PSI - Issue 13

Valentin Tkachenko et al. / Procedia Structural Integrity 13 (2018) 1396–1401 Author name / Structural Integrity Procedia 00 (2018) 000–000

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not usually assumed during the element designing. The difficulties of such engineering estimation are related to the absence of model of very-high cycle multiaxial criteria. In the paper Bourago et al. (2011) the first estimation of VHCF properties under complex loading is proposed. The authors Bourago et al. (2011) have applied the VHCF multiaxial criteria for critical state estimation of real elements of turbo-jet engine. It was founded out that crack initiation due to high frequency loading may occur during the same or shorter fatigue life of element. At the beginning the early crack growth is still governed by high frequency loading and further a bifurcation is possible with a crack propagation under high cycle or low cycle conditions depending on the location of crack nuclear. Therefore, the study on the thresholds under high frequency loading of structural materials may help to develop more accurate model for fatigue life prediction in VHCF range. This paper is focused on the investigation of near threshold fatigue crack growth and modeling of crack front evolution. The proposed model combines numerical simulations with experimental data and can be used for the first order estimation of fatigue crack shape under ultrasonic loading. 2. Material and experimental procedure The material for ultrasonic fatigue crack growth tests was used the same to previous studies on axial Nikitin et al. (2016) and torsion Nikitin et al. (2015) loadings. It is two-phase titanium alloy VT3-1 (close to Ti6-Al-4V) used for aeronautic application. The specimens for crack growth tests were machined from plateau part of turbo-jet compressor disk. The geometry of specimens was calculated according to ultrasonic fatigue testing concept Bathias and Paris (2004). The flat specimens have a radius of 31 mm in its gage section. The dimensions of the specimen are following: L =106 mm, W =14 mm, H =8 mm with the minimum sickness in the gage section of 3 mm. Edge notch was machined in the plane of specimen gage section at the node of displacements. Ultrasonic crack growth tests were performed on axial piezoelectric machine at 20 kHz operating in laboratory air environment. The monitoring of fatigue crack propagation by the lateral surface was realized by using an optical camera. The ultrasonic crack growth tests needs some modifications in testing procedure and loading parameters determination compare to standard-one. 2.1. Calculation of stress intensity factor (SIF) In the case of VHCF concept the cyclic loading is realized in a resonance regime at the first harmonic of specimen natural frequency. The load parameter in this case is small amplitude displacements (about 3-10 micrometers). An analytical determination of SIF based on handbooks Tida et al. (2000) database is impossible because of testing methods features. The free vibration cyclic loading means a gradient stress distribution along specimens axis with zero values of stress at the specimens ends. Therefore the use of classical formula will give a zero SIF range. Estimation of a crack opening at the ultrasonic frequency is also impossible due to limitations of measuring equipment. The only one accessible way for determination the SIF under ultrasonic loading is numerical simulations. Based on dimensional analysis the following equation to estimate SIF under ultrasonic vibrations was proposed by Bathias and Paris (2004) where d E - dynamic Young modulus,  - Poisson's coefficient, U - amplitude of displacements, a - crack length,   Y a w - dimensionless geometry function. In the principles of ultrasonic fatigue testing it is assumed that crack growth is due to uploading part of loading cycles. The negative values of SIF are not taken into account. In this case the SIF range is corresponding to its maximum value. The dimensionless function is determined by numerical simulation. The model of specimen, fig.1, is build for one-half of specimen with imposed symmetry conditions at the surface that is assumed as not broken section. The crack is simulated by a surface with imposed free boundary conditions. The crack tip line is simulated by ntroducing a special concentrate element with two counters. The stress concentration factors were calculated along the crack tip line. The SIFs were calculated for different crack length with a given displacement of 1 micrometer. After that the dimensionless function was determined by polynomial approximation. 2 (1 )   d E U a Y a w        K  