PSI - Issue 40

A.M. Ignatova et al. / Procedia Structural Integrity 40 (2022) 185–193 Ignatova A.M. at al. / Structural Integrity Procedia 00 (2022) 000 – 000

187

3

2

( )

 

m v

K



1     j j k E 

j

j

(1 )



N

(3)

j

2

(2(1 ) ) k e



j v

 

(4)



k is the fraction of elastic energy spent on fracture, e is the elastic energy of the particle. The presented model allows us to determine only the initial velocity but does not allow one to estimate the velocity in time. The above papers are focused primarily on metal materials. The behavior of ceramic materials that belong to non metallic refractory materials under shock-wave loads is considered in detail in paper of Davydova (2013), where a scenario for the development of damage localization during the origin of rupture areas related to the formation of multiscale self-similar collective modes of ensembles of defects is proposed. Mentioned models allow the prediction of materials responses under impact, while the behaviour of individual fragments remains, as a rule, beyond their limits or is partially covered. One of the reasons for this situation is insufficient experimental data on the behaviour of rupture fragments and their individual velocity. The aim of the study is to experimentally determine the velocity of rupture fragments upon impact on a refractory In the paper of Ignatova (2021), potassium fluorophlogopite is used as an object of exposure, which is mica crystalline and refers to refractory non-metallic silicate materials. This material has a density of 2.8-2.9 g/cm 3 and crystal-chemical formula: KMg 3 [Si 3 AlO 10 ]F 2 and the following composition, wt.%: SiO 2 – 39-43, Al 2 O 3 – 9-12, MgO – 27-30, K 2 О – 7-9, F – 9-12. The compressive strength of potassium fluorophlogopite depends on the length of the layered structural components; with a length of 50-300 microns, this parameter varies in the range from 50 to 10 MPa, respectively. The targets made from mica-crystalline material were shaped in the form of flat plates with a size of 280x160x15 mm (taking into account 70 mm for mounting in the unitholder). The samples were covered with white water-based emulsion paint to illustrate the results of the experiments, with a marking grid with a cell size of 10×10 mm on the samples' surface. A steel ball (Steel 20) with a diameter of 23 mm was used as a projectile. The velocity of the rupture fragments was determined through video recording obtained using a high-speed Photron Fastcam SA5 camera. The maximum shooting speed of the camera was 775,000 fps at a resolution of 128×24 pixels. The high -speed video recording system was equipped with a lighting complex consisting of seven light sources with a power of 1,000 W each to obtain high-quality video shooting with a short exposure time. The video was processed by analyzing frame-by-frame images using the ImageJ-FiJi software program (TrackMate module). The trajectory of each rupture fragment was tracked within provisional coordinates, then the distance traveled by the fragment frame to frame was determined, and the time scale of the shooting, the velocity of the fragments was determined with reference to a certain point in time. The size range of fragments was also established using the ImageJ-FiJi software program (the Analyze particles module) to consider the individual characteristics of the rupture fragments during the analysis of frame-by-frame images. non-metallic silicate material. 2. Materials and methods

2.1. Experimental set-up

The collision of a target made from fluorophlogopite and a steel ball as an was performed using a pneumatic unit (Fig. 1). The steel ball was accelerated in a pipe with an internal diameter of 25 mm and a length of 3,950 mm using pneumatic equipment; a pump with a high-pressure receiver with a volume of 5.2 liters was used. The receiver was