Experimental and numerical investigation on 3D printed PLA sacrificial honeycomb cladding
Introduction
The use of improvised explosive devices in terrorist attacks against civil engineering structures increased significantly during the last decades. When such events occur, the associated blast loads may result on the failure of critical load bearing members, with subsequent social disruption and psychological impact to society, as well as high economic and environmental losses. Therefore, the implementation of strengthening or protective techniques is crucial to mitigate the effects of blast loads on structures and to ensure their survivability. Although the traditional method of protection is the strengthening of structural members, the concept of sacrificial cladding has been extensively investigated [1], [2], [3], [4], [5], [6], [7], [8] due to their reduced mass and high energy absorption capacities. Sacrificial claddings are commonly fixed on the exterior of the structural element and are composed by a crushable core and two skin plates. The objective of the skin plate is to evenly distribute the applied blast pressure to the crushable core and ensure its uniform compression. The crushable core undergoes a progressive deformation under a constant low stress, absorbing most of the blast induced energy and therefore protecting the load bearing element. The crushable core is often materialised with a cellular solid, such as aluminium foam [1], [3], [4], [9], expanded polystyrene [10] and polyurethane foam [11], or a cellular structure with several topologies, including auxetic core [12], [13], tubular core [14], [15], [16], honeycomb [17], [18], and load-self-cancelling core [19], [20].
Recent advances in additive manufacturing technologies allow the manufacturing of complex components which would be impossible with traditional subtractive manufacturing techniques. Among the available processes, the fused deposition modelling extrusion based technique (FDM) is usually used in consumer-level 3D printers. This technique manufactures 3D printed parts through the layer by layer deposition of thermoplastic filaments [21]. The use of 3D printing components as energy absorption structures has grown in interest in recent years due to the high flexibility of the manufacturing process, which allows tailored properties. Several authors [22], [23], [24], [25], [26], [27], [28], [29], [30], [31] have reported on the use of 3D printed structures as energy absorption solutions. Although the majority of the referred studies [22], [23], [24], [26], [27], [28], [29] resorted to experimental quasi-static compression tests to evaluate the energy absorption capabilities of the 3D printed kernel elements, Sarvestani and his team [30], [31] performed both quasi-static three point bending and low-velocity impact tests to achieve the same goal. Additionally, Harris and his co-workers [25] carried out an experimental campaign comprised of quasi-static and dynamic (using an Hopkinson bar) compression tests to verify the energy absorption capacity of metallic hybrid lattice cores. Mainly due to the high flexibility of additive manufacturing, a variety of topologies have been studied and reported in the literature, namely triply periodic minimal surfaces [24], lattice cylindrical structures [27], hierarchical honeycomb [26], auxetic structures [28], [30], honeycomb structures [23], [29], [30], metamaterial cellular cores [31] and lattice structures [22].
In the present study, the nonlinear response of 3D printed PLA honeycomb structures is investigated, both experimentally and numerically, in order to analyse their energy absorption capacity when used as the crushable core of a sacrificial cladding solution. The influence of the relative density on the energy absorption capacity is verified, enabling the development of a tailored sacrificial cladding solution, composed by a crushable core (PLA honeycomb structure of a given relative density and height, in combination with two PLA solid plates) and an aluminium front plate. The dynamic response of the proposed sacrificial solution is experimentally obtained resorting to a previously developed and validated explosive driven shock tube [10], [32], while the corresponding numerical simulations are performed using the commercial finite element software LS-DYNA [33].
The most relevant property for a cellular material, such as the honeycomb structure, is its relative density, defined as the ratio between the density of the cellular material ρ*, and the density of its constituent material ρs. Additionally, according to Gibson and Ashby [34], the mechanical properties of the cellular material greatly depend on the cell shape. As illustrated in Fig. 1, the present research is conducted using a regular hexagon as the unit cell shape to fill the two-dimensional x1-x2 plane. Therefore, assuming that the honeycomb structure has a low density (so that the ratio between the wall thickness t and the edge length l is small) and that the cells are regular, the relative density reduces to definition (1).
A typical stress-strain curve for honeycombs subjected to out-of plane compression, i.e. load applied against x3 direction, is illustrated in Fig. 1(c). This curve may be characterised by an initial elastic phase, usually truncated by elastic or plastic buckling, followed by a plateau regime with almost constant stress, which ends with a densification phase [34]. The plateau stress σpl, along with the densification initiation strain εd, are the most important characteristics of a sacrificial cladding solution, as they control the energy absorption capacity of the solution. Therefore, their correct determination is crucial. Tan et al. [35] proposed a method for the computation of the densification initiation strain through an energy efficiency parameter η, defined in Eq. (2) as function of the nominal stress σ and strain ε.
According to [35], the densification initiation strain corresponds to the point where the efficiency is a global maximum, as presented in Fig. 1(c). Following the determination of the referred strain, the plateau stress can be obtained through the energy equivalence on the plateau regime. In the resulting definition (3), εy stands for the plastic phase initiation strain.
According to [36], when estimating the energy absorption capability of a cellular material, it is common practice to ignore the elastic energy, as well as the energy of the pre-collapse and densification stages. Therefore, the energy absorption of the cellular material may be obtained through Eq. (4). Scaling this value with the mass of the crushed cellular material one obtains the corresponding specific energy absorption, SEA.
Lastly, the efficiency of the sacrificial solution e, is defined according to Eq. (5) as a function of the ratio between the transmitted and applied impulses, and ir, respectively.
Section snippets
Experimental campaign
The present experimental campaign was conducted on 8 × 8 × 9.4 cm parallelepiped 3D printed crushable core samples (see Fig. 1(a)) composed by a honeycomb structure with a height of 9 cm and two solid plates with a thickness of 2 mm. Three different infill geometries were considered, as presented in Table 1. All honeycomb structures were manufactured with a constant wall thickness of 0.43 mm, while the edge length was varied, resulting in relative densities of 5, 7.5 and 10%. On the other
Numerical simulation
The numerical simulations performed on the present study resort to the explicit finite element code LS-DYNA [33], which takes into account both material and geometric non-linearity. The simulations were performed on a dual Intel Xeon X670 at 2.93 GHz and 16 GB of RAM, being computed with 8 nodes in parallel shared memory and double precision. The time step was automatically computed by LS-DYNA, while using a scale factor of 0.6 for the computed time step, as suggested by the user manual [33].
Preliminary tests on the experimental set-up
A preliminary set of experimental tests were conducted, with no sacrificial cladding, to verify the influence of the set-up on the obtained results. Fig. 9 presents the experimental records of both the force sensor and the pressure transducer, together with the numerically simulated response of the force sensor. The influence of spurious vibrations of the set-up on the force sensor’s measurements is readily observable in the experimental curve (black line in the figure). Nonetheless, as
Conclusions
Experimental tests (EDST) and numerical simulations (LS-DYNA) were used in the present study to analyse the nonlinear response of 3D printed PLA honeycomb structures subjected to out-of-plane blast loading, in order to estimate their energy absorption capacity when used as the crushable core of sacrificial cladding solutions. The influence of the honeycomb relative density on its nonlinear response was also verified. The findings of this research allow to conclude that:
- 1.
Both the force peak and
Acknowledgements
This work was supported by contracts SFRH/BD/115599/2016 and PTDC/ECI-EST/31046/2017 with the Portuguese funding institution FCT - Fundação para a Ciência e Tecnologia.
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