PSI - Issue 16

Zinovij Nazarchuk et al. / Procedia Structural Integrity 16 (2019) 169–175

170

2 Zinovij Nazarchuk, Olexandr Andreykiv, Valentyn Skalskyi, Denys Rudavskyi / Structural Integrity Procedia 00 (2019) 000 – 000

Keywords: delayed fracture; macromechanisms of material delayed fracture; acoustic emission signals; residual life of structure elements.

1. Introduction

Delayed fracture of structural materials is dangerous due to difficulties in their prediction and diagnostics. Since such fracture is caused by the defects formation or association (vacancies, dislocations, pores, microcracks, macrocracks) during which the elastic waves are irradiated, AE method is the most effective to reveal delayed fracture of structural elements under a long-term static loading. To detect such fracture of structural elements, AE method has been used by Andreykiv et al. (2001), Nazarchuk et al. (2017), Skalskyi et al. (2018). However, it was only a qualitative diagnostics of the process and its initiation. To quantify the material delayed fracture, it is necessary to determine the AE parameters dependences on the parameters of this process. First of all, it concerns the acoustic signals generation theory creation during the elementary fracture acts, in particular the micro and macro defects formation, their growth and association. In this paper we give an example of creating such theory for the case of the high-temperature creep cracks propagation in structural materials. On this basis, an example of quantitative diagnostics of this process is given. This allows determining the parameters based on which it is possible to estimate the residual life of the structure element under long static load and, thus to prevent its unexpected fracture. In the studies of Andreykiv et al. (2009, 2011, 2015a, 2015b, 2017a) the energy approach for creating mathematical models of structural materials delayed fracture under the influence of mechanical, physical and chemical factors is developed. It is based on the first law of thermodynamics: the energy components balance in the loaded engineering system, as well as on their change rates balance. A number of mathematical models (Andreykiv et al. (2009, 2011, 2015a, 2015b, 2017a)) have been created and on this basis the methods for determining the structural elements residual life under mechanical loading (long-term static, cyclic and shunting) and other factors (high temperatures, hydrogen-containing and corrosive-aggressive environments, neutron irradiation) have been developed. Based on these methods the residual life of bimetal structural elements of oil reactor, gas pipelines, etc. was calculated (Andreykiv et al. (2015c, 2016, 2017b)). As an example, here is described the mathematical model of a high-temperature creep flat crack propagation in an infinite body and the period of subcritical crack growth is determined. The model essence is the following. Let us consider a metal body with a crack area S 0 , under long-term loading and high temperature (Fig. 1, a). We assumed that the crack is macroscopic, and the external tension stresses are applied in the way that the stress-strain state is symmetrical relative to the crack plane, and in the vicinity of the crack tip it is described only by the stress intensity factor K I . The problem is to determine the time t = t  when the high-temperature creep crack reaches the critical size and the body fractures. To solve the problem, we apply the energy approach (Andreykiv et al. (2017a)) and based on it we obtain the dependence for determining the subcritical growth period of the high-temperature creep crack 2. Energy approach in delayed fracture mechanics of structural materials

1



   

                        t L c m c t t d A t A    / } 0, ,0 {2 1 1 0 1  

         t t d  0, ,0

(1)

1 1 L

 

dt dS

.

c

L

The initial and final conditions should be added to the equation (1) to complete the mathematical model   0 0, 0 t S S   ;   * * * , t t S t S   ; . ( ) * c t S    (2)