On single aluminum crystals under cyclic loadings, fresh slip lines appeared during the reversed loading, lying very close to, but not coincident with the slip lines formed in the forward loading. These slip lines indicate the start of extrusion or intrusion as commonly observed in fatigue specimens. An initial stress field is present in all metals. The initial stress field favorable to the aforementioned sequence of slip is one having a positive shear stress in one thin slice P and a negative one in a closely located thin slice Q. A forward loading causes a positive shear stress, which is of the same sign as the initial shear stress in P, but of opposite sign to that in Q. Hence the shear stress in P will reach the critical value first to cause slip. Due to the continuity of the stress field, slip in P relieves not only the positive shear stress in P but also in Q. This has the same effect as increasing negative shear stress in Q. During the reversed loading, Q has the highest negative shear stress and hence slides. Similarly, this slip causes P to be more ready to slide in the next forward loading. This process is repeated to cause a monotonic alternate sliding in P and Q. In this way, an extrusion or intrusion is nucleated. A crack can be started from an intrusion. The thin slices P and Q are considered to be in a most favorably oriented crystal located at a free surface. An initial stress field giving positive shear stress in P and negative in Q is calculated from an assumed initial inelastic strain field which, in turn, can be caused by distribution of dislocations. The buildup of plastic shear strain in P and Q causing the start of extrusion or intrusion is shown.
Inversion analysis of the complex initial stress field of an extra-long tunnel based on “overlapping partition-integration”
