## 4 Failure Modes
### Failure Dominated by Joint 2: S-90-30  
The crack propagation patterns and AE parameters of the S-90-30 specimen are presented in Figure 5. When the stress is loaded to 17.72 MPa, variations in the strain field at the joint tips are observed (Figure 5a); specifically, joint 2 exhibits a relatively low strain value with no macroscopic cracks observed, while wing cracks initiate at its tip. Macroscopic cracks aligned with joint 1 emerge, with the coplanar strain band at its inner tip extending to the soft-hard interface, and light-colored strain bands appear between the joints. Examining the AE parameters during stage I (Figure 5b), the ringing count reaches 6.1 \(\times\) 10\({}^{3}\) (Time = 140 s), with the \(b\)-value rapidly fluctuating upwards and downwards over a short period. Observing the crack proportions during stage I (Figure 5c), the cumulative tensile crack proportion rises to 20.73%, while the real-time tensile crack proportion remains around 92%. The specimen undergoes a certain degree of damage dominated by tensile failure during stage I, primarily due to the coplanar tensile cracks initiating at the tip of joint 2. As the stress climbs to 19.98 MPa, approaching the peak strength, the principal strain field during stage II (Figure 5a) reveals that the cracks at the tip of joint 1 propagates towards both tips, forming macroscopic cracks. The cracks located at the tip of joint 2 within the wing continue to propagate, with the wing's inner tip cracks transgressing the layer boundary, ultimately evolving into tensile cracks. A coplanar shear strain band initiates at the outer tip of joint 2 and extends towards the right tip of the specimen. The color of the strain bands between the joints deepens, and their range expands. As stage II progresses, the alternating rise and fall rate of the \(b\)-value increases, indicating an acceleration in the frequency of large and small failures occurring alternately. The damage to the specimen accelerates. Observing the AE parameters (Figure 5c), the cumulative tensile crack proportion rises from 20.73% to 34.05%, while the real-time tensile crack proportion remains stable at around 92%. It indicates that the damage during stage II is dominated by tensile failure. With the stress loaded to 18.89 MPa, stage III begins. Observing changes in the principal strain field (Figure 5a), the tensile wing cracks at the inner tip of joint 2 propagate downwards, approaching the bottom of the specimen. Under shear action, the coplanar strain band at the outer tip of joint 2 overlaps with the shear strain band on the right side,  
Figure 5: Principal strain field and AE parameter profiles of the S-90-30 specimen: (**a**) principal strain field; (**b**) stress-strain curves, \(b\)-value, and AE counts; (**c**) shear-tension cumulative crack proportion and real-time tensile crack proportion. leading to crack coalescence and extension to the right tip of the soft layer. This causes the stress to drop from 19.98 MPa to 18.89 MPa. The rapid climb in the \(b\)-value indicates the occurrence of small failures due to crack coalescence. The AE counts rapidly climb to approximately 18 \(\times\) 10\({}^{3}\) during stage III, indicating severe damage to the specimen. As the stress declines to 18.50 MPa, stage IV commences. Observing the principal strain field during stage IV (Figure 5a), the wing cracks at the inner tip of joint 2 propagate to the bottom of the specimen. Out-of-plane tensile cracks initiate at the inner tip of joint 2. Meanwhile, the tensile strain band generated at the upper tip of joint 1 overlaps with the coplanar strain band initiated at the inner tip of joint 2, leading to crack coalescence and inter-joint crack penetration. It results in a drop in stress from 18.89 MPa to 18.50 MPa. Examining Figure 5b, the \(b\)-value and AE counts exhibit minor changes during stage IV. Observing the crack proportions (Figure 5c), the cumulative tensile crack proportion climbs to approximately 55%, while the real-time tensile crack proportion remains around 94%.