13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- number of about 25 sorts of ferrous materials and their heat-treatment conditions in the present stage. As a result, it is found that the equation is materialized with less than 10% of error. 5. Conclusions (1) A fatigue strength diagram is formulated and characterized as a function of the equivalent cyclic stress ratio (REQ-ratio). The REQ-ratio is derived from a hypothesis of cyclic plastic adaptation that reflects micro-mechanical behavior of a fatigue slip band. (2) The graphic method estimating REQ-ratio based on the hypothesis of the plastic adaptation is developed in the present paper. REQ-ratio materializes a similitude relation between the fatigue strength diagrams of the notched and un-notched specimen in the case where the notch depth is comparatively large size of mm-order (where the notch size effect is negligible). It means that REQ-ratio can be applied as a main variable to the formulation of the fatigue strength diagram. (3) The notch behavior is characterized and mapped by making the notch root radius and depth into variables. The notch size effect is systematically considered on the basis of the notch behavior map and the size effect factor is proposed for each of the fatigue strength σw1 and σw2 . (4) The formulation of the fatigue strength diagram can be extended to the case of the extremely small size notch, such as the depth of 10 and 100 µm-order, where the size effect is dominant, and finally the generalized equations expressing the fatigue strength diagrams are proposed. These equations are applied to regression analyses on fatigue data of practically used metallic materials. As a result, it is found that the equations are materialized with less than 10% of error. References [1] H. Matsuno, Y. Mukai, A stress parameter for correspondence between notched and un-notched specimen fatigue data: strength of fatigue macro-crack initiation at a notch root in plates and round-bars, Proc. APSCFS & ATEM'01, JSME-MMD, Oct. 20-22, 2001, JSME No. 01-203, 394–399. [2] U. Essmann, U. Gösele, H. Mughrabi, A model of extrusions and intrusions in fatigued metals, I. Point-defect production and the growth of extrusions, Phil. Mag. A, 44-2 (1981) 405–426. [3] E.A. Repetto, M.A. Ortiz, A micromechanical model of cyclic deformation and fatigue-crack nucleation in f. c. c. single crystals, Acta Materialia, 45 (1997) 2577–2595. [4] J. Polák, J. Man, K. Obrtlik, AFM evidence of surface relief formation and models of fatigue crack nucleation, International J. Fatigue, 25 (2003) 1027–1036. [5] G. Sines, Failure of materials under combined repeated stresses with superimposed static stresses, Tech. Note 3495, National Advisory Committee for Aeronautics, Washington, DC, (1955). [6] D. Taylor, A Mechanistic Approach to critical-distance methods in notch fatigue, Fatigue Fract. Engng Mater. Struct., 24 (2001) 215–224. [7] H. Kitagawa, S. Takahashi, Fracture mechanics approach to very small fatigue crack growth and to the threshold condition, Trans. JSME. A, 45, 399 (1979) 1289–1303. [8] H. Matsuno, A new interpretation of notch-sensitivity in fatigue of metals, Proc. 9-th International Fatigue Congress, May 14-19, 2006, Atlanta, Georgia, USA. [9] Y. Murakami, M. Endo, A geometrical parameter for the quantitative estimation of the effects of small defects on fatigue strength of metals, Trans. JSME, A, 49, 438 (1983) 127–136. [10]H. Nisitani, M. Endo, Unifying treatment of notch effects in fatigue, Trans. JSME, A, 51, 463 (1985) 784–789.
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