The Hall-Petch relation describes the relationship between the yield strength and grain size of metals. Metals exhibit a linear increment in their yield strength, depending on the inverse square root of the grain size. The knowledge of the effects of the grain size on the yield strength of the metals such as aluminum is a necessity in material selection for various applications. The grain sizes in most cases are determined by the different material processing technologies available. Severe plastic deformation (SPD), which is one of the effective methods to produce fine microstructures, is capable of giving a grain size smaller than 5 μm. Many researchers have seen the SPD processing technique as being capable of producing high performance metals with significantly increased strength.
Research conducted by Dr. Takayuki Koizumi and Professor Mitsutoshi Kuroda from Yamagata University in Japan focused on investigating the effects of the grain size on the yield strength of aluminum. They used two groups of samples. The samples in the first group contained successively refined grains produced by equal-channel angular pressing (ECAP). The samples in the second group were first subjected to 8 ECAP passes and then they were annealed step by step to coarsen the grains. The research work is currently published in the journal, Materials Science and Engineering A.
Briefly, the authors commenced their work by performing tensile tests on all the samples to be used in the experiments. The dislocation-related strengthening was evaluated using the Taylor equations after using the Williamson-Hall method to obtain the dislocation densities. On the other hand, grain size-related strengthening was determined by subtracting the friction stress and dislocation-related strengthening from the observed yield strength. Eventually, a comparison of the amount of grain size-related strengthening in the samples and the conventional Hall-Petch relation was made.
From the conducted experiments, the authors observed consistency in the amount of grain size-related strengthening in the samples having grains refined by ECAP and the conventional Hall-Petch relation. Furthermore, an extra grain size-related strengthening was observed clearly in the annealed samples with the grain sizes below 10 μm.
Although their experiments were performed using pure aluminum only, the experimental data for the dislocation densities and yield strength of aluminum alloy given in the literature showed that alloys undergo smaller grain size-related strengthening effect as compare to pure metals. Additionally, the refining and coarsening approaches for the grains, equal grain sizes give different grain size-related strengthening relative to the yield strength. Several factors were put forward to explain the difference observed in the grain size-related strengthening. The primary reason was however seen to be the shifts in the grain boundary characteristics as a result of the annealing process.
Koizumi, T., & Kuroda, M. (2018). Grain size effects in aluminum processed by severe plastic deformation. Materials Science and Engineering: A, 710, 300-308.Go To Materials Science and Engineering