PSI - Issue 25

E. Solfiti et al. / Procedia Structural Integrity 25 (2020) 420 – 429 E. Solfiti and F. Berto / Structural Integrity Procedia 00 (2019) 000–000

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fracture profile outlines the boundaries of some bounded units (same as the deformation units), even parallel to the load direction, and departing from di ff erent locations near the notch. Gu et al. (2002) suggested that these units first rotate along the load direction and then the slippage appears until the final pull-out. Leng et al. (1998) supposed that the tensile strength is mainly governed by the internal pressure of trapped air and developed a simple theoretical model that related the tensile strength to the density and the flake sizes: σ = kP i ρ d , being P i the air pressure and d the theoretical pristine flake size. It can explain the linear relation among density and flake sizes. Finally, it has been found that the essential work applied with the plane stress hypothesis, can characterize properly FG sheets tensile strength. Khelifa et al. (2018) developed also a first numerical FE model to simulate commercial FG foil with 1 mm thickness and compared the results with experimental nanoindentation data. The constitutive equation applied to the model is that of an isotropic elasto-plastic material. The elastic properties carried out are reported in the previous lines and they are consistent with data from furnisher, but they need further confirmation since no comparable experimental data are available (Chen and Chung (2015) applied nanoindentation on lower density FG foils). The visco-elastic behavior of a material can be substantially measured by the loss tangent tan δ (or loss factor) where δ is the phase-lag angle between the dynamic stress applied and the subsequent strain. Given the layered microstructure, the viscous component of CEG becomes more relevant at lower densities. For example loss tangent values up to 0.187 were found in flexural tests of FG with density equal to 1 . 1 g / cm 3 , against 0.019 or 0.021 of pure aluminum and Zn-Al alloy respectively (Luo and Chung (2000)). Even tan δ = 0.92 when ρ = 0 . 35 g / cm 3 (Chen and Chung (2013). Despite rubbery materials are known to be excellent dumping materials and they show values for tan δ up to 0.7, when normalized respect on the e ff ective solid phase, the expanded graphite results to be again better (Chen and Chung (2013). Indeed, the cell walls of CEG and FG are made of multiple layers (approximately 60, as shown by Chen and Chung (2013)), depending on the intercalate stages, and they are shared between two or more cells allowing a certain amount of relative displacement both within the single wall and relative to the cell walls. The cells can be viewed as volumes interlocked at the edges that stretch and flatten upon loading. An engineering shear strain up to 35 for exfoliated graphite compacts and up to 12 for FG with ρ = 0 . 86 g / cm 3 was found to exist between the only cell walls by (Chen and Chung (2015)). The volume fraction of the solid phase within a graphite compound (also referred to as solid content) a ff ects both the elastic and viscous part of the response (see fig.7). As it increases, the layered are tightened and the relative displacement is hindered. The storage and loss modulus increase both in flexural and compressive tests in the in-plane direction at low frequencies, in opposite manner to the loss tangent (Chen and Chung (2012, 2013); Luo and Chung (2000)). Viscous character is higher in flexural load given the in-plane preferred orientation of graphite layers Chung (2014). Hence, to loosen the bondings means to enhance the sliding of the cell walls and to dissipate more energy by the friction forces. Xiao and Chung (2016) modeled low density CEG with interfacial friction theory, allocating each cells with 4 parallel Voigt elements, and showing that the contribute on the internal sliding stems primarly from the one among the cell walls rather then the negligible inter-layer one. 3.3. Visco-elastic behavior

4. Conclusion

The previous discussion can be summarized in the following points:

• the microstructure of FG is almost totally outlined: the deformation units have a preferred orientation and they result directly from the worms compaction. The larger the original flake size, the larger the exfoliated volume and more e ff ective the load distribution; • anisotropy e ff ects among the in-plane and out-of-plane is evident in all the quantities such as strength, modulus, deformation and conductivities; • the compression / recovery behavior is due to both trapped air and internal bending of fixed deformation units. Elastic and plastic behavior coexist. Compression modulus and strength are known but still to be better con firmed by further testing in a wider range of density ;