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.