PSI - Issue 68

Saeid Hadidimoud et al. / Procedia Structural Integrity 68 (2025) 788–794 Saeid Hadidimoud et al./ Structural Integrity Procedia 00 (2025) 000–000

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4. Conclusions The comprehensive study of limit load in presence of cracks and residual stresses provided design curves for a wide range of crack configurations of pressurized vessels in presence of residual stress fields. Additionally, the analyses validated existing analytical solutions for thick-walled cylinders by comparing them with FEM results. The numerical study presented the effect of strain hardening on the limit load of the structure, leading to an increase in the load-carrying capacity of the vessel. FE studies showed increasing crack depth led to a reduction in the limit load of cylinders. Design curves for shallow and deep cracks were presented and compared. Numerical studies showed axial cracks were particularly sensitive to internal pressure, whereas circumferential cracks were more excited by axial loading. External cracks showed greater impact on reducing the limit load of cylinders compared to the sealed internal cracks. However, in thick-walled cylinders with axial cracks, an internally pressurized (open) crack led to the highest reduction in limit load. Autofrettage was also simulated to assess the effect of residual stresses on the limit load of cylinders. The most significant influence of residual stresses on the limit load of cracked cylinders was observed in the case of external hoop cracks, in both open-end and closed-end cylinders. A complementary study is underway to investigate the influence of crack configurations and residual stress fields on fracture resistance of defective vessels from the viewpoint of fracture mechanic’s approach. Alongside the current study of limit load, the fracture mechanics approach will provide and additional design tool to enable prediction of failure and/or fracture resistance of pressure vessels containing defects and residual stresses and serve as a complementary element of the digital twin model for this purpose. Zerbst, U., Ainsworth, R. A., Schwalbe, K. H. , 2000. Basic principles of analytical flaw assessment methods. International Journal of Pressure Vessels and Piping, 77(14–15), 855–867. Gangling, L., et al. , 1988. Elastoplastic analysis of an open-ended cylinder from the twelve polygonal yield condition. International Journal of Pressure Vessels and Piping, 33, 143–152. Gao, X.-L., 1992. An exact elasto-plastic solution for an open-ended thick-walled cylinder of a strain-hardening material. International Journal of Pressure Vessels and Piping, 52(1), 129–144. Dixon, R. D., & Perez, E. H., 2008. “Elastic-Plastic Solutions for Open-End Thick Walled Cylinders Subjected to Internal and External Pressures.” Proceedings of the ASME 2008 Pressure Vessels and Piping Conference, Volume 5: High Pressure Technology; Nondestructive Evaluation Division; Student Paper Competition, Chicago, Illinois, USA, July 27–31, 2008, pp. 13–19. ASME. Gao, X.-L., 2007. Strain gradient plasticity solution for an internally pressurized thick-walled cylinder of an elastic linear-hardening material. Zeitschrift für angewandte Mathematik und Physik, 58(2), 161–173. Hales, R., Budden, P. J., 1998. An alternative method for estimating the time to initiation of Type IV cracking in R5 (Vol. 7). Nuclear Electric Report EPD/GEN/REP/0323/98. Gloucester, UK. Ainsworth, R. A., 2000. The limit load for an uncracked cylinder under pressure, bending and end load. British Energy Report E/REP/GEN/0027/00. Gloucester, UK. Lei, Y., Budden, P. J., 2005. Limit load solutions for a cylinder with a circumferential crack under combined internal pressure, axial tension and bending. J. Strain Anal. 39, 673–683. Gao, Z., Cai, G., Liang, L., Lei, Y., 2008. Limit load solutions of thick-walled cylinders with fully circumferential crack under combined internal pressure and axial tension. Nuclear Engineering and Design, vol. 238, no. 9, pp. 2155–2164. Parker, A., 2001. Autofrettage of open-end tubes—pressures, stresses, strains, and code comparisons. Journal of Pressure Vessel Technology, vol. 123, pp. 271–281. Perry, J., Aboudi, J., 2003. Elasto-plastic stresses in thick-walled cylinders. ASME Journal of Pressure Vessel Technology, vol. 125(3), pp. 248– 252. Perry, J., Perl, M. , 2008. A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage. Perry, J., & Perl, M., 2006. A 3-D model for evaluating the residual stress field due to swage autofrettage. Proceedings of the ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. Volume 5: High Pressure Technology, Nondestructive Evaluation, Pipeline Systems, Student Paper Competition, Vancouver, BC, Canada, July 23–27, 2006, pp. 91–98. ASME. References