## 5 Results and Discussion
### Discussion  
It has been argued [4; 6; 7; 16; 42; 43] that leaving \(K_{III}\) out of \(K_{eq}\) may lead to an imprecise crack path and crack initiation [12]. However, when using full-field measurement nonlinearities, such as fatigue-induced plasticity, crack flank interlocking, rugosity, and trapped debris are already accounted for [7; 31]. In these cases, including full-field measurements allows the capture of such a degree of plasticity. This means these SIFs could not be calculated from numerical simulations [44]. The proposed method captures the full extent of SIF and SIF ranges. So, in that sense, SIFs are deemed as effective. However, negative \(K_{I}\) values do not make physical sense. For negative relative displacements to occur, the crack lips would need to penetrate each other, which is physically impossible. Figures 6a and 7a show a strong nonlinearity between the loading and unloading paths in mode I. One differential aspect of the applied axial load is the full inversion. So, one might need to pay close attention so as not to incorrectly interpret it as a negative \(K_{I}\) value instead of a SIF range. So, the growing negative \(K_{I}\) values shown in sample R-030 under negative load show a limitation of the proposed method and can be interpreted as crack lips touching each other. However, for sliding modes II and III, the negative sign indicates the relative displacements change directions. According to Equation (9), such  
Figure 8: R-030 (in-phase tension–torsion) results comparison between COD and LSM methods: (a) \(K_{I}\), (b) \(K_{II}\), (c) \(K_{III}\). direction provides the direction of the crack kinking angle [25]. It is also observed that sliding modes develop in opposite directions, confirmed by the two methods. This may be attributed to one sliding mode that can dissipate energy faster than the other one, most likely credited to rugosity [44]. Moreover, [PERSON] et al. [11] recently acknowledged the interaction and possible overlapping between mode III and other modes. Similarly, a rise in \(K_{II}\) implied a reduction of \(K_{I}\) and vice versa, and [PERSON] et al. [6] found a coupling effect between modes I and III, and recently [PERSON] et al. [23] confirmed such coupling for I and II, II, and III, and I and III at least for a composite material. With that in mind, Figure 9 represents a crack with three opening modes where the displacement vector over the surface is plotted as \(\delta\), the displacements in each direction are plotted as \(\delta_{i}\), and \(\alpha\) and \(\Psi\) are the in-plane and out-of-plane crack kinking angles, respectively. If the value of total displacement \(\delta\) stays constant but changes direction, the ratio of modes II and III will change. Furthermore, Equation (14) shows the relation between displacement and SIF; hence, a change in displacement creates a shift in SIF. Although such behavior may not impact the fatigue crack growth rate if Keq stays the same, it undoubtedly will impact SIFs' values and the crack propagation, as recently discussed by [PERSON] et al. [31]. If \(K_{II}\) rises, it favors \(\alpha\) growth (in-plane direction), whereas if \(K_{III}\) goes up, \(\Psi\) growth is favored (out-of-plane direction). Moreover, microscopic crack growth was not studied. This paper shows a method to calculate the \(K_{III}\), so FCG is fully accounted for and not underestimated at the macro level. This is important as [PERSON] [16] observed that mild steel exhibiting mode III displacements tends to branch to mode I cracks that most likely would produce faster FCG. Nonetheless, CP prediction for 3D cracks is a challenging task [12]. This paper proposes a method to calculate mode SIF III to be included in such estimation. Figure 9: Sliding displacements over the crack’s fracture plane. Adapted from [6].