PSI - Issue 36

Nataliya Yadzhak et al. / Procedia Structural Integrity 36 (2022) 401–407 Nataliya Yadzhak, Oleksandr Andreykiv, Yuri Lapusta / Structural Integrity Procedia 00 (2021) 000 – 000

402

2

half-length of crack

l

( ) II III p l + half-length of crack with fracture process zone at mixed mode II+III loading ( )* II III l + half-length of critical crack at mixed mode II+III loading N number of load cycles ( )* II III N + critical number of load cycles (lifetime) at mixed mode II+III loading i R  stress ratio in CTOD parameters W strain energy II W mode II strain energy III W mode III strain energy is W elastic component of i W (1) ( ) ip W l part of the work of plastic deformations depending only on the crack length l (2) ( ) ip W t part of the work of plastic deformations that depends only on time t and is generated by the body during its unloading and compression of the fracture process zone 0 i  experimental constant ifc  critical CTOD it  crack tip opening displacement (CTOD) ith  threshold CTOD

max it  maximum CTOD per cycle min it  minimum CTOD per cycle  fracture energy it 

specific work of plastic deformations in the fracture process zone

( ) II III fc  + specific fracture energy under the mixed mode II+III loading  shear modulus  Poisson’s ratio II  mode II loading III  mode III loading ip  average shear stress in the fracture process zone

Throughout this paper, the index i in the symbols corresponds to the loading mode and can take the following values: i II = (for the mode II loading); i III = (for the mode III loading); i II III = + (for the mixed mode II+III loading); / i II III = (for mode II or mode III loading). 1. Introduction Structural elements of long-term operation are subjected to various loading types, in particular, static, fatigue and manoeuvre. Further, the loading types can be subdivided by directions and other properties. Determination of the loading direction about the crack contour is essential, if the structural element contains a crack, especially a plane crack. In many cases, this complex loading can be approximately reduced to a combination of main loading modes. Among others, the mixed mode II+III loading plays a significant role in modelling of a wide range of industrial processes. However, the modelling procedure can be complicated by the existence of small cracks, which according to Miller’s hypothesis ( Miller (1987)) may be present in materials already at the manufacturing stage. Thus, the account of the small fatigue cracks becomes important in the lifetime prediction of structural elements under mixed mode II+III. Contrary to small cracks, the mixed mode II+III long crack growth has already been considered by a number of scholars. Zhao (1987) extended Griffith’s approach to mixed mode problems and derived t he maximum energy release rate criterion in general form, which is applicable for a combination of the main loading modes. Despite its accuracy compared to experimental data, the criterion is formulated in the parameters of stress intensity factors (SIF), similarly to the elliptical criterion by Nie (2020), and thus, is invalid for small cracks. Mixed mode II+III problems have also been analysed based on the J  approach and the eff K  concept, which confirmed the invalidity of the K  approach already for higher load levels (Vojtek et al. (2014), Vojtek et al. (2015)).