Comparison of low and high frequency fatigue tests

Abstract The paper presents the results of low and high frequency fatigue tests carried out on nodular cast iron. The specimens of synthetic nodular cast irons from three different melts were studied in the high cycle fatigue region (from 105 to 108 cycles) using fatigue experimental equipments for low and high frequency cyclic loading. Low frequency fatigue tests were carried out at frequency f ≈ 120 Hz using the fatigue experimental machine Zwick/Roell Amsler 150HFP 5100; high frequency fatigue tests were carried out at frequency f ≈ 20 kHz using the ultrasonic fatigue testing device KAUP-ZU. Both fatigue tests were realised at sinusoidal cyclic push-pull loading (stress ratio R = −1) at ambient temperature (T = 20 ± 5 °C).


Introduction
The fatigue has been a predominating fracture mode of loadbearing machine members. Therefore, through the years, its prevention has become a fundamental design criterion. Although fatigue has been studied extensively over many years and excellent reference books are now available, further study is warranted because the knowledge base is partly obsolete and new materials and treatment are being continuously developed. Fatigue testing is usually performed to estimate the relationship between the amplitude of stress and the number of cycles to failure for a particular material or component. Fatigue testing is also conducted to compare the fatigue properties of two or more materials or components. In either case the reliability of any decisions based on the results of a fatigue testing program is directly related to the manner in which the experiments are designed and analysed (BOKŮVKA O. 2002).
Fatigue tests are usually preformed using low frequency cyclic loading with frequencies in the range from f  10 to 200 Hz. A norm prescribes the number of cycles Nf = 10 7 or 10 8 for determination of the fatigue characteristics. If it is necessary to determine the fatigue characteristics at higher number of cycles, it is extremely time demanding and expensive. Recently, the material research has been oriented on the questions of the verification of fatigue properties in the gigacycle regimes of loading. There have been developed new testing apparatus, methods and techniques with the aim to achieve the experimental data at the number of cycles Nf = 10 9 and more.
One of the possible directions is the application of experimental methods of high frequency cyclic loading for determination of the fatigue properties in materials (BOKŮVKA O. 2014, ULEWICZ R. 2017).
Time and economical effectiveness of determination of the fatigue characteristics by high frequency cyclic loading is evident from the Tab. 1. The time demands of low frequency cyclic loading (LFCL) with frequency f  120 Hz are compared with high frequency cyclic loading (HFCL) with frequency f  20 kHz. The contribution deals with comparison of the fatigue properties of nodular cast iron at high and low frequency fatigue testing.

Experimental material and methods
The specimens from three melts of nodular cast iron were used for experiments. The melts have been different by charge composition (Tab. 2). The basic charge of individual melts DOI: 10.30657/pea.2017.17.03 was formed by different ratio of pig iron and steel scrap and by different additive for the regulation of chemical composition (metallurgical silicon carbide or ferrosilicon) (COPI K. W. 2003, ZHANG W. H. 2009). For modification and inoculation, modifier FeSiMg7 and inoculant FeSi75 were used in the same amount for all the melts. The metallographic analysis of specimens from experimental melts was made with the light metallographic microscope Neophot 32. The specimens for metallographic analysis were taken out from the cast bars and prepared by usual metallographic procedure (KONEČNÁ R. 2014  The fatigue tests were realised according to STN 42 0362 at low and high frequency sinusoidal cyclic push-pull loading (stress ratio R = -1) at ambient temperature (T = 20  5 °C). Low frequency fatigue tests were carried out at frequency f  120 Hz using the fatigue experimental machine Zwick/Roell Amsler 150HFP 5100 (Fig. 1a). High frequency fatigue tests were carried out at frequency f  20 kHz using the ultrasonic fatigue testing equipment KAUP-ZU (Fig. 1b).
For a given material the ralationship between the applied amplitude of cyclic stress and the number of cycles to failure is customarily identified from its S-N diagram (Wöhler curve) in which the stress amplitude is plotted with the corresponding number of cycles to failure using a semi logarithmic scale. The number of cycles that the metal can endure before failure increases with a decreasing stress amplitude and for some engineering materials (including nodular cast iron) the Wöhler curve becomes horizontal at a certain limiting stress known as the fatigue limit (fatigue strength). Below the fatigue limit the material will not fail in an infinite number of cycles (VĚCHET S. 2001). For both fatigue tests (low frequency cyclic loading and high frequency cyclic loading), ten specimens from each melt were used to obtain the relationship between the applied amplitude of cyclic stress and the number of cycles to failure (Wöhler curve) and to determine the fatigue strength. a) specimen for low frequency cyclic loading b) specimen for high frequency cyclic loading

Experimental results and discussion
Microstructure of the specimens from experimental melts is shown in the Fig. 3  Mechanical properties (tensile strength Rm, elongation A, absorbed energy K0 and Brinell hardness HBW) are connected with the microstructure of the specimens, especially with the character of matrix (content of ferrite and pearlite) and also with the size and count of graphitic nodules (Tab. 4). For the fatigue tests, ten specimens from each melt were used to obtain Wöhler fatigue curves σa = f(N) and determine fatigue strength σc.
The results of fatigue tests (Wöhler curves) obtained at low frequency cyclic loading (f  120 Hz) are shown in Fig. 4. The number of cycles to failure increases with a decreasing stress amplitude.
The values of fatigue strength σc determined for N = 10 7 cycles in comparison with tensile strength Rm are given in Tab. 5. The fatigue strength in analysed specimens of nodular cast iron increases with an increasing tensile strength.   The results obtained at high frequency cyclic loading are in a good agreement with the results obtained at low frequency cyclic loading. In both cases, the fatigue strength σc increases with an increasing tensile strength Rm.

Conclusions
The norm prescribes the number of cycles Nf = 10 7 (for steels and cast irons) to determine the fatigue characteristics. Nowadays, some experimental institutions deal with fatigue testing in the gigacycle regimes of loading (i.e. at the number of cycles Nf = 10 9 and more). The main problem of higher number of cycles is time demand of testing. Therefore, new testing apparatus, methods and techniques have been developed whereby the experimental methods for determination of the fatigue properties at high frequency cyclic loading have a predominant position. High frequency fatigue testing with frequency f  20 kHz is not so time demanding as low frequency fatigue testing with frequencies f  10 to 200 Hz.
The application of high frequency cyclic loading is characteristic with the significant time, energy and work saving. Moreover, the results obtained at high frequency cyclic loading are in a good agreement with the results obtained at low frequency cyclic loading. They are utilizable in the field of materials engineering and treshold states of materials.