It is well known that fatigue cracks remain closed during part of the load cycle under constant- and variable-amplitude loading. It seems that Elber's effective stress intensity factor range produced by a crack opening stress is in successfully good agreement with experimental fatigue crack propagation behaviour under various loading including constant-, block-, and spike-loading from a huge amount of tests. Recently, J. C. Newman introduced the interesting calculation model of the crack opening stress which was based on the Dugdale model, but was modified to leave plastically-deformed material along the crack surfaces as the crack advances.
However in his model, he neglected the stress re-distribution in the region of crack ahead in the calculation of crack opening load which leads to the occurrence of the re-distribution. Moreover, he also neglected the elastic deformation for the materials along the crack surfaces.
In this paper, Newman's calculation model is modified to solve the above problems. By the way, from the physical point of view, the idea that crack-opening stress is a limit stress for a fatigue crack propagation proposed by Elber comes to question. We considered that a fatigue crack does not propagate if a local part in the vicinity of a crack tip remains elastic, i. e., a plastic strain does not accumulate at a crack tip. This limit loading stress is named “consuming stress S_cs” which was confirmed to have nearly the same value as the crack opening stress by our calculation results. Various kind of case studies including constant-amplitude, spike and step down (for the threshold phenomenon) loading were carried out by using the model. These calculation results suggest the following phenomena.
(1) S_cs value increases rapidly just after fatigue crack initiates from a natural sharp defect. This result supports the phenomenon that fatigue crack can easily initiate from a sharp crack even if the length is small because of a large effective stress range.
(2) S_cs value reaches constant value approximately as a crack advances under constant-amplitude loading.
(3) S_cs value changes in accordance with the behaviour of acceleration and delayed retardation of a crack propagation after a spike over-loading.S_cs
(4) Phenomenon of threshold crack propagation seems to be able to be explained by the S_cs value under step down loading.