Micromechanics of an extrusion in high-cycle fatigue

Abstract

A most favourably oriented crystal located at a free surface of a f.c.c. polycrystal under cyclic tension and compression of high-cycle loading is considered. An extrusion in this crystal is shown to be caused by a positive slip in one thin slice P and a negative slip in a closely located slice Q. An initial tensile strain eⁱ _αα in the thin slice R sandwiched between P and Q causes an initial compressive stress ζⁱ _αα in R and a positive initial shear stress ζⁱ _αβ in P and a negative one in Q. (The repetition of the subscript in Greek letters in this paper as above does not denote summations.) Slices P, Q and R, the slip direction α and the normal to the slip plane β all make 45° with the free surface. The elongation in R induced by this initial strain is called the ‚static extrusion‘. The difference between the resolved shear stresses in P and Q causes the build-up of plastic shear strain in P and Q, and hence the extrusion growth. As the extrusion grows, the initial compression in R decreases, resulting in a decrease in the extrusion growth rate. This decrease in compression in R tends to activate a second slip system to slide. The plastic strain due to slip in this second slip system has a tensor component e”_αα, which has the same effect as the initial strain eⁱ _αα in causing the positive and negative resolved shear stresses in P and Q, and hence the additional extrusion growth. In the present study, with consideration of the secondary slip in R, the extrusion is shown to grow far beyond the static extrusion. A similar conclusion can be made for the growth of an intrusion.