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Fibre-reinforced plastics based on high-strength synthetic fibres are used in many industries as a structural material. In some cases, a composite structure can be subject not only to static/cyclic loading, but also to impact. Under normal operation conditions, composite structures are most often subjected to low-velocity impacts (hail, tool drop, gravel from vehicle wheels, impacts from auxiliary equipment, birds, etc.). Similar phenomena often occur during the operation of aircraft, wind generators, ship elements and bridge elements [1, 2, 3, 4]. To provide further safe operation of composite structures, there are requirements for the residual static strength of composites in the presence of impact damages. In cases related to emergency situations, where the requirements for ensuring the integrity/tightness of the structure are imposed, the tasks of high-velocity impact interactions are also widespread [5-10]. For example, fragments formed by rotor blades fracture must be localized by the aircraft engine protective case to prevent the fuselage damage [5]. To date, a plenty of studies have been published on the experimental and computational analysis of the composite material impact loading features among which several review works [11-16] can be highlighted that quite fully reflect and structure the accumulated experience in this field. Despite the large number of publications devoted to FRPs impact loading, there are almost no works on the random nature of the perforation process of the layered composites under high-velocity impact. When a projectile interacts with a target, there are two outcomes that indicate the target damage, and they are perforation or non-perforation (failure or resistance) [17, 18]. It is believed that at each projectile velocity Vi the target behaviour has a binary result (response) U, where U=1 if perforation takes place and U=0 if no perforation occurs. There is also a zone of mixed results (ZMR), which is characterized by two limit velocities V0 and V100. When using a probabilistic approach, V0 determines the projectile velocity, corresponding to the zero probability of target perforation, and V100 determines the upper limit of the zone of mixed results and corresponds to the velocity at which the target is perforated with a 100% probability. When designing composite structures that can be subject to high-velocity impact, engineers are faced with the task of determining rational configurations of composite targets that would guarantee no perforation over the entire expected operating range of projectile velocities [19, 20]. In [19], using a simple protective barrier consisting of one steel plate as an example, it is presented that the solution to this problem comes down to determining the thickness of the plate for which the value V50 will exceed the design velocity VD by a certain amount. Figure 1 shows the dependence of target perforation probability on the initial projectile velocity. The average value of projectile velocity in the zone of mixed results is V50 (the projectile velocity at which the probability of target perforation is 50%), and the standard deviation σ characterizes the width of the zone of mixed results. Velocity V0 is calculated based on the results of ballistic limit tests. The permissible design velocity VD must be lower than V0 by the design tolerance value ∆. In fact, the value of ∆ is determined by the standard safety factor [19, 20]. Thus, when designing a structure, the value of the permissible velocity VD is lower than the value V0, then this configuration excludes the possibility of target perforation in a given operating range of projectile velocities. For simple structures consisting of, for example, a single steel plate, the width of the zone of mixed results can be quite narrow and amount to about 5 m/s. However, for more complex structures (multilayer and heterogeneous), which include structural composites, the width of ZMR can be several tens of meters per second [19]. Fig.1. Perforation probability vs projectile velocity The works [21-27] present various approaches to processing experimental data to obtain estimates of V0, V50 and V100. Unfortunately, it was not possible to find in open sources any estimates of the zone of mixed results width for FRPs, as well as data on the influence of target thickness on it. Meanwhile, this information is extremely important when constructing computational models of deformation and fracture of a composite under high-velocity impact, since ballistic curves are used to verify their parameters [28]. This paper presents an experimental study on the features of the impact interaction of a steel spherical projectile with GFRP specimens with the thicknesses of 4 mm, 6 mm, and 7.3 mm at the velocities near the corresponding ballistic limits. The experimental study was carried out in two stages. At the first stage, based on the results of the first series of impact tests using the Lambert-Jonas approximation [27], ballistic curves and estimates of V50, maximum perforation and non-perforation velocities were obtained for each thickness of specimens. At the second stage, another series of tests for each thickness of specimens, when the initial projectile velocity was selected so that it fell into the zone of mixed results was carried out in order to obtain perforation frequency curves. Based on the results of more than 300 impact tests, estimates of the zone of mixed results width were obtained, which can later be used by engineers and designers when creating critical structures potentially subjected to impact loading during operation.

About the authors

N. A Olivenko

South Ural State University, Chelyabinsk, Russian Federation

E. V Leshkov

South Ural State University, Chelyabinsk, Russian Federation

D. S Zaigraev

Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics, Snezhinsk, Russian Federation

V. P Matash

Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics, Snezhinsk, Russian Federation

S. M Ulyanov

Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics, Snezhinsk, Russian Federation

О. A Kudryavtsev

South Ural State University, Chelyabinsk, Russian Federation

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