Issue 49

Yu. Bayandin et alii, Frattura ed Integrità Strutturale, 49 (2019) 243-256; DOI: 10.3221/IGF-ESIS.49.24 252 nucleation and growth of defects with pronounced transitions at metastability area in terms of the structural variable (the defect density tensor and structural scaling parameter). N UMERICAL SIMULATION OF SILICON CARBIDE BEHAVIOR UNDER SHOCK - WAVE LOADING he wide applications of ceramics have been found due to the high dynamic elastic limit and the ability to absorb the energy at high load intensities. Ceramics show a low level of plastic (viscoplastic) deformation and the elastic- plastic transition in ceramic are associated with the “geometric” contribution of defects to the total strain. Fig. 7 shows a comparison of simulation and experimental results for silicon carbide under shock wave loading [15, 22]. The presented velocity profiles demonstrate the splitting of the shock wave into an elastic precursor and a plastic front. The value of plastic strain for ceramics is much smaller than that observed for metals. Weak sensitivity of the plastic front to the pulse intensity reflects the low contribution of the viscoplastic component, which is associated with low mobility of defects in ceramics. It was noted in [15] that some spall experiments in ceramics show weakly expressed spall pulse. This feature can be associated with a very short time of initiation and size of damage localization zone leading to small changes in the mechanical impedance during the formation of the spall surface. The self-similarity of wave fronts in SiC ceramics was established in [15] and it was shown that the value of the dynamic elastic limit does not depend on time. In this connection, velocity profiles were constructed in time-normalized coordinates for different thicknesses of the samples (Fig. 7). This result demonstrates the self-similarity of shock wave fronts in ceramics, which is due to self-similar patterns of damage kinetics in the metastability area of the nonequilibrium thermodynamic potential for solid with defects. S ELF - SIMILARITY OF SHOCK WAVE FRONTS IN METALS AND CERAMICS or a wide class of materials (metals [1-3] and nonmetals [2]), the fourth power-law universality of plastic wave fronts is established (Fig. 8 and Fig. 9)    * 0 A P   (14) where 0 P is the stress amplitude,  is the exponent equal to four in the strain rate range  *  ~ 10 5 −10 7 s -1 [3]. An explanation for the power universality of plastic wave fronts was proposed in [4], associated with the subjection of relaxation mechanisms to multiscale collective autosolitary modes of defects. It is established that the fourth power-law is violated for vanadium [3, 33]. Comparison of the results of the numerical simulation with experimental data is shown in Fig. 10. With an increase of strain rate at the wave front an asymptotic approximation to the fourth power-law is possible (in the graphs it is indicated by a solid line). C ONCLUSIONS he mechanisms of structural relaxation are associated with collective behavior of mesoscopic defects related to the metastability of nonequilibrium potential of solid with defects and the generation of collective modes responsible for plastic strain and damage localization. These modes represent the self-similar solutions of the evolution equation for the structural variable (defect-induced strain), which determines the relaxation properties of material and scenario of elastic-plastic transition. Spatial-temporal dynamics of these modes (autosolitary and blow-up dissipative structures) can be initiated at appropriate load condition (shock wave rise) and could provide the anomalous relaxation ability of nonlinear system “solid with defects” in the conditions of the specific type of criticality – structural-scaling transition. The metastability “decomposition” leads to the splitting of the wave front on the elastic precursor, the transient area of elastic precursor decay and the steady plastic front due to continuous (structural-scaling) transition between similar types of metastability depending on the shock wave amplitude. Autosolitary wave modes which subject the relaxation properties of shocked materials represent the “universality class” providing the four power universality at the steady shock wave front. The splitting of the wave front starts at the onset of critical behavior in the presence of metastability caused by the T F T