Investigating the influence of material and geometrical factors on bonded joint strength: A parametric CZM analysis of single lap joints

Abstract

Adhesive bonding has become a cornerstone technology in aerospace, automotive, defense, and energy sectors, enabling the integration of lightweight and high-strength assemblies that would be difficult or impossible to realize with traditional mechanical fastening techniques. Beyond weight savings, bonded joints eliminate the need for bolts or rivets that often create stress concentrations, thereby improving fatigue life, ensuring smoother aerodynamic surfaces, and enhancing corrosion resistance. These advantages, however, come with the critical challenge of guaranteeing reliable and predictable structural performance. In aerospace applications in particular, bonded joints must undergo rigorous certification before being deployed in airframe structures, and this requirement necessitates either extensive experimental campaigns or high-fidelity numerical models that can reduce reliance on physical testing. Traditional fracture and fatigue testing approaches are limited by cost, time, and scalability. Each new adhesive, thickness, or joint geometry typically requires dedicated specimen production, fixturing, and long-term test programs. This motivates the increasing reliance on numerical simulation methods that can replicate crack initiation, progressive damage, and failure. Among such approaches, cohesive zone model has emerged as one of the most robust and widely accepted frameworks, bridging the gap between continuum mechanics and fracture mechanics. By embedding cohesive elements along bond interfaces, the model allows traction–separation laws to govern the entire fracture process from elastic loading, through damage initiation at peak traction, to progressive degradation and eventual failure controlled by critical fracture energies. This capacity to replicate mixed-mode fracture, involving both Mode I opening and Mode II shear, makes cohesive zone modeling particularly suited to bonded joint analyses, where real loading scenarios rarely involve pure modes. The main objective of this M.Sc. thesis is to establish a fully automated, parametric cohesive zone model based framework for investigating the interplay of three critical parameters: adhesive thickness, overlap length, and adhesive material type. Unlike many prior studies that focused on one parameter at a time, this work explicitly considers their coupled effects, allowing for a more realistic and comprehensive understanding of structural performance. Four commercially relevant adhesives, namely AV138/HV998, Hysol EA 9361, Sikaforce 7888, and Araldite 2015, were chosen to represent a range from brittle to ductile systems. Their traction–separation properties were derived from literature-based tensile and shear test data, including double cantilever beam and end-notched flexure fracture energies. Importantly, the parameters were not taken as fixed constants but formulated as explicit functions of thickness, capturing both intrinsic fracture toughness and additional plastic dissipation effects in thicker layers. A robust Python scripting infrastructure was developed in Abaqus to automate every stage of the simulation workflow, including geometry construction, mesh generation, cohesive property assignment, job submission, and result post-processing. This automation ensured repeatability and allowed the exploration of large design matrices that would be impractical to evaluate manually. The outputs, including load–displacement curves, ultimate load, dissipated fracture energy and damage variables, were systematically extracted and synthesized into design maps. These maps serve as quick-reference engineering guidelines that identify optimal regions of adhesive thickness and overlap length for each adhesive system. For instance, the ductile Hysol EA 9361 demonstrated a non-monotonic response with optimum performance in the 0.20–0.30 millimeter thickness range, while the brittle Araldite 2015 performed best with thin bond-lines and shorter overlaps. While the parametric study itself yields valuable insights, the thesis advances one step further by integrating multi-objective optimization into the framework. Using ModeFRONTIER as the optimization environment, adhesive thickness, overlap length, and adhesive type were treated as decision variables, while the objectives were defined as maximizing both ultimate load and energy dissipation. A constraint was imposed on minimum damage progression to ensure structural integrity and avoid solutions that rely on premature cohesive failure. The MOGA-II evolutionary algorithm was employed, chosen for its ability to handle nonlinear and discontinuous responses typical of cohesive zone based simulations The optimization campaign generated approximately 997 unique design points, of which only 273, representing about 27 percent, converged successfully due to the intrinsic numerical challenges of modeling progressive damage in brittle adhesives. Among these, 98 solutions, representing about 10 percent of the total runs, satisfied all objectives and constraints, forming the final Pareto-optimal set. The results confirmed several important trends. Adhesive thickness does not exhibit a simple monotonic relationship with performance, since depending on the adhesive type, increasing thickness can enhance ductile energy absorption but diminish peak load capacity. Overlap length consistently plays a dominant role in determining strength, though beyond a critical threshold additional length contributes little to further performance gains. Adhesive selection emerges as the most influential parameter, dictating whether trade-offs between energy and load are favorable or limiting. Visualization of the Pareto fronts highlighted how engineers can navigate between conflicting objectives. When prioritizing maximum load, brittle adhesives such as AV138 or Araldite 2015 may appear attractive. However, when energy absorption and damage tolerance are equally valued, ductile systems such as Hysol EA 9361 or Sikaforce 7888 provide superior balance. These trade-offs underscore the necessity of multi-objective approaches rather than single-metric optimization in bonded joint design. The combined parametric and optimization framework represents the innovative contribution of this thesis. The parametric design maps offer immediate, interpretable guidelines for specific adhesives, while the optimization study delivers Pareto-based strategies that help designers tailor joints to competing performance requirements. Together, they provide a dual-level tool: on one hand, a practical engineering reference, and on the other, a rigorous decision-making foundation for multi-objective structural design. Equally important is the methodological flexibility of the framework. The automation scripts can be readily extended to new adhesives, alternative adherend materials such as composites, or other joint geometries such as double-lap or scarf joints. The incorporation of thickness-dependent cohesive functions ensures transferability to a broad range of industrial scenarios, where bond-line thickness often varies due to manufacturing tolerances. Moreover, the optimization setup can easily accommodate additional objectives, such as minimizing weight or maximizing fatigue life, further aligning with aerospace industry certification needs. In conclusion, this thesis demonstrates that adhesive joint performance cannot be fully understood by varying a single parameter in isolation. Instead, meaningful design insights arise only when material type, geometry, and damage evolution are examined in concert and optimized under realistic constraints. By delivering both parametric guidelines and optimization-based Pareto strategies, this work provides a comprehensive framework that reduces reliance on experimental trial-and-error and accelerates the adoption of adhesive bonding in critical structural applications. The outcomes make a significant contribution to cohesive zone modeling, adhesive joint design, and computational optimization, positioning this framework as a reference methodology for future industrial and academic studies alike.