3. Fatigue tests of aluminum tubes

Rotary bending fatigue tests were performed at the room temperature of 25 °C and an operating temperature of 125 °C to evaluate the effects of the operating environment on the fatigue life of the aluminum tubes. To determine the effects of surface defects occurring during product assembly, V-notches were fabricated on the aluminum tubes for the fatigue tests. The notch sensitivity and material constant used in the Peterson equation were then computed from the fatigue notch factor and the notched tube specimens’ stress concentration factor obtained from the structural analysis.

3.1 Fatigue test specimens

3.1.1 Smooth un-notched and notched tube specimens for fatigue tests

In general, rotary bending fatigue tests involving tube-shaped specimens; the jaw of the fatigue test machine is tightened around both ends of specimen to prevent slip. To perform fatigue tests on tube-shaped specimens using a rotary bending fatigue test machine, metal plugs were inserted into both ends of the aluminum tubes and the specimens were mounted on the jaw. The aluminum tube specimens were designed to undergo fatigue failure at their central area during the fatigue tests.
Static structural analysis was conducted to determine the location of the fatigue failure that occurs when metal plugs are inserted into the aluminum tubes in the unprocessed state. A 3D model was created in the commercial finite element analysis package ANSYS (V19.1, USA) for the aluminum tubes; the external diameter of the tube was 15.88 mm and its thickness was 1.9 mm, and metal plugs were inserted into both its ends. Symmetric boundary conditions were applied, and the analysis was performed using a 1/4 model. A mesh was generated using hexahedral elements from the 3D model; the number of nodes and elements produced were 30,000 and 10,000, respectively. In accordance with online database MatWeb, the aluminum tubes used in the structural analysis had a modulus of elasticity of 125 GPa and a Poisson’s ratio of 0.33. In our previous study, tensile tests were conducted at room temperature to obtain the load-displacement curves of the Al3003-O aluminum tubes, and the tensile strength and yield strength were derived using stress-strain curves acquired from tensile tests. The basic structural steel provided in ANSYS was used as the material of the metal plug. As the boundary condition, a bending moment of 300 N·mm was introduced at one end of the tubes (Fig. 5).
The structural analysis of the tubes in the unprocessed state showed that fractures did not occur at the center of the tubes owing to a uniform distribution of high stress even at the surface (Fig. 6(a)), and the distribution of fractures during the fatigue tests was thus assumed to be random. Therefore, considering the site of distribution of high stress on the surface, it was designed as a concave test specimen(R 200mm ) whose tube center thickness was reduced to 0.94 mm . The previously mentioned boundary conditions were assigned to the finite element model to determine whether fractures occurred at the centers of the tubes. The specimens were then fabricated using the design, which exhibited high stress mostly in the central area (Fig. 6(b)).

3.1.2 Notched tube specimens for fatigue tests

Owing to their geometric characteristics, surface defects (surface scratches, dents, etc.) occurring in aluminum tubes used to manufacture heat exchangers in air conditioners induce stress concentration and lower fatigue life. To predict the fatigue life in relation to surface defects, notched tube fatigue specimens were prepared by introducing V-notches in the aforementioned tube specimens, where a surface dent is defined as a dent having a notch angle of 90 ˚, a notch radius of 0.02mm, and a depth of 0.115 mm (Fig. 7).

3.2 Rotary bending fatigue tests

A four-point rotary-bending fatigue-test equipment (KDMT-250, Korea) was used for the fatigue test (Fig. 8). The stress ratio was −1 because the mean stress of the cyclic loading profiles was 0 in the rotary bending test. After locking the specimens, the eccentricity was measured using a dial gauge to ensure a value of 0.05 mm or less; the frequency of rotations was set as 1800 rpm. The bending stress experienced by the tubes due to the bending load was calculated as shown by
\(\sigma_{\max}=\frac{16\times D\times L\times P}{\pi\left(D^{4}-d^{4}\right)}\)(4)
where \(P\) is the load of the pendulum, L is the distance between loading points (200 mm ), and \(d\) and \(D\) are the internal and external diameters of the aluminum tubes, respectively. The digital caliper(Mitutoyo, Japan) was used to accurately measure the internal and external diameters of the tubes. The fatigue test was performed while varying the stress under two temperatures (25 °C and 125 °C) and notched (notch angle of 90 ˚, notch radius of 0.02 mm, and depth of 0.115 mm) conditions. The fatigue tests were performed for a total of 10 specimens. Each test was concluded when the specimens experienced fractures or reached the fatigue limit (1 × 107 cycles). As predicted from the specimen design, fractures were observed in the central areas of the specimens (Fig. 8).

3.3 Fatigue test results

3.3.1 Comparison of fatigue life at 25 ˚C and 125˚C

The S–N curves for the aluminum tubes were obtained at room temperature (25 °C) and at the heat exchanger operating temperature of 125 °C (Fig. 9(a)). Based on the S–N curves at the two temperatures, a linear equation was obtained on the log–log scale and converted to a decimal scale as follows.
Temperature of 25 °C: \(S_{\max}=113.96\ \times\ {N_{f}}^{-0.043}\)(5)
Temperature of 125 °C:\(S_{\max}=108.97\ \times\ {N_{f}}^{-0.050}\) (6)
The fatigue limits (defined as the stress at 1 × 107cycles) were 57.19 MPa at 25 °C and 49.02 MPa at 125 °C, resulting in a temperature modification factor of 0.86, which was calculated by dividing the fatigue limit at 125 °C by that at 25 °C.
The results of the fatigue tests in relation to notches in the aluminum tubes are shown in Fig. 9(b). As explained earlier, the S–N curve was fitted by the following equation.
Temperature of 125 °C, notched:\(S_{\max}=49.058\ \times\ {N_{f}}^{-0.032}\) (7)
The fatigue limit, which was defined as the fatigue strength at 1 × 107 cycles, was found to be 29.37 MPa. The alternating stress value for the notched specimen was lower than those of the smooth specimens. The notch modification factor, which was calculated by dividing the fatigue limit of the notched specimens by that of the smooth specimen(results of heat exchanger operating temperature of 125 °C), was 0.60, resulting in a fatigue notch factor (\(K_{f}\)) of 1.67 that is an inverse of the notch modification factor.

3.3.2 Determination of material constant

By deriving the material constant (\(a\)) from the Peterson equation, we can estimate the fatigue notch factor (\(K_{f}\)) under different notch conditions. First, the stress concentration factor was obtained for notched tubes through a structural analysis in ANSYS (V19.1, USA). V-notches, measuring notch angle of 90 ˚, 0.02 mm in notch radius, and 0.115 mm in depth, were introduced onto standard smooth specimens, and a bending moment of 300 N·mm was applied to one end of the tubes. The results of the structural analysis showed that the notched specimens had a maximum stress of 13.69 MPa (Fig. 10). The stress concentration factor, which was calculated using the ratio of the average stress (5.02 MPa) in standard un-notched specimens to that of notched specimens, was found to be 2.73.
When the stress concentration factor (\(K_{t}\) = 2.73) of the notched tube specimens was obtained through structural analysis, and the notch radius (\(r\) = 0.02 mm ) and the fatigue notch factor, which were calculated based on the results of fatigue tests (\(K_{f}\) = 1.67), were substituted into the Peterson equation (Eq. (8)), the material constant (\(a\)) was found to be 0.03mm. Therefore, because \(K_{f}\) in relation to the notch radius (\(r\)) can be easily obtained by the Peterson equation,
\(K_{f}=1+\left(\frac{K_{t}-1}{1+\frac{a}{r}}\right)\) (8)
it is possible to predict the decrease in the fatigue limit due to various notch sizes.