PSI - Issue 14

L.R. Botvina / Procedia Structural Integrity 14 (2019) 26–33 L.R.Botvina / Structural Integrity Procedia 00 (2018) 000 – 000

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Many dependencies (both kinetic and parametric) of the deformation and fracture characteristics are similar to the curves shown in Fig. 1. These include creep curves (for different stresses or temperatures), deformation curves (for different loading rates or temperatures), kinetic curves of fatigue crack growth, wear curves, the dependencies of internal friction in material, and swelling caused by irradiation, etc. The initial stage ( I ) on the fracture kinetic curves may be absent. This is most often due to the difficulty in the recording of this stage because it requires finer measurement than registration of fracture processes at stages II and III . However, the other trends are preserved. The extent of stage II (section of the curve between points A and B , Fig. 1) decreases as P increases over rather broad range. Close to Pc , the dependence of the lifetime on P , and the scatter of the experimental points increase. In the case of fatigue, a similar family of fatigue crack length growth curves for different stress amplitudes is used to plot kinetic fatigue fracture diagrams (Fig.1b), described in their middle part (on the AB section) by the well known Paris equation: ⁄ = ∆ (1) where ⁄ is the growth rate of the fatigue crack, Δ K is the range of the stress intensity factor, m is an exponent that depends on the material and experimental conditions and for many structural materials varies from two to four. The comparison of the fracture kinetic curves presented in Fig. 1a with the isotherms for the liquid-gas phase transition plotted in pressure ( p ) vs. density ( ρ ) coordinates shows that the fracture curves have a shape similar to the isotherms at different temperatures. On each of the fracture curves, as on the liquid-gas isotherms, we can isolate an initial section (0 - τ 1 ) within which the first derivative of the characteristic K decreases; the second steady-state stage (τ 2 - τ 1 ), for which dK/d τ is almost constant and the third stage where the development of the process is unstable and the derivative dK/d τ increase. The effect of the parameter P is characterized by the fact that with an increases in P , the extent of the second steady-state stage of the fracture process decreases and the first derivative of the characteristic K increases. For the critical values of P c and τ c , t he second stage on the curves disappears (τ 2 - τ 1 =0) and the third stage follows the first stage. In this case, the time dependence of the characteristic K becomes close to linear, as does the isotherm p=f ( ρ) when the critical temperature is achieved under the liquid-gas transition conditions. By analogy to the liquid-gas phase transition, the closeness to the critical point of the fracture process (in this case, to the point with coordinates P c , τ c ) is defined by the difference τ 2 - τ 1 (Fig . 1a). This difference may serve as an order parameter for the fracture process of a solid. In this case, we can probably assume that the process itself undergoes the phase transition at the point with coordinates P c , τ c . What can we say about phase transition in this case? The fracture mechanisms are different under different conditions. However, all of them are connected with nucleation and gradual accumulation of different types of damage. At the initial stage of fracture (region I in Fig. 1a), pores are only nucleated, and the damage process is not yet developed, a dislocation structure is formed which causes strain-hardening of the material. Accordingly, we can consider that at stage I the material does not contain pores or contains significantly less of them in comparison with the number of defects at the order stages. At stage II , the accumulation of pores is going on and the material can be considered as a “two - phase” one, i.e. consisting of damaged and undamaged volu mes. At stage III the rapid growth of pores, the formation of macrocracks and fracture are going on. Thus, the dashed curve in Fig. 1a, similar to coexistence curve for the liquid-gas phase transition, separates the “two - phase” region in which the specimen consists of pores or microcracks and sections of undamaged material. Such a representation of the two- phase structure of a solid under loads is close to Frenkel’s idea which considers a typical crystal of a monoatomic substance as a binary material consisting of proper atoms and vacancies which are “atoms” of the second substance (voids). If the material is a two-phase one at the steady state stage of fracture, we can assume that upon achievement of critical conditions, a “phase transition” occurs with for mation of a new phase: a macrocrack. In the crystallization process, the role of pores is played by particles of the solid phase already crystallized from the melt; therefore the steady state stage on the crystallization curves (plotted in viscosity of the melt vs. fraction of solid phase coordinates) is connected with development of a two-phase structure, and the extent of this stage (determined by the volume fraction of the solid phase) is the order parameter of the crystallization process.