*3.1. Experimental Results*

To discuss the crack size effect on stress evaluation, the *H*p(*y*) signal, corresponding to different stresses, should be collected in advance with the tensile test, so the preload was determined based on the mechanical properties of material, as shown in Table 1. In this study, the load interval is 6 kN, and the loading rate is 0.5 kN/s. When the preload was reached, the load was held about 120 s, and then the sample was taken down from the CMT2502 testing machine. After that, the sample was placed on the platform, and the *H*p(*y*) signals were sequentially collected along detection lines. Comparing the *H*p(*y*) signals, it can be seen that although the sizes of cracks are different, the change regulation of the *H*p(*y*) signal is very similar as stress changes. Therefore, when the groove depth is 3.0 mm, the *H*p(*y*) signals of the sample along seven detection lines, corresponding to different stresses, are shown in Figure 4.

From Figure 4a, it can be seen that when the stress is 0 MPa, the distribution of *H*p(*y*) signal is irregular, and its amplitude is in the range of <sup>−</sup>2.6~67.8 (A·m<sup>−</sup>1). For the result, it can be known that the amplitude is in the range of intensity of the geomagnetic field, thus the initial *H*p(*y*) signal effect on stress evaluation can be ignored. From Figure 4b–e, it can be seen that as stress increases, the amplitude of the whole *H*p(*y*) signal increases gradually, and the *H*p(*y*) signal mutation, corresponding to groove, also becomes more obvious gradually. Compared with the amplitude of *H*p(*y*) signal in Figure 4e, it can be seen that the amplitude in Figure 4f decreases as stress increases. Comparing *H*p(*y*) signals in different detection lines, it can be seen that when the stress is the same, the *H*p(*y*) signals and its changes are basically the same. Based on that result, the *H*p(*y*) signals along the middle line are analyzed and shown in Figure 5.

**Figure 4.** *H*p(*y*) signals under different tensile loads. (**a**) 0 MPa, (**b**) 75 MPa, (**c**) 150 MPa, (**d**) 225 MPa, (**e**) 337.5 MPa, (**f**) 375 MPa.

**Figure 5.** *H*p(*y*) signals corresponding to different stresses.

Figure 5 shows that when stress is 0 MPa, the *H*p(*y*) signal appears nearly as a horizontal line. As stress increases, the *H*p(*y*) signals present linear distribution, then turn anticlockwise and approximately intersect at one point, which is defined as zero crossing point in this paper. For the mutation of *H*p(*y*) signal, corresponding to groove, it can be seen that when the groove size is different, the mutation degree also changes, so it can be used to evaluate the stress. Therefore, the mutation of *H*p(*y*) signal, corresponding to groove, was extracted and defined as magnetic intensity gradient *K*, which was calculated with Equation (1).

$$K = \frac{H\_p(y)\_{\text{max}} - H\_p(y)\_{\text{min}}}{\Delta l} \tag{1}$$

where *H*p(*y*)max and *H*p(*y*)min are the maximal and minimal values of *H*p(*y*) signal, Δ*l* is the spacing between the location of *H*p(*y*)max and *H*p(*y*)min.

For different crack sizes, the *K* of *H*p(*y*) signal was calculated based on Equation (1). It can be seen that when the depth of groove is the same, the relationship between *K* and groove width is very similar. For that reason, not all the experimental results were shown in this paper, and only when the groove depth is 3.0 mm, the relation of *K* and groove width was shown in this paper.

When the stresses are different, the curves of *K* and groove width were shown in Figure 6. It can be seen that as groove width increases, the change regulation of *K* is very similar, and it presents in the form of parabola. When stress is 337.5 MPa, which is the yield strength of material, the *K* reaches the maximal value. Based on that, the value of *K* and groove width is fitted with quadratic polynomial function.

**Figure 6.** Relation of *K* and width of groove.

Similarly, for discussing the depth effect on stress evaluation, the relation of groove depth and *K* was analyzed. For that purpose, the *H*p(*y*) signals, corresponding to the same widths and different stresses, were collected, and its *K* was also calculated. Comparing experimental results, it can be seen that although groove depths are different, the change regulation of *K* is very similar as stress increases gradually. In view of that, when groove widths were 2.0 mm and 3.0 mm, which were the common widths, the results of *K* and groove depth were shown in Figure 7.

As shown in Figure 7, it can be seen that the relationship of *K* and groove depth is nearly linear, and the slope between *K* and groove depth increases gradually as stress increases. When stress reaches 337.5 MPa, the slope reaches the maximal value, and then becomes smaller as stress increases further. To discuss the influence of stress on the value of *K*, the result of *K* and stress was fitted with linear function. In this study, the fitting coefficient was defined as *KF*, so the relationship between *KF* and stress was determined and shown in Figure 8.

**Figure 7.** Relationship of *K* and groove depth. (**a**) 2.0 mm, (**b**) 3.0 mm.

**Figure 8.** Result of *KF* and tensile stress.

As shown in Figure 8, it can be seen that although the groove widths are different, the change regulation of *KF* is basically the same as stress increases. In detail, when the stress is 337.5 MPa, the *KF* corresponds to the maximal value, and it decreases obviously as stress increases further. For the same stress, the *KF* increases gradually as the groove width increases.
