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

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This paper addresses the question of mixed mode II+III small crack modelling from the perspective of the energy approach. The suggested model is built in deformation parameters of CTOD, that allows us to correctly describe the

small crack propagation. 2. Problem statement

Consider a thick infinite plate with a tunnel crack, located normally to the plate surface (Fig. 1). In the centre of the crack, a Cartesian coordinate system Oxyz is introduced with the Ox axis directed normally to the crack contour, the Oy axis – along the crack contour, and the Oz axis – orthogonally to the crack plane. At infinity, the plate is subjected to the simultaneous action of two types of loading:

• fatigue loading of intensity II  applied normally to the crack contour causes mode II, and • fatigue loading of intensity III  applied parallelly to the crack contour generates mode III.

Fig. 1. Scheme of a thick cracked plate under mixed mode II+III loading.

These two loading types result in a mixed mode II and III acting on the plate facilitating the crack propagation. The problem consists in the determination of the number of cycles ( )* II III N N + = , that leads to crack propagation from the initial 0 2 l to the final ( )* 2 II III l + length, which causes fracture of the plate. 3. Development of the model The solution of this problem is sought based on the energy approach proposed earlier by Shata and Terletska (1999) and widely applied for lifetime determination of various structural elements and loading conditions, e.g. flat fatigue cracks (Rudavs’skyi (2015)), fatig ue cracks (Andreikiv et al. (2017)), high-temperature creep (Andreykiv and Sas (2006)), corrosion fatigue (Andreikiv and Shtayura (2019)). According to this approach, the crack growth is considered to be jump-like, and the crack propagation rate is defined as a length of a small crack jump c l  over a large number of cycles c N  , which makes this relation continuous. Then, based on the first law of thermodynamics, the energy balance is given by (Andreikiv and Sas (2006)): A W = +  , (1)

and the energy rate balance is as follows (Andreikiv and Sas (2006)):

dA d dW dN dN dN  = +

(2)

.