Structural-temporal theory of fracture as a multiscale process

Steady plastic wave fronts and scale universality of strain localization in metals and ceramics

“…where  is the temperature factor, 0 U is the characteristic value of the energy of the interatomic bond rupture, 0i  is the characteristic relaxation times,  is the generalized thermodynamic force, which in the Zhurkov model coincides with the applied stresses [12,14]. In the works of the authors [6,18], the dependence of the relaxation times on the accumulated strain in the form…”

“…These collective modes have the nature of self-similar solutions for the evolutionary equation of damage kinetics (autosoliton modes in the case of the development of plastic instability and dissipative structures for damage localization) and play the role of "collective variables" that subordinate the spatialtemporal dynamics of the behavior of condensed matter under intense impacts. The formation of self-similar plastic wave fronts [2,3], instability and damage-failure transitions in metals and ceramics [9][10][11][12][13][14][15], kinetic regularities of spall fracture in metals and ceramics [12,15,16] can be regarded as the most striking manifestations of such space-time dynamics. The listed effects are studied theoretically [6,11,13,[16][17][18][19][20][21][22] on the basis of developed continuum models reflecting the role of metastability, collective modes of defects on the relaxation properties of solid and damage-failure transition scenario.…”

The Numerical Model of Dynamic Mechanical Behavior of Brittle Materials Based on the Concept of the Kinetic Theory of Strength

“…The T parameter is a physical one and usually characterizes process of formation and development of the main crack (fracture) in a sample or a fragment of material or formation of system of micro-fractures that cause macroscopically inelastic behavior of this fragment. It is obvious that the time parameter T depends on the scale, and hierarchy of the corresponding scales is associated with hierarchy of elements of the internal material structure [50][51][52]. According to Zhurkov, this parameter is associated with thermal fluctuation effects in the crystal lattice and defined by the temperature and applied load.…”

Relations between Parameters of Fracture Processes on Different Scale Levels

“…When solving the problems of fracture mechanics, it is necessary first of all to set the key features that determine the fracture event itself, corresponding to specific tests, for example, to consider the formation of microcracks in a sample or its macroscopic fragmentation as the fracture thereby implicitly determining the representative volume of the fracture. Thus, depending on the type of loading action, fracture can occur at different scale levels [1,2]. The scale on which the fracture is implemented determines the values of the strength parameters of a material or the mechanical characteristics critical for this level.…”

“…The parameters τ and d calculated in this way, nevertheless, do not allow us to obtain an adequate structural−time model of UAD.During the dynamic tests on SHPB, a marble sample was under impact pulses the intensity and duration of which were much higher than that in the experiments on UAD. The sizes of the fracture regions in the two types of tests differed by orders of magnitude; i.e., the two types of fracture considered were implemented at different scale levels to which different space−time elementary (representative) volumes correspond[2]. Thus, there is a fundamental problem of determining…”