# Structure and Mechanical Properties

## ABSTRACT

The multiscale structure, materials properties, and mechanical responses of the turtle shell (Terrapene carolina) were studied to understand the fundamental knowledge of naturally occurring biological penetrator-armor systems. The structure observation and chemical analysis results revealed that the turtle shell carapace comprises a multiphase sandwich composite structure of functionally graded material having exterior bone layers and a foam-like bony network of closed-cells between the two exterior bone layers. Although the morphology was quite different, the exterior bone layers and interior bony network possessed comparable hardness and elastic modulus values of ~1 GPa and ~20 GPa, respectively. Compression and flexure test results showed a typical nonlinear deformation behavior recognizant of man-made foams. The mechanical test results revealed that the interior closed-cell foam layer plays a significant role on the overall deformation behavior of the turtle shell. The finite element analysis simulation results showed comparable agreement with the actual experimental test data. This systematic study could provide fundamental understanding for structure-property phenomena and biological pathways to design bio-inspired synthetic composite materials

Author(s): Hongjoo Rhee, Mark F. Horstemeyer, Y. Hwang, H. Lim, H. El Kadiri, W. Trim

Corresponding Author: Hongjoo Rhee

## STRUCTURE

Fig. 1. Multiscale hierarchy and structure of the turtle shell; (a) a morphology of the turtle shell carapace, (b) a costal scute showing the successive growth pattern, (c) a crosssectional view of the carapace showing composite layers, (d) an SEM micrograph of a fracture surface, (e) an SEM micrograph of a cell structure, and (f) an SEM micrograph of a fibrous structure inside of the cell.

Structure observations on the turtle shell revealed a multiphase composite material that is arranged by a multiscale hierarchy. Such a multiscale hierarchical structure of the turtle shell carapace is depicted in Fig. 1. The turtle shell comprises a series of connected individual plates covered with a layer of horny keratinized scutes (Fig. 1a–b). The scutes are made up of a fibrous protein called keratin that also comprises the scales of other reptiles [5]. These scutes overlap the seams between the shell bones and serve to reinforce the overall protection to the shell. The carapace is made of a sandwich composite structure of functionally graded material (FGM) having relatively denser exterior layers and an interior fibrous foam-like layer (Fig. 1c–d). SEM micrographs clearly revealed such fibrous structure inside of the cell (Fig. 1e–f).

The internal structure of the turtle shell was nondestructively observed by using an X-ray computed tomography (CT) and obtained images are provided in Fig. 2. The X-ray CT was carried out by using a v|tome|x by phoenix|x-ray. The X-ray CT images clearly showed that the pores within the interior foam-like layer of the turtle shell carapace were closed-cell type and randomly distributed. In addition, the results obtained from the in-house image analyzer software revealed that the porosity levels of the relatively denser exterior, interior foamlike layer, and whole turtle shell carapace including all three layers were 6.86%, 65.5%, and 48.9%, respectively.

Figs. 3 and 4 show the microstructure observation and chemical analysis results obtained from various surfaces of the turtle shell. Three different layers of the outermost keratin layer, right underneath the keratin layer, and the inside surface of the turtle shell carapace were observed and analyzed by using an SEM and an energy dispersive X-ray (EDX) spectroscopy technique, respectively. These layers have different surface microstructures and chemical compositions. The EDX analysis showed that the outermost keratin layer mainly consists of carbon (C), oxygen (O), nitrogen (N), and sulfur (S) that are main constituents of the protein. The result is not surprising since the keratins are a family of fibrous structural proteins, also called scleroproteins. Unlike the outermost keratin layer, right underneath the keratin layer and the inside surface of the turtle shell carapace contained abundant additional minerals as indicated by the presence of calcium (Ca, 15–20 wt.%), phosphorous (P, 7–10 wt.%), sodium (Na), chlorine (Cl), and magnesium (Mg) that are known to be main components of the bone.

 Fig. 2. (a) A side sectional view and (b) a top sectional view of the turtle shell carapace coupon obtained from X-ray CT single slice scan showing randomly distributed closed-cell pores within the foam-like interior layer. Fig. 3. SEM micrographs obtained from different surfaces of the turtle shell carapace; (a) the outermost keratin layer, (b) underneath the keratin layer, and (c) inside surface. Fig. 4. Chemical analysis results obtained from different surfaces of the turtle shell carapace; (a) the outermost keratin layer, (b) underneath the keratin layer, and (c) inside surface.
Fig. 5. SEM micrographs obtained from the fracture surface of the turtle shell carapace; (a) bony layers and (b) inside of the closed-cell (fibers). Fig. 6. Chemical analysis results obtained from the fracture surface of the turtle shell carapace; (a) bony layers and (b) inside of the closed-cell (fibers).

The microstructures and chemical analysis results obtained from different locations of the fracture surfaces of the turtle shell carapace are provided in Figs. 5 and 6. The chemical compositions obtained from the exterior layers and the network (e.g. closed-cell wall) region within the foam-like interior layer were quite similar to those can be found in Fig. 4b–c. The fibers inside of the closedcell also showed an accordant chemical composition (Fig. 6b), which implies that they include “bony” fibers. The microstructure observation and chemical analysis results obtained from various locations of the turtle shell clearly revealed that the turtle shell carapace is made of a sandwich composite structure having exterior lamellar bone layers and an interior bony network of closedcell fibrous foam layer.

## MECHANICAL PROPERTIES

Experimental results obtained from the nano- and microindentation tests on the side surfaces of the turtle shell carapace are provided in Fig. 7. The results showed that the exterior layers and interior bony closed-cell walls possess comparable hardness and modulus values. Hardness and elastic modulus values obtained from the nano-indentation tests ranged from 0.8–1.1 GPa and 18.3– 24.8 GPa, respectively; whereas, the average hardness value obtained from the Vickers hardness tests was about Hv100 that corresponds to 0.98 GPa. There were small variations in hardness and elastic modulus values from experiments due to the roughness of the specimen. The nano-indentation test results reflect highly localized micromechanical properties that may contain porous or impurities in its texture. Since the regions of indentation are so small that local impurities or defects can induce uncertainties in the measurements. This effect is minimized under Vickers hardness test set-up and the exterior layers and closed-cell walls within an interior layer possessed comparable hardness values.

For quasi-static compression tests, two different types of coupon specimens including all three layers and then only a bony exterior layer were prepared. The effect of strain rate on the mechanical behavior of the turtle shell was compared with respect to the different density levels and the raw data obtained from the tests is illustrated in Fig. 8a. The lower five curves (represented by lines with symbols) were obtained from the test specimens including all three layers (two exterior and an interior layers); whereas the upper six curves were obtained from the specimens only containing a relatively denser exterior layer. Top three curves (in symbols) among those six curves were obtained from thinner specimens and the bottom three curves (in lines) represent thicker specimens. The thickness difference between those two regimeswas about 15%. The favorable deformation mechanism of the turtle shell carapace under quasi-static compression test conditions can be explained by importing that of synthetic foams and/or honeycombs since fundamental structures of the test specimens are similar to those of such cellular solids. At small strains, the specimenswere deformed in a linear elastic manner due to the cell wall bending. Soon after the initial linear elastic deformation, a plateau of deformation was reached, because of the buckling of the cellwalls. After such a plateau of deformation, another period of linear deformation was proceeded since a densification occurred resulting in a rapid increase of compressive stress. When comparing the specimens containing the exterior region only, the thicker specimens showed a similar deformation yet much weaker behavior than those can be observed in the specimens including all three layers; whereas the thinner specimens showed almost a linear compressive deformation behavior simply because of the density and structure differences. Most of discernible pores within exterior layer are distributed near the region between the exterior layer and interior foam-like layer. Fig. 8b provides the comparison of specific energy absorption obtained from the quasi-static compression test results (Fig. 8a). Density and porosity levels of the test specimens were already considered in this normalized data. The energy absorption ability of the turtle shell carapace increased with increasing strain rate for a given density level. The composite layers including all three layers showed better energy absorption ability compared to the exterior layer for any given strain rate. In addition, such composite layers possessed a considerable amount of plateau of deformation that is a model index of good energy absorbing materials. The combining information of these two plots in Fig. 8 is very important to design the optimum energy absorbing composite material. For example, composite foam materials can be tailored to give the best combination of properties for a given package by choosing the right combination of the cell wall materials, relative density, reinforcement phases, and so on.

Flexure tests using a three-point bending mode were carried out on a coupon specimen sampled from the turtle shell carapace and compared with finite element simulation results. The specimens were cut as longitudinal and transverse directions of the turtle shell, and no apparent difference in the stress–strain relations with respect to the different orientations were noted. The flexural stress (σf), flexural strain (εf), and Young's modulus in bending (EB) for the rectangular specimens can be extracted by fitting the test data into the following formulas: $Insert formula here$

where, M is the maximum bending moment, c is the distance from center of specimen to the outer fibers, I is the moment of inertia of the cross-section, F is the applied load, L is the support span, d is the depth of test specimen, b is the width of test specimen, D is the maximum deflection of the specimen center, and m is the slope of the tangent to the initial straight line of the load deflection curve. Comparisons between three-point bending test results obtained from the experimental data and FEA simulations using ABAQUS software are depicted in Fig. 9 with the FEA simulation conditions listed in Table 1. The flexural stress versus strain curve showed a similar pattern to those obtained from the compression tests. Young's modulus, in this case, was determined by the slope of the initial linear elastic deformation curve. The FEA simulation results for a chosen actual test condition of EB=7.1 GPa are shown. The FEA simulations employed both single shell three-layer element and a discrete three-layer element in the region of initial elastic deformation. The EB values obtained from the initial simulations were much higher than that obtained from actual tests in both cases, since the material properties were measured without considering any effect from voids or pores in the outer shells as well as the inner core from the indentation tests. However, the exterior bone layer inevitably contained small voids, and the interior foam layer was basically a closed network of pores. Therefore, the FEA simulation results showed much stiffer stress versus strain responses than the experiments as shown in Fig. 9a. When the void volume fraction was considered, the FEA results showed much closer results as illustrated in Fig. 9b. Based on the void volume fraction in the turtle shell, the overall material properties could be estimated using an equivalent inclusion idealization and then adopted in the finite element model. By using modified material properties, the FEA simulation results gave better comparisons with experimental test results (Fig. 9b); the three-discrete layer approach captures strain reversal through-the-thickness direction if the soft core material is located between hard face sheet materials like a sandwich structure.