PSI - Issue 72

A.F.L. Macedo et al. / Procedia Structural Integrity 72 (2025) 61–68

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models based on continuum mechanics often fall short, finite element method (FEM) analyses are commonly used, despite their limitations, such as mesh dependency. Approaches that consider materials’ fracture toughness are particularly effective for bonded joints. CZM have proven highly effective in analyzing bonded joints. The CZM approach integrates principles from material strength and fracture mechanics to predict damage initiation and propagation, providing a comprehensive understanding of damage leading to structural failure (Rocha and Campilho 2018). Key parameters in CZM include elastic stiffness, cohesive strength, and fracture toughness ( G C ). Accurate predictions depend on correctly estimating these parameters and laws. However, studies showed that good predictions can be achieved even when using less precise cohesive law shapes (Antunes et al. 2021). Various fracture tests are available today to estimate G C in different pure-mode components, such as G IC and G IIC , as well as in mixed-mode scenarios, where both tensile and shear fracture energies ( G I and G II ) are considered. The fracture envelope concept helps link pure-modes under mixed-mode loading, allowing for predictions of crack growth. To measure pure or mixed-mode toughness, several methods can be used. For G IC , Double-Cantilever Beam (DCB) tests are commonly used because they are straightforward to fabricate and require only standard tensile testing equipment (Sekiguchi et al. 2017). G IIC is typically measured using End-Notched Flexure (ENF) tests, but alternatives like 4-Point End-Notched Flexure (4ENF) and End-Loaded Split (ELS) tests are also effective (Wang et al. 2023). For mixed-mode loading, tests such as SLB, Asymmetric DCB (ADCB), and Mixed-Mode Bending (MMB) are used (Pohlit 2007). The SLB test, introduced by Yoon and Hong (1990), is easy to execute and involves a three-point bending setup where the shorter lower adherend induces both tension and shear at the crack tip. Various methods, from linear-elastic fracture mechanics to the J-integral, are available in the literature to estimate G I and G II . The SLB test has been increasingly utilized to analyze bonded joints, both experimentally and numerically. Oliveira et al. (2020) investigated the t A effect on the mixed-mode behavior of a ductile polyurethane adhesive using the SLB test, highlighting that the compliance-based beam method (CBBM) is particularly effective to estimate G I and G II . Szekrényes (2012) used the J-integral with the SLB test to analyze G I and G II and validated the results with the Virtual Crack Closure Technique (VCCT) and FEM analysis, noting some limitations of classical plate theory in these calculations. Davidson et al. (2012) analytically derived G I and G II for sandwich panels using DCB and ENF tests, applying these data in CZM models to simulate crack propagation in SLB specimens, demonstrating that pure-mode CZM parameters can effectively predict mixed-mode behaviors. Lee et al. (2013) enhanced SLB adhesive joint performance through micro-patterning, with CZM modelling showing an error margin of 8% in predicting failure loads, supporting its use in bonded joint design. Santos and Campilho (2017) conducted both experimental and CZM modelling studies on the SLB test to assess the mixed-mode behavior of adhesives ranging from brittle to ductile, confirming the data's applicability for joint design. Ji et al. (2012) focused on the influence of t A on interfacial G I and G II , determined via the J -integral, and the estimation of CZM laws through the direct method. They observed that increasing t A led to higher G I , G II , and tensile cohesive strength ( t s 0 ), while shear cohesive strength ( t n 0 ) decreased. This work focuses on the numerical analysis of how t A influences the mixed-mode fracture process in adhesive joints. Experimental data from SLB tests is used, involving composite adherends and a ductile adhesive, with t A ranging from 0.1 to 2.0 mm. The study includes a comparison between experimental and numerical P -  curves for validation purposes, followed by the estimation of CZM laws and validation of the fracture envelope across all t A . 2. Experimental and numerical details 2.1. Materials SEAL ® (Texipreg HS 160 RM) unidirectional carbon-epoxy pre-impregnated laminas were used to produce the adherends for SLB joints, with a unit thickness of 0.15 mm. Twenty layers were manually stacked. After, the assembly was placed in a heated plate press to cure under pressure (2 bar) at 130 ºC for 1 hour. The elastic-orthotropic constants of a unidirectional sheet are available (Oliveira et al. 2020). The SLB joints were bonded using a ductile polyurethane adhesive. Toughness and mechanical properties were obtained from a study by Faneco et al. (2017). The mold used to produce the specimens allows six samples to be produced at once, and they were tested in accordance with the French standard NF T 76-142. A servo-hydraulic machine was used to carry out the tests, obtaining the parameters Young's modulus ( E ), tensile yield stress (  y ), tensile strength (  f ), and tensile failure strain (  f ). Fig. 1 illustrates the tensile stress-strain curves (  -  ) of the adhesive. The shear tests, obtained previously (Faneco et al. 2017), determined