PSI - Issue 33

R.F.N. Brito et al. / Procedia Structural Integrity 33 (2021) 665–672 Brito et al. / Structural Integrity Procedia 00 (2019) 000–000

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provide similar structural behavior, stepped lap joints are easier to manufacture and to analyze due to their geometry, resembling a series of single-lap joints (Crocombe, 2005), hence is broader use. As in other joint configurations, joint strength ( P m ) depends on factors such as bond-line thickness and area, substrates and adhesive material properties, etc. For stepped lap joints, the number and size of steps also influence P m (Durmuş and Akpinar, 2020; Ichikawa et al., 2008). Nomenclature of stepped-lap joints. The amount of variables within the stepped-lap joints has led to multiple parametric studies to identify their influence on P m (Chowdhury et al., 2016; Ichikawa et al., 2008). Although these studies can be done analytically using closed-form solutions like those developed by Hart-Smith (1973), experimentally, or using numerical techniques like the Finite Element Method (FEM), being the latter more frequent in the literature (Ramalho et al., 2020), mainly because it allows visualizing stresses and strains. Moreover, FEM capabilities were extended with the Cohesive Zone Model (CZM), which uses damage laws and an especial element type, hence to be used together with FEM. Several damage laws had been developed, being the triangular law the most common because of its simplicity. A more detailed description of the CZM fundamentals and its application to adhesive joints was reported by Campilho (2017). Modeling adhesive joints using CZM generally provides a good agreement with experimental data (Durmuş and Akpinar, 2020), hence its widespread use. However, the CZM laws require the critical strain energy release rates for tensile and shear ( G IC and G IIC , respectively), and the respective toughness of the material, which had to be obtained experimentally. Furthermore, the application of CZM for modeling interlaminar failure of Carbon Fiber Reinforced Polymer (CFRP) substrates on Single-lap joints (SLJ) has been investigated with promising results (Sun et al., 2020). The interlaminar fracture or delamination is the damage of the CFRP matrix caused by normal stresses (  y ) within the substrates (Neumayer et al., 2016). Stepped-lap joints can be composed of metallic and CFRP substrates. Under quasi-static loading conditions, the joints composed by CFRP-CFRP substrates present higher strength ( P m ) than their aluminum-CFRP counterparts even with some specimens presenting delamination (Machado et al., 2018). Under impact conditions, the performance of CFRP is also higher than those with aluminum substrates; nevertheless, joints with steel substrates have higher strength (Valente et al., 2019). Furthermore, the strength of CFRP-CFRP joints can also be affected by non-linearities in the stacking of the composite layers, as determined from a numerical parametric study (Wu et al., 2018). In addition, stepped-lap joints with three steps presented a better behavior than those with more steps (up to 10) (Wu et al., 2018). Although a few studies about the behavior of stepped-lap joints exist, little information is available on how the overlap length ( L O ) influences P m and the mechanical behavior of this type of joint. Moreover, being this joint configuration somehow similar to a series of SLJ, it is expected to have an increase in P m as a function of L O . This work aims to investigate the influence of the L O on the overall mechanical behavior of this type of joint. This effect was investigated experimentally and numerically on joints with CFRP-CFRP substrates and bonded with a ductile adhesive. The numerical investigation was carried out using the FEM considering a triangular CZM traction separation law for determining the numerical P m . Furthermore, numerical models solely of FEM were performed to obtain the stress distributions at the mid-bond line. 2. Materials and Methods 2.1. Materials The analyzed joints consisted of CFRP substrates bonded with a ductile adhesive, the Araldite ® 2015. The substrates were produced in-house from carbon-epoxy composites (SEAL ® Texipreg HS 160 RM. Legnano, Italy) of 0.15 mm thick. The final composite sheets were hand-layered using a [0 20 ] layup and cured in a hot-plate press (1 h at 130ºC and 2 bar) (Ribeiro et al., 2016), resulting in 3 mm thick sheets. The mechanical properties (orthotropic) of the final composite sheets were determined in previous work, as reported by Ribeiro et al, (2016), and are listed in Table 1. The composite sheets produced were later cut to the sizes required for the substrates using a circular abrasive saw. Similarly, the adhesive was characterized experimentally in previous work, as reported by Campilho et al., (2013), and its mechanical properties are listed in Table 2, including the toughness in tensile and shear necessary for the CZM modeling. Further details of the experimental characterization of the adhesive are described by da Silva et al., (2012), and Faneco et al., (2017).