Modelling the transition from strengthening to softening due to grain boundaries

Published data on pure Cu at or close to its saturation state of deformation suggests a Hall–Petch relation of flow stress at ambient temperature in the range of grain sizes 1  μ m  > d > 10  nm [W. Blum, Y.J. Li, J. Chen, X.H. Zeng, K. Lu, Int. J. Mater. Res. 97 (2006) 1661–1666] while for elevated temperatures ultrafine-grained Cu produced by severe plastic deformation exhibits softening relative to conventional grain sizes d > 10 μ m [Y.J. Li, X.H. Zeng, W. Blum, Acta Mater. 52 (2004) 5009–5018]. Presuming grain boundaries as impenetrable dislocation obstacles, these observations are rationalized by (i) a reduction of the mean slipped area and corresponding shift in the main location for dislocation storage from grain interior to boundaries with decreasing d; (ii) thermally activated dissolution of dislocation dipoles occurring faster at boundaries than within the grain interior owing to different coefficients of diffusion. A simple statistical dislocation model is derived from these ideas and compares to experimental results in semi-quantitative agreement.