Abstract
One of the important problems respecting the X-ray method of stress measurement is concerned with the residual stresses induced in polycrystalline metals by plastic deformation. Many experimental results that have so far been obtained by the X-ray method show that the axial residual stresses induced by uniaxial deformation do not satisfy the macroscopic equilibrium over the cross section of a specimen. Moreover, the magnitude and sign of the fictitious stress depend upon the crystallographic plane that is to be used to diffract the X-ray beam. For example, the axial residual stress of a specimen of α-iron deformed in tension is approximately in equilibrium if measured with respect to {211} by Cr-Kα radiation. On the other hand, if measurements are made with respect to {220} by Fe-Kα, the residual stress distribution will not satisfy the equilibrium giving a fictitious tensile stress. A fictitious compressive stress will be obtained if measurements are made with respect to {310} by Co-Kα.
Since the lattice spacing is taken as gage length when measurement of stress is made by the X-ray method, the two following factors are considered to account for the above-mentioned fictitious stresses.
(1) The lattice strain of each crystal constituting a polycrystalline aggregate is inevitably influenced, so far as compatibility must be satisfied, by the elastic and the plastic deformation behavior of the surrounding crystals.
(2) The information to be obtained by the X-ray method is restricted to those select crystals which are correctly in the direction that will satisfy Bragg's condition.
The first fundamental interpretation of the fictitious residual stress phenomenon was proposed by Greenough. He introduced a relationship between the microscopic residual stress resulting from uniaxial tension and the residual lattice strain measured by X-rays. However, his theory does not seem to be adequate for such metals as α-iron since he assumes elastic isotropy, and the theory is based on Taylor's theory, in which plastic anisotropy is not considered.
In the present investigation, the fictitious residual stress induced in polycrystalline α-iron by uniaxial plastic deformation was theoretically interpreted considering elastic and plastic anisotropy. The analysis is based on the following assumptions:
(1) Each crystal constituting an aggregate under plastic deformation is of equal strain.
(2) In the loading condition, the stress in each crystal corresponds to the flow stress in the multiple slip region of a single crystal with the same orientation.
(3) The elastic constants of a polycrystalline aggregate are calculated from those of the constituent crystals according to the Reuß or the Voigt model.
The theoretical result thus obtained will efficiently elucidate the published experimental results qualitatively.
