Abstract
Hall–Petch strengthening has been widely used in materials science, but its mechanism is not very clear yet, some inverse phenomena were observed. This paper gives a fractal approach to explanation of the Hall–Petch effect, revealing the value of the fractal dimensions is the key factor: when it is larger than one, the Hall–Petch effect is predicted; while when it is smaller than one, an inverse Hall–Petch relationship is obtained. The fractal theory can also explain the nano-effort (size effort) in nanotechnology and spider silk’s strength.
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