4. Discussion
The purpose of this study was to analyze the effects of surface defects
(notches), operating temperature, and the number of re-welding on the
static strength and fatigue characteristics of the aluminum tubes
(Al3003-O) used in heat exchangers of air conditioners. In the present
study, the grain size grew and hardness decreased as the number of
re-welding increased because a heat-affected zone was created in the
specimens due to a welding temperature of approximately 600 ℃ and
multiple weldings. The result that the correlation between the grain
size and the hardness was observed to be nonlinear suggests that the
heat-affected area of the aluminum tubes shows a significant
deterioration in the hardness even when welded only once; this is
expected to be accompanied by a decrease in the mechanical strength. As
repeated welding causes the strength of the aluminum tubes to decrease
further, in order to avoid the creation of more heat-affected zones, it
is better to add new tubes or to extend existing ones instead of
repeatedly welding the same area. Regarding the underlying mechanism of
the relation between the hardness and the grain size, the density of the
grain boundary generally decreases with increasing grain size, and
hence, the hardness decreases owing to the increased mobility of
dislocation. In other words, grain boundary acts as an obstacle to
dislocation movement. The smaller the grain size, the more grain
boundary exists. As a result, the movement of dislocation is disturbed
and the hardness increases.
Moreover, the relation between the mechanical strength (i.e., yield
stress) and grain size of a metal has previously been formulated by the
Hall-Petch equation, \(\sigma_{y}=\sigma_{o}+k_{y}d^{-0.5}\) where\(\sigma_{y}\) is the yield stress, \(\sigma_{o}\) is the stress for
dislocation motion, \(k_{y}\) is a material constant, and dis the grain
size. In the absence of considerable work hardening effect of material,
this equation can be modified to relate the hardness (\(H_{v}\)) and
grain size (d) by \(H_{v}=H_{o}+k_{H}d^{-0.5}\) where \(H_{o}\) and\(k_{H}\) are material constants. According to the Hall-Petch equation,
the mechanical strength can be directly converted to the hardness.
Therefore, a decrease in the hardness with increasing number of
re-welding makes the material less strong and more ductile. This result
can affect the fatigue strength of the material. It has been well known
that ductile material generally provides a good fatigue resistance in
the low-cycle fatigue region where most of the fatigue life is occupied
by the crack propagation than crack nucleation due to a considerable
amount of plastic deformation. Furthermore, in the present study, when
unheated, the hardness of the material is based on both work hardening
and grain size, but materials with heat history (0, 1 and 5 times
re-weldings) are re-crystallized, thus the hardness values are related
only to the grain size. Nevertheless, the current results showed a poor
correlation (\(R^{2}\) = 0.866) between the hardness (\(H_{v}\)) and
grain size (\(d^{-0.5}\)) by the Hall-Petch equation, indicating that
the hardness would be better related to the grain size by the equation,\(H_{v}=H_{o}+k_{H}d^{-\alpha}\) which has three parameters
(\(H_{o}\), \(k_{H}\), and \(\alpha\)).
The effects of temperature and notched conditions on the fatigue of the
Al3003-O aluminum tubes used in heat exchangers of air conditioners were
also observed. The fatigue limit of 49.02 MPa measured in a heat
exchanger operating temperature of 125 °C was lower than that obtained
from those with at a room temperature of 25 °C, resulting in a
temperature modification factor of 0.86 that the fatigue life of
aluminum tubes of are affected even when the operating temperature
(125°C) is maintained. The kinetic energy of molecules in the aluminum
tube rises whose generates an active molecular motion when the
temperature increases. In particular, the spacing between molecules is
increased which results in a lower binding force, the probability of
breaking the bond between molecules increases when an external load is
applied. Therefore, the grain size increases at the high temperatures a
thereby the slip deformation accelerates and a significant deterioration
of fatigue strength of aluminum tubes. However, the fatigue limit of
notched specimens was lower than that of un-notched specimens, thus
resulting in a fatigue notch factor of approximately\(K_{f}\)= 1.67. From this fatigue notch factor obtained from experimental
measurements and the stress concentration factor (\(K_{t}\) = 2.73) of
the notched tube specimens (\(r\) = 0.02 mm ) obtained from
structural analysis, the material constant \(a\) = 0.03 mm that
could be used in the Peterson equation was computed. Therefore, for
Al3003-O aluminum tubes with diverse notch sizes, it is possible to
predict \(K_{f}\) that leads to calculations of decreased fatigue limits
due to various notch sizes. For example, for another notch size of \(r\)= 0.5 mm , \(K_{t}\) can be computed from structural analysis.
Then, by inserting this \(K_{t}\), \(r\) = 0.5 mm , and \(a\) =
0.03 mm into the Peterson equation, \(K_{f}\) for this notch size
can be calculated. By using the material constant a of the aluminum
tubes (Al3003-O) calculated in this study, the fatigue notch factor\(K_{f}\) can be re-calculated for the aluminum tubes with varying notch
sizes (\(r\)), and hence a decrease in the fatigue limit can also be
predicted for those aluminum tubes with diverse notches.