d has a relationship with ψ

Transcription

1 Principle of X-Ray Stress Analysis Metallic materials consist of innumerable crystal grains. Each grain usually faces in a random direction. When stress is applied on such materials, the interatomic distance of the crystal lengthens or diminishes. The variation of this crystal plane spacing d has a certain relationship with the angle ψ which is the angle made by the normal of the specimen surface and that of the crystal plane. X-ray stress measurement systems measure this variation and calculate the stress. d has a relationship with ψ 1

2 Bragg Law The Bragg law defines the relation of diffraction of X-rays by a crystal grating as follows. nλ = 2d sinθ where λ is the wavelength of X-rays, θ is the diffraction angle. Stress Calculation With measuring variations of θ made by changing various angles of ψ, the stress σ can be calculated from the following equation. (2θ ) σ = K (sin 2 ψ ) where K is called stress coefficient which is determined according to the material. In other words, by plotting 2θ values measured at varied ψ angles on 2θ-sin 2 ψ diagram, the inclination can be obtained. When this inclination is multiplied by K, the residual stress value is obtained. 2

3 Principle of X-ray stress measurement Measurement example of residual stress 3

4 Example of 2θ -sin 2 ψ line diagram Features of X-Ray Stress Measurement Measuring residual stress non-destructively Very good correspondence of the measured value with that obtained by the mechanical method (strain gauge method) Employment of the parallel X-ray beam geometry permits sample alignment with ease. The stress measured is located about 10 μm deep from the surface. Stress distribution in the depth direction can be measured with high accuracy. Local residual stress can be measured. Surface treatment of samples is important Computer-aided automatic operation Computer-aided calculation and analysis 4

5 Moiré interferometry Two beams of coherent light are used to illuminate the specimen grating obliquely at symmetrical incident angles ±α. Reference grating The two beams interfere, creating a reference grating in the zone of their intersection. This reference grating is called a virtual reference grating, because no real physical reference grating is present. The frequency of the virtual reference grating, f r, is given as f r = (2/λ) sin α λ is wavelength of the light source α is the incident angle of the light beams 5

6 Specimen grating The specimen grating is firmly bonded to the specimen. When loads are applied to the specimen, the surface deformation is transferred to the grating with high fidelity. The deformed specimen grating and the virtual reference grating interact to form a moiré pattern, which can be viewed and photographed using the camera. In moiré interferometry, the initial frequency of the specimen grating, f s, is half that of the virtual reference grating, i.e., f s = f r /2 The reference grating controls the sensitivity of the measurements. Moiré fringes The specimen grating and the virtual reference grating interact to form a moiré pattern. The interaction can produce the U-displacement and V- displacement fields. They represent the in-plane displacement of every point on the specimen surface as contour maps of equal displacement fringes. V field U field 6

7 Displacement analysis For each point in the fringe pattern U= N x /f r V = N y /f r U and V are components of the displacement in the x and y directions. N x and N y are fringe orders when lines of the reference grating are perpendicular to the x and y direction and f r is the frequency of the reference grating; f r =2400 lines/mm is typical. The fringes orders are determined either manually or with the aid of digitizing techniques. Strain analysis For strain analysis, relative displacements are of interest rather than absolute displacement. Once the fringes are assigned a fringe order, the displacement map has been constructed and engineering strains may be determined from the strain-displacement relations as follows: U 1 Nx V 1 Ny ε x = = [ ] εy = = [ ] x f x y f y U γxy = y V + x 1 Ny = [ f x N + y x ] 7