# Fiber Bragg Gratings Based Cyclic Strain Measuring of Weld Toes of Cruciform Joints
## 4 Results  
### Time History  
The data directly measured by FBG is the changes in the grating Bragg wavelength at the testing point. The relationship between the testing point strain \(\varepsilon\) and the measured value can be expressed as Equation (11). \[\varepsilon=(\lambda_{\alpha}-\lambda_{stat})\times 1000/k_{\varepsilon} \tag{11}\]  
where \(\lambda_{co}\) is the real-time wavelength value collected by FBG, \(\lambda_{stat}\) is the initial wavelength value when the FBG is unloaded, \(k_{\varepsilon}\) is the strain sensitivity coefficient of FBG. Table 4 shows that the Bragg wavelength used in this paper is between 1530 and 1555. Here, \(k_{\varepsilon}\) is set to be 1.2 pm/\(\mu\varepsilon\). According to Equation (11), the testing signals at all the testing points were processed, and the strain time history of testing points were obtained, and the corresponding curves were drawn. Figure 10 shows the strain time history curve of the testing point 0#. According to Table 4, the testing point 0# is located on the surface of the specimens' thin plate, which is far away from the weld toe. It is mainly used to verify nominal stress during the testing process. From Figure 10, the testing point 0# generally exhibits a constant amplitude strain of R = 0 and \(\varepsilon_{\max}\) is 986 \(\mu\varepsilon\). Considering E = \(2.06\times 10^{5}\) MPa  
Figure 8: Cyclic strain testing system. Figure 9: Testing points arrangement and specimen fracture. given in Table 1, \(\sigma_{\text{max}}\) = 203.1 MPa can be calculated, which is satisfying with the maximum nominal testing stress 200 MPa. So it indicates that the FBG has sufficient testing accuracy and reliability. At the end of the test, as the crack size approached gradually to the critical size, the strain near this testing point was rapidly increased. When the specimen broke instantaneously, the strain fell to zero quickly. The duration of the broken stage is extremely short, with only about 19.9 s, which corresponds to the instantaneous fracture of the specimen. Figure 11 shows the strain time history curve of testing point 3#, where Figure 11a is the overall signal curve. It can be seen that the overall strain time history of this testing point can be divided into three phases: the \"strain decline\" phase (Early phase), the \"strain stationary\" phase (Mid phase), and the \"strain rise and falls sharply\" phase (Final phase), among which the \"strain stationary\" phase lasts a long time, accounting for about 52% of the total time. In the \"strain stationary\" phase, \(\varepsilon_{\text{max}}\) = 1078 \(\mu\varepsilon\), \(\varepsilon_{\text{min}}\) = -81 \(\mu\varepsilon\), \(\Delta\varepsilon\) = 1159 \(\mu\varepsilon\). \(\varepsilon_{\text{max}}\) is slightly higher than the nominal testing strain, and \(\text{SCF}_{\varepsilon}\) = 1.09, \(\text{SCF}_{\Delta\varepsilon}\) = 1.18. It is worth noting that there is a small amount of compression strain in the stable phase. Figure 11b shows the signal curve of the early phase. In order to make the strain trend more clearly, one strain cycle in Figure 11b is extracted from sequential 13 actual loading cycles. It can be seen that both the \(\varepsilon_{\text{max}}\) and \(\varepsilon_{\text{min}}\) in one cycle gradually decrease until they become stable in the \"strain stationary\" phase, indicating that the material near this testing point has obvious cyclic hardening characteristics, which leads to the weakening of SCF. In the first cycle in Figure 11b, \(\varepsilon_{\text{max}}\) = 1990 \(\mu\varepsilon\), \(\varepsilon_{\text{min}}\) = 616 \(\mu\varepsilon\), \(\Delta\varepsilon\) = 1374 \(\mu\varepsilon\). Then, \(\text{SCF}_{\varepsilon}\) = 2.02, \(\text{SCF}_{\Delta\varepsilon}\) = 1.39 can be calculated according to Equations (2) and (4). Compared with the \(\text{SCF}_{\sigma}\) of the corresponding testing point in Table 3, \(\text{SCF}_{\varepsilon}\) is very close to \(\text{SCF}_{\sigma}\), which is mainly due to the small portion of plastic strain in total strain.