## 3 Results and Discussion  
### Numerical Simulations  
#### 3.1.1 Quenching Process  
The quenched T-type rib shows compressive residual stress at its outer layers and tensile residual stress at the internal layers both for the longitudinal and transverse residual stress, as shown in Figure 5. The thermal stress resulting from the temperature gradient in different positions of the component in the heating and cooling stages contributes to the formation of residual stress during the quenching process. The variation of residual stress can be explained as follows: severe shrinkage appears at the outer surface with the high temperature of the component, while there is little strain at the internal layer at the initial stage of the quenching. Inconsistent strain between the outer and internal layers impedes the shrinkage at the outer surface, resulting in tensile residual stress at the outer layers and compressive residual stress at the internal layers. The temperature at the internal layers starts to decrease due to the stable cooling velocity and the shrinkage at the internal layers increases compared to that at the outer layers. The tensile to compressive stress distribution from the outer to internal layers changes gradually. During the final stage of quenching, the temperature at the outer layer decreases to room temperature while there is still shrinkage at the internal layer during the cooling stage. According to the volume invariance, the strain at the outer layers hinders the continuous contraction of the internal layers, thus causing compressive residual stress at the outer layers and tensile residual stress at the internal layers.  
Figure 4: Principle of contour method: (**a**) Initial stress before cutting; (**b**) Stress after cutting; (**c**) Calculation of the initial stress.  
Figure 5: Residual stress distribution of quenched T-type rib: (**a**) Longitudinal residual stress; (**b**) transverse residual stress.  
The residual stress shows a lamination distributional type at the thickness direction because of the directional heat transfer during the quenching process. The area with the stiffener shows an asymmetrical distribution of residual stress at the thickness direction of the T-type rib while that of the smooth area without the stiffener is symmetrical. Two paths (depicted in Figure 5) are plotted to describe the distribution of residual stress in the area with and without the stiffener, as shown in Figure 6. The smooth area shows approximately equal longitudinal and transverse residual stress and this is similar to the distribution of residual stress for a quenched plate. The residual stress changes from \(-210\) MPa at the surface to 190 MPa at the center point of the smooth area. Nevertheless, there is a distinct difference between the longitudinal and transverse residual stress at the center point of the area with the stiffener. The longitudinal stress varies from \(-230\) MPa to 200 MPa while the transverse stress changes from \(-230\) MPa to \(145\) MPa, and the maximum tensile stress locates at 40-50 mm from the bottom surface. The stiffened area shows larger longitudinal stress compared to that of the smooth area. The existence of the stiffener increases the temperature gradient and strain inhomogeneity, thus inducing larger longitudinal residual stress. The stiffened area can be equivalent to the quenching process with larger thickness compared to the smooth area. Due to the internal balance of residual stress, larger longitudinal residual stress will give rise to smaller transverse residual stress at the stiffened area.