The Principle of Strain Reconstruction Tomography: Determination of Quench Strain Distribution from Diffraction Measurements

The evaluation of residual elastic strain within the bulk of engineering components or natural objects is a challenging task, since in general it requires mapping a six-component tensor quantity in three dimensions. A further challenge concerns the interpretation of finite resolution data in a way that is commensurate and non-contradictory with respect to continuum deformation models. A practical solution for this problem, if it is ever to be found, must include efficient measurement interpretation and data reduction techniques. We describe the principle of strain tomography by high-energy X-ray diffraction, i.e. reconstruction of the higher dimensional distribution of strain within an object from multiple scans in lower dimensions, and illustrate the application of this principle to a simple case of reconstruction of an axisymmetric residual strain state induced in a cylindrical sample by quenching. The underlying principle of the analysis method presented in this paper allows generalisation to more complex situations.