Photon Factory Activity Report 2004 #22 Part B (2005)
Instrumentation and Technique

16A1/2002S003

Modification of projection-type X-ray microscope for stress imaging
Kenji SAKURAI* and Mari Mizusawa
National Institute for Materials Science, Sengen, Tsukuba, Ibaraki 305-0047, Japan
Introduction
It is extremely important to evaluate mechanicalfailures of infrastructure materials using non-destructive
techniques. One of the most promising ways is stressanalysis by means of the X-ray diffraction techniqueusing the sin2ψ-2θ procedure, which is the measurementof the Bragg peak position (2θ) as a function of thesample orientation (ψ) [1]. Since the technique gives
only an average value, one has to carry out an XY scan of
the sample in order to obtain the stress distribution. Thisis not practical because of the very long measuring time.
This report describes the modification of the
instrumentation of a projection-type X-ray microscope [2],which is a tool for efficient imaging.
Theoretical background
X-ray stress analysis is based on the use of latticespacing as a strain gauge. For each inclination of thesample, defined by two angles ϕ and ψ, the strain ε in thedirection normal to the diffraction planes, is related to thecorresponding lattice spacing d, which is linked directly
to the diffraction angle 2θ by Bragg's law. The relation
between the strain ε and the stress tensor components isthen derived through a micro mechanical approach to thematerial. Using the equilibrium conditions of the freesurface, i.e., plane stress, the following equation, called
the sin2ψ law, is obtained:E ∂(ε φψ )σx =(1)
1 + ν ∂(sin 2 ψ )where σ, E and υ are the stress of interest, Young’s
modulus and Poisson's ratio. So far, most experiments
have been performed with a fixed X-ray wavelength. Thismeans that the 2θ angular scan should be performed todetermine the diffraction angle for each ψ angle, which
has been usually scanned by changing the inclination of

the sample to the incident X-ray beam. On the other hand,
one might notice that equation (1) can be rewritten as∂λE 1
σx =(2)
1 + ν λO ∂ (sin 2 ψ )where λ and λ0 are the X-ray wavelengths giving Bragg
peaks at certain diffraction angles, for the cases with andwithout strains, respectively. This indicates that the stressis given by the incident X-ray wavelength scan to find theBragg peaks at certain several detector angular positions(2θ), which can control ψ even when the sample iscompletely fixed.
Modification of instrumentation
2D diffraction imaging can be performed even without
an XY scan of the sample, when a projection-type X-ray
microscope is employed. Quite a wide incident X-ray
beam (typically, 8mm(H)×0.2mm(V)) arrives at quite
small angle incidence, around 1 deg., to irradiate thewhole view area of the sample. The detector is a CCD
camera with an internal collimator plate. The camera canbe fixed, as diffraction peaks are obtained by amonochromator scan instead of a normal angular scan ofthe detector. One can see which parts of the sample
become bright when the X-ray wavelength comes acrossthe expected Bragg condition.
Figure 1 shows a schematic view and also photos of theprojection type X-ray microscope modified for residual
stress imaging. So far, the experiments have been usually
done at around 90 deg, which has the advantage ofminimizing the distance from the sample surface to thedetector. The main modification of the instrumentation
made here is to fit the microscope for variable 2θ angles(60~120 deg). The distance of the camera needs to belengthened to avoid mechanical interferences with thesample when the angle diverges from 90 deg.
References[1] V.Hauk: "Structural and ResidualStressAnalysis
byNondestructiveMethods", Elsevier, Amsterdam (1997);
I.C.Noyan, J.B.Cohen, "Residual Stress Measurement
byDiffraction
andInterpretation", Springer-Verlag, NewYork (1987).
[2] K.Sakurai and M.Mizusawa, Photon
Factory Activity Report 2003, #21, p.260(2004).
*sakurai@yuhgiri.nims.go.jp

Figure 1 Projection-type X-ray microscope specifically modified for stress imagingexperiments. The experiment consists of repeated exposures during the incident X-ray
wavelength scan. The scans are performed for different ψ, i.e., 2θ angle. The incident
angles of X-rays are fixed the whole time.

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