Bending behaviour of auxetic multicellular beam structures

In recent years, thin-walled beam structures have been widely popular in many engineering applications such as aviation, aerospace, military, automotive and construction due to their light weight, excellent load carrying ability and energy absorbing capability as well as their cost-effective advantage. In the event of an accident to land and air vehicles, the protection of structural integrity is the most important issue in engineering applications, since the structural integrity of the vehicle may be damaged as well as the parts may be damaged under the influence of complex stresses consisting of both dynamic and static external loads. In general, high mechanical expectations lead to an increase in the weight of structures, which not only reduces the performance of vehicles but also leads to an increase in fuel consumption. In this context, different geometries have been developed to improve the mechanical efficiency of load-carrying components. Honeycomb structures consist of hexagonal or regular polygonal shaped geometries consisting of interconnected cells. These structures are used in many areas of engineering applications because they exhibit higher load carrying capability (high mechanical efficiency) with lower weight than other geometries. Although there are applications to improve the mechanical performance of thin-walled beam structures with honeycomb cross-sectional structures, the combination of high stiffness and load carrying capability with sufficient weight saving is limited. Therefore, it is inevitable to develop materials/structures with unique design and unusual mechanical properties for structures with high mechanical efficiency. Auxetic materials have negative Poisson's ratio. Unlike conventional materials, materials with negative Poisson's ratio tend to expand under tensile stress and contract under compressive stress. Auxetic materials are rarely observed as structures found in nature in the microstructures of tree sap, corals, and sponges. By mimicking these excellent mechanical properties of auxetic materials, the mechanical performance of engineering designs can be improved by reducing or eliminating structural damage. Several auxetic materials and structures have been demonstrated, theoretically designed and fabricated. Advances in additive manufacturing (AM) techniques make it possible to produce materials with complex cellular architectures. In this study, the focus is on the development of lightweight and high load-carrying cross-sections for beams subjected to bending. The deformation behavior, load carrying and energy absorption capabilities of honeycomb structures with positive and negative Poisson's ratio cross-sections and hybrid geometries consisting of at least two different honeycomb structures are investigated experimentally, numerically and theoretically. The study consists of three main parts. In the first section, the deformation behavior and mechanical performance of the hollow thin-walled beam structure under three-point bending behavior are investigated in detail and the cause of damage is discussed in depth. Then, the bending behaviour of square (Squ), hexagonal (Hex), octagonal (Octa) and auxetic (Aux) multicellular beam structures with the same beam dimensions, number of cells and height were investigated by finite element method. A comparative study of the load carrying and energy absorption capabilities between structures with negative and positive beam cross-sections has been carried out using the nonlinear finite element code LS-DYNA. The results of the finite element analyses are compared with the experimental results of the Aux beam structure with auxetic cross-section produced from 316L stainless steel (Direct Melting Laser Sintering-DMLS) by additive manufacturing method. The material parameters used in the finite element method were used in the same way as the data obtained from tensile tests according to ASTM E8/E8M-15a standards by additive manufacturing method. The numerical and experimental results were found to be in good agreement. In the hollow beam structure (BT), it was shown that fracture occurred in the upper corner of the part due to buckling and folding effect in the contact area of the indenter. For the Squ, Hex and Octa beam structures, fracture occurred due to localized stress caused by buckling of the cell walls in the upper regions where the indenter contacts. On the other hand, the cross-section of the structure consisting of auxetic cells was less laterally deformed under bending load and the walls were found to be oriented towards the center. Thus, despite the high displacements, the local buckling effect could be minimized. This resulted in a limited decrease in the cross section moment of inertia. As a result, a structure with higher load carrying capacity and consequently higher energy absorption capacity was obtained. In assessing the performance of different cell sections, the effect of beam volume and damage displacement on the change in the cross-section moment of inertia was analyzed and a dimensionless quantity "Failure Sensitivity" (FS) was defined. According to the results, the calculated FS was found to be the highest for the hollow beam (HT) and the lowest for the solid beam, as expected. Aux beam has the lowest failure sensitivity among the multicellular beam structures. In addition, as another approach to express the mechanical properties of the structures with respect to the solid beam, the bending performance index (BPI) was defined as the ratio of the failure sensitivity of the multicellular structure to the failure sensitivity of the solid structure. Similarly, the BPI of the Aux beam was found to be the best after the solid beam. As a result of the analyses, the specific load carrying (SLC) capacity of the Aux structure is 45.6%, 29% and 11.4% higher than that of the Hex, Squ and Octa beam structures, respectively. In addition, in terms of specific energy absorption (SEA) capacity, it performed 11.3, 3.8 and 1.8 times better than the Hex, Squ and Octa honeycomb multicellular beams, respectively. Accordingly, it is understood that the auxetic cross-section exhibits higher mechanical performance under wide range displacement. Interestingly, in the first part, it was found that the beam with negative Poisson's ratio cells can change the direction of deformation in the cross section and the structure remains capable of carrying loads at wide displacement ranges. In the second section, the study is focused on the effect of the auxetic cell arm angle and functional grading of the cell wall thickness on the beam performance. In this context, the effect of 55, 65, 75 and 85-degree cell wall angle and wall thickness for three types of functionally graded cases of the beam structure in which the auxetic cells are orientated along the beam axis are systematically investigated in an experimental and numerical way. By increasing the angle of the unit cell wall with constant beam weight provided that the beam structure's load carrying ability and energy absorption capability are improved up to a certain point with the change in the negative Poisson's ratio of the Aux beam cross-section. Although larger values of the cell wall angle provided a limited improvement in the bending performance of the beam, damage occurred at lower displacements. By increasing the unit cell wall angle from 55 degrees to 75 degrees, it was found that the bending performance of the Aux beam structure improved SYT and SEA by 11% and 12.4%, respectively. Based on the best cell angle (75) obtained, it is found that if the cell wall thicknesses of the structure are increased by functional grading from the neutral axis to the outer wall, it is possible to realize further improvements in specific values, SYT and SEA, 19.4% and 25.4%, respectively, despite the increase in the beam weight. In the third section, the design of Aux multicellular beams and a hybrid (AuxOcta) beam design (new for the literature) with auxetic and octagonal cells is investigated. Auxetic structures were manufactured with 316L stainless steel by DMLS additive manufacturing method. Three-point bending test results show that the cross-section of the Aux beam structure shows gradual local deformation, while the deformation of the cells in the cross-section of the AuxOcta beam is spread throughout the cross-section. Furthermore, the cell wall thicknesses were optimized from the neutral axis to the outer wall to improve the load carrying and energy absorption capacities of the AuxOcta structure. This optimized AuxOcta structure (AuxOcta-G) offers superior bending performance according to the test results. Compared to the Aux structure, the improvement in the specific load carrying capacity (SLC) of the AuxOcta-G structure is 15% for 5 mm displacement, while the improvement in the specific energy absorption (SEA) capability reaches about 16%. The Finite Element Method (FEM) results showed that the AuxOcta and AuxOcta-G structures offer a desirable deformation behaviour over a wide displacement range. This study is expected to provide a basis for future investigations of auxetic and/or hybrid beam design with a cross section of negative Poisson's ratio.