Advanced numerical tool for fatigue and humidity degradation prediction in adhesive joints


Several techniques are available for joining materials together in various engineering applications. However, adhesive joints have recently attracted significant attention of researchers owing to their excellent strength to weight ratio property. Unfortunately, adhesive joints are susceptible to different failures due to loading conditions. To this note, researchers have been looking for various alternative methods to effectively predict joint behaviors under various loading and environmental conditions, so as to promote their use in critical structures. Thus, the finite element method has been identified as a promising solution.

Presently, the cohesive zone model is widely used for finite element analysis. It has been adopted by adhesive joints to model adhesive layers as it relates the material stress with the corresponding displacement between adjacent nodes. Besides, it is easy to implement and produces accurate results. Consequently, environmental factors such as humidity in a joint significantly influence the material parameters which may result in degradation. Humidity degraded joints can be modelled through cohesive zone model taking into consideration the traction-separation law.

Generally, fatigue analysis using cohesive zone model involves progressive damage application to the element. A formulation based on the experimental details is used to mimic the fatigue degradation. The damage variable is considered as a function for numerous fatigue cycles. Just like the initial methods, the main challenge remains controlling the fatigue damage parameters leading to less accurate results. In addition, the cycle-to-cycle approach involves complex and time-consuming computations thus limiting the accuracy of the obtained results.

Recently University of Porto scientists: Dr. Marcelo Costa, Dr. Lucas F M da Silva, Dr. Guilherme Viana and Dr. Raul D S G Campilho developed a finite element method based on the cohesive zone model for modelling adhesively bonded joints. The joints were subjected to fatigue and degradation by humidity. Consequently, the authors incorporated different types of traction-separation laws including exponential and trapezoidal. Furthermore, humidity degraded joints were modelled using a general law for property degradation as a function of the humidity content. On the other hand, modelling fatigue was based on experimental data relationship to ensuring reproducibility of the results. The authors aimed at simplifying the whole modelling systems to ensure more accurate results. Their work is published in the journal, International Journal of Fatigue.

The research team observed that the trapezoidal separation law was the most suitable approach for modeling experimental data for the aged and unaged samples. The number of cycles to the failure of the specimens were correctly predicted using fatigue degradation method. Also, both the numerical and experimental results were similar. This was attributed to the possibility of implementing different types of traction-separation law such as exponential, trapezoidal and triangular as well as a full cohesive zone model. However, the trapezoidal cohesive zone model resulted in more accurate values closer to the experimental results. Furthermore, MATLAB interface proved to be effective for speeding up the simulation process, extraction and visualization of the results.

The study by Dr. Marcelo Costa and his colleagues at University of Porto will advance modeling of joints subjected to different degradation and fatigue conditions thus an effective way of minimizing joints and structural failures. It will also enable design of specific joints with desired requirements and precision. The proposed technique can also be used for modelling an array of experimental conditions as well as a platform for including additional loading modes and further fatigue considerations.

About the author

Lucas F M da Silva is currently Associate Professor with Aggregation at the Department of Mechanical Engineering of the Faculty of Engineering of the University of Porto and Director of the Integrated Master in Mechanical Engineering. He obtained his PhD in bonding of composites from the University of Bristol (UK) in 2004. He leads the Adhesives Group, composed of post-docs, PhD students and MSc students. He has published 226 ISI papers (191 as author and 35 as editor) and 24 books (9 as author and 15 as editor) mainly on adhesive joint mechanics. His papers were cited 6136 times and correspond to an h-index of 43 (SCOPUS, 8/12/2018).

One of his papers obtained the SAGE Best Paper Award 2010 and Donald Julius Groen Prize 2010 (both awards given by Institution of Mechanical Engineers). He received in 2013 and 2018 the Award of Scientific Excellence by the Faculty of Engineering of the University of Porto.

He is editor in chief of The Journal of Adhesion, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications and University of Porto Journal of Engineering. He is also co-editor of two Springer book series (Advanced Structured Materials and Springer Briefs in Engineering: Computational Mechanics). He is member of the editorial board of International Journal of Adhesion and Adhesives and Journal of Adhesion Science and Technology. He is reviewer of 63 ISI journals.

He organises international conferences on adhesive bonding (Structural Adhesive Bonding every odd year and Industrial Applications of Adhesive Bonding every even year), advanced joining processes (every odd year) and materials (Materials Design and Applications every even year). He founded and leads the Portuguese Adhesion Society that belongs to European Adhesion Societies Group (EURADH).

He has 9 pending patents. He developed a software for designing adhesive joints available online (jointdesigner). He is consultant of several international companies (e.g. Alstom, Nagase Chemtex, John Deere).

About the author

Marcelo Costa graduated with a PhD in Mechanical Engineering at the Faculty of Engineering of the University of Porto, where he also previously received his MSc in Mechanical Engineering. His main area of interest targets adhesive bonding, starting with the development of a web application for the design of adhesive joints during his MSc thesis (available online: During his PhD, the focus consisted on the effect that different environmental factors, such as moisture, exerted on the static mechanical performance of adhesive joints as well as on the long-term fatigue behavior of such joints. Extensive experimental testing allowed for a numerical tool to be developed: a cohesive element for use in ABAQUS that allows for the modelling and prediction of the behavior of adhesive joints subjected to moisture and fatigue. His scientific contributions include 16 published papers (7 as first author), 3 book chapters and 26 contributions to scientific conferences.

About the author

Raul D S G Campilho was born in 1979. In 2003 he graduated in mechanical engineering at Instituto Superior de Engenharia do Porto (ISEP), Porto, Portugal. He completed his M.S. degree in 2006 and his Ph.D. in 2009, both in Faculdade de Engenharia da Universidade do Porto (FEUP), Porto, Portugal. Campilho currently serves as an Assistant Professor at ISEP, where he teaches in the areas of mechanical engineering.

He is an active researcher in the fields of numerical modeling, finite element methods, cohesive zone models for fracture behavior, natural and artificial composite materials and adhesive joint design. He currents supervises PhD and MSc students.

He has published 147 ISI papers and 8 books mainly on adhesive joint mechanics including composites. His papers were cited 2623 times and correspond to an h-index of 29 (SCOPUS, 24/11/2018). He is reviewer of many ISI journals.

About the author

Guilherme Viana was born in 1990. In 2013 he graduated in mechanical engineering at Faculdade de Engenharia da Universidade do Porto (FEUP), Porto, Portugal. During his PhD, which he finished in 2018, he studied the effect of extreme temperatures, environmental humidity on the static and impact behaviour of adhesive joints. He developed a cohesive zone model that can predict the mechanical behaviour of adhesive joints taking into account their environmental degradation. During his PhD, he actively contributed to several international scientific conferences. He is author to 13 published papers and 3 book chapters.

He currently works at Airbus, Filton as a consultant in the area of sealant products.


Costa, M., Viana, G., Créac’hcadec, R., da Silva, L., & Campilho, R. (2018). A cohesive zone element for mode I modelling of adhesives degraded by humidity and fatigue. International Journal of Fatigue, 112, 173-182.

Go To International Journal of Fatigue

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