Cyclic Strength and Nonlinear Material Fracture Mechanics (by the example of steels)
It was shown that a material fatigue fracture diagram can be viewed as a locus of points with $σ$ and $\sqrt l$ coordinates' product equal to $K_{1c}/2$, and $σ$ and $l$ product -- to $G_{1c}/2$, where $K_{1c}$ and $G_{1c}$ are non-linear fracture mechanics force and energy criteria. It was established that the average number of interatomic bonds destroyed within one alternate stress $\nabla_{1cs}$ cycle is directly proportional to $σ$ that is twice as large as a peak value of $σ^a$. It was found that low-cycle fatigue is characterized by $σ>σ_{0.2}$ and $σ_{1cs}> 1$, high-cycle fatigue -- by $σ= σ_{0.2}$ and $\nabla_{1cs} = 1$, and giga-cycle fatigue -- by $σ< σ_{0.2}$ and $\nabla_{1cs} < 1$. An individual interatomic bond cannot be destroyed part by part but as a single unit. The latter means that in giga-cycle fatigue a single interatomic bond is destroyed within several cycles rather than within a single cycle. The factors $F$ (collapsibility) and $R$ (resistibility) were proposed and mentioned as essential material physical constants. The introduced notion $\nabla_{1cs}$ and the established linear nature of $\nabla_{1cs}$ relationship allow to: a) clarify the fatigue crack growth physical nature in low-, high- and giga-cycle fracture zones; b) determine the nature of a fatigue fracture diagram disruption; c) plot the fatigue fracture diagram using the results obtained in a single specimen cyclic strength test with a selected value of $σ\ge σ_{0.2}$. For giga-cycle fatigue it is important (with similar purpose in mind) to determine this dependence for $σ< σ_{0.2}$. It is recommended to use $G_{1c}$ criterion to find the $l_{cr}$ length value which in contrast to $K_{1c}$ has a clear physical nature.