Compression and shear behaviour of graded chiral auxetic structures

Highlights

• experimental testing of graded chiral auxetic structures under compression and shear loading.

• development and validation of the computational models

• calculation of shear and Young’s modulus of analysed auxetic structures.

• evaluation of influence of graded porosity on the mechanical response of auxetic chiral structure.

Abstract

Graded chiral auxetic cellular metal structures were produced from copper alloy powder using Selective Electron Beam Melting (SEBM) technique and tested under compressive and shear loading conditions. The predesigned geometry of chiral structures has a variable chiral amplitude through the length of the specimens, which results in graded porosity of the analyzed auxetic structures. The deformation mechanisms and mechanical response were evaluated with compression and shear testing at two loading velocities. The infrared thermography has been used to track the evolution of plastic deformation in the specimens. The deformation process under compression loading starts in the area with the largest chiral amplitude and then continues through the whole height of the specimen. The shear loading shows two significantly different groups of responses, which are affected by local defects causing the start of failure in different parts of structure. The results of experimental testing were further used for validation of developed finite element models of chiral structures. The influence of graded porosity on the mechanical response of chiral structures was evaluated with parametric computational simulations and compared to the non-graded structure with constant chiral amplitude and same weight. The non-graded auxetic structure offers a stiffer response due to deformation uniformly distributed through the height of the specimens but fails abruptly at lower strains.

Introduction

Auxetic cellular structures are modern metamaterials, which exhibit a negative Poisson's ratio (Caddock and Evans, 1989). The consequence of negative Poisson's ratio is particular deformation behaviour (material expands in lateral direction when stretched, and vice versa, when compressed) contributing to enhancement of mechanical properties useful in many fields of engineering, medicine, fashion and sport (Novak et al., 2016). The auxetic materials have improved shear performance (increased shear modulus) (Yang et al., 2004), damping properties, sound (Scarpa et al., 2004) (also with control of acoustic band gaps Krödel et al., 2014) and energy absorption (Chan and Evans, 1998, Yang et al., 2013;Novak et al., 2019) of structural components and the possibility to predefine crack propagation path (Kramberger et al., 2019), which makes them particularly useful for many modern multifunctional applications. They are being increasingly studied for use as cores in composite sandwich plates for ballistic protection in combination with cover plates made from other materials in body and vehicle armour applications (Imbalzano et al., 2015; Imbalzano et al., 2015). They have the potential to reduce the impact forces upon small (e.g. elbow) or large affected area (e.g. leg, human torso) as flexible pads (Lakes, 1993), which can also be used for sports applications (Sanami et al., 2014). The advantage of auxetic sandwich plates to deform in a convex shape (synclastic curvature) is exploited in automotive and aerospace engineering (Lakes, 1987; Evans, 1991). Additionally, a morphing wing can be established in aerospace engineering by use of auxetic structures (Airoldi et al., 2012). The use of different auxetic textiles is also studied (Sloan et al., 2011; Dobnik Dubrovski et al., 2019; Wang and Hu, 2014;Jiang et al., 2015). Furthermore, graded porosity can enhance the mechanical and acoustic properties of the auxetic structures even more (Lim, 2002), which was shown in the case of gradient honeycombs (Lira and Scarpa, 2010), Kirigami sandwich structures (Hou et al., 2014), blast protection panels (Novak et al., 2019), shock absorbers (Al-Rifaie and Sumelka, 2019) and also in the case of aero engine fan blades (Lira et al., 2011). Some of the graded auxetic structures were also tested under high strain rate loading, where the gradation is more important due to the inertia effects (Novak et al., 2018).

Most of the research of auxetic cellular structures has been so far performed under uniaxial tensile or compression loading conditions (Scarpa et al., 2005; Duncan et al., 2016; Novak et al., 2018;Carta et al., 2016). The elastic mechanical properties were determined also for hexagonal crystals (Gorodtsov and Lisovenko, 2019) and 3D re-entrant structures using analytical and finite element approach (Shokri Rad et al., 2014). However, the auxetic cellular structure can be used in other loading scenarios, like shear and torsion. The shear loading investigations of auxetic cellular structures are very limited, mostly due to complex fixtures needed for experimental tests. The shear experimental testing of missing rib auxetic structures was done recently (Jin et al., 2019), where authors also performed parametric computational studies to investigate the relationships between the physical design parameters and the key model parameters. The theoretical and computational investigation of shear resistance of auxetic structures was reported in Doyoyo and Wan Hu (2006), where authors determined that the auxetic cores are structurally less stiff under longitudinal loads and stiffer under transverse loads. The transverse (out-of-plane) shear properties of a novel centre symmetric honeycomb structure was evaluated using analytical and finite element models in Lira et al. (2009). The out-of-plane shear modulus of auxetic honeycomb structure was analyzed with computational simulations also in Scarpa and Tomlin (2000). The shear modulus of re-entrant copper foam was evaluated using experimental tests in Li et al. (2013), where it was shown that shear modulus increased with increasing volumetric compression ratio, and showed a small hump of shear modulus near the point corresponding to the Poisson's ratio minimum. The transverse elastic properties of chiral honeycombs were determined in Lorato et al. (2010) using the analytical approach.

As it can be concluded from the above state-of-the-art review, there is a clear need for further investigations of shear response of auxetic structures. This study is thus concerned with experimental and computational determination of shear mechanical properties and deformation behaviour up to failure of three-dimensional graded chiral auxetic copper structures at two loading rates for the first time.