Stress Distribution and Tomographic Profiling with Energy Dispersive X-Ray Scattering

Abstract

Two novel and potentially powerful, x-ray scattering techniques for tomographic profiling of composite materials and for profiling residual strain variation, versus depth, in a specimen are presented. The techniques utilize a high intensity/energy “white” beam synchrotron source and monitor the energy dispersive scattering from a fixed micro-volume as the specimen is scanned through it. The tomographic profiles based on the net scattered intensity and exploiting absorption coefficient/scattering-power variations, can be contrast enhanced by selectively monitoring scattering from specific crystal structures in a composite material. The strain profiling technique is shown to chronicle the detailed internal the stress variation over several mm's of steel. The initial state residual stresses, the effect of a cantilever spring imposed external stress, and their interplay in elastic/plastic deformation are discussed.

In situ strain profiling of elastoplastic bending in Ti–6Al–4V alloy by synchrotron energy dispersive x-ray diffraction

“…2, involves the incident radiation scattering at a fixed angle 2 ͑3°in this study͒. [1][2][3][4] The energies, E, of the Bragg peaks are given by E = ͓d hkl sin͔͑͒ −1 , where d hkl is the interplanar spacing associated with the ͑hkl͒ reflection of interest. Here = 0.5hc, where h is Plank's constant and c is the speed of light.…”

“…In the conventional units, where d hkl is measured in Angstroms and E in keV, one has = 6.199 Å keV. [1][2][3][4][5][6][7][8] At a given position inside a specimen the value of an interatomic spacing ͑d͒, as determined from the energy ͑E͒ of a given Bragg line, can be used to determine the elastic strain value e = ͓͑d −…”

“…At the small angle used, the total length of the GV along the x 2 direction is approximately ͑d i + d s ͒ / sin͑2͒. 1 In this experiment the d s value was set larger than d i to extend the GV in the x 2 -symmetry direction. This increases the scattered signal and the number of grains averaged over the GV.…”

“…The size of the diffraction/GV in strain profiling along x 3 was 60 m. The incident and diffracted beam collimation has also been discussed at length elsewhere. [1][2][3][4] Figure 4͑a͒ is a schematic of a typical tensile elastoplastic stress ͑͒ and strain ͑͒ curve ͑adapted from Ref. 21͒, which is used to define the terms used in the mechanical analysis presented herein.…”

“…Recent advances in synchrotron based high energy x-ray diffraction techniques allow one to nondestructively profile strain variations on a microscopic scale as a function of depth within bulk specimens and coatings. [1][2][3][4][5][6][7][8][9][10][11] Such diffraction techniques probe the changes in atomic interplanar spacings, and hence only the elastic portion ͑ e ͒ of the strain. The total elastoplastic strain ͑͒ is given by = e + p ͑1͒…”