## 3 Numerical Analyses and Results
This implies the validity of numerical approach and methodology utilized in this research for determining the fracture parameters of the BISBB specimen. Figure 6: Variations of geometry factors with mode mixity parameter in the BISBB specimen and for different geometry and loading conditions. (**a–c**) Al-Adhesive-Alumina, (**d–f**) Alumina-Adhesive-Al, (**g–i**) Al-Adhesive-Al, (**j–l**) Alumina-Adhesive-Alumina. Figure 7: Corresponding values of pure mode I and pure mode II geometry factors for the analyzed specimens with different _u/W_ and _S/W_ ratios. (**a,b**) Al-Adhesive-Alumina, (**c,d**) Alumina-Adhesive-Al, (**e,f**) Al-Adhesive-Al, (**g,h**) Alumina-Adhesive-Alumina. Figure 8: Variations of \(T^{\star}\) with crack inclination angle for the analyzed BISBB sample and for different \(a\)/W and \(S\)/W ratios. (**a–c**) Al-Adhesive-Alumina, (**d–f**) Alumina-Adhesive-Al, (**g–i**) Al-Adhesive-Al, (**j–I**) Alumina-Adhesive-Alumina. Under mixed I/II loading, fracture initiation occurs along a kinked direction relative to the original plane of crack. The direction of fracture initiation (\(\theta_{0}\)), depends on the mode mixity and fraction of tensile/shear deformation. Variations of \(\theta_{0}\) for different crack inclination angles (or mode mixities) in the investigated BISBB samples are shown in Figure 10. It is seen that this angle increases from zero (for pure mode I condition) to an angle of approximately 70\({}^{\circ}\) (for pure mode II condition). For each crack inclination angle (\(\alpha\)), the fracture initiation direction (\(\theta_{0}\)) varies in a narrow range depending on the adherent types and also \(a\)/W and \(S\)/W values. Figure 9: Variations of Biaxiality ratio (\(B\)i) parameter for different mode mixities, geometrical and loading parameters in the investigated BISBB specimen. (**a–c**) Al-Adhesive-Alumina, (**d–f**) Alumina-Adhesive-Al, (**g–i**) Al-Adhesive-Al, (j–l) Alumina-Adhesive-Alumina. Figure 10: Variations of fracture initiation angle (\(\theta_{0}\)) for mixed mode I/II loading of BISBB specimen for different a/W and S/W ratios. (**a–c**) Al-Adhesive-Alumina, (**d–f**) Alumina-Adhesive-Al, (**g–i**) Al-Adhesive-Al, (**j–l**) Alumina-Adhesive-Alumina. The adherent material types located in the left- and right-hand side of the BISBB specimen subjected to mixed mode I/II loading may also affect the fracture behavior and change the calculated fracture parameters. Figure 11 presents the influence of different permutations of adherent materials on the fracture parameters of the analyzed BISBB specimen. It is seen that the location of adherent materials in the left and right side of the crack or adhesive slightly changes the fracture parameters, but among them the mode II stress intensity factor (\(Y_{\text{II}}\)) is more sensitive to the change in the type of adherent materials. The effect of adherent material type on the shape and size of crack tip plastic region was also investigated based on the results obtained from the finite element analyses of the BISBB specimen. Figures 12 and 13 compare the shape and size of the plastic zone for three mode mixities (i.e., pure mode I with \(\alpha=0^{\circ}\), mixed mode I/II with \(\alpha=30^{\circ}\) and pure mode II with \(\alpha=40^{\circ}\) and \(44.5^{\circ}\)) of specimens with four permutations of adherent materials. It is seen that the size of plastic zone depends on the mode mixity. The largest size of plastic zone belongs to pure mode I whilst mixed mode loading has the smallest size of plastic zone. Also, according to the results shown in Figures 12 and 13, the location of adherent materials had no noticeable effect on both shape and size of bi-material adhesive bounded joints under different mode mixities of the BISBB specimen. It is finally noted that we demonstrated the ability of the BISBB test specimen for producing any desired mode I and II mixity using several finite element analyses.