Auxetic lattice truss cores fabricated of LayWood

Abstract

Lattice truss cores are used to reduce the mass and increase the strength of sandwich boards. These panels are typically manufactured from metal or carbon composites. As a rule, they do not exhibit auxetic properties. Auxetic structures have several extraordinary mechanical properties. The aim of this study was to manufacture lattice auxetic cores from a biodegradable material and determine their elastic properties. The structures were produced from LayWood Olive, a composite containing polylactic acid and 40% wood dust. The cores had comparable relative densities, but their geometry and number of cells differed. As a result of uniaxial compression in individual lattice truss cores, it was shown that the cores whose cells were square in the top view were isotropic. In contrast, cores with rectangular cells were strongly orthotropic. Moreover, the Poisson’s ratio changed depending on the cell size and rib angle. Among the cores that exhibited isotropic properties, the lowest Poisson’s ratio and modulus of elasticity were recorded for the structure composed of 49 cells with ribs that were 2 mm thick. The highest Poisson’s ratio and modulus of linear elasticity were found with the orthotropic structure composed of 15 cells with ribs that were 3 mm thick. This paper was based on numerical calculations that were verified by experimental studies.

Full Article

Auxetic Lattice Truss Cores Fabricated of LayWood

Jerzy Smardzewski,^a,* Krzysztof W. Wojciechowski,^b and Artur Poźniak ^c

Lattice truss cores are used to reduce the mass and increase the strength of sandwich boards. These panels are typically manufactured from metal or carbon composites. As a rule, they do not exhibit auxetic properties. Auxetic structures have several extraordinary mechanical properties. The aim of this study was to manufacture lattice auxetic cores from a biodegradable material and determine their elastic properties. The structures were produced from LayWood Olive, a composite containing polylactic acid and 40% wood dust. The cores had comparable relative densities, but their geometry and number of cells differed. As a result of uniaxial compression in individual lattice truss cores, it was shown that the cores whose cells were square in the top view were isotropic. In contrast, cores with rectangular cells were strongly orthotropic. Moreover, the Poisson’s ratio changed depending on the cell size and rib angle. Among the cores that exhibited isotropic properties, the lowest Poisson’s ratio and modulus of elasticity were recorded for the structure composed of 49 cells with ribs that were 2 mm thick. The highest Poisson’s ratio and modulus of linear elasticity were found with the orthotropic structure composed of 15 cells with ribs that were 3 mm thick. This paper was based on numerical calculations that were verified by experimental studies.

Keywords: Auxetic; Lattice truss cores; LayWood; Experiment; FEM

Contact information: a: Department of Furniture Design, Faculty of Wood Technology, Poznan University of Life Sciences, Poznan, Poland; b: Institute of Molecular Physics Polish Academy of Sciences, Department of Computational Physics of Complex Systems, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland; c: Poznan University of Technology, Faculty of Technical Physics, Institute of Physics, Piotrowo 3, 60-965 Poznań, Poland; Corresponding author: jsmardzewski@up.poznan.pl

INTRODUCTION

Composite sandwich structures are widely used in various fields because of their high specific strength and modulus, high temperature resistance, and damping, etc. The cores can be comprised of prismatic elements (honeycomb, textile, and corrugations), an assembly of struts (tetrahedral, pyramidal, and Kagome), or shell elements (egg-box) (Wadley et al. 2003). There is additional space in the core to allow the use of a multi-functional filler, which facilitates special engineering applications (Wang et al. 2018). Core plates with auxetic properties (i.e. having a negative Poisson’s ratio) are particularly attractive. Auxetic systems exhibit the unusual and useful property of becoming wider rather than thinner when uniaxially stretched. Grima et al. (2013) presented a mechanism to generate auxetic behavior at tailor-made values, which may be implemented in composite manufacture using readily available materials. Huang et al. (2017) developed a novel honeycomb design with a negative Poisson’s ratio. It was composed of two parts (a reentrant hexagonal component and thin plate) that provided separate contributions to the in-plane and out-of-plane mechanical properties. The authors focused on the in-plane mechanical properties of the auxetic cellular structure. The transverse shear properties of a novel centrosymmetric honeycomb structure were studied by Lira et al. (2009). The cellular structure features a representative volume element (RVE) geometry, allowing in-plane auxetic deformations, and multiple topologies to design the honeycomb for multifunctional applications. In contrast, composite sandwich structures with lattice truss cores have been attracting increasing attention because of their superior specific strength/stiffness and multi-functional applications (Wang et al. 2014). Many researchers have emphasized the preferred fabrication methods for these structures and the conceptual basis for topology selection, as well as the attributes of the best load supporting structures. Unfortunately, none of these structures exhibit auxetic properties. Additionally, none of these materials were made of wood or wood composites.

Polymer hierarchical truss materials with low relative densities have been fabricated for compressive tests (Wu et al. 2017). The results are very useful for designing ultra-lightweight hierarchical truss materials with high specific strength at low density in order to avoid the deficiencies of this structural configuration. Compressive and shear tests were conducted to investigate the mechanical properties and the failure mechanism of a new composite pyramidal lattice structure made of unidirectional carbon fibre (epoxy laminate). The experimental results show that the new composite has some significant advantages compared with other existing composite pyramidal lattice structures. Wu et al. (2016) improved the strength of truss lattice sandwich structures by optimizing the topology structure. As a result the hourglass lattice sandwich structure may be considered as a promising candidate in high specific strength lightweight structures. Xu et al. (2016) presented a new method to form graded corrugated truss core sandwich structures based on an auto-cutting and mould-press process. Results showed that the distributions of the truss cores strongly affect bending behavior of sandwich beams. In paper (Wang et al. 2018) the authors showed that the mechanical behaviour of the pyramidal lattice truss core sandwich panels made from carbon fibre reinforced composites materials, depends on the relative density of the core and the material properties of truss members. Based upon the previous work (Gao et al. 2013) the authors designed and fabricated a strengthened pyramidal truss core with an interlacing laminate form of adjacent nodes to solve the problem of core-separation failure and fully justify the potential of cross-bars. Dong and Wadley (2015) investigated octet-truss lattice structures made from balanced [0/90] carbon fiber reinforced polymer (CFRP) laminates using a simple snap-fit method. Their isotropic response may provide new opportunities for ultra-lightweight multiaxial loaded structures. Those authors developed a simple snap-fit and vacuum brazing method to fabricate three-dimensional space filling octet-truss lattice structures from Ti–6Al–4V alloy sheets. These truss lattices exhibit excellent mechanical properties compared to other cellular materials. The study (Xu et al. 2015) introduced a novel concept of combining graded material and a lattice truss core to form graded lattice truss core sandwich structures, which is based on the stitching and hot-press process. In the study (Li et al. 2011) the mechanical performance of an all-composite pyramidal lattice truss core sandwich structure was investigated. Sandwich structures were fabricated with a hot compression molding method using carbon fibre reinforced composite T700/3234. The pyramidal truss core sandwich structures consisting of CFRP face sheets and aluminum alloy cores were described in the paper (Zhang et al. 2013). The aim of this hybrid concept is to maximise the specific bending stiffness/strength as well as provide an excellent energy absorption ability. Pingle et al. (2011) developed collapse mechanism maps for the shear response of sandwich panels with a stainless steel core comprising hollow struts. Quasi-static uniform compression tests and low-velocity concentrated impact tests were also conducted to reveal the failure mechanisms and energy absorption capacity of two-layer carbon fibre composite sandwich panels with pyramidal truss cores (Xiong et al. 2012).

The literature review shows that layered structures with lattice truss cores are known. These are: corrugated core constructions (Wadley et al. 2003), graded corrugated truss (Xu et al.2015, 2016), two-layer pyramidal truss sandwich core (Xiong et al. 2012), pyramidal core (Li et al. 2011; Gao et al. 2013; Yang et al. 2014), hollow pyramidal core with the four tubes (Pingle et al. 2011), diamond weave, egg box (Wadley et al. 2003), tetrahedral, double layer Kagome ‘lattice trusses (Yungwirth et al. 2008), 2-D lattice truss core (Wang et al. 2014), X-type lattice truss core (Wang et al. 2018), octet-truss lattice structures (Dong et al. 2015; Dong and Wadley 2015). The applied models are distinguished by symmetry and periodicity in two mutually perpendicular directions. Just a few works (Yungwirth et al. 2008; Li et al. 2011; Xiong et al. 2012; Zhang et al. 2013l; Feng et al. 2016) refer to symmetrical arrangements of pyramidal cores. In these works, the broader base of a single cell is square. This suggests that the cores should have isotropic properties. However, there is a lack of broader discussion of structures with orthotropic properties useful in constructions made of wood or wood-based composites. In addition, the literature review shows that the mechanical properties of sandwich panels with pyramidal cores have been tested many times. They were subjected to bending, compression and shearing. However, the elastic properties of the cores have not been determined. It has not been established whether these are conventional or auxetic structures. The term “auxetic” defines a class of materials that exhibit a negative Poisson’s ratio, which causes a counter-intuitive expansion under tension rather than contraction (Evans et al. 1991). These materials have been shown to possess enhanced toughness and hardness, as well as absorb sound and vibrations better than their non-auxetic counterparts (Greaves et al. 2011). The atypical elastic behavior of auxetic materials is enabling advancements in a broad range of technologies such as high-performance armor, extremely precise sensors, and impact-resistant composites (Alderson 1999). Therefore, it would be important to determine the elastic properties of the lattice core in iso- and orthotropic systems and to demonstrate their auxetic characteristics. In addition, the works discussed were related to structures made of metal, carbon fibers or polymers. The possibility of using them in the design of biomaterial constructions is very limited. They are an additional difficulty in recycling. Therefore, new natural materials are being sought, which can ensure the use of wood-based sandwich panels in the construction.

In fact, the mechanical properties of LayWood are small in relation to metals, carbon fibers or polymers. However, compared to the properties of the paper core, even the auxetic one, the obtained elastic constants are far from being satisfactory (Smardzewski 2013). They can therefore guarantee that multilayered sandwich panel with lattice LayWood core will be distinguished by higher stiffness and strength compared to the honeycomb panels with a paper core.

The aim of this study was to develop new lattice truss core structures with auxetic properties made of wood composite. In particular, it was decided to determine numerically and verify experimentally the elastic properties of the developed structures.

MATERIALS AND METHODS

Models

Five types of lattice truss core models differing in cell shape and size were prepared for the analyses (Fig. 1). Cores A, B, and C are distinguished by periodic geometry in the Cartesian coordinate axes X and Y. Cores D and E are characterised by differing rib slope in the X and Y axes. When selecting the shape, it was decided that cores A, B, and C should exhibit isotropic properties, while cores D and E should be orthotropic. The height of all cores was identical at H=10 mm. The lattice ribs were 3, 2, 4, 2.5, and 3 mm in thickness for structures type A, B, C, D, and E, respectively. Table 1 also presents relative densities of the modelled structures calculated based on solid models designed using the Autodesk Inventor Professional©. Solid models were printed in the Fused Deposition Modelling (FDM) technology with 3D Flashforge printers (FlashForge Corporation, China) (Fig. 2). The solid X-type print option was applied. The used filament was LayWood Olive (3D Drukujesz, Poland), i.e. a composite of PLA and 40% wood dust, with the filament diameter of 1.75 mm and printing temperature of 210 ºC to 220 ºC. During printing, it was used a nozzle with a diameter of 0.1 mm. The thickness of the first layer was equal 0.27 mm and the thickness of next layers 0.14 mm. The temperature of platform was 110 ºC, and the temperature in the extruder 210 ºC. Printing proceeded without the use of supports. For these settings, the average printing time was 15 hours. Five samples were prepared for each model, providing a total number of 25 samples.

Table 1. Relative Cell Density

Fig. 1. The shape and dimensions of lattice truss cores

Fig. 2. 3D prints

Materials

Mechanical properties of the filament differ from those of the printed material. For this reason it was decided to determine stress-strain characteristics for the printed material using samples with the shape and dimensions specified in Fig. 3. Samples were printed in the FDM technology using the solid X-type print option. A total of 10 samples were prepared. Samples were subjected to uniaxial tension testing using a Zwick 1445 universal testing machine (Zwick, Germany). Longitudinal and transverse strains were measured by the pattern matching method (Digital Image Correlation) using the Dantec Dynamics system (Dantec Dynamics A/S, Denmark). Based on the recorded direct results, the stress-strain characteristics were plotted for the printed material, while the modulus of linear elasticity and Poisson’s ratio were determined (Fig. 4).

Fig. 3. The shape and dimensions of samples for uniaxial tension testing

In order to include plasticity in numerical calculations for selected cells, the experimental stress-strain dependence had to be converted for LayWood (Fig. 4) after the linear elastic range was exceeded. First the linear elastic range was determined establishing the linear equation for this section. As shown in Fig. 4, the slope of the straight line corresponds to the value of the modulus of linear elasticity for LayWood equal to E_L=601.29 MPa (tensile strength MOR = 10.03 MPa, Poisson’s ratio υ=0.36). Next true stress σ_T and the logarithmic plastic strain ε_L, required in the FEM algorithm, were calculated using the equations given below:

 (1)

where  , true stress,  logarithmic strain, E_L= modulus of elasticity of LayWood, σ = engineering stress, and ε = engineering strain.

For the plastic range in Fig. 4 above the straight line the graph for σ _T=f(ε _L). was plotted. The converted engineering data obtained from the tensile test for LayWood were used to verify their quality. Thus an analogous sample as that in Fig. 4 was modelled in the Abaqus v.6.15 system. The model was ascribed the elastic modulus E_L and respectively determined stresses and strains from the plastic range. Figure 4 presents also tension curves for LayWood samples from experimental tests and numerical calculations. On this basis it was assumed that data conversion was successful and the obtained results are reliable and they were used in further numerical calculations.

Fig. 4. The stress-strain curve for tensile strength of LayWood

Tests

Printed lattice truss core models were subjected to uniaxial compression in the Y direction and next in the X direction. The diagram for loading and the testing stand are presented in Fig. 5. The tests were conducted using the edge detection method (Digital Image Correlation – DIC) and the IMAQ Vision software (National Instruments, Nederland). Prior to measurements the sample was subjected to preload loading with the force of 5 N. The aim was to eliminate slacks and geometric imperfections of printed structures. Reference images were produced in such a state. Next the load was gradually increased by 10 N accurate to 1 N. For each new value of force one photograph was made. Loads were interrupted when the value of 60 N was reached for the X direction and force at failure for the Y direction. Based on edge detection (Fig. 6) the digital image analysis method was applied to determine the numbers of pixels in reference sections of 10 mm in length (accurate to 0.02 mm). The same technique was used to measure the length and width of the core before and after strain. Next using the dependencies given below:

Poisson’s ratios υ_yx, υ_xy were determined, where: dX denotes narrowing, dY elongation, X core width, and Y core length. Moreover, for each of the orthotropic directions the moduli of linear elasticity E_y, E_x were established based on the equations,

where F_y,x is the load of the core in the direction of the Y and X axes, respectively, and H denotes core height.