Towards a further understanding of dislocation pileups in the presence of stress gradients

This study is an essential complement and extension to the stress-gradient concept recently proposed by Hirth. An analytic method is presented for studying the behaviour of double-ended dislocation pileup in the presence of various stress gradients by solving a singular integral equation based on the continuous approximation of dislocations. Four special cases of double-ended pileup in the presence of stress gradients are discussed in detail. The corresponding dislocation distribution, the length of pileup, the total number of dislocations within the pileup and the force on the leading dislocations at the pileup ends are derived, respectively. It is shown that both the number of dislocations and the force on the leading dislocation in a pileup are sensitive to the relative magnitude of stress near the dislocation source and both are less than that in constant stress case. Of particular importance, it is indicated that the small-scaled materials subjected to a stress involving a gradient would be stronger than that under a constant stress. Applied to wire torsion and foil bending, the stress gradient model predicts an increase in the initial yielding, which is in reasonable agreement with the recent experimental data. The proposed stress gradient concept may provide a new physical insight into the size-dependent plasticity phenomena at small length scale.     

On the comparative assessment of ratcheting-induced dislocation density in 42CrMo4 steel by X-ray diffraction profile analysis and hardness measurement

The phenomenon of ratcheting occurs under the influence of non-zero mean stress during cyclic loading; it singificantly reduces the low cycle fatigue life of engineering structures. The present investigation deals with a detailed comparison on the estimation of dislocation densities in the 42CrMo4 steel induced by ratcheting using two different methods, i.e. X-ray diffraction (XRD) profile analysis and hardness. The dislocation densities in the ratcheted specimens were assessed using XRD profile analysis following the modified Williamson–Hall method as well as hardness measurements following the modified Nix and Gao model. The results showed that dislocation density increased in the ratcheted specimens as compared to the unratcheted ones and increase in accumulation of ratcheting strain was correlated with the increase in dislocation densities in the ratcheted specimens. It was established that both hardness and X-ray diffraction profile analysis methods can very effectively be used to assess the dislocation densities in the ratcheted specimens.