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Conference Papers Year : 2023

Statistical mechanics of fracture phenomena and brittle-to-ductile transitions


The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctua-tions, especially in micro- and nano-devices as well as in rubberlike and biological materials. However,temperature effects, in particular on the brittle thermo-activated fracture and on the brittle-to-ductiletransition, 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 fractureand brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable non-linear elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion [1], ultimately describingthe fracture as a genuine phase transition. With regard to the brittle-to-ductile transition [2,3,4], we obtaina complex critical scenario characterized by a threshold temperature between the two fracture regimes,an upper and a lower yield strength, and a critical temperature corresponding to the complete break-down. The proposed fracture models are implemented by means of the spin variable approach, useful todeal with arbitrarily non-convex potential energies [5]. This method has been largely applied to severalsituations including the physics of muscles [6], the folding of macromolecules [7,8,9], the adhesion orpeeling processes [10,11], and the phase transformations in solids [12]. In the context of fracture, it allowsto distinguish between the intact, softened and broken states of the discrete elements and therefore todirectly follow the propagation of cracks in given materials and structures.
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hal-03969496 , version 1 (02-03-2023)


  • HAL Id : hal-03969496 , version 1


Andrea Cannizzo, G. Florio, G. Puglisi, Stefano Giordano. Statistical mechanics of fracture phenomena and brittle-to-ductile transitions. 26emes Rencontres du non-linéaire, RNL 2023, Mar 2023, Paris, France. ⟨hal-03969496⟩
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