Abstract: Various adhesive strengths are governed by the intensity of the singular stress field generated at the interface edge, referred to as the Intensity of Singular Stress Field (ISSF). When the singular stress fields in a test specimen and an actual structure are geometrically similar, strength evaluation based on ISSF has been shown to be highly effective. However, since the singular stress field varies depending on the local geometry at the adhesive edge, the ISSF method cannot be directly applied to joints with different edge geometries.

In this study, a unified approach for evaluating adhesive strength under different singular stress fields is proposed by introducing a fictitious edge interface crack at the adhesive interface edge.

(1) The proposed edge interface crack, whose length is less than 1% of the adhesive layer thickness, establishes a one-to-one correspondence between the stress intensity factor (SIF) of the crack and the ISSF of an interface edge without a crack. For example, the adhesive strength of butt joints varying with adhesive layer thickness can be represented by a constant critical value K_1c of the edge interface crack.
(2) In the proposed edge interface crack method, direct comparison becomes possible even when the singularity indices at interface edges differ, because the SIF has a common physical unit. Furthermore, the dominant fracture mode—debonding or shear failure—can be readily identified from the relative magnitudes of K₁and K₂.
(3) To evaluate adhesive strength for different local geometries, an exact general solution for the stress intensity factors of an edge interface crack applicable to butt joints is derived, and its usefulness is demonstrated as follows.
(4) For lap joints with different edge geometries, the nominal average fracture stress may differ by more than a factor of two. It is shown that these differences can be consistently explained by a constant critical value K_1c using the edge interface crack method.
(5) Based on numerous experimental results, the nominal average fracture strength of butt joints is approximately twice that of lap joints. By introducing a fictitious edge interface crack with a crack length a=10^-4 mm at the interface edge, the adhesive strengths of butt joints (BJ) and lap joints (LJ) can be directly compared. The obtained critical values are $K_{1c}^{(B,ave)} = (12.2 \pm 4.70) \times 10^{-2}$ $\text{MPa}\sqrt{\text{m}}$ for butt joints and $K_{1c}^{(L,ave)} = (67.9 \pm 24.8) \times 10^{-2}$$\text{MPa}\sqrt{\text{m}}$ for lap joints, giving $(K_{1c}^{(L,ave)}/K_{1c}^{(B,ave)}) \approx 5.5$, indicating that lap joints exhibit higher strength than butt joints, consistent with common engineering understanding.
(6) Since the strengths of butt joints and lap joints can be expressed by constant values of K_1c or K_2c, and considering the ratio $(K_{1c}^{(L,ave)} / K_{1c}^{(B,ave)}) \approx 5.5$, the strengths specified for JIS standard specimens with adhesive thickness h=0.1mm were predicted. The predicted ratio $\sigma_c^B(\text{JIS}) / \tau_c^L(\text{JIS}) = 1.65$ agrees well with the experimental ratio $\sigma_c^{(B,ave)} / \tau_c^{(L,ave)} \approx 1.7$.

These results demonstrate that the edge interface crack method provides a practical and unified framework for evaluating adhesive strength across different geometries and loading conditions.

Keywords : Adhesive strength, butt joint, lap joint, singularity index, stress intensity factor, edge interface crack.

Biography: Professor Kazuhiro Oda is a faculty member in the Mechanical Engineering Program, Faculty of Science and Technology, Oita University. He received his Ph.D. in Engineering from Kyushu Institute of Technology in 1995. His research interests include strength of materials, elasticity, and fracture mechanics, with a particular focus on stress analysis and singular stress fields at dissimilar material interfaces and strength design of adhesive structures. After completing his doctoral studies in 1995, he served as a Research Fellow of the Japan Society for the Promotion of Science (JSPS) and later joined Tokuyama College of Technology, where he held positions as Associate Professor and Professor. In 2012, he moved to Oita University as Professor in the Faculty of Engineering (now the Faculty of Science and Technology). He is currently engaged in research on advanced strength evaluation methods for adhesive joints and stress intensity factor analysis for orthotropic dissimilar materials. Professor Oda also serves as Special Assistant to the President for Industry–Academia Collaboration, promoting partnerships between the university and industry. He was a Board Member of the Society of Materials Science, Japan (2020–2024). With numerous publications and contributions, he is recognized as one of the leading researchers in fracture mechanics–based design of dissimilar material joints. In 2025, he received the Society of Automotive Engineers of Japan’s Technical Paper Award.