Although there are different methods for measuring residual stress in a material. However, I would like to know the detailed procedure of measuring Residual stress through X - ray diffraction technique.
If you have access to a general service of X-ray diffraction, you may ask whether they have a specific equipment for measuring residual stresses. This kind of equipment incorporates the required software to do all calculation (as Amrit Raj Paul explains to you). This is my recommendation to get performant results.
Concerning the application of the Hooke's law, you have to pay attention to the potential anysotropy of your material, which eventually could not be negligible in the welded area.
As you have to work in reflection mode because the X-ray has only a limited deep penetration (except High-energy X-sources), you should properly prepare the surface of the sample in the area in which you will do the measurements. A good metalographic polishing should be required.
There is numerous techniques for measuring or calculate residual stress. Williamson Hall (WH) is a rather simply method that can give you a first look, however you can upgrade this aproximation with the so-called Modified Williamson Hall (MWH). Another method is the Warren Averbach (WA), this is mathematically more rigourous than WH and WHM.
Despite the availability of the WH and WA method I sugest you to measure it, the sin^2psi method (square sin of psi) is reliable and commonly used.
As Prof. Jose San Juan says, the limited depth penetration of laboratory X-rays makes the technique very susceptible to polishing induced stress, so special care is needed for sample preparation.
For more information, in the Noyan and Cohen book you'll find all the information that you are looking (DOI: 10.1007/978-1-4613-9570-6)