Page 196 - Failure Analysis Case Studies II

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There were several types of defect seen in the fracture surface here, including a large weld line,
cold slug fragments and voids. The latter are especially likely to form at or near a thickening of
the tank wall (e.g. Fig. 7). Judging by the several white stains observed on the buttress surface
immediately above the lateral corner, it is likely that there were several very slow leaks before the
final, catastrophic failure when the cracks propagated catastrophically. The bead would have
formed during this phase of the failure. It was possible to quantify the effect of the several
weakening mechanisms at work in the failure. The initiating mechanisms are:
1. the geometric stress concentration at the buttress corner;
2. internal voids;
3. fragments of cold slug adjacent to the corner; and
4. frozen-in strain due to cold tool or cool melt conditions when moulded.
The maximum tensile stress to which the outside of the side wall is exposed can be estimated by
simply assuming that the tank can be modelled by a cylindrical pressure vessel. The maximum
stress developed in such a vessel is the hoop stress, which acts around the short periphery of the
tank, at right angles to the long axis of the tank. It is the most serious stress experienced by a
cylindrical pressure vessel or tube, and is twice the longitudinal stress. It is reasonable to use the
hoop stress as the critical stress imposed on the tank, since the crack has propagated in a
longitudinal direction, i.e. under the influence of a hoop stress. It is given by the equation

Hoop stress = p.D/2t (1)
where p is the internal pressure, D the diameter of the cylinder and t the wall thickness. Taking D
as ca 45 mm and t as 2.5 mm together with the value ofp as 25 psi, then the hoop stress is thus
about 225 psi or about 1.55 MN m-*, a relatively benign stress for a material with a measured
tensile strength of ca 80 MN m-2.
The stress concentration at the buttress corner can be modelled by a standard figure provided
by Peterson [5], which represents a notch in bending for various geometries. Inserting the measured
values for the three geometric parameters - r, the radius of curvature at the corner = ca 0.01 mm;
d, the thickness of the section = 2.5 mm and D, the thickness of the buttress = 30 mm - then the
critical ratios for interpolation on the graph are: r/d = ca 0.004 and D/d = ca 12.
Using the value of r/d of ca 0.004, then interpolation gives the stress concentration factor, K,
(the ratio of real to nominal applied stress) as
K, = 4.2 (2)

If the spherical void occurs in this zone, then the K, value will be about 2, but it is likely to be
an underestimate, since they vary greatly both in shape and inner surface. If flatter and elongated,
then a more realistic model is that of a penny-shaped crack [6]. The K, factor varies from about 2
up to greater than 11 on this stress concentration diagram, depending on the ratio t/r, where t is-
the minimum radius and r the radius of the circular cavity. This was the most difficult parameter
to estimate since direct measurement was difficult and impracticable with the available microscopic
data. Taking a pessimistic value of say, t/r = 20, then the K, value will be about 6, so the net stress
factor could be
K, = (6 x 4.2) - 25 (3)