damaged surface grows as a result of the opening of microcracks. The development of the main crack leads to the complete fracture. Changes of the damage parameters at the observed stages of multiple fracture are shown in Fig. 5. It follows from the graphs that the critical situation appears at reaching the area of damages (ω*) close to 10%, when the microcrack opening increases, density of defects decreases as a result of their coalescence, and concentration criterion falls to the constant value (k~1.5). The value of ω*=10% is close to the threshold of percolation for many systems; therefore, changes at the third stage precede the critical event (specimen fracture). With reaching ω*, the exponential relation, which describes the cumulative distributions of microcracks and acoustic emission signals, becomes close to the power relation, and exponents in these relations reduce. 2.6. Activation energy of fracture process An analysis of the established regularities of changes in exponents of the functions describing the statistical distributions allows us to connect them with a change in another important parameter of kinetic process, namely, in the activation energy of fracture. According to Arrhenius – Zhurkov equation of [11], the lifetime (t) of solids is the function of the activation energy of fracture process U(σ), the absolute temperature T, the energy of a thermal motion R and obeys the exponential relation: 0 0 (σ) exp U U t t RT ⎡ − ⎤ = ⎢ ⎥ ⎣ ⎦ (5) This relation may be obtained from a correlation 0 lg lg (σ) / t t b T = + , where b( )σ is the slope of dependence lgt 1/T − , (σ) (lg ) / (1/ ) b b t T = =Δ Δ , or ( ) 0 exp β/ t t T = , where β 2.3b = . Multiplying the numerator and denominator of the exponential function index by the Boltzmann constant and denoting βk U= leads to (Eq. 5). Thus, the activation energy is evaluated on the slope coefficient b of creep curves plotted in semi logarithmic coordinates [12]. The stress dependence of the activation energy of fracture of polymethylmethacrylate, which was plotted using these data [13], showed that the activation energy decreases with increasing the stress and the stress dependence of activation energy corresponds to the exponential relation with the exponent equal to 0.02 and R2=0.98. Similar decrease of the slope coefficient with increasing the load or specimen displacement is presented in Fig. 2 c. The activation energy of solids is traditionally related (by the analogy with that of chemical reactions) to the energy given for the overcoming of inter-atomic interaction by thermal fluctuations. Although the fracture process in the whole is determined by the strength of atomic bonds in the region of fracture localization, this approval calls for the special confirmation. Indeed, the slope coefficient of strength dependencies obtained for laboratory specimens is the macroscopic parameter revealing the kinetics of initiation and accumulation of microcracks and growth of a macrocrack. These processes are connected to changes in the fracture process zone size and damage accumulation in this zone. Therefore, the decrease in the activation energy with increasing stress may be a consequence of considered above regularities of damage accumulation in the fracture process zone that are due to the interaction of defects resulting in a decrease in the slope coefficients of statistical distributions. This assumption is confirmed by an analysis performed in [6, 13], which showed an interrelationship between the activation energy and exponents in power law equations characterizing the fracture development, namely, in both the Paris relation and the equation based on the phase transition theory.
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