PSI - Issue 41

590 A.M. Ignatova et al. / Procedia Structural Integrity 41 (2022) 589–597 2 Ignatova A.M., Yudin M.V., Voronov V.L, Ignatov M.N., Gladky I.L., Inozemtsev A.A., Naimark O.B. / Structural Integrity Procedia 00 (2019) 000–000 fluorphlogopite. It has been established that the change in the velocity of fragments in time corresponds to the hyperbolic function; a coefficient has been proposed to calculate the change in the velocity of potassium fluorphlogopite fragments break-off in time. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the MedFract2Guest Editors. Keywords: non-metallic material; cracks; fracture; impact; fragmentation; image analysis. Introduction. According to the conventional classification, the major types of fracture are as follows: brittle fracture; fracture with development of radial cracks; granulation; plastic hole expansion; plug shearing; petal-shaped hole formation (Lamon, 2016). Solid brittle materials, including hard-melting non-metallic materials, exhibit only the first three types. Such fracture occurs through fragmentation. Properties of the material, impact velocities and fracture conditions determine the parameters of fracture fragments, including their velocity. The total of fracture fragments constitutes a fragmentation field. In literature, the fragmentation field is seen as a single object possessing the characteristics of its own, specifically (Barenblatt, 1964):  propagation velocity (often assumed as the leading fragment velocity);  fragmentation field bursting cone angle;  equivalent area of fragment effect;  mass distribution of fragments;  fragmentation field fluence. A fragmentation field can contain fragments in a wide variety of shapes and sizes; therefore, it would be a oversimplification to consider them as a single object. Practical determination of material properties requires assessment of velocities of individual fragments and patterns of their change with time (Stefanov, 2005). Besides, individual velocities of fracture fragments following an impact are crucial for evaluation of the hazard they present after emission. Some sources are known to have looked into this problem; so, (Goncharov et al, 2017) suggest a model for prediction of fracture parameters of a target and projectile shell based on the following equation: � � � � � � � � � � ��� � � � , (1) where V 1 is velocity of the contact surface between the impactor and the fixed target at the moment of impact, This model does not take into account the impact angle and external factors affecting the 'target-impactor' system. In (Kiselev snd Yarunichev, 2009), describing a collision between two particles, the suggested model, unlike others, enables prediction of the velocity and quantity of fragments forming the fragmentation field. Therefore, velocity of each fragment m α j at the moment of impact (particle fracture) is composed of velocity V determined by equation (2), and velocity v j α of emission from the point of collision. � � � � �� � � � � � � � � ��� � � �� � � , (2) 2 Ignatova A.M., Yudin M.V., Voronov V.L, Ignatov M.N., Gladky I.L., Inozemtsev A.A., Naimark O.B. / Structural Integrity Procedia 00 (2019) 000–000 fluorphlogopite. It has been established that the change in the velocity of fragments in time corresponds to the hyperbolic function; a coefficient as been proposed to calculate the ch nge in the velo ity of potassium fluorphlogopite fragments break-off in time. © 2022 The Autho s. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of MedFract2Guest Editors. K ywords: non-metallic material; cracks; fracture; impact; fragmentation; image analysis. Introduction. According to the conventional classification, the major types of fracture are as follows: brittle fractu e; fracture with development of radial cracks; granul ti ; plastic hole expansion; plug sh aring; petal-shaped hole formation (Lamon, 2016). Solid b ittle materials, incl ding hard-melting non-metallic materi ls, exhibit only the first three types. Such fracture occurs through fragmentation. Prope ties of the material, impact velocities and fractur conditions determine the pa amete of fracture fragments, including their velocity. The total of fracture fragments stitute a fragm n ation field. In liter ture, the fragmentation field is seen as a single object possessing the haracteri tics of its own, specifically (Ba enblatt, 1964):  propagation vel city (often assumed as the leading fragment velocity); fragmentation field bursti g cone angle; equivalent area of fragme t effect; mass distribution of fragments; fr gmentation field fluenc . A fragmentation field can contain fragments in a wide variety of shapes and sizes; therefore, it would be a oversimplifica ion to consider them as a si gle object. Pract cal determination of material p operties requires asse s ent of velocities of individual fragme ts and pa terns of their change with time (Stef nov, 2005). B sides, individual velocities of fracture fragments followi g an impact are cru ial for evaluation of the hazard they pres nt after emission. So e ources are known to have looked into this problem; so, (Goncharov et al, 2017) suggest a model for prediction f fractu parameters of a target and projectile shell ba ed on the following equation: � � � � � � � � � � �� � � � , (1) where V 1 is velocity of the contact surface between the impactor and the fixed target at the moment of impact, ρ j , ρ t , ar material d nsities of the impactor and the surface, respectively, U j , U t , are p rticle v loc ties of the impactor and target mate ial, resp ctively. This model does not take into account the impact angle and external factors affecting the 'target-impactor' system. In (Kiselev snd Yarunichev, 2009), describ ng ollision betwe n two particles, the sugg s ed model, unlike oth rs, enables prediction of the velocity and quantity of fragme ts formi g the f agmen ation fi ld. Therefore, velocity of each fragment m α j at the moment of impact (particle fracture) is compos d of veloci y V d termin d by equation (2), and velocity v j α of emission from the point of collision. � � � �� � � � � � � � � ��� � � �� � � , (2) © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the MedFract2Guest Editors. ρ j , ρ t , are material densities of the impactor and the surface, respectively, U j , U t , are particle velocities of the impactor and target material, respectively.

V is total velocity of the two particles after collision; V 1 is velocity of the first particle before collision; V 2 is velocity of the second particle before collision; M 1 is mass of the first particle before collision; M 2 is mass of the second particle before collision; V is total velocity of the two particles after collision; 1 is ve ocity of the firs particle b fore collision; 2 second particl before collision; M 1 i mass of the fir t particle before c llisi n; 2 second particl before collision;