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Phase diagram of brittle fracture in the semi-grand-canonical ensemble

T. Mulla1, S. Moeini1, K. Ioannidou1,2,3, R. J.-M. Pellenq1,2,4, and F.-J. Ulm1,2,*

  • 1Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2MIT-CNRS-AMU Joint Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3Laboratoire de Mcanique et Gnie Civil, CNRS Universit de Montpellier, 34090 Montpellier, France
  • 4Department of Physics, Georgetown University, Washington DC 20057, USA

  • *Corresponding author: ulm@mit.edu
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Phys. Rev. E 103, 013003 – Published 13 January, 2021

DOI: https://doi.org/10.1103/PhysRevE.103.013003

Abstract

We present a simulation method to assess the quasistatic fracture resistance of materials. Set within a semi-grand-canonical Monte Carlo (SGCMC) simulation environment, an auxiliary field—the bond rupture potential—is introduced to generate a sufficiently large number of possible microstates in the semi-grand-canonical ensemble, and associated energy and bond fluctuations. The SGCMC approach permits identifying the full phase diagram of brittle fracture for harmonic and nonharmonic bond potentials, analogous to the gas-liquid phase diagram, with the equivalent of a liquidus line ending in a critical point. The phase diagram delineates a solid phase, a fractured phase, and a gas phase, and provides clear evidence of a first-order phase transition intrinsic to fracture. Moreover, energy and bond fluctuations generated with the SGCMC approach permit determination of the maximum energy dissipation associated with bond rupture, and hence of the fracture resistance of a widespread range of materials that can be described by bond potentials.

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Outline

Information

Phys. Rev. E 103, 013003– Published 13 January, 2021
  • Received 1 June 2020
  • Revised 2 October 2020
  • Accepted 21 December 2020
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