Delamination Testing of Additive Manufactured Sandwich Structures with Lattice Truss Core

Sandwich structures possess a high bending stiﬀness compared to monolithic structures with a similar weight. This makes them very suitable for lightweight applications where high stiﬀness to weight ratios are needed. Most common manufacturing methods of sandwich structures involve adhesive bonding of the core material with the sheets. However, adhesive bonding is prone to delamination, a failure mode which is often diﬃcult to detect. In this paper, the results of delamination testing of fully additive manufactured (AM) AlSi10Mg sandwich structures with pyramidal lattice truss core are presented. To characterise the bonding strength, climbing drum peel tests and out-of-plane tensile tests are done. The thickness of the faces and the diameter of the struts is 0.5 mm, while the core is 2 mm thick. The inclination of the struts is 45 ◦ . To predict the expected failure loads and modes, analytical formulas are derived. The analytics and tests are supported by ﬁnite element (FE) calculations. From the analytic approaches, design guidelines to avoid delamination in AM sandwich structures can be followed. The study shows, that critical ratios for face sheet thickness to strut diameter can be determined, to deﬁne if the structure tends to delaminate under certain loads. Those ratios are mainly inﬂuenced by the strut inclination. The peel tests resulted in face yielding, which can also be followed from the analytics and numerics. The out-of-plane tensile tests didn’t damage the structure.


Introduction
Sandwich structures show outstanding properties, especially regarding bending and buckling behaviour. Usually, two thin face sheets are adhesively connected to a much thicker core structure. A lot of different core structures were developed in the past. The most commonly used are honeycombs and foams. The adhesive bonding is often responsible for the failure of sandwich structures and can in many cases be traced back to delaminations, which can occur due to local damages of the adhesive connection or local buckling of the face sheets. Furthermore, especially in the case of honeycomb core structures, the bonding surface is small and therefore the maximum transferable load too. To increase the bonding strength, an increase of the bonding surface would be reasonable. But, whereas the specific weight is proportional to the vertical tensile module and the tensile strength, the peeling resistance of the skin/core bonding is not exceedable.
Depending on the type of adhesive, the force that an adhesive fillet can transfer is equal to the tensile strength of a 0.08 -0.1 mm thick foil. Thicker foils are therefore inappropriate for increasing strength properties. This can only be achieved by smaller cell sizes [1]. With the establishment of new manufacturing processes, such as additive manufacturing (AM), alternative approaches for sandwich structures are attractive. By using lattice structures for the sandwich core, the sandwich can be printed as a single part and by this a direct connection between the core and the faces is established.
First fundamental investigations about sandwich structures with lattice cores were presented by Wicks & Hutchinson [2,3]. They show that truss core sandwich structures have high flexibility in designing the structural behaviour. Compared to honeycomb structures, much better structural properties against bending and compression loads, regarding stiffness or strength, can be achieved. Regarding cellular structures, especially the work of Gibson & Ashby [4,5] shows basic formulations for the mechanical properties of lattice structures as a function of the relative cell density. They show that different elastic properties of sandwich structures scale linearly with the relative density of the core. For sandwich structures with tetrahedral and pyramidal core under 3-point bending, Deshpande & Fleck [6,7] derived equivalent expressions. The results are extended by the research of Evans et al. [8,9] and Chiras et al. [10] for shear and compression loads. Zok et al. [11] show that main failure mechanisms of pyramidal truss core sandwich panels are face sheet yielding, face sheet buckling, core member yielding and core member buckling. Basic studies about failure modes of sandwich structures have been done especially by Zenkert et al. [12,13,14]. They show that sandwich beams under quasi-static and fatigue bending loads tend to delaminate for the most tested configurations. Some research focuses on methods to stop these delaminations instead of avoiding them.
Other approaches focus on the creation of sandwich structures with high transverse stiffness and strength [17,18] to avoid delaminations. Furthermore, Jakobsen et al. [19] show an alternative approach. They reroute the delamination to confine it to a predefined zone in the sandwich. By this, they are able to stop the propagation of the delamination. According to the authors knowledge no studies have been performed yet on fully AM sandwich structures with lattice core. Since the delamination behaviour of such structures has not been investigated, this study focusses on a specific geometry.
The main objective of this research is the development of simple criteria for avoiding delaminations in AM sandwich structures with pyramidal cores. For this, the bonding strength and delamination resistance is investigated. Analytical preliminary considerations regarding peeling strength of sandwich structures with lattice core are supported by FE studies and by physical tests. Fig. 1 shows the considered AM sandwich structure.

Methods and Materials
In the following section the used specimens, material and associated test methods are presented. Furthermore, analytical formulations are derived to predict the expected failure loads and modes. This formulations can be used as rough design guidelines to avoid delamination.

Materials and Specimens
All structures are made of AlSi10Mg via Laser Powder Bed Fusion (LPBF) using an EOS M290 printer. The nominal geometric parameters of the structures are summed up in Table 1. Due to manufacturing restrictions, a face sheet thickness t f = 0.5 mm, a core thickness t c = 2 mm, a strut diameter of d = 0.5 mm and a relative strut angle of ω = 45 • are used. A total sandwich height of h = 3 mm results. The radius of the struts is defined using r. Fig. 2 shows a schematic sketch of a lattice unit cell with its face sheet section. To describe the structural properties of the lattice core, simple calculation methods can be used for strength and stiffness. The in-plane Young's Equations for the out-of-plane Young's modulus and shear modulus can be derived using the stiffness method, assuming pinned struts as shown for example in [6]: Due to the overlapping of the struts, the bonding surface between the core and the face sheets cannot assumed to be circular, as shown in Fig. 3. Since no nondestructive measuring method is accessible, the nominal bonding surface can be extracted from the CAD-model, which was used for the manufacturing, or derived analytically using the following assumption: properties, material properties for the calculations are determined doing tensile tests. The specimens are produced from AM sandwich structures by separating the face sheets from the core structure and afterwards milling them to a bone shape. Using the presented equations and the extracted material data, the following sandwich properties are derived:

Preliminaries and Experimental Set-Up
Throughout the study, two test strategies are used to characterise the delamination behaviour of AM sandwich structures: out-of-plane tensile tests and climbing drum peel tests. Furthermore, the tests are supported by numerical FE calculations to get a better understanding about the failure mechanisms. First, the main failure mechanisms for the core structure are determined. Failure can happen at three different zones: failure at the connection point or a failure of the strut itself. Considering one unit cell with pinned struts, as shown in Fig. 2, a load in 3-direction (out-of-plane) results in an axial strut force of: The failure zone is only a function of the strut angle ω. This can be derived by comparing the strut stress with the stress in the connection surface. Under a tension load in 3-direction F 3 , the resulting stresses in the struts σ s and the stress in the connection σ c can be calculated as followed: Under the condition that the struts are slender, and by this, no bending influence has to be considered, simple assumptions can be derived for the predicted failure mechanism. For σ s = σ c a critical value ω = 35.26 • results. For lower angles, the struts will fail before the connection. For larger angles, the connection will fail before the struts. This relation is shown in Fig. 5. In the following sections the experimental set-up and the expected analytical determined values are shown.

Out-of-Plane Tensile Test
As shown in  cardanic bearing, is constructed (Fig. 6).
The face sheets of the specimens are adhesively bonded with the bearings. A 3M Scotch-Weld EC-9323-2 high strength epoxy adhesive is used. The strength of the adhesive is specified with 29 MPa, which results in a higher maximum load compared to the expected strength of the connection between the lattice core and the face sheets. The specimens are cut from large AM plates using a band saw. Due to these circumstances the outer geometry of the specimens varies and can be found in Table 3. Furthermore, the resulting maximum allowable forces, before the strength of the adhesive would be exceeded, are shown. All these force are much higher in comparison to the binding strength between face sheets and core, assuming the lowest ultimate strength of R m ≈ 250 MPa from Fig.4, which results in a maximum force of F max, core = 2.125 kN. Since the exact ultimate strength is unknown, the expected failure loads of the three specimens should be in the range of 2 − 3 kN, assuming that the load is evenly distributed on the connection points and the plastic stress distribution is homogeneous. The final test set-up is shown in Fig. 7.
The displacement of the machine, as well as the force in the load cell, are documented. Additionally, the tests are monitored with a DIC technique, using a GOM Aramis 4M system, which allows measuring three-dimensional displacements and strain information of a surface by measuring absolute and relative multiple point movements.

Climbing Drum Peel Test
The climbing drum peel test" is a method to determine the resistance of bonded sandwich cores against peeling forces acting perpendicular to the surface layer. The drum transforms the vertical force of the testing machine into a moment so that the connection between the face sheets and the core is directly loaded. This test is the only way to characterise the direct bonding strength. The tests are done according results, which has to be carried by the specimen. If the stresses get higher than the critical stress, the face sheets will delaminate. This value is known as specific peel moment and can be calculated according to DIN 53295 as followed: The force F 1 is the force needed to deform the face sheet itself and has to be sub-   Since for ductile materials failure occurs in the plastic area, the plastic case will be used. Fig. 9 shows a submodel for two rows of the sandwich structure. The applied bending moment will result in reaction forces F R = M/a at the connection points if pinned struts are assumed. The distance between two unit cells is a. By this, a general relation to avoid delamination can be established: This relation is shown in Fig. 10. If delaminations should be avoided, the ratio of t f /d should be lower than the in Fig. 10 shown critical ratio. The critical value for ω is the value where the failure mode changes from strut failure to joint failure (see A total number of 3 specimens is tested. In Table 4 the specific geometric parameters are summed up. Furthermore Fig. 11 shows a sketch of the specimens and Table 5 the resulting expected relevant cross sections. R m = 350 MPa is used. The number of cells n was successively decreased since no delamination could be incited with high cell numbers. Fig. 12 Fig. 13a and 13b.

Results and Discussion
Out-of-Plane Tensile Test Fig. 14 shows the results of the out-of-plane tensile tests. Additionally, Fig. 15 shows a picture of one of the specimens right before failure and after failure. The results show slight differences regarding the stiffness. This is mainly attributed to tolerances from manufacturing, which are specified with ±100 µm, which could result in differences regarding the strut diameters and therefore to differences in the stiffness (see Eqs. 1 and 2) since they are square depending on the diameter. The failure load of all three tested specimens lies between 3.8 -4 kN. No failure in the core structure was detected. For all specimens, the adhesive fails before the core breaks. All failure loads are smaller than expected, which could be attributed to an irregular moistened adhesive surface. Nevertheless, from the measured loads it can be followed that the connection is at least as strong as the materials strength (Fig.   4). Assuming the connection surface of one unit cell to be, as specified in Fig. 3, A c ≈ 0.34 mm 2 and the resulting total connection surface A C = n × A c = 8.5 mm 2 .
This would result in a connection strength, of at least σ u > 440 MPa, which is not Based on the numerical FE simulations, the first zone to undergo full plastic deformation is the joint between the face and the struts, as shown in Fig. 16. This is also the expected critical zone according to Eq. (6) and (7).

Climbing Drum Peel Test
Fig . 17 shows the force-displacement curves of the climbing drum peel tests. Furthermore, in Fig. 18 the measured force is related to the specific widthb (Fig.11), to avoid that results are misinterpreted by different geometries. Additionally, Fig.   19 shows a picture of specimen 1 and Fig. 20 of specimen 3 after testing. Both specimens show a failure in the face sheets. Since the face sheets fail, before they have rolled up sufficiently, the evaluation following DIN 53295 cannot be done. Nevertheless, it can be followed that no delamination will occur with the used geometry. For specimen 3, the number of cells in one row (in the rolling axis) was reduced. The face sheet did not fail immediately and therefore the evaluation for the peel moment can be done according to DIN 53295 to M peel = 279.62 Nmm/mm. However, the face sheet did not delaminate, but broke parallel to to cell row in rolling direction (see Fig. 20) and by this the result is not meaningful.
Based on the numerical FE simulations, the first zone to undergo full plastic deformation is the face sheet, as shown in Fig. 21. This is also the expected critical zone according to Eq. (9) since t f /d = 1 < 3.2. In the second simulation, with 2, the connection is expected to fail, as seen in the stresses of Fig. 13b. This corresponds too to the simplified model presented in Eq. (9).

Conclusion
In this study investigations of the delamination behaviour of fully additive manufactured sandwich structures with pyramidal lattice grid core were performed. In future studies, the models will be expanded to assume a inhomogeneous stress distribution on the joints and struts.