PSI - Issue 52

Chen Zhou et al. / Procedia Structural Integrity 52 (2024) 234–241 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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et al. 2018). However, the sandwich structure has some obvious weaknesses, such as a large stiffness difference between the face sheet and the core, which leads to easy damage at the interface between the face sheet and the core. Typically, the fracture pattern of the interface between the face sheet and core is mixed mode fracture. Some test configurations for mixed mode fracture have been developed, such as the single cantilever beam (SCB) test (Saseendran et al. 2020), mixed-mode bending (MMB) test (Quispitupa et al. 2010), and DCB-UBM test (Sørensen et al. 2006). The SCB test does not require complex test equipment, but the mode mixity that can be produced is very limited. The MMB and DCB-UBM specimens can generate larger mode mixity by changing the loading position and the moment ratio, respectively, but require more complicated test equipment. In addition, the DCB-UBM test can produce more stable crack propagation than the MMB test (Sørensen et al. 2006). The DCB-UBM test was proposed by Sørensen et al. (2006) for mixed mode fracture mechanics characterization of adhesive joints, laminates, and multilayers, and a particular loading fixture based on steel wires was developed at the same time. Lundsgaard-Larsen et al. (2008) applied this test method to sandwich structure. Later, Kardomateas et al. (2013) gave the closed-form algebraic expressions for ERR and mode mixity of the DCB-UBM sandwich specimen. In addition, the test equipment of DCB-UBM was optimized by Berggreen et al. (2018). The new equipment is easy to operate and can produce a greater mode mixity. There are many studies on the DCB-UBM test under static loading, but few reports on the DCB-UBM test under dynamic loading, because the dynamic load in the experiment is not well controlled. However, with the rapid development of numerical methods, we can use numerical methods to investigate the fracture characterization of DCB-UBM specimens under dynamic loading. The primary goal of this paper is to investigate the fracture characterization of DCB-UBM specimens under dynamic load, and a new numerical method named the MCSDE method is proposed to calculate ERR and PA by relative surface displacement. The paper is organized as follows: First, the implementation of the MCSDE method is introduced. Next, the accuracy of the MCSDE method is verified. Finally, the fracture characterization of the DCB UBM specimen under dynamic load is investigated based on the MCSDE method. 2. Numerical implementation method Due to the face sheet and core of a sandwich structure are typically made of different materials, oscillation singularity will occur near the crack tip (Hutchinson and Suo 1991). Commonly used numerical methods for solving this complex interface fracture problem are the Virtual Crack Closure Technique (VCCT, Krueger 2004), the Crack Surface Displacement method (CSD, Matos et al. 1989), and the Crack Surface Displacement Extrapolation method (CSDE, Berggreen 2004). Krueger et al. (2013) summarized the advantages and limitations of the above-mentioned methods, and pointed out that the CSDE method is a promising method due to CSDE method can effectively avoid the numerical error zone by extending the linearization, the result is therefore relatively stable. However, the results of the CSDE method depend on the slope of the extrapolation curve, and the linear extrapolation of the transition zone is no good fit in some isolated cases (Berggreen 2004). Therefore, we proposed a modified CSDE (MCSDE) method that makes the result more stable. The MCSDE method uses surface displacement δx and δy to horizontally extrapolate the values before the numerical error zone to the crack tip, which effectively avoids the influence of the extrapolation curve slope on the results. The schematic diagram of the MCSDE method is shown in Fig. 1. The computational formulas for ERR and PA based on surface displacements are as follows: The PA , defined as the ratio between mode Ⅰ and mode Ⅱ stress intensity factors of a bi -material interface crack, can be expressed by Eq. (1) (Zhou et al. 2023). ( ) 22 11 arctan ln arctan 2 x y H H h           = − +       (1) where ε denotes the oscillatory index and can be expressed as 1 1 ln 2 1      −  =    +  (2) where β is D undur’s parameter, and H 11 and H 22 are bi-material parameters. Further details can be found in the work    