Abstract
This paper describes the results of a series of finite element analyses performed to investigate the suitability of the coefficient of the J-CTOD relationship, dn, as a parameter to quantify constraint. Analyses have been performed which employ the modified boundary layer solution to demonstrate the relationship between the T-stress, Q and dn parameters. Analyses have also been performed to analyse the effects of constraint in strength mismatched welded three-point bend specimens. These results are compared with predictions of constraint made using values of dn derived from slip-line field solutions. Material strength overmatching is shown to cause a significant loss in constraint, whilst undermatching increases constraint. On the whole, predictions of the effects of constraint from slip-line field solutions are shown to agree with the measured constraint levels obtained using the finite element method, although the results from highly undermatched joints are not as accurate as the others examined. This is shown to be due to the effect of the base material outside the weld on the crack tip stress fields. By employing a two-material idealisation of the modified boundary layer formulation, using elastic T-stresses to model the constraint due to the specimen geometry and the normalised load parameter, J/hσYw, to control the size of the plastic zone relative to the thickness of the weld material, it was possible to reproduce the complex stress fields encountered in each of the specimens.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ainsworth, R.A. and O'Dowd, N.P. (1995). Constraint in the failure assessment diagram approach for fracture assessment. Journal of Pressure Vessel Technology 117, 260-267.
Al-Ani, A.M. and Hancock, J.W. (1991). J-dominance of short cracks in tension and bending. Journal of the Mechanics and Physics of Solids 39, 23-43.
Anderson, T.L. (1989). Crack tip parameters for large scale yielding and low constraint configurations. International Journal of Fracture 41, 79-104.
ASTM Standard Test for JIc, A Measure of Fracture Toughness. Annual Book of ASTM Standards, E813-88, American Society for Testing and Materials, Philadelphia, USA, 1988.
Betegón, C. and Hancock, J.W. (1991). Two-parameter characterization of elastic-plastic crack tip fields. Journal of Applied Mechanics 58, 104-110.
Bilby, B.A., Howard, I.C. and Li, Z.H. (1992). Prediction of the first spinning cylinder test using ductile damage theory. Fatigue and Fracture of Engineering Materials and Structures 16, 1-20.
Burstow, M.C. and Ainsworth, R.A. (1995). Comparison of analytical, numerical and experimental solutions to problems of deeply cracked welded joints in bending. Fatigue and Fracture of Engineering Materials and Structures 18, 221-234.
Burstow, M.C. and Howard, I.C. (1996). Predicting the effects of crack tip constraint on material resistance curves using ductile damage theory. Fatigue and Fracture of Engineering Materials and Structures 19, 461-474.
Burstow, M.C. and Howard, I.C. (1997). Constraint effects on crack growth resistance curves of strength mismatched welded bend specimens. In Mis-Matching of Interfaces and Welds (Edited by K.-H. Schwalbe and M. Koçak), pp. 357-369. GKSS Research Center Publications, Geesthacht, FRG.
Burstow, M.C., Howard, I.C. and Ainsworth, R.A. (1998). The influence of constraint on crack tip stress fields in strength mismatched welded joints. Journal of the Mechanics and Physics of Solids 46, 845-872.
Edmunds, T.M. and Willis, J.R. (1977). Matched asymptotic expansions in nonlinear fracture mechanics-III. Inplane loading of an elastic perfectly-plastic symmetric specimen. Journal of the Mechanics and Physics of Solids 25, 423-455.
Hutchinson, J.W. (1968). Singular behaviour at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 16, 13-31.
Joch, J. and Ainsworth, R.A. (1994). Relationships between the J-integral and the crack tip opening displacement for stationary cracks in weldments at plastic collapse. Fatigue and Fracture of Engineering Materials and Structures 17, 1175-1185.
Joch, J., Ainsworth, R.A. and Hyde, T.H. (1993). Limit Load and J-Estimates for Idealised Problems of Deeply Cracked Welded Joints in Plane-Strain Bending and Tension. Fatigue and Fracture of Engineering Materials and Structures 16, 1061-1079.
Kirk, M. T. and Dodds, R. H. (1993). The influence of weld strength mismatch on crack-tip constraint in single edge notch specimens. International Journal of Fracture 63, 297-316.
Larsson, S.G. and Carlsson, A.J. (1973). Influence of non-singular stress terms and specimen geometry on smallscale yielding at crack tips in elastic-plastic materials. Journal of the Mechanics and Physics of Solids 21, 263-277.
Leevers, P.S. and Radon, J.C. (1982). Inherent stress biaxiality in various fracture specimen geometries. International Journal of Fracture 19, 311-325.
Li, Z.H., Pugh, A.C., Howard, I.C. and Yates, J. (1996). The assessment of cracks in welds between dissimilar materials - an application of the ductile damage model. Departmental Report, Department of Mechanical Engineering, the University of Sheffield.
Milne, I., Ainsworth, R.A., Dowling, A.R. and Stewart, A.T. (1988). Assessment of the integrity of structures containing defects. International Journal of Pressure Vessels and Piping 32, 32-104.
O'Dowd, N.P. and Shih, C.F. (1991). Family of crack-tip fields characterized by a triaxiality parameter - I. Structure of fields. Journal of the Mechanics and Physics of Solids 39, 989-1015.
O'Dowd, N.P. and Shih, C.F. (1992). Family of crack-tip fields characterized by a triaxiality parameter - II. Fracture applications. Journal of the Mechanics and Physics of Solids 40, 939-963.
O'Dowd, N.P. and Shih, C.F. (1995). Two-parameter fracture mechanics: theory and applications. Proceedings of the 24th National Symposium on Fracture Mechanics (Edited by J.D. Landes, D.E. McCabe and J.A.M. Boulet), ASTM STP 1207, pp. 21-47.
PD6493 (1991). Guidance on methods for assessing the acceptability of flaws in fusion welded joints. British Standards Institution, London.
Rice, J.R. and Rosengren, G.F. (1968). Plane strain deformation near a crack tip in a power-law hardening material. Journal of the Mechanics and Physics of Solids 16, 1-12.
Rooke, D.P. and Cartwright, D.J. (1976). A Compendium of Stress Intensity Factors, HMSO, London.
Sherry, A.H., France, C.C. and Goldthorpe, M.R. (1995). Compendium of T-stress solutions for two and three dimensional cracked geometries. Fatigue and Fracture of Engineering Materials and Structures 18, 141-155.
Shih, C.F. (1981). Relationships between the J-integral and the crack opening displacement for stationary and extending cracks. Journal of the Mechanics and Physics of Solids 29, 305-326.
Shih, C.F., O'Dowd, N.P. and Kirk, M.T. (1993). A framework for quantifying crack tip constraint. Constraint Effects in Fracture (Edited by E.M. Hackett, K.-H. Schwalbe and R.H. Dodds), ASTM STP 1171, pp 2-20.
Sun Jun. (1993). Stress triaxiality constraint and crack tip parameters. Engineering Fracture Mechanics 44, 789- 806.
TOMECH (1991). User's Guide. Department of Mechanical and Process Engineering, the University of Sheffield.
Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24, 109-114.
Zhang, Z.L., Hauge, M. and Thaulow, C. (1996). Two-parameter characterization of the near tip stress fields for a bi-material elastic-plastic interface crack. International Journal of Fracture 79, 65-83.
Rights and permissions
About this article
Cite this article
Burstow, M., Howard, I. & Ainsworth, R. The Effect of Material Strength Mismatching on Constraint at the Limit Load of Welded Three-Point Bend Specimens. International Journal of Fracture 89, 117–142 (1998). https://doi.org/10.1023/A:1007480827982
Issue Date:
DOI: https://doi.org/10.1023/A:1007480827982