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The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nano-devices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.