抄録
In the previous papers, the authors have reported on the change in half-value breadth of diffraction line of (200), (310), (211) and (110) atomic planes in fatigue process by using CoKα radiation. It was found that the change in half-value breadth of diffraction line of (200) atomic plane was the largest, while that of (110) plane was the smallest, although general mode of the change in half-value breadth was quite similar. At the same time we studied the changes in residual stress and microstructure during fatigue process, and we considered qualitatively, on the basis of the experiments, that the change in half-value breadth was correlated to the slip mechanism of crystal in fatigue phenomena.
In this paper, an interpretation is presented on the diffraction plane dependence of the change in half-value breadth, which is based on the idea that each crystal in the polycrystalline aggregates is particularly fitted for slip according to its orientation. In the discussion, it is assumed that the diffraction planes lie in parallel with the specimen surface according to the experimental condition of goniometer and that the X-rays diffracted by severely slipped crystals have large line broadening, while those by unslipped crystals remain as sharp.
The orientation factor μ is given by
μ=cosφcosα,
where, φ: the angle between slip plane normal and stress axis
α: the angle between slip direction and stress axis
In order to get the mean value of μ of an atomic plane with respect to a slip system, μ is intergrated with respect to λ, where λ is the angle of the direction of the stress axis to the orientation of each crystal, that is,
μ=1/2πΣni=1{∫λiλi-1μidλ},
where, λ0=0, λn=2π
Calculating μ of the atomic planes (200), (310), (211) and (110) with respect to each of the three slip systems {110}, {211} and {321}, and taking the maximum values of μ for each atomic plane, we have 0.482, 0.469, 0.460 and 0.435 for (200), (310), (211) and (110), respectively.
On the other hand, the values of μ have been obtained by the graphical method. The distribution of the orientation factor μ has been determined on stereographic projection by the other author. The geometrical orientation of probable diffraction plane can be determined on the same figure as a trace of orientation. Using this figure, we can determine the distribution of μ along the trace of orientation. From this, we decided the mean value of μ for the aforesaid atomic planes at 0.485, 0.486, 0.484 and 0.436 corresponding to (200), (310), (211) and (110) diffraction planes, respectively. μ values determined by both the methods of calculation and graphical procedure are tabulated, and it is found that μ values are very close between both the methods. After all, we see that μ of (200) plane is the largest and that of (110) plane is the smallest. It is expected, therefore, that μ is one of the important factors which affect the diffraction plane dependence of the change in half-value breadth during the fatigue process.
The above discussion is based on the observation of half-value breadth of diffraction lines from atomic planes parallel to the surface. It is probable that, if the above interpretation is right, the diffraction plane dependence for atomic planes not parallel to the surface would be different from the above observation. This has been proved by the experiment.
