Interpretation of Nanoscale Softening in Terms of Dislocation-Accommodated Boundary Sliding Farghalli A. Mohamed, University of California, DMR Fig. 1. Yield strength as a function of the inverse square root of the grain size for Cu. The curve representing dislocation accommodated boundary sliding intersects the straight line representing the Hall-Petch behavior at about d c = 25 nm. Fig. 2. Yield strength as a function of the inverse square root of the grain size for Cu. Experimental data are superimposed on Figure 1. Analysis. The new model for deformation is based on the concept of dislocation accommodated boundary sliding. According to the model, strain during the creep of nc-materials is produced by boundary sliding while the creep rate is governed by the time for the climb of a dislocation along the boundary until annihilation occurs. The rate equation is given by: Equations (1) and (2) are applied [-] to examine whether nanoscale softening can be predicted. (2) Prediction. As shown in Figure 1, the curve representing dislocation accommodated boundary sliding (Eq.2) intersects the straight line representing the Hall-Petch behavior (Eq.1) at about d c = 25 nm. Accordingly, for d larger than about 25 nm, strength is determined by the Hall-Petch relation whereas for d is smaller than about 25 nm, strength is governed by dislocation-accommodated boundary sliding as defined by Eq.2. Significance. The results are significant since they show that by combining conventional Hall-Petch behavior for larger grains and a new deformation process based on dislocation-accommodated boundary sliding for smaller grains, nanoscale softening can be predicted; and that the critical grains sizes d c for nc-Cu is 25 nm. The present prediction is consistent with the trend of experimental data and the value for d c reported for Cu. Introduction. In general, as the grain size, d, is refined, the strength increases according to the Hall-Petch relation: (1) where  o is a friction stress and c is a constant. Hall-Petch behavior holds to grain sizes well within the nanoscale range. However, experimental observations have suggested that when the grain size of some nc-materials falls below a critical value in the nanoscale range, the strength decreases, i.e., nanoscale softening (an inverse Hall-Petch behavior) occurs. Nanoscale softening has been attributed to the occurrence of Coble creep, the absence of dislocation pile-ups at the ultrafine grain sizes, the operation of Coble creep with a threshold stress, or the application of composite models. Purpose. The present investigation was undertaken to examine whether a new deformation model [+] for nc-materials can provide a possible explanation for nanoscale softening. [+] F.A. Mohamed and M. Chauhan, Metallurgical and Materials Transactions A, (2006), 37a (12), [-] F.A. Mohamed, Metallurgical and Materials Transactions A, (2007), in press. Comparison with experimental trends. Experimental data reported for Cu along with the stress vs. curve that was constructed in Figure 1 are given in Figure 2. An examination of this figure shows that despite the presence of scatter, the agreement between prediction and experimental data is reasonably good in terms of the positions of the datum points in the softening regime and the predicted value of the critical grain size. It is most likely that the sources of the scatter are related to the variation of the grain size in samples, and the use of two different techniques, X-ray diffraction (XRD) and transmission electron microscopy (TEM), in measuring the grain size of the material.