PSI - Issue 42

F. Cesarano et al. / Procedia Structural Integrity 42 (2022) 1282–1290 F. Cesarano, M. Maurizi, C. Gao, F. Berto, F. Penta, C. Bertolin / Structural Integrity Procedia 00 (2019) 000 – 000

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2. Materials and methods Given the cost-effectiveness and practicality of the FDM method used in the literature [2, 5, 6], this method was also taken as a starting point and used in this work, combined with PLA, the most widely used filament for 3D and 4D printing techniques [1, 2]. In addition to the classic properties of PLA, it should be pointed out that inhomogeneous elements with anisotropic properties are generated during the FDM process. Casavola et al., 2016 [8] described the mechanical behaviour of components obtained with FDM using classical laminate theory, calculating the values of the elastic modulus in the longitudinal direction and transverse to the fibre direction for a single-layer test specimen for different fibre inclination angles (Fill-density = 100%). They also derived the Poisson's coefficient and shear modulus experimentally. On the other hand, in Baker et al., 2017 [9], due to the biaxial symmetry (XY plane of isotropy), a transversely isotropic material model was developed to simulate the response to thermal and mechanical loads, obtaining the coefficient of thermal expansion (once passed the transition temperature) and the glass transition temperature. Consequently, this characterization of the PLA (shown in Table 1) makes it possible to obtain more accurate numerical simulations (in bold are the properties used in the finite element analysis in this work). 185 ± 5 * − 57 ± 1 The first theoretical method on which this research is based is the bi-material strip theory [10, 11, 12], which is as close as one can find in theoretical terms to a bending deformation of a multilayer component. To calculate flexural curvature ( ) to measure and catalogue the curvatures obtained in the performed experiments, in analogy to the bi material strip theory, the geometric equation (1) was exploited in this contribution: = 2sin [ −1 (δ⁄ )] √ 2 + δ 2 where δ is the maximum deflection obtained from the bending acting on the component, and is the abscissa to which the maximum deflection corresponds. The second theoretical method that accompanied this research is the classical theory of laminates [10, 11, 12], which, combined with the numerical method, i.e. the FEA, supports the experimental characterization of the phenomenon (SME and viscoelastic behaviour [5]). Then, there is the experimental method, which can be divided into the specimens' production process (stage (a) in Fig. 1) and the thermal stimulus's application process (stage (b) in Fig. 1). The production process is realized through a 3D printer (Prusa I3 MK3S) and the corresponding slicer to create the various specimens; on the other hand, the thermal stimulus is applied in a gravitational convection oven (Fisherbrand). Once the choice of materials and methods used has been made, it is pointed out that of all the available studies, the composite specimens proposed in van Manen et al. 2017 [ 2 ] and Yu et al. 2020 [ 5 ] are those that best suit the objective of this research; namely, the quantitative and mathematical analysis of unidirectional SMPs as a function of temperature and time. For example, it is possible to obtain pure bending deformation by printing a bi-layer plate with one layer having the fibres' orientation at 0° and 90° [ 5 ]. As a result, the default settings of the 3D printing slicer were changed to allow the production of these samples in this particular way. Table 2 shows the modification of the main parameters used to produce the specimens. (1) Table 1: PLA's Young modulus, Poisson's ratio and shear modulus [8] - Coefficients of thermal expansion and glass transition temperature [9] Samples Young's Modulus (GPa) Poisson's ratio ( 12 ) Shear modulus ( 12 ) (M Pa ) CTE ( ° −1 ) (° ) - - 185 ± 5 * 10 −6 57 ± 1 0.330 1246.57 ± 32.21 185 ± 5 * − 57 ± 1 0.330 1246.57 ± 32.21 185 ± 5 * 10 −6 57 ± 1 0.330 1246.57 ± 32.21 PLA Wire 3.38 3.12 2.86 2.77 PLA 0° PLA 45° PLA 90°