Fatigue Crack Propagation in Low-Carbon Steel under Doubly-Repeated Stress

Discussion from Distributions of Residual Stress and Plastic Strain Ahead of Crack Tips

Abstract

A new method of the X-ray microbeam diffraction technique was used to measure the local residual stress near the fatigue crack tip. The residual stress was compressive at the crack tip and changed to tensile away from the crack tip. The shape of the residual stress distribution ahead of the crack tip was found to agree with the analytical result derived by using Rice's rigid plastic strip model, although the maximum compression at the crack tip was lower than that expected from the analysis. The calculated distance from the crack tip to the point where the residual stress changed from compression to tension was 1.5∼2 times as long as the distance measured by the X-ray method.
Three kinds of plastic regions were observed ahead of the fatigue crack tip, i.e., (1) the region calculable from Dugdale's equation (ζ-region), (2) the slip band region (ξ-region), and (3) the substructure-formed region where the formation of substructure was evidently observed by the X-ray microbeam method (η-region).
Fatigue crack propagation under doubly-repeated stress was discussed on the basis of the results of microscopic observations mentioned above. The influence of stress cycling at the first stress level on the propagation rate under the second stress level was quantified with a parameter κ as
κ=K_p/K,
where K is the applied stress intensity factor and K_p is the value of the stress intensity factor obtained by substituting the measured value of dl/dN into the K vs. dl/dN relation for the constant stress amplitude fatigue. Five components were first considered to affect the κ value as
κ=1+Δκ_r+Δκ_d+Δκ_s+Δκ_b+Δκ_p
where Δκ_r, Δκ_d, Δκ_s, Δκ_b and Δκ_p represent the contributions of residual stress, fatigue damage, strain hardening, the blunting of the crack tip and the profile of the crack front within the specimen thickness, respectively.
Several examples of the variation of κ with the increment λ of the crack length after the time of stress change were measured for fatigue with a high-low drop of the stress amplitude. These variations were explained with three values: a negative value of Δκ_r in the region with the compressive residual stress, a positive value of Δκ_d in η_v-and ξ_v-regions, and a negative value of Δκ_s in the region of ξ_v<λ<ζ_v. As λ approached to ζ_v, the κ value became unity.
In the case of stress-raise fatigue, the variation of κ with λ was explained by a negative value of Δκ_d in η_v-region and a positive value of Δκ_s in the region of ξ_v<λ<ζ_v.