## 3 Numerical Analyses and Results
However, by moving towards pure mode II loading condition the magnitude of \(Bi\) parameter reduces showing the non-significant influence of \(T\)-stress on the fracture of this specimen. The absolute value of Biaxiality ratio parameter increases by increasing the crack length ratio and loading span ratio for smaller crack inclination angles (\(\alpha<30^{\circ}\)) and conversely its magnitude reduces by increasing a/W and S/W for \(\alpha>30^{\circ}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S/W** & **a/W** & **Permutation** & **Pure Mode II Inclination Angle** \\ \hline \multirow{6}{*}{0.5} & \multirow{2}{*}{0.3} & Al-Adhesive-Alumina & 40\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Al & 50\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Al & 50\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Alumina & 40\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 33\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Al & 37\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Al & 37\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Alumina & 33\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 31\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 50\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Al & 55\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 50\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 40\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Al & 44.5\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 40\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Alumina & 40\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 36\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Al & 38.5\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Al & 38.5\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Alumina & 36\({}^{\circ}\) \\ \hline \multirow{6}{*}{0.7} & \multirow{6}{*}{0.3} & Al-Adhesive-Alumina & - \\ \cline{3-4}  & & Alumina-Adhesive-Al & - \\ \cline{3-4}  & & Al-Adhesive-Alumina & - \\ \cline{3-4}  & & Alumina-Adhesive-Al & - \\ \cline{3-4}  & & Al-Adhesive-Alumina & - \\ \cline{3-4}  & & Alumina-Adhesive-Alumina & 47\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 41.5\({}^{\circ}\) \\ \cline{3-4}  & & Alumina-Adhesive-Alumina & 44\({}^{\circ}\) \\ \cline{3-4}  & & Al-Adhesive-Alumina & 41.5\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pure mode II crack inclination angles for the BISBB specimen. Figure 4: Variations of mode I geometry factor (Y\({}_{\rm I}\)) with crack inclination angle (\(\alpha\)) for different BISBB specimens and different geometrical and loading conditions. (**a–c**) Al-Adhesive-Alumina, (**d–f**) Alumina-Adhesive-Al, (**g–i**) Al-Adhesive-Al, (**j–l**) Alumina-Adhesive-Alumina. It should be noted that the single-material and homogenous short bend beam specimen was analyzed in previous papers of the authors [11; 12; 13] using the same finite element modeling and software. Since the crack in the BISBB sample was assumed in the adhesive part and this part was assumed to behave as elastic linear material, the framework of linear elastic fracture mechanics (LEFM) would be applicable and valid for analyzing the fracture behavior of the BISBB specimen. The J-integral method therefore provides accurate results for fracture parameters of linear elastic materials as demonstrated in several research papers [11; 12; 15; 16; 22; 26; 28; 30; 33; 37; 38; 39; 40; 41; 42; 43]. It is also pointed out that by considering the same mechanical properties for all adherent and adhesive parts, the fracture parameters  
Figure 5: Variations of mode II geometry factor (\(\Upsilon_{\rm II}\)) with crack inclination angle (\(\alpha\)) for different BISBB specimens and different geometrical and loading conditions. (**a–c**) Al-Adhesive-Alumina, (**d–f**) Alumina-Adhesive-Al, (**g–i**) Al-Adhesive-Al, (**j–I**) Alumina-Adhesive-Alumina. reported earlier by the authors for the SBB specimen are obtained [11; 12].