High Strain Rate Behaviour of Auxetic Cellular Structures

Abstract

Auxetic cellular structures are modern metamaterials with negative Poisson’s ratio. The auxetic cellular structures build from inverted tetrapods were fabricated and experimentally tested under dynamic loading conditions to evaluate the effect of strain rate on their deformation mode. The Split-Hopkinson Pressure Bar (SHPB) apparatus was used for testing at strain rates up to 1,250 s, while a powder gun was used for testing at strain rates up to 5,000 s. The homogeneous deformation mode was observed at lower strain rates, while shock deformation mode was predominant at higher rates. The results have shown that the strain rate hardening of analysed auxetic specimens is prominent at higher strain rates when the shock deformation mode is observed, i.e. when most of deformation occurs at the impact front. Relevant computational models in LS-DYNA were developed and validated. A very good correlation between the computational and experimental data was observed. Introduction Auxetic cellular structures are novel metamaterials with negative Poisson’s ratio – they tend to expand in lateral direction when subjected to tensile loading and vice versa in the case of compression loading [1]. This behaviour can be beneficial in many applications, especially in the crashworthiness, ballistic protection and energy absorption applications [2]. The mechanical behaviour of auxetic structures is well characterised and understood for quasi-static loading conditions, but not so much for dynamic and impact loading due to insufficient experimental characterisation attempts so far. Past studies were mostly concerned with the quasi-static elastic behaviour of uniform auxetic structures at very small strains [3] and limited ballistic resistance study [4]. Mechanical behaviour of some particular auxetic structures was characterised by uniaxial quasi-static compressive and tensile tests [5–10]. The Split-Hopkinson Pressure Bar (SHPB) experiments were also carried out for auxetic cellular structures fabricated with additive manufacturing, including also polymer fillers [11]. There is a clear need to test the auxetic cellular structures also under high strain rate loading conditions to comprehensively evaluate their behaviour also at highly dynamic loading. Especially since there are many applications where these metamaterials can be used efficiently. Explosion Shock Waves and High Strain Rate Phenomena Materials Research Forum LLC Materials Research Proceedings 13 (2019) 25-30 https://doi.org/10.21741/9781644900338-4 26 Specimens fabrication The specimens build from inverted tetrapods were used in this research. Inverted tetrapods (Fig. 1a), are assembled in a particular way to define the geometry of the investigated specimens (Fig. 1b-c). The specimen’s inverted tetrapod dimensions were (Fig. 1a): a = 3.5 mm, h = 3 mm, dh = 0.5 mm, while the circular cross-section diameter of the struts was in range from 0.38 to 0.53, depending on the porosity (Table 1). Two types of specimens were analysed in this work: a) short and b) long specimens. The difference between the analysed types of specimens was in length in X2 direction (Table 1). The specimens were fabricated from the Ti-6Al-4V alloy powder by the selective electron-beam melting method (SEBM) at the Institute of Materials Science and Technology (WTM), University of Erlangen-Nürnberg, Germany [12]. Figure 1: Geometry of auxetic specimens build from inverted tetrapods: a) inverted tetrapod, b) geometry in orthogonal views and c) fabricated specimen Table 1: Specimens data Short specimens Dimensions [mm] |X1| × |X2| × |X3| Mass (std. dev.) [g] Density [g/cm] Porosity p [-] Middle porosity 15.6 × 19.2 × 18.7 3.45 (0.023) 0.62 0.86 Long specimens Dimensions [mm] |X1| × |X2| × |X3| Mass (std. dev.) [g] Density [g/cm] Porosity p [-] High porosity 15.6 × 40.5 × 18.7 4.67 (0.138) 0.40 0.91 Middle porosity 7.24 (0.051) 0.61 0.86 Low porosity 9.04 (0.075) 0.76 0.83 High strain rate experimental testing High strain rate experimental testing was performed using two different experimental devices: a) Split Hopkinson Pressure Bar (SHPB) apparatus at the State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, China and b) the powder gun at the Institute of Pulsed Power Science, Kumamoto University, Kumamoto, Japan. The achieved loading velocities were 25 m/s and 220 m/s using the SHPB and the powder gun, respectively. The loading velocities correspond to the strain rates up to 1,250 s and 10,000 s for short specimens and 5,000 s for long specimens, respectively. In the case of powder gun experiments the mechanical response was evaluated with the PVDF gauge (Piezo film stress gauge, PVF2 11125EK, Dynasen), as in previous experiments described by Tanaka et al. [13]. A homogenous h