PSI - Issue 13

Tomasz Tomaszewski / Procedia Structural Integrity 13 (2018) 1756–1761 Author name / Structural Integrity Procedia 00 (2018) 000–000

1759

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factor α k equal to 1.05. The test specimen size was changed by reducing the geometrical dimensions relative to the standard specimen. The specimens were sampled from a metal sheet of 4 mm thickness. Fixed parameters of the technological process were maintained.

R

Table 1. Specimen dimensions. Type of geometry t [mm]

Ra 0.32

w 2

w 1 ± 0.05

w 1 [mm]

w 2 [mm]

R [mm]

l [mm]

S o [mm 2 ]

Standard spec. Minispecimen

4

7

14

25 18

100

28

1.4

2.5

5

35

3.5

t

l

Fig. 2. Geometry of the flat smooth specimen for fatigue testing made of steel 1.4301.

The fatigue tests were carried out for a symmetrical sinusoidal cycle ( R = -1). For loads with a different σ a / σ m ratio, two-parameter σ a -N characteristics are recommended (Ligaj and Soltysiak (2016)). The fatigue tests were carried out in the range of high-cycle fatigue with controlled stress. The criterion ending the fatigue test was macro-crack on the specimen. The proposed test conditions aimed at determining the impact of the size effect in the geometrical perspective. This required carrying out tests for tension, compression load and four-point bending. A clamp for symmetrical bending ( R = -1) was designed and manufactured. The clamp featured adjustment of the supports position and thickness of the installed specimen. As a result, the tests were performed on a single clamp, which was adapted to the specimen size. For the purpose of eliminating the eventual impact of employing the clamp, the supports spacing and the force applied were sized identical to the specimens. The experimental points for the presented fatigue characteristics σ a -N were approximated to linear regression line in bilogarithmic system and Basquin equation (Table 2). A graphical presentation of the results is shown in Fig. 3.

Table 2. Fatigue characteristic σ a - N parameters.

Linear regression line log σ a = a log N + b

Basquin relation C = N ( σ a ) β

Correlation coefficient, R 2

Type of geometry

a

b

C

β

Axial loas

Standard specimen

-0.0399 -0.0558 -0.0804 -0.1103

2.578 2.695 2.986 3.232

2.78ꞏ10 64 1.87ꞏ10 48 1.29ꞏ10 37 1.92ꞏ10 29

25.00 17.91 12.42

0.983 0.932 0.951 0.980

Minispecimen

Bending load

Standard specimen

Minispecimen

9.05

4. Verification of the analytical model The statistical model with a critical volume was implemented for the experimental data obtained in a high-cycle fatigue range. The tests included acid-resistance steel 1.4301 specimens showing susceptibility to changes in cross-sectional area. In accordance with the size effect theory, the susceptibility is more pronounced in bending loads than in axial loads. Linear regression can be used for a small number of extreme points (initial tests) (Strzelecki and Sempruch (2016)). The experimental points (two specimen sizes) were approximated to a regression line (Fig. 3). The fatigue strength for axial loads and bending loads were different. The fatigue characteristics σ a -N were analysed using the statistic test of parallelism of slopes. The characteristics for bending load are not parallel. The hypothesis was rejected that assumed the equality of slope coefficient a . Despite the different values of the a coefficient for axial load, the characteristics are parallel. The value of the difference in fatigue strength is defined as the cross-section size coefficient K HC . The mean value for axial stress is at a level of 1.086, and equal to 1.275 for bending stress. The model with a critical volume was applied for estimating fatigue life for the standard specimen. The calculations were performed basing on fatigue characteristic σ a -N obtained for the minispecimen and four-point bending. According to the (3) equation, fatigue life was calculated for a cross-sectional area of the standard specimen. The regression line obtained based on experimental tests of the standard specimen was deemed as the reference