# Effect of the Depth of Decarburized Layer in SKL15 Tension Clamp on Fatigue Strength
## 2 Investigation of Cause of Fatigue Crack
### Decrease in the Fatigue Strength Due to Decarburized Layer  
Several researchers have confirmed that the fatigue strength of steel is lowered by the decarburized layer [2,6]. However, opinions on the degree of reduction in the fatigue strength depending on the depth of the decarburized layer differ among researchers. According to [PERSON] et al. [2], when the decarburization layer is present to an effective degree, a constant endurance limit of 325 MPa is seen regardless of the strength of the material. This means that due to the low strength of the decarburized layer, the cracks are  
Figure 3: SEM photographs of decarburized layers: (**a**) Specimen #7; (**b**) uncracked specimen.  
Figure 2: Results of measuring the depth of decarburized layers.  
generated even under a low stress range in the decarburized layer, and this crack plays a role in the initial crack, which grows into the base metal. [PERSON] and [PERSON] [6] determined the change in the fatigue strength according to the depth of the decarburized layer using a fatigue test on plain carbon steel. As the depth of the decarburized layer increases, the fatigue limit of the material decreases (Figure 4). This appears to be because the \(\Delta K_{l}\) generated at the crack tip increases as the depth of the decarburization layer increases if the size of the initial crack in the decarburization layer is assumed to be the same as the depth of the decarburization layer.  
Assuming that the fatigue crack occurs in a much lower stress range than the base metal due to the decrease in the strength of the decarburized layer, in terms of fracture mechanics, the deeper the decarburized layer, the deeper the crack. In the case of a first mode crack, \(\Delta K_{l}\) generated at the crack tip, as in Equation (2), has a large value as the depth of the crack increases and the range of stress acting on the crack surface increases.  
\[\Delta K_{l}=S_{r}\sqrt{\pi a}F_{c} \tag{2}\]  
where \(S_{r}\) is the stress range, \(a\) is the crack depth, and \(F_{c}\) is the correction factor. The correction factor is determined according to the type of load acting on the crack, the member shape, and the shape of the crack. According to [PERSON] and [PERSON] [7], in order for cracks to grow in cracked steel, the \(\Delta K_{l}\) generated at the crack tip must exceed the fatigue threshold stress intensity factor range (\(\Delta K_{th}\)), which is equivalent to Equation (3).  
\[\Delta K_{th}=7(1-0.85R)\text{ MPa}\cdot\sqrt{\text{m}} \tag{3}\]  
where \(R\) is the stress ratio, which is the ratio between the minimum and maximum stress under constant stress amplitude. The fatigue threshold stress intensity factor range (\(\Delta K_{th}\)) is independent of the depth of the crack and is determined by the stress ratio. Thus, as the decarburized layer thickens, the stress range leading to \(\Delta K_{th}\) decreases, reducing the fatigue strength. Therefore, the research results of [PERSON] and [PERSON] [6], which show the deeper the decarburized layer, the weaker the fatigue strength, can be considered to be valid. However, the degree of fatigue strength reduction according to the depth of the decarburized layer may vary depending on the shape of the member and the type of load; thus, the results of [PERSON] and [PERSON] [6] cannot be directly applied to the tension clamp. Therefore, the \(\Delta K_{th}\) of  
Figure 4: Decrease in fatigue limit with respect to the depth of decarburization layer (reproduced from [PERSON] and [PERSON], 1958.)  
the tension clamp material, the shape of the member, and the section force acting at the location where the fatigue crack has occurred must be known to determine the fatigue strength of the tension clamp.