OPTIMIZATION OF TI6Al4V AUXETIC STRUCTURES R. Acevedo 1 *, R. Kolman 2 , M. C. Fredel 1 , E. C. Santos 3 *ruben.acevedo@rocketmail.com 1 Department of Mechanical Engineering, Universidade Federal de Santa Catarina 2 Institute of Thermomechanics of the Czech Academy of Sciences, 3 Zeiss Introduction XVIII SBPMAT 2019 Objective: Optimization of four structure parameters - L, H, W, and Θ. Two optimal solutions are pre-defined: 1) Minimal stiffness with minimal mass; 2) Maximal stiffness with minimal mass. Besides, the correlation between geometric parameters will be established. Finally, the effect of these parameters in Poisson's ratio will be observed. To implement simulations and analysis, a Finite Element Method – ANSYS 19 – is used for prediction of mechanical behavior of the auxetic Ti6Al4V structure. Material and Methods • Optimization of the main structure parameters that affect Poisson’s ratio by static simulations in ANSYS 19; • Determination of optimal parameters for minimal and maximal stiffness. References [1] Mott, P.H. Physical Review B, 80, 2009 [2] Lim, T.C. Eng. Materials series, 2015 [3] Yang, L. Materials Sci. & Eng. A, 558, 2012 [4] Wang, X. Int. Journal of Mech. Sci. 2017 [5] Wang, X.T. Wang, B. Li, X.W. Ma, L. Mechanical properties of 3D re-entrant auxetic cellular structures. 21 st International conference on composite materials, 2017. Conclusions An optimization of geometric parameters was successfully implemented in an auxetic Ti6Al4V structure. A swift change in parameter values can produce auxetic parts with completely diverse mechanical behavior: minimal stiffness is obtained with W minimized and H/L maximized; inversely, an auxetic structure having maximal stiffness is obtained as W is maximized and H/L is set to a minimum. Acknowledgements L W θ Nevertheless, there is a class of materials which present a negative Poisson ratio, those are called auxetic (first introduced by Evans), derived from the Greek word auxetikos , defined as “that which tends to increase”. Auxetic behavior can be either intrinsic or obtained by several re-entrant geometries [2]. These geometries can also be extended in 3D. Figure 1 shows two geometries that present auxetic behavior. In this study, an auxetic geometry was chosen, especially due to its easiness in parametrization and promising early simulation results. Elastic behavior of this structure has been studied in [3,4]. Typically, most of the materials have a Poisson’s coefficient between 0,2 and 0,4. Poisson’s coefficient is a non-dimensional ratio defined as the fraction between longitudinal elongation and lateral compression after a uniaxial traction effort. This coefficient allows the characterization of matter contraction perpendicular to the applied effort direction [1]. Considering only isotropic materials, the values for this elastic constant are comprised in the [-1, 0.5] interval. Fig. 1. Auxetic geometries Fig. 2. Auxetic structure under analysis. H W L θ Results and discussion • Optimization of geometric parameters After the creation of a 2D parametric model containing the four main geometric dimensions – L, H, W and θ – a load of 1 N was applied in the right edge of the structure (Fig. 2). Further on, the corresponding elastic deformation was measured in x and y directions. The combined influence of parameter θ and H/L ratios on the Poisson coefficient was studied by fixing W values, shown in Fig. 3. -11 -9 -7 -5 -3 -1 1 5 25 45 65 85 105 Poisson ratio (ν) θ (°) H/L=2 H/L=2,5 H/L=3 Results and discussion In the following, the combined influence of parameters W and θ was studied by fixing H/L=2. Poisson’s coefficient curves can be observed in Fig. 4. -24 -19 -14 -9 -4 1 5 25 45 65 85 105 Poisson ratio (ν) Poisson (W=0,1 mm) Poisson (W=0,5 mm) Poisson (W=1,0 mm) Poisson (W=1,5 mm) Poisson (W=2,0 mm) Θ (°) To ensure the validity of previous results, a comparative analysis, g3, with the analytical solution (in elastic regime) proposed by Wang [5] was then performed. This analytical formulation uses all geometric parameters of this structure and corresponding material properties E, G and ν (in this case, for Ti6Al4V). -4 -3 -2 -1 0 1 15 35 55 75 95 Poisson ratio (ν) θ (°) Poisson (Analytical) Poisson (FULL2D-PSTRESS) Poisson (FULL2D-PSTRAIN) Comparing simulation results with the analytical solution (g3), it can be observed a good agreement for θ > 35°. As in the [15,35] angle interval, a significant difference appear: for instance, as θ =24°, Poisson ratio is equal to -2,75 (analytical) and -3,50 (plane stress/strain simulation). For θ < 15° , the analytical formulation does not provide usable data. Parameters: H/L=2; W= 1 mm Fig. 3: Poisson ratio dependance on H/L and θ Fig. 4: Poisson ratio dependance on W and θ Fig. 5: Poisson ratio analytical solution vs FEM simulation