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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For the base radius, surface breaking flaws of 1 x 5mm produce a RF = 1.12 and 5 x 25mm embedded flaws (p = 1.5mm) RF = 1.46. For the base centre (with no FAD), surface breaking flaws of 1 x 5mm produce a RF = 1 / K r = 1.15 and 5 x 25mm embedded flaws (p = 1.5mm)RF = 1.49. In the case of embedded flaws in the base radius this is highly conservative as stress linearization across the flaw demonstrates crack closure. Pessimistically, the K r value used in the plot is based on linearization across the section which is conservative for this particular, non-linear, stress distribution. For the other cases, the e ff ects of low constraint are used to demonstrate the avoidance of brittle fracture. This was achieved by enhancing K mat following guidance in Annex N BS7910 (2019). The largest enhancement was from a K mat = 34MPa.m 0 . 5 toK c mat = 116.2 MPa.m 0 . 5 due to a 5 x 25mm embedded flaw in the base centre. This adjustment was made by cracked body modelling for T-stress of embedded flaws, as no solutions for embedded flaws are available in BS7910 (2019). Similarly, considering the smaller flaw size of 2 x 7mm also relies on an enhanced K c mat = 86.4MPa.m 0 . 5 . For surface flaws in the base centre, applying Annex N solutions BS7910 (2019) produce a T-stress of -280 MPa andaK c mat = 43.8MPa.m 0 . 5 , resulting in K r = 1.0. This was solved using a cracked body model to K c mat = 50.5MPa.m 0 . 5 andK r = 0.87. It is evident that the improved T-stress value of -410 MPa, calculated from a geometry specific cracked body model is used to demonstrate the acceptability of surface flaws 1 x 5mm or less. Whilst this approach is within the guidance provided in BS7910 (2019) some of the values of K c mat are particularly large. This is likely to be a result of applying large elastic stresses 2.2 times greater than the yield stress, which result in large negative T-stress values and consequently, significant gains in K c mat . Conversely, applying large elastic stresses is also likely to be overpredicting K I , see Annex R BS7910 (2019). The plasticity at the crack tip resulting from elastic bending stresses in the base centre and exceeding the yield stress has been accounted for in the simplest manner by direct application of those stresses into the calculation of K I . Considering the e ff ects of plasticity in the base, results in low plastic strains developing in localised areas of the inner and outer surface of the base centre and internal radius. This will have the e ff ect of relaxing the overall stress in the base and although the crack tip would still be yielding, plastic relaxation e ff ects may reduce the crack driving forces i.e. J or K J - possibly to an extent where constraint e ff ects are not required or by consideration of the elastic-plastic Q-parameter and K J prove satisfactory - potentially with greater margins. Related to this discussion is whether the stresses are load or displacement controlled - the base down drop and re sponse of the base assessed here is considered displacement controlled. Because the vibratory response does not result in significant elastic follow-up. This may be useful to analysts in assessments of type B packages where demonstra tion of margins due to more onerous loading conditions could be conducted using approaches suited to displacement controlled loading. A method for demonstrating the avoidance of brittle fracture of a package for transporting radioactive material has been presented in this paper. The worked examples provided on the base stresses, due to a base down drop at 1.2m at -40 ◦ C, show how to make a demonstration of the avoidance of brittle fracture following the procedure in BS7910 (2019). New inspection and maintenance procedures for the 1647B are currently being developed. Observations on accounting for constraint e ff ects in the presence of high secondary stresses have been made and the possibility of increasing margins by accounting for plastic relaxation e ff ects have been discussed. Further work on this is currently underway. The flat plate solutions for bending provided in Annex N BS7910 (2019) for dealing with constraint e ff ects have been safely extrapolated from using cracked body modelling for surface flaws with small a / B ratios. Cracked body modelling has been used exclusively for calculating T-stress in embedded flaws and structures under biaxial loading. 8. Conclusions

9. Acknowledgements

The authors would like to thank Dr. Rob Kulka (formerly TWI) for his review and assistance in development of this approach.