The Influence of Alloying Elements on Impurity Induced Grain Boundary Embrittlement
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I.
INTRODUCTION
RECENTLY, Stark and Marcus ~have developed a thermodynamic model which describes the effect of impurity (I) grain boundary segregation on the grain boundary cohesive energy. The development of the model was based upon a detailed nonequilibrium thermodynamic analysis of the grain boundary segregation process. This nonequilibrium model directly and simply provides a numerical estimate of the grain boundary cohesive energy change associated with impurity grain boundary segregation. However, it has been recognized that understanding the role of alloying elements (A) of the transition series is of great importance to predict and control grain boundary embrittlement in Fe alloys since the complex grain boundary embrittlement behavior is often encountered with the presence of alloying elements in Fe alloys. The effect of alloying elements on grain boundary embrittlement can be classified into the direct effect and the indirect effect. The indirect effect arises from the grain boundary cohesive energy change induced by the change in impurity grain boundary segregation due to the existence of the I-A interaction in Fe alloys. The I-A interaction and its effect on impurity grain boundary segregation has been rationalized by the Guttmann model. 2 However, the direct effect of alloying elements which arises from the grain boundary cohesive energy change induced by their own grain boundary segregation has as yet to be considered. The main purpose of this study is to investigate the combined direct and indirect effect of alloying elements on impurity-induced grain boundary embrittlement. Therefore, the nonequilibrium model will be extended to Fe-I-A ternary systems. This will be followed by the experimental study on high purity Fe-P, Fe-P-Mn, Fe-P-Mo, and Fe-P-W alloys for the evaluation of the extended model. In order to determine grain boundary strength, the method recently developed by Kameda et al. 3'4 will be adopted. D.Y. LEE is Senior Research Engineer with General Dynamics Corporation, P.O. Box 748, Fort Worth, TX 76101. E.V. BARRERA, Graduate Research Assistant, J.P. STARK, Professor, and H . L . MARCUS, H.L. Kent, Jr. Professor, are all with the Department of Mechanical Engineering, The University of Texas, Austin, TX 78712. Manuscript submitted September 13, 1983. METALLURGICAL TRANSACTIONS A
II.
THE EXTENDED NONEQUILIBRIUM MODEL
It is assumed in the development of the nonequilibrium model that the grain boundary ( G B ) region consists of the boundary (B) and boundary matrix interface ( B M ) regions as shown in Figure 1. Also, the thicknesses of these B and B M regions are assumed to be atomic in nature. The development of the extended model is presented in detail in Appendix B. The final result of the extended model can be expressed as: 6H oB = 6 H B + 6 H BM = 6HB, + 6H~,M - ("-H~ + H ~ - H v ~ ) 6 U ~ _
(m-~
+ I-1~ -
I-1~)6U~ t
[1]
Where 8H aB, 8H B, and 6H BMare enthalpy changes in GB, B, and B M during grain boundary segregation, respectively, ~ and "HAM are the partial molar mixing en
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