Adhesive bonding community shows a continued interest in using bridging mechanisms to toughen the interface of secondary bonded joints, especially in the case of laminated composites. Due to snap-back instability that occurs during fracture, confusions may exist when identifying the toughening effect experimentally. The true toughening effect may be overestimated by lumping all energy contributions (kinetic energy included) in an overall effective toughness. Here, fundamentals for bridging to enhance fracture resistance are explored through the theoretical analysis of the delamination of a composite double cantilever beam (DCB) with bridging. Specifically, we establish a theoretical framework on the basis of Timoshenko beam theory and linear elastic fracture mechanics to solve the fracture response of DCB in the presence of discrete bridging phases. We elucidate the crack trapping and the snap-back instability in structural response during the crack propagation. We identify the contribution to the overall toughness observed numerically/experimentally of both the physical fracture energy and other types of dissipation. The associated toughening mechanisms are then unveiled. Furthermore, we study the effects of property of the bridging phases on the snap-back instability, based on which, we propose a dimensionless quantity that can be deployed as an indicator of the intensity of snap-back instability. Finally, we identify the role of geometrical properties, i.e. the substrate thickness and the arrangement spacing of the bridging phases, in the snap-back instability and the macroscopic fracture toughness of a DCB. This work provides, from a theoretical point of view, an essential insight into the physics related to the structural response of DCB with discrete toughening elements.

粘合剂粘合界对使用桥接机制来强化二次粘合接头的界面表现出持续的兴趣，尤其是在层压复合材料的情况下。由于断裂过程中发生的回弹不稳定性，在通过实验确定增韧效果时可能会存在混淆。通过将所有能量贡献（包括动能）集中在整体有效韧性中，可能会高估真正的增韧效果。在这里，通过对带桥接的复合双悬臂梁 (DCB) 分层的理论分析，探讨了桥接以提高抗裂性的基本原理。具体来说，我们在Timoshenko梁理论和线弹性断裂力学的基础上建立了一个理论框架来解决离散桥接相存在下DCB的断裂响应。我们阐明了裂纹扩展过程中结构响应中的裂纹捕获和回弹不稳定性。我们确定了物理断裂能和其他类型的耗散对数值/实验观察到的整体韧性的贡献。然后揭示相关的增韧机制。此外，我们研究了桥接相的性质对回弹不稳定性的影响，在此基础上，我们提出了一个无量纲量，可以用作指示回弹不稳定性强度的指标。最后，我们确定几何属性的作用，即 基体厚度和桥接相的排列间距，在 DCB 的回弹不稳定性和宏观断裂韧性方面。从理论的角度来看，这项工作提供了对与具有离散增韧元素的 DCB 结构响应相关的物理学的基本见解。