PSI - Issue 16

Zinovij Nazarchuk et al. / Procedia Structural Integrity 16 (2019) 169–175 171 Zinovij Nazarchuk, Olexandr Andreykiv, Valentyn Skalskyi, Denys Rudavskyi / Structural Integrity Procedia 00 (2019) 000 – 000 3

Here (0, )   t – a current crack tip opening for the average stress t  in the process zone;  c – critical crack tip opening (0, ,0)   t ;  – current coordinate along the crack front length L ; A 1 , m ,  0 – the high-temperature creep characteristics of the material (Andreykiv et al. (2009)).

3. Determination of creep crack growth subcritical period using the acoustic emission parameters

During the research of the structural elements residual life under long-term static loading it is important to determine the size of the initial defects, the kinetic diagrams parameters for the high-temperature creep cracks growth (values  0 , m , A 2 t ,  c ) and then on the basis of the mathematical model (1), (2) to estimate the residual life (the period of the high-temperature creep crack subcritical growth) t = t  . However, determination of the defects initial sizes and the parameters  0 , m , A 2 t ,  c , which must be found for the already exploited structural element material, is associated with significant technical difficulties (Nazarchuk et al. (2017)). Therefore, we will create a calculation model for estimating the residual life (the period of high-temperature creep crack subcritical growth) of structural elements under long-term static load using the parameters of the signals of AE (SAE), which are measured directly on the loaded element surface. The model essence is the next. Let us consider a three-dimensional body that is weakened by a flat macrocrack S 0 with a smooth convex contour L , which is tensioned at infinitely distant points by equally distributed long-term stresses of intensity p directed perpendicularly to the crack plane (see Fig. 1, a). We have assumed that such body is influenced by a homogeneous high-temperature field, which causes the high temperature creep in the process zone near the crack edge, which in turn causes the crack propagation. The task is to determine the crack growth kinetics and to estimate the subcritical crack growth period t  . As known (Andreykiv et al. (2017a)), the new formed defects area S (the crack growth area) can be determined by the sum of acoustic emission signals amplitudes A i :     n i i S A 1 (3) Here  – is the material AE constant, which is empirical (Andreykiv et al. (2017a)); n – the number of AE signals registered during the crack propagation. Is shown in the study (Andreykiv et al. (2017a)) that under the pure tension the planar creep crack area S change slightly depends on the crack contour geometry, and the crack contour during its propagation approaches to the circular form. Therefore, in this case, the crack area critical size S  is determined by taking into account the Irwin criterion – the stress factor K I critical value K CC in case of high-temperature creep: Hence, based on the formulas (3) and (4) we can write the equation for the SAE amount n determining that the crack radiates during its subcritical growth       n i T CC i A p K S 1 4 4 2 . (5) As follows from the foregoing, the growth jumps of the crack along its contour for high-temperature creep for a microisotropic material can be considered approximately the same for different incubation periods of their propagation. Therefore, the microfracture areas i s that generates each SAE are suppose to be on average the same (here we consider them as microcircles s i  const = s a (Fig. 1, b)). For real materials where the structure local parameters, the microfracture areas and, accordingly, the AE signals amplitude vary considerably, such an assumption would seem to 4 4 2 CC S p K    . (4)