Here, on the assumption that the classical grain boundary segregation theory would be applied to the case of this study, namely, carbon in ferritic steel, the Hall-Petch coefficient was compared with the concentration of carbon at grain boundary. According to the MacLean's theory, 17) solute carbon concentration segregated at ferrite grain boundary at 973 K is calculated by following equation:In this equation, [at%C], Q and R are the total carbon concentration in solid solution, the activation energy of carbon for grain boundary segregation and the gas constant, respectively. As for the value of Q, 78 kJ/mol estimated by Grabke 18) was taken. Figure 6 shows relationship between k y and segregated carbon content calculated by Eq. (3). k y value tends to increase linearly with increasing segregated carbon content, which suggests that grain boundary segregation of interstitial alloy elements significantly prevents the yielding of ferritic steel. Only 60 ppm carbon causes marked grain boundary segregation to 80 at%, resulting in the enlargement of the k y from 100 (in IF-steel) to 550 MPa · mm 1/2 . The solubility of carbon was reported to be approximately 60 ppm even at ambient temperature 19) in Fe-C binary alloy. Therefore, it could be understood that the similar k y values, around 600 MPa · mm 1/2 , have been reported in lots of previous studies on grain refinement strengthening of ferritic steels except for IF-steels. On the other hand, it is known that nitrogen has less tendency to cause grain boundary segregation in steel, as compared to carbon. [20][21][22] This agrees well with the experimental results that k y is hardly influenced by nitrogen. The enlarged k y by nitrogen mentioned above might be due to the large amount of solute nitrogen in austenite matrix leading to the high concentration of nitrogen at grain boundary even though the segregation coefficient is small.
Conclusions(1) IF-steel has a low Hall-Petch coefficient of approximately 100 MPa · mm 1/2 . The Hall-Petch coefficient of ferritic iron monotonously increases with increasing solute carbon content, and it levels off at 550-600 MPa · mm 1/2 when the solute carbon content reaches 60 ppm. On the other hand, the solute nitrogen hardly affects the Hall-Petch coefficient.(2) The increase in Hall-Petch coefficient by solute carbon seems to be derived from the grain boundary segregation of carbon atoms. The small effect of solute nitrogen on Hall-Petch coefficient could be explained by the less tendency of nitrogen atoms to cause grain boundary segregation. ISIJ, Tokyo, Japan, (1991), 762. 12) V. G. Gavriljuk, H. Berns, C. Escher, N. I. Glavatskaya, A. Sozinov and Yu. N. Petrov: Mater. Sci. Forum, 318-320 (1999)