Statistical representation of the microstructure and strength for a two-phase Ti–6Al–4V

The strength of materials is a function of the direction of the tensile/compression test, which means, the measured strength values can be different in different directions. This discrepancy comes from the microstructure and morphological features of the material which gives it an apparent anisotropy. This study uses a layered fast spherical harmonics formulation to represent the full map of two-point statistics for two-phase materials and the statistical distribution of the strength variation. In a recent study by the authors, the strength of a two-phase microstructure of Ti–6Al–4V alloy was measured. These microstructures were used in the current study for calibration and validation of the model and the statistical variation of strength. This approach is fast and efficient due to using spherical harmonics, furthermore, the model can output strength in all directions simultaneously rather than a single direction.