Behaviour of Shear Thickening Fluids in Ballistic Textiles: A Review

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1 Behaviour of Shear Thickening Fluids in Ballistic Textiles: A Review Dakshitha Weerasinghe 1 ¹Department of Textile and Clothing Technology, Faculty of Engineering, University of Moratuwa, Sri Lanka Abstract Bo armour has been used as a protective measure in warfare for a very long time. However in place of wooden sticks, knives, swords and arrows used at the time, assault rifles, snipers, handguns, Improvised Explosive Devices (IED) and other explosives are used e to the exponential development of weaponry after World War-II. With the advance of weaponry have emerged novel materials for protecting oneself from the increasingly advancing threat levels. High-performance fibres woven into ballistic textile structures was a beginning in this regard. Supplementary components like coatings, ceramic/steel plates and laminated composites are used commonly to reinforce the textile structure to heighten its performance. Shear-thickening-fluid-enhanced ballistic textiles is one such promising research area for high-performance bo armours. A Shear Thickening Fluid (STF)/dilatant is a non-newtonian liquid which will momentarily change its liquid state to a solid state temporarily upon impact or high rate of shear loading, such as the impact loading caused by a high-velocity projectile. This behaviour can be explained using formation of hydroclusters and order-disorder theory. This paper delivers a systematic review of the shear thickening behaviour and mechanism of shear thickening fluids in textile structures, implications, their present stature and what the future holds. Keywords shear thickening fluid (STF); bo armour; non-newtonian liquid; dilatant; viscosity I. INTRODUCTION A Newtonian liquid is a liquid obeying the Newton hypothesis which postulates that the shear stress is proportional to the deformation rate or the shear rate [1]. A liquid which does not obey this hypothesis is called a non-newtonian liquid, where the shear stress is not proportional to the shear rate. If τ, γ and μ refer to the shear stress, shear rate and the constant coefficient of proportionality-namic viscosity, respectively, for a Newtonian liquid τ = γ μ (1) proportionality will be true in contrast to a non -Newtonian liquid where τ / γ will not necessarily be a constant and is called as apparent viscosity [2]. Fig.1 2-D fluid element subjected to shear deformation This can be illustrated for a 2-D fluid element subjected to a shear force as shown in Fig. 1 where the parallelogram in dotted lines depicts the deformed element after δt time. Here, for small δγ values, tan(δγ) δγ (2) which yields δγ= δl / δy (3). Since δl= δu. δt where δu is the flow velocity and δγ denotes the deformation, δγ= (δu. δt) / δy (4). Therefore, dγ = (5) dt where dγ is the velocity gradient and is the rate of deformation, which can be denoted dt more generally as γ. For a 2-D fluid element in shear, since shear stress is directly proportional to the rate of deformation which yields τ yx α (6); which transforms eq. (6) to Page 182

2 τ yx = μ (7) where μ is the constant of proportionality-namic viscosity, which is applicable for Newtonian liquids. Here, τ yx stands for the shear stress acting on the y-plane in the x-direction. This scenario of shear thickening is of particular interest in bo armour-related applications and will be further discussed in terms of its behaviour, mechanisms and manipulating the parameters of a dilatant to obtain desired outcomes. Why it s of profound interest is that by incorporating textile structures with dilatants or STFs, the ballistic performance can be remarkably increased [3] [5] and holds promise for the future of armour materials [6]. II. SHEAR THICKENING BEHAVIOUR AND THEORIES Shear thickening in simple terms is the abrupt increase of apparent viscosity of a non- Newtonian liquid caused e to the shear rate above some critical value. The STF is generally a biphasic dispersion where one phase consists of particles down to nano level (fumed silica, kaolin, Calcium Carbonate, PMMA, corn starch etc.) and the other is the medium in which the particles are dispersed (Polyethylene glycol, water, Glycerin etc.) [4], [7] [9]. The impact of a bullet on a surface can be considered as a loading, causing an extremely high shear rate on the surface. Therefore, on a surface containing STF its the abrupt increase of apparent viscosity will render the non-newtonian liquid solidified in a matter of milliseconds or even less [10]. But it should be noted that there isn t any fluid layers physically in between fabrics but instead, the fabrics can be impregnated with the STF. Srivastava et al. [3] have investigated the effect of varying parameters such as Silica concentration and padding pressure on the ballistic performance. A remarkable advantage of this technology over nonflexible ceramic or steel plates used in the armor materials [11] is that the STF used will remain in the liquid state unless hit by a bullet or met with a sudden impact, thereby imparting more flexibility and mobility to the armour. The shear thickening behaviour itself is complex. It can be explained using two main theories, order-to-disorder transition (ODT) and hydronamic cluster (or hydrocluster) formation [5], [12] [14]. Hoffman [15] has carried out pioneering research to support the order-to-disorder transition theory. The theory suggests the following. The inception of shear thickening past a critical shear rate is e to the disorder of the layered flow structure of the fluid, thereby restricting movement [13]. Upon increasing shear the particles in the dense colloidal dispersion, moving in layers are pulled out of the said layers, jamming into one another thereby increasing the apparent viscosity abruptly. Force couples generated by van der Waals forces, electric double layer repulsion, and the shear stress between ordered layers of the fluid are thought to be the driving forces supporting the theory. Using light scattering it was shown that hexagonallyordered layers dislocate into a disordered state[16]. On the other hand, Bra et al. [17] have simulated the flow behaviour of a colloidal suspension using a Stokesian Dynamics approach where shear thickening was predicted without any layering, in conflict with the order-to-disorder transition theory. The same theory suggests the cause for shear thickening to be the formation of clusters composing of compactly grouped particles clustered upon shear forces. Thus formed hydroclusters getting larger with the increasing shear, short range lubrication forces cause the increase in apparent viscosity [16]. This theory was backed by experiments carried out by Bossis et al. [18] where it was observed that shear thickening occurs as shear forces make the particles form into Page 183

3 compact groups. Moreover, the simulations have also shown that any shear ordering in advance is not necessary for shear thickening. III. RHEOLOGY OF STF In the introctory chapter it was mentioned that for non-newtonian liquids the ratio of shear stress to shear rate will not necessarily be constant, as opposed to Newtonian eq. (7). For non-newtonian liquids, the shear stress and rate of deformation are not linearly proportional [2]. Therefore, for non-newtonian liquids eq. (6) will take the form τ yx α n (8) for some values of n. introcing a constant of proportionality to eq. (8) it can be rewritten in the form τ yx = k. n = k.. = η (9) where η=k. (10). Here, the molus is taken so that τ yx will have the same sign as the velocity gradient. This can explain the phenomenon of increasing viscosity of a non-newtonian liquid as the shear rate increases. Two cases of n in eq. (10) shall be considered; n>1 and n<1. n=1 will be eq. (7) itself. From eq. (10), the term k. strictly increases with the increasing deformation rate, when n>1. Plotting the shear stress, τ yx vs. deformation rate, according to eq. (9) will yield the graphs shown in Fig. 2. Newtonian case, with the gradient of the graph marked as μ in eq. (7) is named Newtonian, n>1 case as Shear-thickening and n<1 as Shear-thinning in Fig. 2, respectively. The dotted curve shows the case of Bingham plastics where according to the graph, a certain shear stress has to be overcome to create any kind of flow. Concrete, grease, ketchup and chocolate are examples and will not be further discussed since it s not related to ballistic textiles [2]. Fig. 2 Newtonian and non-newtonian time-invariant fluids [19] Shear thickening behaviour is of importance in ballistic bo armours and will be discussed further (n>1). For n>1, the gradient of the graph strictly increases, sometimes even causing discontinuities in viscosity increasing [2], [5], [10], [20] [23]. For some fluids, η in eq. (10) can be time-dependent. I.e. η can increase or decrease with the time. For this type of fluids the apparent viscosity is dependent on the ration for which it s subjected to shearing in addition to the fact that it s a function of the deformation rate and previous kinematic history Page 184

4 [24]. Moreover, liquids in which η decreases with time are called thixotropic and liquids that show an increase in η, rheopectic (or antithixotropic or negative thixotropic). To explain the rheology in deeper terms, a 3-D fluid element can be considered where a stress tensor with 9 components can be used to represent stresses [1]. For a vector such as force, only three components will be sufficient but for a stress, it has two considerations force and area, by the definition of stress. Therefore, how the area on which the force acts is oriented to the direction of the force must be taken into consideration. This distinguishes stress into normal and shear stresses therefore having to use a stress tensor. Stress tensor can be denoted in a compact manner as follows. (Cauchy) Stress Tensor; σ xx τ xy τ xz σ = τ yx σ yy τ yz. τ zx τ zy σ zz Here, σ ij and τ ij denote the normal and shear stresses, respectively. These stresses can be marked on a graphical diagram as shown in Fig. 3 Fig. 3 Stresses on a 3-D Fluid element Stress tensor σ, takes a direction v as input and proces the stress σ (v) on the surface normal to this vector for output, thus expressing a relationship between these two vectors [25]. As far as a ballistic impact is concerned, a bullet hitting on the STF-enhanced armour surface can be thought of causing a flow of the STF in the direction v and proces the stress perpendicular to the direction of the same, i.e. the stress on the surface of the armour itself. IV. CONCLUSIONS With the increasing threat levels given the advanced weapon systems, there s an imminent need in the market for high-performance bulletproof vests. Shear thickening is currently being used as a novel technique incorporated to soft bo armours and holds profound promise for the future. It is therefore of vital importance to gain an understanding about the complex behaviour of STF used in liquid bo armours. REFERENCES [1] F. R. Eirich, Rheology. Theory and Applications, vol. 1. New York: Academic Press Inc, [2] Alexander Ya. Malkin and Avraam I. Isayev, Rheology, Third Edit. ChemTec Publishing, Page 185

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