The fatigue crack growth rate DA / D N and the stress intensity factor at the crack tip under different stress ratios were calculated Δ K data is plotted in double logarithmic coordinates, as shown in Figure 1.

It can be seen from Figure 1 that the curve of the relationship between fatigue crack growth rate and stress intensity factor at the crack tip of 42CrMo steel presents “s” shape in the double logarithmic coordinate. These two key points divide the curve into three parts. There are three stages of fatigue crack growth, including low speed growth stage, stable growth stage and high speed growth stage. Compared with the curve of stress ratio r = 0.1, the two key points of the curve of stress ratio r = 0.6 are obvious, and the three stages of crack growth are also clear.

In the low-speed growth stage, the stress intensity factor at the crack tip increases Δ When k is less than the lower threshold value of fatigue crack growth of 42CrMo steel, the crack almost does not propagate and the curve develops vertically. The curve of stress ratio r = 0.1 is not very obvious at this stage. This is because the stress range is large and the load changes violently at this time. As a result, the crack propagation rate is relatively large at the beginning of propagation, and the crack propagation directly transits from the low-speed propagation stage to the next stage.

The stress intensity factor (SIF) at the crack tip increases from initial initiation to slow growth Δ K is also gradually increasing. The condition of crack initiation is the stress intensity factor at the crack tip Δ K is greater than the threshold of fatigue crack growth. Along with the crack tip stress intensity factor Δ When k continues to increase, the crack growth rate also presents an increasing trend, and the fatigue crack growth enters a stable growth stage. At this stage, the fatigue crack growth rate DA / D n is related to the stress intensity factor at the crack tip Δ K shows a linear relationship in logarithmic coordinate system. This stage is the key part in the study of fatigue crack growth and the basis for predicting the residual life of structural parts. Many scholars have carried out research on this stage. Paris rule [63] reveals the relationship between the fatigue crack growth rate DA / D N and the stress intensity factor at the crack tip Δ Where Paris formula is as follows:

Where:

A-crack length, mm;

N-fatigue cycles;

Da / D n – crack growth rate, mm / cycle;

K-stress intensity factor, MPA · m ^ 0.5;

C. M – material constant.

The formula can be obtained by taking logarithms on both sides of the formula at the same time.

The fatigue crack growth rate DA / D N and the stress intensity factor at the crack tip in the stable growth stage of the test data with the stress ratio r = 0.1 and 0.6 are calculated Δ K is plotted in double logarithmic coordinate system and fitted linearly. The result is shown in Figure 2 below.

In Figure 2, r = 0.1, the intercept of fitting line is LGC = – 8.44, the slope is m = 3.53, and the correlation coefficient is r = 0.99725. At this time, the equation describing the crack growth of 42CrMo steel compact tensile specimen in stable growth stage can be obtained by calculation when the stress ratio r = 0.1.

The formula is transformed into Paris formula.

In Figure 2, r = 0.6, the intercept of fitting line is LGC = – 4.19, the slope is m = 0.48, and the correlation coefficient is r = 0.96065.

At this time, the equation describing the crack growth of 42CrMo steel compact tensile specimen in stable growth stage can be obtained by calculation when the stress ratio r = 0.6.

The formula is transformed into Paris formula

As the fatigue crack growth test continues, the fatigue crack length continues to grow Δ When k is greater than the upper threshold of fatigue crack growth of 42CrMo steel compact tensile specimen. The growth trend of the curve becomes close to exponential growth, and the fatigue crack growth enters into the high-speed growth stage. At this stage, the fatigue crack growth rate suddenly increases and increases exponentially, which also leads to the rapid increase of the fatigue crack size, and finally leads to the fracture of the compact tensile specimen. The duration of this stage is very short, which indicates that the fatigue crack of 42CrMo steel will grow abruptly and dangerously at this stage.