Page 115 - Failure Analysis Case Studies II

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2.1. Calculation of the limiting stress, aZul
Graphical creep rupture data provided for different thermoplastics materials (Figs 5-1 0 in DVS
2205, Part 1) allow the corresponding creep rupture stress, K, to be evaluated at the design lifetime
and the intended service temperature. A maximum permissible stress, nzul (‘zul’ is the abbreviation
of ‘zulassig’, the German for ‘permissible’) is then calculated by multiplying K by a series of factors
which take into account the effects of type of welded joint, any chemical interaction between the
container and its contents, the specific strength of the container material, any fluctuating loading
and the degree of hazard of the contents.
Details of the calculation of the limiting stress for the failed tank are set out in Appendix 1.
From this we get that the maximum permissible stress Ievel, azul, for a 25-year life of polypropylene
copolymer similar to that used in the failed tank at 20°C is

nZu1 = 2.54Nmm-’ (1)

2.2. Calculation of wall thickness

The required wall thickness, s, of the container at different depths, h, from the surface of the
contents in the full container can now be determined from the standard equation for hoop stress,
Go, as a function of the static head pressure, p, exerted by the contents at those depths. The basic
equation for the wall thickness, s, is derived in Appendix 2 and is

where d is the container diameter and g is the acceleration due to gravity. In DVS 2205, Part 2 [5],
by putting aml = in eqn (2), three cases are considered. These are:

(i) for containers with constant wall thickness

(ii) for containers with graded wall thickness, s, at depth h, (e.g. Fig. 2, which approximates to
the dam wall type of structure referred to in Part I of this work [4])

where (h, - h,, ,) 2 500 mm.
The factor C in (i) and (ii) takes into account the constraining effect of the joint with the base
of the container in case (i) and the similar effect of change of wall thickness in case (ii). The
value of C varies between C = 1 and C = 1.82. For a flexible base and/or a gradual change in
wall thickness, C = 1 can be used. For a rigid base and/or large and abrupt changes in wall
thickness, the value of C = 1.82 should be applied (this is the equivalent of the corrections to
the radial expansion arising from the solution of Timoshenko and Woinowsky-Kreiger [33
discussed earlier).