PSI - Issue 52

A.D. Cummings et al. / Procedia Structural Integrity 52 (2024) 762–784 A. Cummings / Structural Integrity Procedia 00 (2023) 000–000

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(b)

(a)

Fig. 4. Base drop (height 1.2m) - Maximum principal stress in (a) Base centre (b) Base internal radius

6. Analysis of stresses in the base

Fig. 5 shows the maximum principal stress contour plots in the base centre and base radius at times corresponding to their respective peaks. Stress Classification Lines (SCLs) are shown in the plots from which the stress distributions across the sections are plotted and stresses are characterised into elastic crack driving forces. Although the stresses are cyclic, they are short term, and the number of cycles is very small. A crack initiation assessment of the largest transient peak stress will therefore bound any other failure mode of the base.

6.1. Stress linearization and classification

Fig. 6 shows the stress distribution and linearised stresses at the centre of the base. It is evident that the base is in bending and therefore the stresses exactly in the base centre are acting equally in biaxial bending. From this stress distribution, stress linearization was performed across the section as described in BS7910 (2019). The stresses are initially resolved into a local coordinate system before extracting the stress distribution across the section using Hyperworks (2021). The coordinate system is selected by the user and their choice of SCL. Provided the SCL is exactly perpendicular to the maximum principal stress, in this case it is, the extracted stresses and principal stresses are equivalent. Fig.6b shows the principal stress tensor plot overlaid on the maximum principal stress contour plot from which it is clear that the maximum principal stress is exactly perpendicular to the SCL and therefore the extracted stresses are equivalent to the principal stresses. From the distribution σ 0 and σ 1 are obtained (see Fig. 6a) and bending and membrane stresses are calculated following BS7910 (2019):

1 2

( σ 0 + σ 1 )

(11)

σ m =

And:

1 2

( σ 0 − σ 1 )

(12)

σ b =

The base centre stresses at the outer surface are σ m = 92MPa and σ b = 753 MPa. The bending stress is over twice the static yield stress (340 MPa). Fig. 7a shows the highly non-linear stress distribution resulting from the peak stress in the internal base radius. At a depth of 10mm into the package body the peak stress has decayed to approximately 400 MPa and the stress through the rest of the section is linear. The stress is artificially high due to the rigid contents striking the elastic body. In reality a small amount of plasticity and work hardening would reduce the peak stresses. Nevertheless, this elastic stress distribution at 3.5ms, has been used to calculate K I , σ ref and thus the plastic collapse ratio, L r . Two methods have been used to characterise the stress distribution. Peak stresses do not contribute to plastic collapse at local discontinuities BS7910 (2019) therefore, the bending and membrane stress have been obtained using the in-built stress linearization tools in Hyperworks (2021). This method applies the rules in ASME FFS-1 / API579-1