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.