In the residual stress measurement with X-ray, the measured lattice strain εψ is not proportional to sin2ψ when a steep stress gradient exists in the surface layer, because the X-ray penetrating depth becomes shallower with increasing ψ. This means that the traditional sin2ψ method, which is based on the linearity of εψ-sin2ψ diagram, is hardly adoptable for such cases. The purpose of the present work was to find out a method of analysing such a state of residual stress precisely.
Two methods were used to analyse the diffraction profile: The first is the Warren's method including the“powder pattern power theorem”and the theory of“small coherent domains and strains”. The second is the sum-up method of each sub-profile coming from thinly divided layers and having a normal distribution pattern of which location and standard deviation relate to macro- and micro- strains, respectively. From these analyses, it was found that the diffraction profiles from the layer with steep gradient of residual stresses became more asymmetric with increasing gradient and with decreasing breadth of diffraction line. It was noticed further that the strains calculated from the peak positions and the medians of half width of profiles began to deviate essentially from those calculated from the centroids as the stress gradient increased.
The physical meaning of the weighted averaging method was studied in detail and it was concluded that in this method a more precise result would be obtained when the position of centroid was used instead of the peak or the median of half width of the diffraction profile.
