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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Table 3. Base stress linearization Location, stress

Across section

Across surface flaw (1x5mm)

Across embedded flaw (5x25mm) p = 1.5mm

[MPa]

[MPa]

[MPa]

Base centre σ m Base centre σ b Base radius σ m Base radius σ b

92

N / A N / A

N / A N / A

753 101 277

-9665 10851

-5409 6519

The next step is to classify the stresses as primary or secondary stresses in order to assess their contribution to plastic collapse. The yield stress applied to the elastic-plastic model of the package base was progressively reduced and shows that the base radius stresses are primary stresses and an estimate of F y = L r , u = 0.5 - 0.75, Fig. 8(a)-(b). The estimated L r , u in the base radius is not particularly accurate for this case because it involves plasticity accumulated through several cycles of the base vibrations and the plots shown are immediately after the first cycle.

(a)

(b)

(d)

(c)

Fig. 8. Base drop (height 1.2m) - Base internal radius stress classification (a) F y = 0.5 (b) F y = 0.75 (c) F y = 0.25 (d) F y = 0.1

Further reduction of F y did not cause through thickness yielding of the centre of the base, Fig. 8(c)-(d). At F y = 0.25 the plasticity in the base radius forms a large plastic hinge whereas at the centre of the base the plasticity does not fully develop through the section, Fig. 8(d). When F y = 0.1 the plastic hinge in the base radius serves to protect the centre of the base from further plasticity. The stress pulse occurs as a result of a finite amount of energy imparted into the base and as a consequence would result in very limited plasticity in the vicinity of any crack. Therefore the stresses in the base centre are treated as secondary stresses as they do not contribute to plastic collapse. However, further investigation was carried out to decide how to calculate K I and whether to correct for plasticity e ff ects due to the large, secondary, bending stresses. An elastic-plastic simulation of the uncracked 1647B (with quasi static properties) shows that a pool of yielding may occur in the centre of the base, Fig. 9. The Sintap (1999) procedure discusses plastic redistribution of large secondary stresses and suggests that elastic based calculations of K I are likely to be overly conservative. Annex R of BS7910 (2019) provides similar guidance for large secondary stresses and points to R6 (2001) procedures to calculate an elastic-plastic K s J . Therefore, for this assessment, the guidance in Sintap (1999) (section III.2.3.2) and BS7910 (2019) Annex R was followed, and elastic stresses were conservatively used to calculate K I .