The impact of twin lamella thickness distribution on strength and endurance limit in nanotwinned copper

• The effect of the distribution of lamellar twin thicknesses on nt-Cu is studied.
• The deviations of models from experiments are ascribed to the thickness dispersion.
• The effect of SFE on fatigue cracking is revealed by an extended dislocation model.

The lamellar twin thicknesses in grains of nanotwinned (nt) metals form a population of stochastic nature. The sizes are a set of random variables which might be approximated by a lognormal distribution. The different sizes can lead to different accommodations of inclined dislocation pile-up at the twin boundaries (TBs) or different situations of TBs migrations arising from dislocation nucleation and gliding along TBs. Therefore, only a consideration of the mean thickness in the investigations on the mechanical properties-twin thickness relation is not enough, and the effect of dispersion of the distribution should be investigated. Moreover, with decreasing twin thickness, first the yield stress of nt-copper follows the Hall–Petch (H–P) relation, then the smaller size leads to softening induced by de-twinning. However, by now a complete description of the strength-twin thickness effect over a wider range of 4–100 nm of twin thicknesses in nt-metals is rare. In the great mass of past references, the strengthening and softening stages were separately investigated by different models, which induces that the fitting curves of strengthening and softening stages could neither be smoothly connected nor correspond well with the experimental data at the critical stage of the strengthening–softening transition. In this paper, the analytical expressions for yield strength and endurance limit as the functions of the distribution of lamellar twin thicknesses are provided. The theoretical results could be compared with experimental data over a wider range of twin thicknesses in a simple and approximate manner, and they show good agreement with each other. Furthermore, the effect of stacking fault energy (SFE) on fatigue cracking is revealed by an extended dislocation model.