PSI - Issue 40

I.A. Bannikova et al. / Procedia Structural Integrity 40 (2022) 32–39 I. A. Bannikova at al. / Structural Integrity Procedia 00 (2022) 000 – 000

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The observed regularities suggested that water under these loading conditions behaves as a quasi-plastic non Newtonian condensed matter. Moreover, the asymptotic law for spall strength shows similarity to the spall strength of a solid known as the “dynamic branch” of spall failure. It was shown in Naimark, (2004) that the existence of the length spectrum H C L iL  gives rise to anomalous dispersion properties due to localization kinetics of numerous blow-up damages. Tubular alumina samples were another object for experimental and theoretical studies. The failure of ceramic tubular sample ( 2 3 Al O ) into 2D and 3D fragments was caused by the EEW-induced shock wave in distilled water (Fig. 2, a) and involved two main stages. At the first stage, vertical cracks were formed along the height of the sample, as a result of stretching the tube in the radial direction (which was confirmed by video recording of the failure dynamics (Bannikova et al (2015)). The mechanism for the formation of 2D fragments corresponds to the model of thin shells failure developed by Mott (1947), according to which the size distribution of fragments is influenced only by the loading intensity (in our case, this is the specific energy). Cracks and their branching were also observed at the edges of 2D fragments (Fig. 2, b). A similar process of dynamic crack propagation was observed in the striking PMMA rods by Bellendir et al. (1989), Naimark and Uvarov (2004). Here, an increase in the load provides a transition from the single crack propagation to crack branching and, accordingly, to the fragmentation, which was observed in these experiments. It was shown that the development of multi-site fracture with increasing stress corresponds to the transition from kinetics of the exponential type (characteristic of quasi-static loading) to a "dynamic branch", which shows a weak dependence of the failure time on the applied stress. At the second stage, the formation of horizontal cracks was studied. Analysis of the sample structure showed that the initial porosity of the ceramics directly affects the formation of 3D fragments (Bannikova et al. (2016)). The initial defects (porosity) are activated by the shock -induced stress in ceramics, which leads to the damage-failure transition. The results obtained can be compared with data on liquids, showing that the cavitation (porous) structure of liquids also affects fracture and spall strength. The presence of the second peak on the profile (Fig. 3, a) of the compression wave recorded by the VISAR interference system (Fig. 2, a) indicates that 3D fragments were formed due to the fragmentation of 2D objects in the form of a multiple spall (Bannikova et al. (2016)).

a c h a r a c t e r i s

b c h a r a c t e r i s

Fig. 2. (a) scheme for measuring the free surface velocity; (b) Microbranches near the fracture surface of a 2D fragment, by a HIROX KH-7700 microscope.

t i c p a r a m e t e r

t i c p a r a m e t e r

Self-similar patterns of the fragmentation statistics were established in the range of specific loading energy (4÷ 22 J/g) by Bannikova et al. (2016). It is shown that the size distribution of fragments can be described by two functions: the distribution of 2D fragments – by the exponential function; the distribution of 3D fragments by the power function (Fig. 3, b). The study also provided evidence that the distribution and mechanism of formation of 2D and 3D fragments are affected not only by porosity, but also by loading energy and geometry of the cylindrical specimen. It was shown in Bannikova et al. (2015) that the mass (size) distribution of fragments is transformed into a power-law distribution with an increase in the specific fracture energy for thin-walled shells with a characteristic parameter * 1 k  under conditions of shock wave loading due to electric wire explosion in a liquid. In the case of shock-wave loading of thick-walled shells with * 1 k  , the mass (size) distribution of fragments is described by the