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Introduction Composite materials made of high-performance fibres are well known for their remarkable strength and low weight. Compliant composites with thermoplastic matrices (resin content does not exceed 20% by weight) are widely used in lightweight structures for ballistic protection [1]. Aramids and UHMWPEs (Ultra-High-Molecular-Weight-Polyethylene) are two most commonly used fibre types for armour applications [2]. Until recently, ballistic tests of real panels have commonly been used for determining their ballistic performance [2-5]. At the same time, such experiments can be very expensive especially when a range of thicknesses, configurations or projectiles is considered. On this reason, various numerical methods along with finite element codes are used to quantify interaction between composite panel and projectile. They allow to perform assessment of panel impact resistance and provide useful information about penetration process. The numerical simulation of composite materials under impact loading conditions can be performed at different levels. On the macromechanical level, a composite laminate is considered as a continuum orthotropic material with linear or non-linear mechanical behaviour. The main advantage of the modelling on the macromechanical level is a high computational efficiency. On the other hand, the continuum approach does not allow to catch delamination of the panel and fibres-matrix debonding. Nevertheless, such approach was widely implemented both into finite element and into finite difference codes like ABAQUS, LS-DYNA, ANSYS AUTODYN etc. and used by many researchers to simulate ballistic impact onto ceramic/composite [6-9] or fully fibre composite armour [10-16]. On the micromechanical level an explicit modelling of fibres and matrix elements is performed. Constituent modelling could provide great predictive capabilities but even now, computational power of modern supercomputers is not enough for simulating real-size composite target at the fibre scale. It should be noted that this approach might be used for some specific investigations [17] or as a part of multiscale simulations [18, 19]. All the mentioned above reasons are making mesoscale simulations widely used for analysis of composite materials behaviour. In this case, consolidated plies or fibre bundles are considered. Thus, it is possible to use simpler material models and fracture criteria for fibres bundles and a matrix. The interaction between a “failed” composite (which can behave like a dry woven fabric) and a projectile is also much easy to take into account using a mesoscale model. The yarn-level modelling was successfully used to simulate ballistic impact onto high-strength fabrics [20-23]. Among the mesoscale simulations of fibre composite materials, several works should be certainly mentioned. Gopinath et al. [24] investigated deformations of a clamped woven fabric rectangular laminate impacted at normal incidence by a full metal jacket projectile. Kevlar® yarn bundle and polymer matrix were modelled as a 3-D continuum with contact interfaces between the layers. Bresciani et al. [25] used similar approach for simulating ballistic impacts against Kevlar® 29 plain-woven fabrics with an epoxy matrix. Gama and Gillespie Jr. [26] proposed a layered model with tiebreak contacts for assessment of the damage evolution and penetration of thick-section plain weave S-2 glass/SC15 laminates. Chocron et al. [27] developed a numerical model for UHMWPE that captures the essential physics (wave propagation) during the 0.30 cal. FSP impact. The model bundles fibres in a strip as solid elements with orthotropic properties. All the models use different tiebreak contacts which significantly influence on material performance. At the same time, the authors mentioned that it is difficult to determine real properties of the interface between layers at high-strain rates and only approximate assessments are possible. In our work we developed yarn-level models for two most widely used composite armour-grade materials: aramid fabric with plane weave structure/thermoplastic matrix and Dyneema® HB80 UD laminate. Proposed models have two significant differences from the previous models presented above. Firstly, both models use combination of shell (for yarns) and solid (for resin) elements. Using of shell elements instead of solid elements for the yarns allows to reduce an overall computational cost of the models and realistically catches dynamic processes in fibre bundle [23]. The second feature is using of common nodes between yarns and matrix instead of contact algorithm that decreases an overall amount of contacts and more realistically reflects a material structure. The models successfully reflected the main failure modes in the real panels including the fracture of fibres, delamination, fabric/matrix debonding, yarns pull-out, etc. A reasonable agreement between the numerical and experimental ballistic curves was obtained. The organization of the paper is as follows: the data about materials and results of ballistic tests are presented in Section 2. The numerical models of the composite materials are described in Section 3. The results of numerical simulations are discussed in Section 4. Section 5 gives a conclusion. 1. Materials and ballistic tests 1.1. Composite laminates In this work, two types of composite panels were investigated. The first type of panel was made of single layers of Dyneema® HB80 prepreg. Each single layer of Dyneema® HB80 with the areal density of 145 g/m2 manufactured by DSM (Netherlands) is a (0/90)2 lay-up composed of approximately 84% fibres (in weight) and 16% polyurethane matrix [27]. Ultra-high-molecular-weight polyethylene (UHMWPE) [28] fibres SK76 are used for prepregs [29]. The second type of composite material was an aramid plain weave fabric KV110P/low density polyethylene (LDPE) composite. The aramid fabric with areal density of 110 g/m2 was produced by JSC «Kamenskvolokno» (Russian Federation) [30]. LDPE films with a thickness of 0.040 mm and areal density of 38 g/m2 were placed between fabric layers and used as a thermoplastic matrix. Aramid fabric composite panels were heated up to 145 °C and conditioned at this temperature for 2 h to minimize the temperature gradient. Then all the panels were pressed using the program: 0 … 13 MPa/1 min; 13 MPa/10 min; 13 MPa … 0/1 min. UHMWPE composite panels were heated only to 125 °C due to low melting temperature of PE fibres and pressed under the same program. All the panels had dimensions of 85×85mm. Table 1 contains a brief information about the manufactured laminates for ballistic tests. Table 1 Properties of the panels for ballistic tests Material Areal density (kg/m2) Average thickness of panel (mm) Number of layers KV110P/LDPE 4,01 3,72 27 Dyneema® HB80 4,35 4,70 30 1.2. Ballistic testing Ballistic tests were conducted according to GOST R 50744-95 [31] using 6.35 mm tempered steel ball with a mass of 1.05 g. A special gunpowder stand for acceleration of projectiles with terminal velocity up to 900 m/s was used. More details about the experimental setup and testing procedures could be found in [32, 33]. Initial (before an impact) and residual (after a target perforation) velocities of the projectile were measured during the experiments. Then the experimental data were fitted by least-square regression according to the classical Lambert-Jonas equation [34]: (1) where A, V50 and k are three regression parameters. Vr and Vi are the residual and initial velocities of the projectile, respectively. V50 defines incident impact velocity at which there is 50% probability of partial penetration and 50% probability of perforation [4] and it is close to ballistic limit velocity VBL (maximum initial projectile velocity which does not cause full perforation). Therefore, it can be assumed that . Table 2 contains the values of the regression parameters for the both types of the tested composite panels. Table 2 Lambert-Jonas equation parameters for the composite panels Material V50 (m/s) A k KV110P/LDPE 656 0,87 4,401 Dyneema® HB80 511 1,003 3,089 Fig. 1 shows the residual velocity vs. initial velocity curves according to Lambert-Jonas fits with actual tests measurements. a b Fig. 1. Ballistic curves for the composite panels: a - Dyneema® HB80; b - KV110P/LDPE The panels made of the aramid fabric demonstrated a reducing of back face deflection with the increase of the projectile velocity (Fig. 2). Fig. 2. KV110P/LDPE panels impacted at different velocities On the front side of all KV110P/LDPE panels, there is a buckling area of front layers with a specific cruciate form (Fig. 3). Dyneema® HB80 laminates were deformed significantly after the ballistic tests. Fig. 4 shows the back and the front sides of the panel impacted at a velocity of 771 m/s. It is clearly seen that the impact caused extensive delamination of the panel and fibres pull-out (Fig. 4, b) as well as buckling and fibre-matrix debonding of the front side layers (Fig. 4, a, dashed lines) and fibres fracture. Fig. 3. Buckling area (limited by dashed lines) on impacted side of KV110P/LDPE panel a b Fig. 4. Dyneema® HB80 laminate impacted at a velocity of 771 m/s: a - the front side; b - the back side The experiments showed that during ballistic impact there were several fracture modes in thermoplastic composites. It is difficult to reproduce all the observed deformation and failure mechanisms using continuum approach, and mesoscale models seem to be promising in this case. 2. Descriptions of mesoscale models The mesoscale models for both (plain weave and cross-plied) architectures of the ballistic composites were created using commercial finite-element package ANSYS and LS-PrePost. All the computations were performed with LS-DYNA finite element code using the supercomputer «RSC Tornado SUSU» [35]. 2.1. Geometry The first step to create the geometry of the models was to determine fibres and matrix content by weight. It was mentioned that the Dyneema® HB80 single layer (i.e. four plies) had an areal density of 145 g/m2. Densities of UHMWPE fibres and Polyurethane matrix were assumed equal to 970 kg/m3 [27, 28]. A simple estimation provides a layer thickness of 0,157 mm. KV110P/LDPE panels had 74% aramid fibres by weight and a layer thickness of 0,138 mm. Areal density of a layer was 148 g/m2. It was assumed that densities of an aramid fibres and LDPE matrix were 1440 kg/m3 [4] and 937 kg/m3. Representative volume elements (RVE) were used to construct the composite architectures. Both architectures were meshed using square shell elements (ELFORM = 10) to represent the yarns and 8-nodes solid elements (ELFORM = -1) for the matrices. The RVE for the Dyneema® HB80 single layer consists of bundling fibres into strips with width of 1 mm (Fig 5, a) and gap between the strips of 0,19 mm filling with a matrix. As in the previous paper [35] four plies were consolidated into two because of computational reasons so the strip thickness was 0,0784 mm. The RVE for KV110P/LDPE lamina (Fig 5, b) was a bit more complicated due to a plain weave structure of the aramid fabric. According to the manufacturer data [30], KV110P aramid fabric with an areal density of 110 g/m2 has about ~170-180 strands in the warp and weft directions on each 100 mm. In this regard, the width of the yarn bundle was equal to 0.5 mm. a b Fig. 5. Representative volume elements: a - for Dyneema® HB80; b - for KV110P/LDPE A yarn thickness was 0,08 mm: each two layers were consolidated into one in order to reduce a computational cost of the model. This approach was successfully used for the modelling of aramid fabric [37]. The gap between adjacent yarns was 0,05 mm. KV110P has enough dense weave structure and it was assumed that LDPE matrix fills only pores between yarns and does not impregnate fibre bundles. Thus LDPE matrix between aramid strands was not explicitly modelled and taken into account using special option MAREA in card *SECTION_SHELL (MAREA is a non-structural mass per unit area). For the RVE presented in this paper MAREA was 18,9 g/m2. The geometry of the representative volume elements allows to perform not only full scale simulations of a target but also to use symmetry properties and consider only a ¼ part of a model. Shell and solid elements in both RVE had common nodes. In addition, RVE for Dyneema® HB80 with an increased width of strips (2 mm) was also created to determine sensitivity of the model on the mesh size. 2.2 Material models and contacts The main advantage of mesoscale models is a possibility to use simple constitutive models of materials. Simulations of the ballistic impact onto Dyneema® HB80 were performed with resin properties taken from [27]: the material was assumed to be a homogenous isotropic and perfectly elastic plastic (*MAT_PLASTIC_KINEMATIC). Young modulus of matrix was 70 MPa, Poisson ratio of 0.45, yield strength of 3.5 MPa and failure at an effective plastic strain of 10%. The material of the fibres was linear elastic up to failure (*MAT_LINEAR_ELASTIC). In previous paper [35], the UHMWPE Young modulus of 200 GPa was used according to Utomo [38]. Recent research [39] showed that a value of 120-130 GPa is more realistic. On this reason, the simulations of Dyneema® HB80 were performed with a fibre Young modulus of 132 GPa and fibre failure stress of 3,8 GPa (Chocron et al. [27]). The polymer matrix in KV110P/LDPE composite was also modelled using perfectly elastic plastic material model with Young modulus of 400 MPa, Poisson ratio of 0.45, a yield strength of 12 MPa and failure at an effective plastic strain of 10%. An aramid yarn’s modulus of elasticity was equal to 130 GPa [32]. A failure stress was increased to 4,5 GPa (on ~30% more than the static value [32]) because in paper [40] it was shown that fibres strength increased at high strain rates. The projectile material being considered was a steel with a linear elastic behaviour, elastic modulus of 200 GPa and Poisson ratio of 0.3. Two contact algorithms were used. The first type being specified for projectile-composite interaction was *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE. The second contact type was *CONTACT_AUTOMATIC_SINGLE_SURFACE to define fibre-fibre interaction. Values of friction coefficient being used for the all simulations are presented in Table 3. Table 3 Values of friction coefficients used in the simulations Material Friction coefficient Projectile-Composite Fibre-Fibre Dyneema® HB80 0,02 [27] 0,02 [27] KV110P/LDPE 0,2 [24] 0,2 [21] Contacts between fibres and matrices were not specified. Fibre-matrix interaction was realised through common nodes in RVE. 3. Results of numerical simulations and discussion Transverse impact simulations on the both types of the composite laminates were performed at different velocities of the projectile. Lambert-Jonas fit curves of the experimental data with actual computational results are shown on Fig. 6. a b Fig.6. Lambert-Jonas fit curves of the experimental data with actual computational results for a - Dyneema® HB80; b - KV110P/LDPE 3.1. Mesoscale modelling of Dyneema® HB80 panel The model with fibres properties taken from the paper of Chocron et al. [27] predicted a stopping of projectile at a velocity of 590 m/s. Thus, the ballistic limit value being obtained was about 590-610 m/s. It should be pointed out that bundling fibres into the strips is only a rough approximation to the real material structure. This fact can explain disagreement between calculated residual velocities and experimental ones. To study the influence of strip width on a projectile residual velocity two runs were performed. Strip widths were 1 mm and 2 mm respectively. The initial projectile velocity was 700 m/s. Fig. 8 compares the velocity vs. time history for the projectile for both computations. It is clear that model with narrow strips demonstrated better performance. Numerical model is sure to be overpredicted with further reducing of strip width. Such a behaviour is a result of simple fibre and matrix material model without thermal effects. They influence greatly on the panel behaviour during impact [41] as UHMWPE fibres have a low melting temperature (about 150 °C) [28]. Thus, it is meaningless to decrease strip width without taking into account thermal softening of the material. Furthermore, computational cost of such model will be enormous. The model with the strip width of 1 mm allows to obtain a realistic panel behaviour, reasonable agreement with the experiments and acceptable computational time. The model predicted formation of buckling area on the front side of the panel (Fig. 7, a) as well as significant deflection of the back side and the delamination on the edges (Fig. 7, b) that agree well with the experimental results (see Fig. 4). 3.2. Mesoscale modelling of KV110P/LDPE panel The proposed mesoscale model of KV110P/LDPE panel also demonstrated both qualitative and quantitative agreement with the experiments. For example, an experimentally obtained ballistic limit velocity for the composite was about 510 m/s (see Fig. 6, b). The models give a value of 480 m/s. Moreover, because of a high melting temperature of aramid fibres (about 550 °C) [39] there is no such a significant influence of thermal effects on the ballistic performance of the panel in comparison with Dyneema® HB80 laminate. In this case, the assumption that a fibre bundle is linear elastic up to failure seems to be realistic. a b Fig. 7. An example of a numerical simulation of Dyneema® HB80 laminate impacted at a velocity of 770 m/s: a - front side; b - back side Fig. 8. Relations between the projectile velocity and time history for the models with different strip widths An example of numerically obtained deformed shape of the panel impacted at a velocity of 550 m/s is shown on Fig. 9. a b Fig. 9. An example of a numerical simulation of KV110P/LDPE laminate impacted at a velocity of 550 m/s: a - front side; b -sectional view A velocity reduction leads to the increase of the back face bulging (Fig. 10) and the area of delamination. It is also seen that the amount of fires subjected to pull-out is negligible even at velocities close to the ballistic limit. This is in a good agreement with experimental data (see Fig. 2). Fig. 10. Sectional view of KV110P/LDPE laminate impacted at a velocity of 500 m/s Conclusion In this paper, mesoscale models of two common compliant armour-grade composites for ballistic impact simulations were developed. RVE approach for constructing composite architecture was used in the models. The models were validated by comparing experimental ballistic curves with experimental ones. Yarn-level modelling of KV110P/LDPE gave a good agreement with experimental data even with consolidated layers. Mesoscale modelling of UHMWPE composite with UD structure is also possible but including thermal effects into calculations can increase their possibilities. Nevertheless, both models can predict the main fracture mechanisms in composite panels and allow to define projectile residual velocities with reasonable accuracy. …………………..

About the authors

O A Kudryavtsev

South Ural State University

Email: kudriavtcevoa@susu.ru

S B Sapozhnikov

South Ural State University

Email: ssb@susu.ru

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