# Fiber Bragg Gratings Based Cyclic Strain Measuring of Weld Toes of Cruciform Joints
## 4 Results
### Stress-Strain Response Curve  
The peak-valley value was extracted from the strain time history collected from the test. According to the material parameters in Table 1, the stress-strain response of testing points can be calculated considering the cyclic behavior and memory effect of the material. Since the total loading cycles of the test were numerous, in order to improve the calculating efficiency and display the figures more clearly, only one peak-valley value was extracted from every 100 sequential cycles. The obtained stress-strain response curve for testing point 3# is shown in Figure 12, in which an obvious shift of stress-strain loops can be seen. If the strain values are amplified, exaggerated hysteresis loops can be generated, shown as the sub-figure in Figure 12. It needs to be mentioned that the stress and the strain in the sub-figure are not of real values, but can help to distinguish the different stages more clearly. Generally, a hysteresis loop is formed due to plastic dissipation when the cyclic stress and strain exceed the yield strength of the material. Although the testing stress is lower than the yield strength of the material in this test, SCF in the weld toe causes the actual stress and strain in the weld toe to exceed the yield strength and then results in hysteresis loop phenomenon. According to the different phases of the testing point 3#, the corresponding stress-strain response curves were drawn, as shown in Figures 13-15. Figure 13 illustrates the \"strain decline\" phase corresponds to 1-80472 loading cycles. It can be seen that as the number of load cycles increases, the stress-strain curve gradually shifts to the lower-left as a straight-line shape which exhibits cyclic hardening behavior. In the sub-figure, it can be seen that the shape of the hysteresis loop is almost unchanged in the first several cycles and then becomes stable in the last several cycles. During the cyclic hardening process, \(\Delta\epsilon\) of different cycles almost equals to 1970 \(\mu\epsilon\) and \(\Delta\sigma\) almost equals to 407 MPa, which reflects the test was conducted under the constant amplitude stress and strain state. However, the maximum stress and strain are decreased with the maximum \(\epsilon_{\text{max}}\) of 1951 \(\mu\epsilon\) and the maximum \(\sigma_{\text{max}}\) of 398 MPa. By calculating, \(SCF_{\sigma}=1.99\), \(SCF_{\varepsilon}=1.98\), \(SCF_{\Delta\sigma}=2.03\), \(SCF_{\Delta\varepsilon}=2.00\), which exhibits strong stress-strain concentration effects. Due to the cyclic hardening behavior, SCF will decrease as the number of cycles increases. Then the strain stress response curve becomes approximate line shape. Figure 12: Strain stress response curve (testing point 3#). Figure 14: Strain stress response curve (”strain stationary” phase for testing point 3\(\#\)). Figure 13: Strain stress response curve (”strain decline” phase for testing point 3\(\#\)). Figure 15: Strain stress response curve (”strain rise and fall sharply” phase for testing point 3\(\#\)). Figure 14 shows the \"strain stationary\" phase corresponding to 80473-458382 loading cycles, which lasts a long time. It can be seen that the stress is almost linear to the strain and lies in the elastic region, indicating that the stress and strain in this phase are lower than the yield strength of the weld material. There is nearly no hysteresis loop in this phase, but the stress-strain curves also shift gradually from top-right to bottom-left. It should be emphasized again here that the loops in the sub-figure are only for showing and are not with the real values of stresses and strains. When the stress-strain cycles are stable, \(\Delta\epsilon=1148\)\(\mu\epsilon\), \(\Delta\sigma=240\) MPa, \(\epsilon_{\text{max}}=1075\)\(\mu\epsilon\), \(\sigma_{\text{max}}=220\) MPa. By calculating, \(\text{SCF}_{\sigma}=1.10\), \(\text{SCF}_{\varepsilon}=1.11\), \(\text{SCF}_{\Delta\sigma}=1.20\), \(\text{SCF}_{\Delta\varepsilon}=1.18\), which exhibits weakened SCF compared with that in the \"strain decline\" phase.