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

406

6

0.3, v =

80769 MPa,  = 97 MPa m,

following material properties and testing constants (Lenkovs ’ kyi (2017)):

5 2.1 10 MPa, E = 

( / ) 12.6 MPa m, II III th K =

1,

0.0082, II III p  = ( / )

( / ) II III fc K =

( / ) II III R  = −

( / )0 II III  =

5 7.6 10 m, −

6 1.29 10 m, −

The problem lies in the determination of the

490 MPa.

( / ) II III fc 

( / ) II III th 

= 

= 

( )* II III N + .

plate lifetime

The solution to this problem is sought based on the proposed model (12). Taking into account the material properties, a mathematical model is derived describing the crack propagation in steel 65Г depending on the intensity of the applied loading II  and III  . In order to evaluate the effect of the simultaneous action of mode II and mode III loading, different combinations of loading intensities are considered. The choice of the loading values aimed to represent the four major loading cases: equivalent low intensity loading ( 100 MPa); II III   = = equivalent loading corresponding to half of the shear yield strength ( 245 MPa) II III   = = ; non-equivalent loading with dominant mode II ( 245 MPa, 100 MPa) II III   = = or mode III ( 100 MPa, 245 MPa). II III   = = For each of these combinations of mode II and mode III loading, the relations are built between the lifetime of the plate and the initial crack length by the model (12) (Fig. 2). The comparison of the relation shows the dominant effect of the mode II loading on the plate lifetime under the mixed mode II+III loading. At equal loading intensities of 100 MPa and 245 MPa, the lifetime is smaller, when the principal loading is causing transverse shear (curve 3 ) as opposed to longitudinal shear (curve 2 ). These results are in agreement with the findings of Vojtek et al. 2015, where the mode III component influences less the mixed-mode crack growth.

Fig. 2. Relation

( II III II III N l + + at the following mode II and mode III loading values: 1 – )0

; 2 –

245MPa,

245MPa



=



=

II

III

; 3 –

; 4 –

.

100 MPa,

245MPa

245MPa,

100 MPa

100 MPa,

100 MPa



=



=



=



=



=



=

II

III

II

III

II

III

5. Conclusions This paper focused on modelling small fatigue crack propagation in thick plates under the simultaneous action of mode II and mode III loading. Based on the energy approach, the mathematical model is developed for the description of small crack propagation and subsequent determination of the plate lifetime. The model is built in deformation parameters of CTOD, while the proposed formulas for mode II and mode III crack tip opening displacements take into account the relative load level of the plate, which is crucial in case of small cracks. In the modelling process, the findings of Murakami on the equivalence of mode II and mode III fatigue crack growth mechanisms are adopted. The proposed model is validated on the problem of lifetime determination of a thick plate with a small crack under mixed mode II+III loading from steel 65 Г (analogue to AISI 1066). For this case, the various combinations of loading amplitudes are considered.