PSI - Issue 28

Theodosios Stergiou et al. / Procedia Structural Integrity 28 (2020) 1258–1266 T. Stergiou et al. / Structural Integrity Procedia 00 (2019) 000–000

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2.2 Constitutive description of substrate material Aluminium 6061-T6, used as target substrate, experiences low sensitivity to plastic strain, together with high sensitivity to the rate of strain and temperature. Such characteristics are inherent to metals with a face-centred cubic lattice. Its ultimate strength is linearly related to the logarithm of the strain rate, showing an increased strain rate dependency above the transitional region of 1 s –1 – 10 s –1 . The relationship of its flow stress and ultimate strength to the temperature is an inverse one. This behaviour is well-documented in the literature (CES, 2009; Lesuer et al., 2001; Marom & Bonder, 1979). A Johnson-Cook associative flow rule was chosen for the prediction of the dependence of the yield stress on the plastic strain, strain rate and temperature (Johnson & Cook, 1985). To capture the effects of these factors on ultimate strength, the Johnson-Cook failure model provides a convenient approach in accounting for damage accumulation in the material in terms of the failure strain. Damage accumulation is then defined as the sum of the ratios of plastic strain increments to the failure strain. Material degradation was implemented employing a linear decrease in the material resistance; the effective stress component was the updated measure of stress to account for material degradation, reaching a null value when damage reached a value of unity. 2.3 Numerical modelling The explicit scheme was used to solve the system of dynamic equations of motion, with deformations calculated at discretised points along the geometry with the FE method. The discretisation of layers of the thin plate target was performed by utilising a combination of a continuum and conventional shell elements. Since the smaller in-plane dimension was more than 28-fold of the through-thickness size, this discretisation was reasonable and provided a right balance of accuracy and computational efficiency. Eight-node quadrilateral elements (SC8) are considered for the continuum shell discretisation, which considers a non-zero through-thickness strain component and can treat local bending better. Double-curved quadrilateral, four-node elements (S4), were employed for general-purpose shell elements. Such elements automatically account for thin- and thick-shell theories and can shift between the two during the analysis if required. Both formulations consider finite membrane strains with displacement interpolation in the elements performed using a second-degree polynomial. Following the mesh- sensitivity analysis, the element size in the vicinity of the impact region was selected as 0.4 mm. The interfacial interaction between the polymer coating and the metallic substrate plate was assumed to follow tangentially the in-plane linear Coulomb friction with a coefficient of 0.1 and a no-penetration contact without bonding in the normal direction. 2.4 System configuration Here the details on the geometrical configuration that was selected in this study are provided. The evaluated model included a rigid spherical projectile of 23.80 mm diameter and a two-layer target. The front layer was a polyurea coating of varying thicknesses up to ℎ � � � mm . Aluminium 6061-T6 was selected as the substrate material, with a constant thickness ( ℎ � � ���� mm ). The ratio of projectile’s diameter to substrate’s thickness, � /ℎ � , of 6.8 is constant throughout this work. An overview of the general configuration and major dimensions of the system under consideration are provided in Fig. 2. In this study, the planar target dimensions remained unchanged, with height, H , and width, W , of 300 mm and 200 mm, respectively. The target was clamped at one of the short edges, in a cantilever arrangement, with the clamping region 160 mm × 50 mm. 3. Results and analysis A projectile velocity of 200 ms �� was selected for our investigation and was the reference for subsequent comparative studies. The rationale behind the choice of impact velocity is that the transition between a global bending response to a more local, deformation-dominant response of thin 6061-T6 aluminium plates was reported to occur in a velocity range on the proximity of the respective impact velocity (Shadbolt et al., 1982). In our study, the four coating thicknesses of 1.2 mm , 3 mm , 5 mm , and 7 mm, were considered, together with an aluminium target of 3.52 mm thickness.