To observe the size effect which cannot be predicted with conventional plasticity theories, Fig. 2 compares the equivalent plastic strain contours for different values of KI (2.27, 7.43 and 10 MPa m1/2). In all cases, differences in contour values are observed. These differences are due to the strain gradient term introduced into the constitutive law via Eq. (7). By comparing the results observed in Fig. 2, it is clear that strain gradient plasticity predicts smaller and narrow plastic zone sizes at the crack tip, for stress intensity factor values smaller than 10 MPa m1/2. CONCLUSIONS Inclusion of the influence of the plastic strain gradient in the flow stress (“strain gradient dependent plasticity”) predicts a fatigue threshold of the correct order of magnitude ('Kth 10 MPam1/2 for steel) without recourse to any other possible contributon to deviatons from the Paris’ law at low 'KI values (crack closure, etc.). REFERENCES 1. Ocaña, I. and Gil Sevillano, J. (1998). J. Phys. IV France 8, 129. 2. Fleck N. A., Muller G. M., Ashby M. F. and Hutchinson J. W. (1994) Acta Metall. Mater. 42, 475. 3. Fleck, N.A. and Hutchinson, J.W. (1997). Advances in Appl. Mech. 33, 295. 4. Narutani, T. and Takamura, J. (1991). Acta Metall. Mater. 39, 2037. 5. Meakin J. D. and Petch N. J. (1974). Phil. Mag. 30, 1149. 6. Dingley D. J. and McLean D. (1967). Acta Metallurgica, 15, 885. 7. Ashby M.F. (1970). Phil. Mag. 21, 399. 8. Mecking H. and Kocks U.F. (1981). Acta Metallurgica 29, 1865. 9. Hutchinson J.W. (2000). Int. J. Solids Structures 37, 225. 10. Estrin Y, (1996). In: Unified Constitutive Laws of Plastic Deformation, pp. 69-106, Krausz A.S. and Krausz K. (Eds.), Academic Press, New York. 11. Estrin Y. (1998). Journal of Materials Processing Technology 80-81, 33. 12. Gil Sevillano J., Van Houtte, P. and Aernoudt, E. (1980). Prog. Mat. Sci. 25, 69. 13. Kocks, U.F. (1976). J. Engng. Mater. Tech. 98, 76. 14. Modelling of mechanical properties and local deformation of high strength multi-phase steels. ECSC Steel RTD Annual Report, March 2000.
RkJQdWJsaXNoZXIy MjM0NDE=