PSI - Issue 43

A.D. Nikitin et al. / Procedia Structural Integrity 43 (2023) 53–58 A.D. Nikitin et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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3. Simulation results The proposed model was used for numerical simulation of the fatigue crack initiation and developing in smooth titanium alloys specimens subjected to VHCF pure torsion loading. The shape of the VHCF torsion specimens and mechanical properties of the material were taken from the experimental work Nikitin et al. (2016), Fig.2. The results of the simulations are also compared with the experimental results of VHCF torsion tests. The stress state in the VHCF specimens was calculated considering the resonant frequency of the specimen. The loading parameter is circumferential displacement applied to resonant part of the specimen. .

a) c) Fig. 2. The result of numerical simulation on the crack development in smooth specimen under VHCF torsion at different magnifications (a) and (b), and result of VHCF torsion tests (c) Nikitin et al. (2016) The frequency of the loading is about 20 kHz. The results of numerical simulations show a clear crack initiation and early crack growth in the gage section of the specimen on the plane of maximum shear stress, Fig.2.-a and -b. The analysis of element solution for damage function have shown that the dominant mechanisms of material destruction is shear. With developing the fatigue crack the fraction of element reaching the critical value of the damage function by shear mechanism is decreasing. Simultaneously, the fraction of elements ‘destructed’ by normal crack opening mechanism is increasing. At a certain moment a spontaneous change in crack propagation plane was observed. The crack turns to propagation on the plane of maximum normal stress with the dominant mechanism of normal crack opening. The same zigzag-type of the fatigue crack was observed in experiments, Fig.2-c. The results of experimental work have shown that some specimens were failure by double zigzag or X-type crack, Fig.3. The X-type cracks are usual for low cycle fatigue and high cycle fatigue but in the VHCF range they are relatively rare. The specimens with X-type cracks are showing the subsurface crack initiation. To investigate this tendency, the set of numerical simulations with internal crack initiation was performed. To shift the crack initiation site into the bulk of the material a hard element was introduce. The mechanical properties of a single element were defined as double of the regular moduli. Under the cyclic loading such element manifest itself as a crack concentration and damage function growth was higher at the vicinity of such element. The results of simulations are presented on Fig.3. The result of numerical simulation shows that the torsion crack is mainly forming on the single plane of maximum normal stress in the case of surface defect. When the defect is in the bulk of material the X-type is forming. Moreover, the initial stage of crack initiation is sensitive to the defect location. The shear stage of initial crack growth is more pronounced for the case of deep defect location, Fig. 3-d. The results of numerical simulations show the principal difference in VHCF crack path depending on the location of crack initiation site. b)