## 3 Numerical Analyses and Results
Variations of geometry factors with \(M^{\rm e}\) are also presented in Figure 6. This Figure shows that complete ranges of mode mixities from pure mode I to pure mode II (i.e., \(0\leq M^{\rm e}\leq 1\)) can be achieved by the BISBB specimen. In this Figure, \(M^{\rm e}=1\) corresponds to pure mode I and \(M^{\rm e}=0\) shows the pure mode II loading conditions. This means that for \(0\leq M^{\rm e}<0.5\) the crack tip deformation of the BISBB specimen is controlled by dominantly shear mode (or mode II). On the contrary, when the mode mixity parameter (\(M^{\rm e}\)) varies from 1 to 0.5, the state of mixed mode I/II stress field for the BISBB specimen is mainly governed by the tensile type or opening mode I fracture mechanism. At \(M^{\rm e}=0.5\) that both \(Y_{\rm I}\) and \(Y_{\rm II}\) components are the same and equal together, a transition between dominantly tensile and dominantly shear mechanisms occurs. This situation for the BISBB specimen is achieved typically at crack inclination angles \(25^{\circ}<\alpha<35^{\circ}\), depending on the adherent types, their permutations, crack length and especially the loading span distances. This angle generally increases by increasing _a/W_ and _S/W_. Figure 7 also presents the corresponding values of geometry factors under pure mode I and pure mode II loading conditions. As expected, the corresponding values of \(Y_{\rm I}\) and \(Y_{\rm II}\) at pure modes I and II conditions become greater by increasing the crack length ratio. Furthermore, for any given _a/W_ value, mode I geometry factor increases by increasing the loading span and conversely mode II geometry factor decreases for longer bottom loading span distances. Also, according to Figure 6, mode II geometry factor is less sensitive to the crack length ratio _a/W_ compared to the Mode I geometry factor for \(M^{\rm e}<0.5\). The variations of non-dimensional \(T\)-stress (\(T^{\star}\)) for different loading conditions and material groups of the analyzed BISBB samples are presented in Figure 8. As seen, the \(T\)-stress is significantly negative for mode I dominant conditions (i.e., smaller values of \(\alpha\)). Under such situations the value of \(T^{\star}\) is sensitive to the crack length ratio (_a/W_). However, by further increasing the crack angle and moving towards pure mode II loading condition, the sensitivity of \(T\)-stress to _a/W_ becomes lesser and the corresponding value of \(T^{\star}\) tends to zero. The absolute value of \(T^{\star}\) increases in the BISBB specimen by increasing the crack length ratio (_a/W_) and loading span ratio (_S/W_). Based on the fracture mechanics literature for bonded components, the non-singular term can play a significant role on mixed mode I/II fracture if the magnitude of \(T\)-stress is high enough compared to the singular terms [26; 27; 28; 29; 30]. A parameter called Biaxiality ratio (Bi) defined as \(Bi=\frac{T\sqrt{\pi a}}{\sqrt{K_{\rm I}^{2}+K_{\rm II}i^{2}}}\) is a suitable measure for comparing the importance of \(T\)-stress relative to the stress intensity factors (\(K_{\rm I}\) and \(K_{\rm II}\)). The variations of this parameter for the analyzed BISBB specimens have been illustrated in Figure 9 for different _a/W_ and _S/W_ and \(\alpha\) values. Under dominantly mode I loading conditions (i.e., \(\alpha<20^{\circ}\)), the value of \(Bi\) is significantly negative and its magnitude increases by increasing the crack length ratio (_a/W_). This reveals that the non-singular stress term (\(T\)-stress) has significant role on the process of dominantly pure mode I brittle fracture of the BISBB specimen. Compared to previously used test samples for investigating mixed mode I/II (such as asymmetric semi-circular bend, four-point bend, Brazilian disc, diagonally square plate, edge crack triangular specimen), the magnitude of \(Bi\) parameter is significantly high [31; 32; 33; 34; 35; 36]. This shows that the effect of \(T\)-stress in the fracture process of BISBB specimen is more pronounced than the other mixed mode samples [32; 33; 34; 35; 36; 37; 38; 39].