On Tanaka‐Mura's fatigue crack nucleation model and validation

Abstract

Tanaka‐Mura's fatigue crack nucleation model is revisited. A dimensional problem is found in their cyclic plastic strain formulation obtained by integration of the displacement function, and hence, it is rederived based on the true strain definition. Using the corrected strain formulation, a new fatigue crack nucleation life expression is obtained, and for the first time, low cycle fatigue lives of several metals and alloys are predicted without resorting to experiments. With such theoretical life as the baseline, other factors such as surface roughness, environment, and even high‐temperature damage mechanisms can be delineated in further studies.

A fatigue crack nucleation model for anisotropic materials

“…As implied by Equation (10), even application of a single stress component may induce dislocation distributions of all modes, depending on the coupling terms in the F matrix. In the previous paper, 6 the author showed that the isotropic formulation can satisfactorily predict the low-cycle fatigue life of polycrystalline materials with appreciable plastic deformation. In this sense, metal fatigue is almost unavoidable under repeated loading of any kind exceeding the lattice frictional resistance t i F .…”

“…In the previous paper, 6 the author showed that the isotropic formulation can satisfactorily predict the low-cycle fatigue life of polycrystalline materials with appreciable plastic deformation. Using the surface energy value of 2.3729 J/ m 2 and Burgers vector of 2.48 × 10 −10 m for pure iron, 6 and the Young's modulus of the orientation (for simple estimation of the single mode II crack nucleation, it is assumed that the F matrix takes the "isotropic" form but with the directional modulus, as reasoned from Ting 13 ), Equation (23) then predicts the fatigue crack nucleation life (applying the same surface roughness factor as in Wu 6 ) is calculated to be 35 963 cycles. Then, only a few dislocation pile-ups exist in the most favorable slip systems, depending on the microstructure, while the rest of the body remains elastic.…”

“…Using the surface energy value of Ni, w s = 2.38 J/m 2 , and assume that the machining surface roughness introduces a factor of R s = 1/3, 6 we rearrange Equation (22) as…”

“…For engineering application, w s may be replaced with w′ s = R s w s , where R s is the surface roughness factor. 6…”

“…[1][2][3][4] Tanaka and Mura originally proposed a model of fatigue crack nucleation in terms of dislocation dipole pile-ups, where vacancy dipoles represent intrusions and interstitial dipoles represent extrusions. 6 Here, the mechanical fatigue refers to fatigue damage without time-dependent deformation, ie, creep, and in absence of environmental effects. Recently, the Tanaka-Mura model has been revisited with a revised formula of dislocation pile-up strain.…”