Depth-resolved stress measurement by x-ray powder diffraction tomography

Currently, two major categories of non-destructive, x-ray based methods exist for measuring depth-resolved stress in poly-crystalline materials. But both involve rather complex setups and suffer from anisotropic gauge volumes with aspect ratios of 1:10 or worse. An alternative approach utilizes a pencil beam and x-ray powder diffraction for tomographic reconstruction of local strain and stress tensor components, achieving a more favorable aspect ratio of 1:1. In 2015, it was mathematically demonstrated that using diffraction data from six points on a single diffraction ring, combined with corresponding sample rotations, allows the tomographic reconstruction of the six strain tensor components. However, it was noted that this idea is experimentally challenging and left open the possibility of using fewer rotation axes.

In our presentation, we will demonstrate that employing a single rotation axis and eight segments on two diffraction rings provides sufficient constrains for the tomographic reconstruction of the six strain and stress tensor components. We have used iterative gradient descent to minimize an appropriate cost function, which includes x-ray elastic constants. We tested this innovative approach using control and shot-peened martensite samples at the ID11 beamline of the ESRF Synchrotron Radiation Facility in Grenoble, France. The results showcase the validity of this approach with achieved stress sensitivities of 20 MPa. The influence of photon shot noise and parallax at the detector will be discussed.

Stress tensor tomography utlizes a comparatively simple setup that is compatible with many existing beamlines, which demonstrates its high potential for applications in materials science.