13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 4. Conclusions Two three-parameter descriptions for the three-dimensional (3D) crack-tip stress fields have been introduced. The three-parameter solution K–T–Tz is developed to describe the linear elastic crack-tip stress state, and the J–QT–Tz is to elastic-plastic crack-tip field. The comparisons of the three-parameter solutions K–T–Tz, J–QT–Tz with the corresponding two-parameter solutions K-T, J–Q and single-parameter solutions K and HRR are presented. It is shown that the three-parameter approaches K–T–Tz, J–QT–Tz can describe the 3D stress fields effectively. Acknowledgments The work is supported by the Fundamental Research Funds for the Central Universities (No. NS2012126), Aviation Science Foundation Project (No. 2010ZA52005), Natural Science Foundation of China (No.50805079). References [1] D.M., Clatterbuck, D.C., Chrzan, J.W., MorrisJr., The influence of triaxial stress on the ideal tensile strength of iron. Scripta Mater. 49 (2003) 1007–1011. [2] W., Guo, Recent advances in three-dimensional fracture mechanics. Key Eng. Mater. 183 (2000) 193–198. [3] G.R., Irwin, Fracture. Handbuch der Physik, 6. Springer-Verlag, Heidelberg, 1958, pp. 551–590. [4] J.W., Hutchinson, Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16 (1968) 13–31. [5] J.R., Rice, G.F., Rosengren, Plane strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids 16 (1968) 1–12. [6] M.L., Williams, On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24 (1957) 109–114. [7] C., Betegon, J.W., Hancock, Two-parameter characterization of elastic–plastic crack tip fields. J. Appl. Mech. 58 (1991) 104–113. [8] N.P., O’Dowd, C.F., Shih, Family of crack-tip fields characterized by a triaxiality parameter—I. Structure of fields. J. Mech. Phys. Solids 39 (1991) 989–1015. [9] N.P., O’Dowd, C.F., Shih, Family of crack-tip fields characterized by a triaxiality parameter—II. Fracture applications. J. Mech. Phys. Solids 40 (1992) 939–963. [10] Y.C., Li, Z.Q., Wang, High-order asymptotic field of tensile plane-strain nonlinear crack problems. Sci. Sin. A 29 (1986) 941–955. [11] Y.J., Chao, S., Yang, M.A., Sutton, On the fracture of solids characterized by one or two parameters: theory and practice. J. Mech. Phys. Solids 42 (1994) 629–647. [12] C., She, W., Guo, The out-of-plane constraint of mixed-mode cracks in thin elastic plates. International Journal of Solids and Structures 44 (2007) 3021–3034. [13] W., Guo, Elastoplastic three-dimensional crack border field—I. Singular structure of the field. Eng. Fract. Mech. 46 (1993) 93–104. [14] W., Guo, Elastoplastic three-dimensional crack border field—II. Asymptotic solution for the field. Eng. Fract. Mech. 46 (1993) 105–113. [15] W., Guo, Elastoplastic three-dimensional crack border field—III. Fracture parameters. Eng. Fract. Mech. 51 (1995) 51–71. [16] J., Zhao, W., Guo, C., She, B., Meng. Three dimensional K-Tz stress fields around the
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