  • width along fracture surface is 0.81 mm (3/3.7)

The lateral diameter of the defect can be estimated in a similar way from Figure 7, Paper 4, assuming that the subcritical pinholes shown in an alternate weld are representative of the critical weld defect. The width of the weld was actually 2.5 mm, so the photograph is magnified by 4.8 (12/2.5) – it is about 5 times bigger than life size. The pin hole in the centre of the crack near the centre of the plate is about 0.5 mm as measured directly, so is actually about 0.125 mm (0.5/4.8) in lateral diameter.

These dimensions can now be used to estimate the stress concentration. Figure 76 shows an elliptical hole of major axis 2a and minor axis 2b. Using the dimensions calculated from the photographs


a/b = 0.8/0.125 = 6.4

Reading from Figure 76 using this value shows the stress concentration factor will be

However, it is worth bearing in mind the curve rises rapidly as a/b increases, so there is uncertainty about the value of Ktg. Also, the lateral diameter of the hole was estimated from an adjacent weld, and could be unrepresentative.

The tensile stress is applied at right angles to the long axis 2a of the hole, which in the case of the tank, will be a hoop stress in the wall. It derives from the hydrostatic force from the contents of the tank. There will be some variation through the thickness of the wall, the maximum stress occurring on the outer surface, which is why the cracks have grown to a greater extent along the outer surface when compared to their inward growth.

The crack grew with successive loading cycles, showing the increased stress concentration with increasing crack size, that between propagation zones 3 and 4 in Figure 5, Paper 4 being the largest, and ultimately critical stage of growth. A crack from zone 4 penetrated through the wall therefore allowing an opening in the weld to release the caustic soda in a jet on to the factory floor.

The subcritical cracks shown in Figure 6, Paper 4 occurred off-centre, where the imposed stresses were lower. The load was greatest at the centre of the vertical weld, which explains why a smaller defect there was critical while larger pinholes elsewhere in the weld never became critical.

Similar comments apply to Figure 7, Paper 4 and it can be inferred that the central crack in Figure 7 was less serious in its stress concentrating effects than the critical crack. The stress will have been roughly the same as in the adjacent panel, but the cracks would have grown at a lower rate.


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