Estimation of elastic stiffness ratio c12/c44 and anisotropy parameter ai in the steels with bcc structure

Abstract

In the dislocation characterization by the modified William-son-Hall method, elastic stiffness ratio cl2/c44 and anisotro-py parameter Ai (=2c44/(c11-c12)) are important parameters to determine the contrast factor. In order to determine the values of elastic stiffness cij we need the information of Young's modulus E∗, shear modulus G∗ in poly crystal, and Young's modulus of single crystal; E100, E110 E111. The values of E∗ and G∗ are experimentally obtained by the resonance method. However, it is not so easy to fabricate single crystal, especially for practically used metals in which many alloying elements are contained. Therefore, we need to estimate the values of E100, E110, E111 in some way. In this paper, the following equations were proposed to estimate these values for the steels with bcc structure. E100 = 0.647 x E∗ Eno = 1.079 x £∗ Em = 1.387 x E∗ Hie coefficient in each equation was determined by the average value of Em/E∗ in pure iron. In the steels with bcc structure (E∗=206 GPa), it was confiiined that c12lc44 and A1 are given by the following equations as a fimction of Poisson's ratio v. c12/c44 =-1.466 + 8.887 x v Ai = 2.885-1.602 x v As a result, == 1.11 and .4,^2.42 are applicable for the modified Williamson-Hall method under the condition; v=0.29.