Abstract
The paper presents a two-terms asymptotic analysis of the near-tip stress fields of sharp V-shaped notches having the bisector inclined with respect to remotely applied tensile stress. Due to their geometry, mixed-load conditions are present at the notch tip. The governing of equations result in a leading order system and a second order system. As known, one of the most significant characteristics of singular stress fields in nonlinear materials is that the solution for mixed-mode loading cannot be expressed as a linear combination of mode I and mode II solutions. When the included angle is greater than 90° (as it generally happens in most welded joints, for example) a satisfactory description of the stresses at the notch tip can be obtained by imposing boundary conditions of the symmetric type in the leading-order system, and boundary conditions of antisymmetric type in the second order system. Finally, simple expressions of the plastic Notch Stress Intensity Factors are reported for a particular geometry, with the aim to explicitly describe the influence of scale effect, nominal stress and material properties on the intensities of the asymptotic stress distribution under nonlinear conditions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atzori, B., Rossetto, E., Rossi, F. and Vaschetto, L. (1987) The fatigue limit of spot-welded lap joints. SAE Technical Paper series, No. 870640.
Atzori, B. Lazzarin, P. and Tovo R. (1999). From the local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints, Fatigue and Fracture of Engineering Materials and Structures 22, 369–382.
Betegon, C. and Hancock, J.W. (1991). Two-parameter characterization of elastic-plastic crack tip fields. ASME Journal of Applied Mechanics 58, 104–110.
Boukharouba, T., Tamine, T., Nui, L., Chehimi, C. and Pluvinage, G. (1995). The use of notch stress intensity factor as a fatigue crack initiation parameter. Engineering Fracture Mechanics 52, 503–512.
Champion, C.R. and Atkinson, C. (1991) A crack at the interface between two power-law materials under plane strain loading. Proceedings of the Royal Society of London A 432, 547–553.
Chen, D.H. and Ushijima K. (in press) Plastic stress singularity near the tip of a V-notch. International Journal of Fracture.
Duva, J.M. (1988). The singularity at tapex of a rigid wedge embedded in a nonlinear material. ASME Journal of Applied Mechanics 55, 361–364.
Duva, J.M. (1989). The singularity at the apex of a rigid wedge after partial separation. ASME Journal of Applied Mechanics 55, 361–364.
Gao, Y. and Lou, Z. (1990). Mixed mode interface crack in a pure power-hardening bimaterial. International Journal of Fracture 43, 241–256.
Hutchinson, J.W. (1968a). Singular behavior at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 16, 13–31.
Hutchinson, J.W. (1968b). Plastic stress and strain fields at a crack tip. Journal of the Mechanics and Physics of Solids 16, 337–347.
Kuang, Z.B. and Xu, X.P. (1987). Stress and strain fields at the tip of a sharp V-notch in a power hardening material. International Journal of Fracture 35, 39–53.
Lazzarin, P. and Tovo, R. (1996) A Unified Approach to the Evaluation of Linear Elastic Stress Fields in the Neighborhood of Cracks and Notches. International Journal of Fracture 78, 3–19.
Lazzarin, P. and Tovo, R. (1998). A Notch Stress Intensity Approach to the Stress Analysis of Welds. Fatigue and Fracture of Engineering Materials and Structures 21, 1089–1104.
Nui L.S., Chehimi, C. and Pluvinage G. (1994). Stress field near a large blunted tip V-Notch and application of the concept of the critical notch stress intensity factor (NSIF) to the fracture toughness of very brittle materials. Engineering Fracture Mechanics 49, 325–335.
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.
Ponte Castañeda, P. (1985). Asymptotic fields in steady crack growth with linear strain-hardening. Journal of the Mechanics and Physics of Solids 35, 227–268.
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.
Sharma, S.M. and Aravas, N. (1991). Determination of higher-order terms in asymptotic elastoplastic crack tip solutions. Journal of the Mechanics and Physics of Solids 39, 1043–1072.
Sharma, S.M. and Aravas, N. (1993). On the development of variable-separable asymptotic elastoplastic solutions for interfacial cracks. International Journal of Solids and Structures 30, 695–723.
Wang, T.C. (1990). Elastic-plastic asymptotic fields for cracks on bimaterial interface. Engineering Fracture Mechanics 37, 527–538.
Wang, T.J. and Kuang, Z.B. (1999) Higher order asymptotic solutions of V-notch tip fields for damaged nonlinear materials under antiplane shear loading. International Journal of Fracture 96, 303–329.
Xia, L. and Wang, T. (1993). Singular behavior near the tip of a sharp V-notch in a power-law hardening material. International Journal of Fracture 59, 83–93.
Xia, L., Wang, T. and Shih, C.F. (1993). Higher-order analysis of crack tip fields in elastic power-law hardening materials. Journal of the Mechanics and Physics of Solids 41, 665–687.
Yang, S., Yuan, F.G. and Martin Chiang, Y.M. (1996). Analysis of elastoplastic sharp notches. International Journal of Fracture 80, 59–71.
Yuan H. and Lin, G. (1994). Analysis of elastoplastic sharp notches. International Journal of Fracture 67, 187–216.
Yuan, F.G. and Yang, S. (1997). Crack-tip fields in elastic-plastic material under plane stress mode I loading. International Journal of Fracture 85, 131–155.
Zhang, N. and Joseph, P.F. (1998). A nonlinear finite element eigenanalysis of singular plane stress fields in bimaterial wedges including complex eigenvalues. International Journal of Fracture 90, 175–207.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lazzarin, P., Zambardi, R. & Livieri, P. Plastic notch stress intensity factors for large V-shaped notches under mixed load conditions. International Journal of Fracture 107, 361–377 (2001). https://doi.org/10.1023/A:1007633612060
Issue Date:
DOI: https://doi.org/10.1023/A:1007633612060