Skip to main content
SpringerLink
Log in

Fracture mechanics solutions to spot welds

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Notch stress, stress intensity factors and J-integral at a spot weld are generally expressed by structural stresses around the spot weld. The determination of these parameters are then simplified as determining the structural stresses that can be calculated by a spoke pattern in finite element analysis. Approximate stress formulas for structural stress, notch stress and equivalent stress intensity factor are given for common spot-welded specimens. With the aid of the formulas, test data in terms of the original load can be easily transformed into the data in terms of the structural stress, notch stress or equivalent stress intensity factor at the spot weld. The formulas also facilitate the transfer of test data across different specimens. A measuring method is given for lap joints. The strain gauge technique developed for the tensile-shear specimen shows that all the structural stress, notch stress, stress intensity factors and J-integral at the spot weld can be determined by two strain gauges attached only to the outer surface of one sheet. The results presented here should be helpful for the analysis and testing of spot welds and for developing measuring methods for spot welds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abe, H., Kataoka, S. and Satoh, T. (1986). Empirical formula for fatigue strength of single-welded joint specimens under tensile-shear repeated load. SAE Paper 860606.

  • Cooper J.F. and Smith, R.A. (1986). Initial fatigue crack growth at spot welds. Fatigue of Engineering Materials and Structures. Publ. Institution of Mechanical Engineers, London.

    Google Scholar 

  • Davidson, J.A. (1983). A review of the fatigue properties of spot-welded sheet steels. SAE Paper 830033.

  • Davidson, J.A. and Imhof Jr E.J. (1983). A fracture mechanics and system-stiffness approach to fatigue performance of spot-welded sheet steels. SAE Paper 830034.

  • Gao, Y., Chucas, D., Lewis, C. and McGregor, I. (2001). Review of CAE fatigue analysis techniques for spotwelded high strength steel automotive structures. SAE Paper 2001-01-0835.

  • Gieske, D. and Hahn, O. (1994). Neue Einelementprobe zum Prüfen von Punktschweißverbindungen unter kombinierten Belastungen. Schweißen und Schneiden 46, 9–12.

    Google Scholar 

  • Grubisic, V. et al. (1994). Verbesserung der Bauteilfestigkeit durch höherfeste Feinblechwerkstoffe und optimierte Fügeverfahren. Fügen im Leichtbau, DVM-Bericht 120, 47–61.

    Google Scholar 

  • Hahn, O., Dölle, N., Jendrny, J., Koyro, M., Meschut, G. and Thesing, T. (2000). Prüfung und Berechnung geklebter Blech-Profil-Verbindungen aus Aluminium. Schweißen und Schneiden 52, 266–271.

    Google Scholar 

  • Hahn, O., Kurzok, J.R. and Rohde, A. (1998). Die Ñbertragbarkeit von Kennwerten einer punktgeschweißten Einelementprobe auf Bauteile. ATZ Automobiltechnische Zeitschrift 100, 228–232.

    Google Scholar 

  • Kuang, J-H. and Liu A-H. (1990). A study of the stress concentration factor on spot welds. Welding Journal 69, 468-s to 474-s.

    Google Scholar 

  • Kurath, P. (1992). Multiaxial fatigue criteria for spot welds. SAE Paper 920668.

  • Lawrence, F.V., Wang, P.C. and Corten, H.T. (1983). An empirical method for estimating the fatigue resistance of tensile-shear spot-welds. SAE Paper 830035.

  • Lee, Y., Wehner, T., Lu, M., Morrissett, T., and Pakalnins, E. (1998). Ultimate strength of resistance spot welds subjected to combined tension and shear. Journal of Testing and Evaluation 26, 213–219.

    Google Scholar 

  • Mabuchi, A., Niisawa, J. and Tomioka, N. (1986). Fatigue life prediction of spot-welded box-section beams under repeated torsion. SAE Paper 860603.

  • Maddox, S.J. (1992). Fatigue design of welded structures. Engineering Design in Welded Constructions, Pergamon, Oxford, England, 31–56.

    Google Scholar 

  • Mizui, M., Sekine, T., Tsuzimura, A., Takasshima, T. and Shimazaki, Y. (1988). An evaluation of fatigue strength for various kinds of spot-welded test specimens. SAE Paper 880375.

  • Pook, L.P. (1975a). Approximate Stress Intensity Factors for Spot and Similar Welds. NEL Report 588.

  • Pook, L.P. (1975b). Fracture mechanics analysis of the fatigue behavior of spot welds. International Journal of Fracture 11, 173–176.

    Google Scholar 

  • Radaj, D. (1989). Stress singularity, notch stress and structural stress at spot welded joints. Engineering Fracture Mechanics 34, 495–506.

    Google Scholar 

  • Radaj, D. (1996). Theory of forces and stresses in spot welded overlap joints, Ingenieur-Archiv 67, 22–34.

    Google Scholar 

  • Radaj, D. and Sonsino, C. M. (1998). Fatigue Assessment of Welded Joints by Local Approaches, Abington Publishing, Cambridge.

    Google Scholar 

  • Radaj, D. and Zhang, S. (1991a). Simplified formulae for stress intensity factors of spot welds. Engineering Fracture Mechanics 40, 233–236.

    Google Scholar 

  • Radaj, D. and Zhang, S. (1991b). Stress intensity factors for spot welds between plates of unequal thickness. Engineering Fracture Mechanics 39, 391–413.

    Google Scholar 

  • Radaj, D. and Zhang, S. (1992). Stress intensity factors for spot welds between plates of dissimilar materials. Engineering Fracture Mechanics 42, 407–426.

    Google Scholar 

  • Radaj, D. and Zhang, S. (1994). Thermal Stress Singularity and Fracture Strength at Bimaterial Crack Tips. Mis-Matching of Welds, ESIS 17(Edited by K-H. Schwalbe and M. Kocak), Mechanical Engineering Publications, London, 177–194.

    Google Scholar 

  • Radaj, D. and Zhang, S. (1996). Anschauliche Grundlagen für Kräfte und Spannungen in punktgeschweißten Ñberlappverbindungen. Konstruktion 48, 65–71.

    Google Scholar 

  • Rice, J.R. (1974). Limitations to the small scale yielding approximation for crack tip plasticity. Journal of the Mechanics and Physics of Solids 22, 17–26.

    Google Scholar 

  • Rupp, A., Grubisic, V. Störzel, K. and Steinhilber, H. (1989). Ermittlung von ertragbaren Schnittkräften für die betriebsfeste Bemessung von Punktschweißverbindungen im Automobilbau. FAT Schriftenreihe 78, Frankfurt.

  • Rupp, A., Grubisic, V. and Buxbaum, O. (1994). Ermittlung ertragbarer Beanspruchungen am Schweißpunkt auf Basis der Ñbertragenen Schnittgrößen. FAT Schriftenreihe 111, Frankfurt.

  • Sheppard, S.D. and Strange, M. (1992). Fatigue life estimation in resistance spot welds: initiation and early growth phase. Fatigue Fract. Engng Mater. Struct. 15, 531–549.

    Google Scholar 

  • Sheppard, S.D. (1993). Estimation of fatigue propagation life in resistance spot welds. ASTM STP 1211, 169–185.

    Google Scholar 

  • Sheppard, S.D. (1996). Further refinement of a methodology for fatigue life estimation in resistance spot weld connections. ASTM STP 1292, 265–282.

    Google Scholar 

  • Simon, G. and Krause, H. (1992). Ñbertragbarkeit der an Einpunktproben ermittelten Schwingfestigkeitswerte auf Mehrpunktproben und bauteilähnliche Proben. Schweißen und Schneiden 44, 27–33.

    Google Scholar 

  • Singh, S., Schmid, G. and Geo, S. (1991). Leichtbau durch optimierte Fügetechnik. in Bauteil’ 91, Metallkonstruktionen und Leichtbau – Möglichkeiten und Grenzen, DVM, Berlin, 407–426.

    Google Scholar 

  • Singh, S. (1992). Fatigue testing of jointed sheet material specimens. IIW-Doc. III-998-92.

  • Smith, R.A. and Cooper, J.F. (1988). Theoretical predictions of the fatigue life of shear spot welds. Fatigue of Welded Constructions, Publ The Welding Institute, Abington, Cambridge.

    Google Scholar 

  • Suo, Z. and Hutchinson, J.W. (1990). Interface crack between two elastic layers. International Journal of Fracture 43, 1–18.

    Google Scholar 

  • Swellam, M.H., Ahmad, M.F., Dodds, R.H. and Lawrence, F.V. (1992). The stress intensity factors of tensile-shear spot welds. Computing Systems in Engineering 3, 487–500.

    Google Scholar 

  • Tada, H., Paris, P. and Irwin, G. (1985). The Stress Analysis of Cracks Handbook. Paris Productions Incorporated and Del Research Corporation.

  • Tomioka, N., Niisawa, J. and Mabuchi, A. (1986). On theoretical analysis of stress at welding flange of spot welded box section member under torsion. SAE Paper 860602.

  • Wang, P.C. and Ewing, K.W. (1988). A J-integral approach to fatigue resistance of a tensile-shear spot weld. SAE Paper 880373.

  • Wang, P.C. and Ewing, K.W. (1991). Fracture mechanics analysis of fatigue resistance of spot welded coach-peel joints. Fatigue and Fracture of Engineering Materials and Structures 14, 915–930.

    Google Scholar 

  • Weibel, K. and Wecker, A. (1994). Vergleich der Schwingfestigkeit verschiedener Fügungen an unterschiedlichen Dünnblechproben. Fügen im Leichtbau, DVM-Bericht 120, 177–189.

    Google Scholar 

  • Weibel, K. and Wecker, A. (1995). Schwingfestigkeit gefügter Dünnblechproben prüfen. Materialprüfung 37, 452–456.

    Google Scholar 

  • Yuuki, R., Ohira, T., Nakatsukasa, H. and Yi, W. (1986). Fracture mechanics analysis of the fatigue strength of various spot welded joints. in symposium on Resistance Welding and Related Processes, Osaka.

  • Yuuki, R. and Ohira, T. (1989). Development of the method to evaluate the fatigue life of spot-welded structures by fracture mechanics. IIW Doc. III-928-89.

  • Zhang, J., Dong, P. and Gao, Y. (2001). Evaluation of stress intensity factor-based predictive techniques for fatigue life of resistance spot welds. SAE Paper 2001-01-0830.

  • Zhang, S. (1995). Forces and Stresses in Seam Welded Overlap Joints. Research Report 95-0005, Daimler-Benz AG, Stuttgart.

    Google Scholar 

  • Zhang, S. (1997). Stress intensities at spot welds. International Journal of Fracture 88, 167–185.

    Google Scholar 

  • Zhang, S. (1999a). Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173-s–179-s.

    Google Scholar 

  • Zhang, S. (1999b). Recovery of notch stress and stress intensity factors in finite element modeling of spot welds. NAFEMS World Congress on Effective Engineering Analysis, Newport, Rhode Island, 1103–1114.

  • Zhang, S. (1999c). Stress intensities derived from stresses around a spot weld. International Journal of Fracture 99, 239–257.

    Google Scholar 

  • Zhang, S. (2000). Thermal stress intensities at an interface crack between two elastic layers. International Journal of Fracture 106, 277–290.

    Google Scholar 

  • Zhang, S. (2001a). Approximate stress formulas for a multiaxial spot weld specimen. Welding Journal, 80, 201-5 to 203-5.

    Google Scholar 

  • Zhang, S. (2001b). T-stress and stress intensities for the interface cracks in some specimen-relevant geometries. International Journal of Fracture, accepted.

  • Zhang, S. (2001c). Stresses in laser welded lap joints determined by outer surface strains. Welding Journal, accepted.

  • Zhang, S. and Radaj, D. (1996). Forces and stresses in seam welded overlap joints derived from outer surface deformation. Engineering Fracture Mechanics 54, 743–750.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research and Technology, DaimlerChrysler AG, 70546, Stuttgart, Germany

    Shicheng Zhang

Authors
  1. Shicheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, S. Fracture mechanics solutions to spot welds. International Journal of Fracture 112, 247–274 (2001). https://doi.org/10.1023/A:1013588929709

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013588929709

Search

Navigation