Experimental and Numerical Analysis of Fatigue during the Cyclic Loading

View current table in a new window

Tables index

Veiw figure View Table

View next table

Table 2. Mechanical properties of the 17 240 steel (designated according to STN)

Download as

View current table in a new window

Tables index

Veiw figure View Table

View previous table

View next table

The predetermined tests were performed for the samples with the specified proportions and these samples were prepared from the austenitic chrome-nickel steel with designation: 17 240 while the given designation is based on the Slovak Technical Standard (STN). The mechanical properties of the mentioned steel were determined on the basis of the static tensile test. The chemical composition (Table 1) and the values representing the mechanical properties (Table 2) of the tested steel are shown in the tables hereinafter ^[1].

Based on the observations, the microstructure of the tested chrome-nickel steel sample (Figure 1) consists of polyhedric austenitic and quite large grains. It is also important to point out that the mechanism of twining is observed in relation to this steel and the occurrence of delta–ferrite particles can be seen in surface layers ^[1].

Figure 1. The microstructure of the 17 240 steel [1]

Download as

Veiw figure View Figure

2.1. Fatigue Test Based on Bending Cycles During the Rotation Movement

The testing procedures were performed for samples with round cross-section and determined radius. It has to be pointed out that the fatigue limit is susceptible to the surface quality and it means that it is reduced if there is the oxidation process on the material surface or if there is any surface roughness after the machining process where the material removal is accompanied with the occurrence of chips. According to the fact mentioned hereinbefore, the polishing procedure was used for the final surface treatment and this given procedure was performed in the direction which was parallel to the longitudinal axis of the rod used for preparation of the samples. The given procedure led to the smooth and polished surface ^[2].

Figure 2. The shape of the tested sample

Download as

Veiw figure View Figure

The testing device SCHNECK was used for performance of the fatigue tests. The given testing process was based on the predetermination of the initial stress (σ₁) for the first one tested rod or sample and the given predetermined initial stress was less than R_estanding for the highest admitted yielding stress for the tested material. In relation to the other tested samples, the gradual decreasing of the stress led to recognition of the values representing the specified number of cycles (N) referring to the condition when the sample was able to withstand the specified number of cycles. After the breakage of the first one tested sample, the gradation scale of the stresses was determined for the each one sample while the loading frequency was still the same. The testing procedure was performed until the critical values of the stress were found out. The mentioned critical values were used for determination of the fatigue limit and they represent the stress at which the sample is able to withstand the number of cycles until it is broken. In the case of one sample, the control testing was carried out to confirm the results. In relation to the given control testing procedure, the loading of sample was less by 10 MPa. All of testing procedures were performed continuously and besides fracture, the visible crack was considered as the end of the mentioned testing process (Figure 3) ^[3].

Figure 3. Sample of the 17 240 steel after the testing procedure – fracture [1]

Download as

Veiw figure View Figure

Figure 4. Sample of the 17 240 steel after the testing procedure – fracture

Download as

Veiw figure View Figure

2.1.1. The Results of Measurement and Numerical Analysis

In relation to the tested rods or samples of the 17 240 chrome-nickel steel, the predetermined initial stress, stress based on gradation scale and results of experimental testing process are shown in Table 3.

Table 3. Results of measurements

Download as

View current table in a new window

Tables index

Veiw figure View Table

View previous table

Based on σ – log N logarithmic system, Wöhler fatigue curve was evaluated on the basis of the obtained results referring to the condition when the tested sample under the specific stress (σ) was able to withstand specific number of cycles (N). The resulting course was approximated by slanting and linear line ^[4].

Figure 5. Wöhler fatigue curve – experimental analysis

Download as

Veiw figure View Figure

2.2. Numerical Analysis

The basic model of the sample was created in the ADINA program (Figure 6). The linear-elastic model was selected for the analysis while the given model was based on the fact that there was the rotation movement of the loading force in the points at the ends of the model around the circumference of the sample with reference to time intervals. The material characteristics, critical conditions were defined and subsequently, the mesh was created. The highest stress concentration was expected in the area where the sample was the thinnest and therefore, the smaller size of element was selected because of higher density of mesh and accuracy of the solution ^[5].

Figure 6. Numerical analysis [3]

Download as

Veiw figure View Figure

Figure 7. Wöhler fatigue curve – numerical analysis

Download as

Veiw figure View Figure

2.2.1. Results of Measurements – Numerical Analysis

The values representing stresses (σ) and individual bending moments (Figure 7) were obtained from the numerical analysis of the model based on finite element method.

3. Discussion

The value standing for σ is the critical loading in relation to the fatigue limit (σ_C). The mentioned critical loading means that the sample was able to withstand the basic number of the cycles (N) without any rupture when the middle stress (σ_m) was used. During the testing procedure, the value of the stress was changed gradually in relation to the individual samples and it corresponds to the alternating regular cycle. It is important to point out that the value representing unbroken sample loaded by the basic number of cycles (N) is equal to the fatigue limit when the σ_m= 0 ^[4].

In relation to the 17 240 chrome-nickel steel, the results obtained from the experimental and numerical analyses were mutually compared using the trend lines of the Wöhler curve referring to the stress and the number of cycles until the breakage. The results for both methods are shown as the curves in the created graph (Figure 8)

Figure 8. Wöhler fatigue curves for both methods [3]

Download as

Veiw figure View Figure