Three-dimensional Voronoi model of a nacre-mimetic composite structure under impulsive loading
Introduction
Accidental and deliberate loads on civil and military structures continue to cause severe damage worldwide, along with catastrophic losses of human life [1], [2]. Consequently, the demand for lightweight high-performance materials has increased significantly in protective structural engineering. Biological structures, meta-materials, woven fabrics, nano-polymers, composite sandwich panels and many others have recently been investigated by structural research engineers because of their unique mechanical characteristics, which make them suitable under a range of extreme applications, namely blast, ballistics, fire and so on [3], [4], [5], [6], [7], [8], [9], [10]. In particular, the two-layer armour system (Fig. 1b) found in mollusk shells [11] is believed to be the most efficient armour system, particularly because it is composed mainly of brittle minerals but boasts a fracture toughness which is several orders of magnitude greater. This biological composite system has been perfected by the animal over millions of years of evolution to protect its soft tissues from loads that may arise from predator bites or extremely high hydrostatic pressure in the ocean. Better understanding of nacre’s load sharing mechanism will lead to the development of a superior composite structure for protective applications.
The armour system found in red abalone shells (and other bivalves and gastropod species) consists of a hard brittle outer calcite layer and a tough nacreous layer at its inner surface [12]. The inner layer (nacre), which is mainly composed of aragonite, a brittle mineral that accounts for 95% of its volume [13], [14], exhibits remarkable toughness. Moreover, nacre shows a hierarchical structure over several length scales (macro to nano). On the most elementary level, many have observed that nacre’s structure resembles that of a brick wall at the micro-scale [15], [16], [17], [18], [19], [20], [21], with polygonal aragonite platelets stacked over several layers and bonded together by a soft organic matrix (Fig. 1c and d). This organic matrix serves as both adhesive and cohesive bonds between nacre’s layers and polygonal tablets, respectively. Most studies in the literature, however, focus only on the influences of the adhesive layer rather than the cohesive bonds between nacre’s grains. Other features believed to contribute to nacre’s remarkable toughness are nano-asperities on the tablet surfaces providing additional sliding friction [22], [23], [24], [25]; mineral bridges at the interface as reinforcements between tablets [17], [22], [26] and waviness on the surfaces of the tablets for strain hardening [11], [27]. The aspect ratio of the platelets is also believed to have a certain influence on the strength and stiffness of the nacreous composite [28], [29].
Other investigations on nacre’s microstructural features (volume fractions, tablet aspect ratio, overlap length etc.) have been conducted in an attempt to link them with its mechanical properties. Dutta et al. [30] claimed that nacre chooses its overlap length to minimize crack driving forces at the interface, thereby delaying crack initiation. Kotha et al. [31] concluded that composites with high toughness can be manufactured from platelets with low aspect ratios through a shear-lag modelling approach. Gao et al. [24] employed Griffith’s fracture criterion to show that mineral platelets become insensitive to flaws at small length scales. Barthelat et al. [32] found that nacre does not achieve steady state crack propagation due to toughness amplification from tablet pullout and subsequent process zone toughening mechanisms. Other investigations have also found that nacre has tremendous ability to arrest crack propagation due to intrinsic and extrinsic toughening mechanisms that operate in front of and behind a developing crack tip, respectively [33]. Flores-Johnson et al. [34] claimed that the performance of nacre-like plates under blast loading is explained by the hierarchical structure, which facilitates globalized energy absorption by interlayered interlocking and delamination.
In summary, the geometric parameters such as tablet aspect ratio, interfacial waviness, overlap length and interlayer interactions of platelets have been found to influence nacre’s toughness. The aforementioned investigations have focused mainly on the localized load sharing mechanisms of nacre activated by tablet sliding under uniaxial tension or pure bending. This raises the question of whether the same mechanisms are activated under transverse loadings such as hydrostatic pressure or blast impulse. There are, however, very limited studies in the literature focusing on this topic both numerically and experimentally. This paper develops a novel nacre-mimetic composite model for simulating the Voronoi-shaped tablets, multilayer structures, grain cohesion and interfacial bonding to address: (1) The influences of the multilayered hierarchical structure of the nacre-mimetic composite on its resistance to impulsive loadings; (2) The impact of laminate staggering on the toughness of the composite; and (3) The size and shape effect of the platelets on fracture resistance. Specifically, the crack propagation patterns in the adhesive/cohesive layers and the energy dissipated via fracture, delamination and plastic deformation will be captured and analyzed. The model consists of a Voronoi-like platelet arrangement resembling red abalone nacre and the nacre-like laminates are bonded together with different overlapping configurations. The composite platelets are modelled with amour-graded Aluminum AA5083-H116, which are adhered together by a Vinylester matrix. A rate-dependent material model is used to simulate the transient responses and plastic deformation of the Aluminum tablets under impulsive loading.
Section snippets
Assembling the nacre mimicking geometry
Barthelat et al. [11] observed that the arrangement of the tablets in each layer of nacre is similar to that of a Voronoi diagram, through optical images of a red abalone specimen (Fig. 1d). Based on these optical images, they have generated a model consisting of two layers of nacre’s tablet structure for finite element analysis. This procedure offers limited control over the geometry and arrangement of the tablets in each layer, making it challenging to develop nacre-mimetic composite systems.
Numerical results and discussions
Fig. 10 illustrates the crack propagation patterns in the adhesive layers of the baseline composite model. A middle cross-section snapshot of the adhesive layers is captured at different times of the dynamic event, showing the damage development history. The failed adhesive elements are hidden to highlight the delamination zone, while they are still kept active to prevent tablet penetration. It can be observed that the crack initiates from the edges of the layer near the blast source and
Influence of the number of nacre-mimetic composite layers
Analysis from the previous section has demonstrated the relatively uniform distribution of damage and energy absorption among the different layers of the composite panel. Nacre’s composite structure (Fig. 1) is actually composed of hundreds of mineral layers to maximize damage mitigation and energy absorption capabilities. A parametric study is conducted in this section to investigate the performances of two (n = 2), five (n = 5) and ten (n = 10) layered composite panels of the same thickness. These
Conclusions
Several nacre-mimicking composite models were developed for investigating the influence of nacre-mimetic microstructural features on the blast resistance of composite panels. The following parameters were assessed in terms of the damage mitigation efficacy of the multilayer nacre-like composite structure: (a) number of staggering composite layers, (b) staggering lengths, and (c) tablet grain sizes. The results showed that by adding more layers to the composite, the integrity of the system was
Acknowledgements
This research was sponsored by the Australian Research Council linkage Grant LP150100906 and by the University of Melbourne Early Career Researcher Grants.
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