Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520, Institut d'Électronique de Microélectronique et de Nanotechnologie (IEMN), F-59000 Lille, France.
Politecnico di Bari, (DMMM) Dipartimento di Meccanica, Matematica e Management, Via Re David 200, I-70125 Bari, Italy.
Phys Rev E. 2023 Mar;107(3-2):035001. doi: 10.1103/PhysRevE.107.035001.
The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nanodevices 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.
脆性和韧性材料的断裂行为会受到热涨落的强烈影响，这在微纳器件以及橡胶状和生物材料中尤为明显。然而，温度效应，尤其是对脆性到韧性转变的影响，仍需要更深入的理论研究。为此，我们提出了一种基于平衡统计力学的理论，该理论能够描述由易碎元素组成的晶格的典型离散系统中与温度相关的脆性断裂和脆性到韧性转变。对于脆性行为，我们得到了温度相关的断裂应力和应变的封闭形式表达式，这些表达式代表了广义的格里菲斯准则，最终将断裂描述为一种真正的相变。关于脆性到韧性的转变，我们得到了一个复杂的临界场景，该场景具有两个断裂模式（脆性和韧性）之间的阈值温度、上屈服强度和下屈服强度以及与完全破坏对应的临界温度。为了展示所提出的模型在描述小尺度热断裂行为方面的有效性，我们成功地将理论结果与 Si 和 GaN 纳米线的分子动力学模拟进行了比较。
