2.2. X-Ray diffraction technique
The sin2w method of X-ray diffraction technique is applicable for plane stress condition, and was therefore used to determine the magnitude of the residual stress to the depth of about 20 lm in the as-welded specimen.
The X-ray diffraction method for lattice strain measurement relies on well established Braggs law illustrated with Eq. (1), where k is the Xray wavelength, d is the interatomic lattice spacing and h is the diffraction angle (Cullity and Stock, 2001; Fitzpatrick et al., 2005).
k ¼ 2d sin h ð1Þ The technique measured elastic stress from diffraction elastic constants determined from measurable elastic strains, assuming linear elastic distortion occured in the contributing crystal lattice plane.
The lattice elastic strain for the reflections (hkl) at angle w are calculated from shift in interatomic lattice spacing (Fig. 2) caused by manufacturing process according to Eq. (2).
The lattice spacing, d is obtainable from wave length and diffraction angle, 2h according to Eq. (2).
The do is the stress free lattice spacing and the dw is the measured stressed lattice spacing (Fitzpatrick et al., 2005).
eðhklÞ
w
¼
d ðhklÞ
w
do
do
ð2Þ
In plane stress condition (where the in-plane stress, rz =0) and considering that biaxial stresses exist, then the tensile force which produces a strain along X direction will have a lateral effect consistent with Hooke’s law and the ratio of transverse to longitudinal strains defines the Poisson ratio, t according the Eq. (3)
The elasticity theory for an isotropic solid shows that the strain along the angle, w could be obtained from Eq. (5).
The Eq. (6) enables the calculation of the stress in any chosen direction from the lattice spacings determined from two measurements, made in a plane normal to the surface and containing the direction of the stress to be determined.
The portable diffractometer used for X-ray diffraction was Proto residual stress analyser. The diffractometer uses Croto
computer software for data processing and analysis of results.
It used Cr Ka2 radiation, which has wavelength of 2.2897 A ° as X-ray anode.
The diffraction angle of the radiation was 156.1. Body Centre Cubic lattice and crystallographic planes, {211} were used for martensitic stainless steel specimen.
Transverse residual stresses at six different points across weld were considered for measurement.