The paper proposes and tests an approach to determine the stress intensity factors (SIF) of cracks subjected to mode III using full-field displacements as opposed to the crack opening displacement (COD) method, which uses only two data points. The proposed scheme fits displacement data into Williams’ series for cracks, solving the equations using the over-deterministic Least Squares Method (LSM). The method is tested in tubes with through-cracks under axial and cyclic torque loading, and both proportional and non-proportional loading. The Digital Image Correlation (DIC) technique measured the displacement fields, and an approach is presented to address the curvature error in the tube samples. The experimentally determined SIF and SIF ranges with the proposed method are compared with respective values found using COD equations showing a pronounced nonlinear variation. It is concluded that for most, both methods agree, and for the LSM, the number of expansion terms in Williams’ series seems to make no difference, exhibiting less noisy results than the COD method and effectively addresses nonlinear variations in SIF calculations across different loading conditions, ultimately enhancing the understanding of crack behavior under mode III loading.