## 1 Introduction  
The importance of mode III in crack displacement has been extensively documented in the literature [1, 2, 3, 4, 5, 6, 7] and its consequence in cylindrical components [8]. Literature results demonstrated [2, 4, 9, 10] that out-of-plane displacements are present, even when direct out-of-plane loading is not applied, generating a crack driving force in the out-of-plane direction. Furthermore, [PERSON] [11] recently noted the lack of literature dedicated to mode III. [PERSON] et al. [12] found that including mode III (along with Poisson's ratio and T-stress) enhanced crack initiation prediction. SIFs can be calculated from displacements obtained through numerical simulation (such as XFEM or DBEM) using weight functions, virtual crack (VCC), J, or the interaction integral technique from a geometric factor (using ASTM or SIF manuals).  
From data acquired through experimental methods, clip gauges are known for their reliable measures and low cost, but in the case of kinked cracks, the displacements given by the COD gauge may not adequately describe the stress field on the crack tip. However, at the time of writing this paper, there are no clip gauges that can simultaneously measure the crack's opening and sliding displacements. One would require clip gauges in addition to a second technique, like strain gauge or extensometers. Nevertheless, one would require separate setups for opening and sliding. The digital image correlation (DIC) technique provides independent full-field displacement measurements in 2D or 3D with the use of two or more cameras. Even for a larger budget, it has become standard equipment in many laboratories. Therefore, such kinds of readings are readily available. Therefore, one can use such experimental measurements and fit them to a stress function; the J integral is a robust method to calculate SIF [13], but one needs to establish strain and stresses before using it, and the VCC is preferred for delamination prediction. Additionally, one needs a method to decompose the J integral values as it gives the total energy used to create a new surface crack regardless of direction [13]. Moreover, despite results demonstrating that mode III displacements appear even when no direct out-plane-loading is applied, there is no robust method to calculate SIF mode III using full-field experimental displacements. Therefore, disregarding mode III can lead to lower equivalent SIF [14], uncertainty in 3D crack initiation and propagation [5], or fracture toughness overestimation [15].  
On the other hand, many schemas have been devised to produce mode III on sample coupons such as tubes and cylinders under torsion [7], rotated beams [16; 17], inclined cracks [18; 19; 20], modified Brazilian disk [21; 22], and modified Arcan [23] among others. A review of some testing fixtures for mode III can be found in [15; 24]. Therefore, the importance that the community gives to testing samples under out-of-plane displacement can be seen. All these methods, along with full-field independent displacements, such as the ones provided with the DIC technique, create the need for a robust method to calculate SIF mode III. The paper shows a scheme to fit full-field displacement fields to [PERSON] equations in mode III and how to solve them with the least squares method (LSM).