Analytical and Three-Dimensional Finite Element Investigation of Multiaxial Loading on Stress Intensity Factor of U-Shaped Spot-Welded Joints
Abstract
Resistance spot-welded joints are widely used in automotive structures and are often subjected to complex loading conditions that can lead to fatigue crack initiation and growth around the weld nugget. To evaluate the fracture-mechanics behaviour and structural integrity of these joints, accurate determination of Stress Intensity Factors (SIFs) is crucial. In the present study, the SIFs for a U-shaped resistance spot welded joint under multiaxial loading are investigated by three-dimensional Finite Element Analysis (FEA) and analytical approaches. We develop a detailed numerical model of the welded sheets and weld nugget in ABAQUS to characterise the local stress field and determine the corresponding SIFs. The numerical predictions are compared with those obtained from the analytical formulations proposed by Zhang and Swellam to assess their accuracy and applicability for the configuration investigated. In addition, the influence of weld nugget diameters and sheet thicknesses on the SIFs is studied systematically. The results show that Zhang's analytical model agrees better with the finite element predictions than Swellam's formulation for the loading and geometric conditions considered. In addition, the calculated SIFs increase with increasing weld nugget diameter and sheet thickness within the investigated parameter ranges. The results provide useful insight into the mixed-mode fracture behaviour of spot-welded joints and help to assess the validity of simplified analytical approaches for multiaxially loaded welded structures.
Keywords:
Multiaxial loading, Mixed-mode fracture, Resistance spot welding, Finite element analysis, Stress intensity factor, Weld nugget diameter, Sheet thicknessReferences
- [1] Pook, L. P. (1975). Fracture mechanics analysis of the fatigue behaviour of spot welds. International Journal of Fracture, 11(1), 173-176. https://doi.org/10.1007/BF00034726
- [2] Radaj, D. (1989). Stress singularity, notch stress and structural stress at spot-welded joints. Engineering fracture mechanics, 34(2), 495-506. https://doi.org/10.1016/0013-7944(89)90161-6
- [3] Zhang, S. (1999). Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding journal-New York-, 78, 173-s. https://s3.us-east-1.amazonaws.com/WJ-www.aws.org/supplement/WJ_1999_05_s173.pdf
- [4] Swellam, M. H., Ahmad, M. F., Dodds, R. H., & Lawrence, F. V. (1992). The stress intensity factors of tensile-shear spot welds. Computing systems in engineering, 3(1-4), 487-500. https://doi.org/10.1016/0956-0521(92)90134-5
- [5] Pan, N., & Sheppard, S. D. (2002). Stress intensity factors in spot welds. Engineering fracture mechanics, 70(5), 671-684. https://doi.org/10.1016/S0013-7944(02)00076-0
- [6] Zhang, Y., & Taylor, D. (2000). Sheet thickness effect of spot welds based on crack propagation. Engineering fracture mechanics, 67(1), 55-63. https://doi.org/10.1016/S0013-7944(00)00029-1
- [7] Lin, P. C., & Pan, J. (2008). Closed-form structural stress and stress intensity factor solutions for spot welds under various types of loading conditions. International journal of solids and structures, 45(14-15), 3996-4020. https://doi.org/10.1016/j.ijsolstr.2008.02.006
- [8] Lin, P. C., & Pan, J. (2008). Closed-form structural stress and stress intensity factor solutions for spot welds in commonly used specimens. Engineering fracture mechanics, 75(18), 5187-5206. https://doi.org/10.1016/j.engfracmech.2008.08.005
- [9] Yu, Z., Ma, N., Murakawa, H., Watanabe, G., Liu, M., & Ma, Y. (2023). Prediction of the fatigue curve of high-strength steel resistance spot welding joints by finite element analysis and machine learning. The international journal of advanced manufacturing technology, 128(5), 2763-2779. https://doi.org/10.1007/s00170-023-11993-y
- [10] Santos, J. I., Martín, Ó., Ahedo, V., de Tiedra, P., & Galán, J. M. (2022). Glass-box modeling for quality assessment of resistance spot welding joints in industrial applications. The international journal of advanced manufacturing technology, 123(11), 4077-4092. https://doi.org/10.1007/s00170-022-10444-4
- [11] Heidrich, D., Zhang, F., & Fang, X. (2021). Fatigue strength of rivet resistance spot welding technique in comparison with self-piercing riveting for multi-material body-in-white structure. Journal of materials engineering and performance, 30(5), 3806-3821. https://doi.org/10.1007/s11665-021-05684-6
- [12] Meilinger, Á., Cserépi, M. F., & Lukács, J. (2024). Behaviour of aluminium/steel hybrid RSW joints under high cycle fatigue loading. Welding in the world, 68(2), 427-440. https://doi.org/10.1007/s40194-023-01663-8
- [13] Prabitz, K. M., Antretter, T., Rethmeier, M., El-Sari, B., Schubert, H., Hilpert, B., ... & Ecker, W. (2024). Numerical and experimental assessment of liquid metal embrittlement in externally loaded spot welds. Welding in the world, 68(10), 2713-2722. https://doi.org/10.1007/s40194-024-01696-7
- [14] Ullrich, M., Wohner, M., & Jüttner, S. (2024). Quality monitoring for a resistance spot weld process of galvanized dual-phase steel based on the electrode displacement. Welding in the world, 68(7), 1791-1800. https://doi.org/10.1007/s40194-024-01720-w
- [15] Lippardt, S. (2023). Influence of the geometry on the fatigue strength of welded joints using the effective notch stress approach. Welding in the world, 67(3), 669-681. https://doi.org/10.1007/s40194-022-01409-y
- [16] Zanetti, M., Babini, V., & Meneghetti, G. (2021). Fat classes of welded steel details derived from the master design curve of the peak stress method. Welding in the world, 65(4), 653-665. https://doi.org/10.1007/s40194-020-01057-0
- [17] Rudorffer, W., Wächter, M., Esderts, A., Dittmann, F., & Varfolomeev, I. (2022). Fatigue assessment of weld seams considering elastic–plastic material behavior using the local strain approach. Welding in the world, 66(4), 721-730. https://doi.org/10.1007/s40194-021-01242-9
- [18] Scacco, F., Zerbst, U., Meneghetti, G., & Madia, M. (2022). Comparison between PSM and IBESS approaches for the fatigue life estimation of weldments. Welding in the world, 66(6), 1251-1273. https://doi.org/10.1007/s40194-022-01284-7
- [19] Yoshihara, Y., Osawa, N., Murakawa, H., & Dai, P. (2025). Study on the estimation method for the mean stress effect on the fatigue strength of welded joints with various failure modes and joint types. Welding in the world, 69(1), 151-167. https://doi.org/10.1007/s40194-024-01815-4
- [20] Brechelt, S., Wiche, H., Junge, J., Gustus, R., Schmidt, H., & Wesling, V. (2023). Increase of electrode life in resistance spot welding of aluminum alloys by the combination of surface patterning and thin-film diffusion barriers. Welding in the world, 67(12), 2703-2714. https://doi.org/10.1007/s40194-023-01614-3