The local strain behavior of cold-rolled HSLA (niobium) steel was investigated in the vicinity of a circular hole for first loading, first unloading, and in the unloaded state after 50 000 and 82 000 cycles by determining εθ as a function of distance from an 0.02-in. (508-μm) circular notch by direct comparison of optical micrographs at approximately ×1000. This technique allows changes in length to be determined to ±0.15 μm which, over a 100-μm gage length, corresponds to an engineering strain resolution of ±0.15%. The resolution is sufficiently high to allow local strain distributions, as calculated from elasticity and plasticity theory, to be compared with the experimental data. A pseudo-plastic solution was developed from the plane stress solution by considering A. E. Green's three-dimensional solution and Neuber's relation between stress and strain concentrations. The monotonic deformation law obeyed by cold-rolled niobium steel was experimentally determined and combined with the pseudo-plasticity result to obtain a quantitative prediction of the local strain behavior on first loading. Experimentally obtained strain behaviors for first loading provide good agreement with the pseudo-plasticity result for each of the strain levels investigated. The strain distribution measured after the first unloading demonstrated that a compressive residual stress is generated during the first cycle. The strain distribution developed by repeated tension loading is also presented and discussed.
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