4.1 Fracture morphology analysis based on fracture mechanics calculation
To further investigate the nature of fatigue crack initiation and propagation behavior, quantitative fracture analysis was performed with the help of fracture mechanics. The stress intensity factor ΔK of the fracture surface of failed specimens was calculated. For surface crack initiation in the present work, Zone I, II can be approximately regarded as a semi-elliptic. The areas of Zone I and Zone II were measured and their square root values\(\ \sqrt{}\text{area}\) , which was obtained by projecting on the plane perpendicular to the loading axial, were used to calculate the ΔK values,given by the equation for surface cracks [16, 39]:
\begin{equation} \Delta K=0.65\sigma\sqrt{\pi\cdot\sqrt{ar\mathbb{e}a}}\nonumber \\ \end{equation}
Where σ is the maximum stress amplitude of cyclic stress for R=-1, and 0.65 is the calculated parameter for surface crack initiation.Figure 9 demonstrates the calculated results of ΔK of Zone I and Zone II together with the values of the applied stress amplitude and the fatigue life. Obviously, the values of ΔK Zone I and ΔK Zone II maintain nearly constant levels regardless of the fatigue strength and the fatigue life. The average ΔK Zone Ivalue was evaluated to 1.44 MPa·m1/2 and the corresponding value of ΔK Zone II was a little higher, about 2.40 MPa·m1/2, respectively. Compared with some previous investigations[40, 41], the ΔK Zone II is slightly lower than that of some conventional magnesium alloys, which is usually considered as a threshold of stable crack propagation. But it is still within the range of the reported crack growth thresholds of magnesium alloys, about 1.2-5.0 MPa m1/2 [40-42]. Therefore, the ΔK value of Zone II can be regarded as the crack propagation threshold of the material, which corresponds to the threshold for stable crack propagation.
Therefore, in the present case, the fatigue failure process of the LZ91 alloy can be divided into three main stages according to the differences in the ΔK values and the characteristics of the fracture surface. As demonstrated in Section 3.3, the crack initiation region (Zone I) presents a relatively special morphology, which is similar to the rough area (RA) and facet morphology of some structural alloys [43-45]. In the titanium alloys [44], the facets were formed due to the inconsistent plastic strain of the two phases in the crack initiation region. Based on this, it can be preliminarily deduced that due to the difference in the plastic deformability of the two phases in the material, the plastic strain was highly concentrated in one of them. Subsequently, the local deformation inhomogeneity of the two phases would lead to the nucleation and initiation of micro-cracks. As the micro-crack grows, the size of the plastic zone at the crack tip gets larger, as well as the stress intensity factor. This would therefore result in a higher level of stress in a local region near the micro-cracks, as compared with neighboring regions. As a result, numerous micro-cracks were initiated, propagated, and then coalesced in Zone II. Namely, the formation of Zone II corresponds to a multi-crack propagation stage in the process of fatigue failure. This is the reason why there are a large number of radial ridges in Zone II, which make it relatively rough. Afterward, when the stress intensity reaches the crack propagation threshold value, namely, the ΔK value of the edge of Zone II, the crack propagation pattern changes again. In some researches of high-strength steels, it was proposed that [46, 47] the ΔKRA (ΔK Zone II in the present case) value corresponds to the relevant threshold for long crack growth. Therefore, the growth pattern of the crack in Zone III switched from the multiple short crack growth to the steady single long-crack growth that follows Paris law.