PSI - Issue 57

Cristian Bagni et al. / Procedia Structural Integrity 57 (2024) 598–610 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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0.3 mm long crack on the polished edge of the joint. The investigation showed that the initiation phase represented a significant portion (between 20% and 70%) of the total fatigue life of the joint. The variability was due to several factors, including load level, overlap length and geometry of the bond edge (square edge or spew fillet). Crocombe et al. (2002), Graner Solana et al. (2007) and Shenoy et al. (2009) used backface strain measurement to study the evolution of the fatigue damage in adhesively bonded joints and to detect crack initiation. All three studies confirmed that crack initiation represents a significant portion of the total fatigue life of an adhesively bonded joint. In particular, Crocombe et al. (2002) observed that the initiation phase was about 50% of the overall fatigue life of the joint. Graner Solana et al. (2007) performed a series of fatigue testes on adhesively bonded 2014-T6 aluminium single lap specimens. The specimens were instrumented with six strain gauges to measure backface strain during the tests. The results of the tests seemed to support the fact that the initiation phase represents a significant percentage of the total life of the joint. Furthermore, they observed that the damage appeared in the fillet of the adhesive as a change in the colour of the adhesive itself, most likely due to the formation of microcracks. Shenoy et al. (2009), instead, concluded that the crack initiation phase was predominant at low fatigue loads, while the crack propagation phase prevailed at high fatigue loads. From the literature, it is evident that detecting crack initiation is still an aspect that has not been fully developed and it is significantly dependent on the techniques used to detect crack initiation and how crack initiation is defined. Shenoy et al. (2010) and Graner Solana et al. (2010) proposed empirical models able to predict the total fatigue life of adhesively bonded joints. The fatigue damage evolution was defined by the former model as a power law of the localised equivalent plastic strain, while by the latter model as a power law of the elasto-plastic strain. The two models were implemented into finite element (FE) analysis software and produced results in good agreement with experimental data. However, the FE selection and the meshing strategies used in the two papers are suitable for the analysis of simple geometries like the lap shear specimens used in the corresponding research work. However, for more complex geometries (for example automotive body-in-white models), the use of 2D plane strain elements like in Graner Solana et al. (2010) is not suitable, while the use of solid elements like in Shenoy et al. (2010) might lead to finite element models that are computationally too onerous. Continuing on the topic of FE modelling of adhesively bonded joints, several modelling approaches and strategies were proposed (see for example Yagam and Das (2006), Campilho et al. (2013), Bedon et al. (2018) and Moreira and Campilho (2019)). However, very few research works proposed an easy-to-use approach for the modelling and fatigue assessment of adhesively bonded joints, that could be used by the transportation industry to analyse full structure models with limited changes to the typical FE modelling strategies and requiring reasonable computational efforts. Heyes et al. (2012) proposed a fracture mechanics-based approach to assess the fatigue performance of adhesively bonded joints. The meshing strategy proposed by the authors was relatively similar to the meshing strategy commonly used by automotive manufacturers for the FE models of their vehicles. However, the proposed method does not produce finite fatigue life estimations, but rather it assesses the fatigue performance of adhesive joints by calculating a safety factor, which is a function of the maximum value of the J-integral at each calculation point and the threshold strain energy release rate. This was mainly dictated by the fact that the research work was based on early generation adhesives whose load-life data was characterised by significant scatter and shallow slopes, potentially leading to unrealistic or very inaccurate fatigue life predictions. Kang et al. (2015) proposed a method for the fatigue life prediction of adhesive joints based on the structural stress method proposed by Rupp et al. (1995), subsequently modified and implemented in nCode software and widely used for the fatigue life estimation of spot welds. The authors proposed to model the adhesive layer using the ‘area contact method’ (ACM). This method enabled finite fatigue life estimations to be made and the use of relatively coarse FE meshes. However, it produced inaccurate high-cycle fatigue life predictions. Furthermore, this is an adaptation of a method developed for spot welds but applied to adhesives and therefore, to properly describe the behaviour of the bonded joint, the size and pitch of the ACM elements as well as the value of nine empirical parameters must be carefully chosen. Finally, Chen et al. (2017) proposed a J-integral based semi-analytical approach for the fatigue life estimation of adhesive joints. However, despite achieving a good correlation between predictions and experimental results, the approach has some limitations. In particular, it cannot be used for tension-compression fatigue loads, because it is based on the J-