PSI - Issue 14

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

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L.R.Botvina/ Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

The fracture mechanics based on the Griffith approach is the basis for an experimental and theoretical analysis of fracture processes. However, it is known that the Griffith equation is an analog of the Gibbs equation used to describe the crystallization process, and as the Griffith equation, follows from the analysis of the balance of total and surface energies. The appearances of a critical crack, as well as the appearance of a critical nucleus of a solid phase, lead to the development of processes of fracture or crystallization that does not require energy supply. The similarity of the J. Gibbs and A. Griffith relations proposed for estimating the critical sizes of the solid phase nucleus during crystallization and the crack length during fracture allow us to consider the processes of failure from the viewpoint of the phase transitions theory. The idea of such an analysis was pronounced by de Arcangelis et al. (1985) three decades ago, but until now there is no agreement of researchers in that what kind of phase transition is realized at the fracture. Moreno et al. (2001) consider fracture as a first-order phase transition, similar to thermally activated fracture in a homogeneous medium, while Zapperi et al. (1997) believe that this question remains controversial similarly to the question of which order parameter characterizes a phase transition upon fracture. Consideration of the fracture processes from the point of view of the phase transitions theory is the only consequence of the noted analogy. Therefore, the question remains what other consequences follow from the analogy of the Griffiths and Gibbs equations, in addition to the possibility of considering fracture from the viewpoint of the theory of phase transition. An attempt to answer these questions will be made in this paper. The order parameter in the liquid-gas phase transition (or liquid-solid phase) is the difference between the density of a liquid and a gas (liquid and solid), characterizing the extent of the two-phase region of the isotherms of the liquid-gas phase transition. This region is bounded by the spinodal curve. At the phase transition point, critical values of density and pressure are reached, the liquid passes into vapor, and the two-phase region disappears. During the fracture, the two-phase region of the damaged and undamaged material is formed at the second stage of stable development of the process. Thus, according to Botvina (1994, 1997), the extent (or duration) of the stable stage of fracture process development can serve as the order parameter of the phase transition upon fracture. In Fig. 1, a we present schematically typical fracture kinetic curves K=f (τ) obtained under a constant value of the parameters P and S defining the test condition (temperature, loading rate, etc.; K is a certain strain and/or fracture property; τ is the time). It is clear that these curves remain similar to each other until a certain critical value of the parameter is reached. For P=P c , the second steady-state stage disappears on the fracture kinetic curves and they become closer to straight lines. 2. The order parameter of phase transitions in the fracture and crystallization processes

Fig. 1. (a) typical time dependencies of a characteristic ( K ) of deformation or fracture for different values of a parameter P governing the loading conditions: I, II, III – stages of damage accumulation; (b) fracture kinetic diagram (rate of change in the K characteristics in function of governing parameter)