International Journal of Fracture

, Volume 209, Issue 1–2, pp 203–222 | Cite as

Elastic vortices and thermally-driven cracks in brittle materials with peridynamics

  • Zhanping Xu
  • Guanfeng Zhang
  • Ziguang Chen
  • Florin BobaruEmail author
Original Paper


Instabilities in thermally-driven crack growth in thin glass plates have been observed in experiments that slowly immerse a hot, pre-notched glass slide into a cold bath. We show that a nonlocal model of thermomechanical brittle fracture with minimal input parameters can predict the entire phase diagram of fracture measured in experiments for the low immersion speed regime. Geometrical restrictions to crack growth commonly found in other approaches are absent here. We discuss a method for determining the appropriate size of the peridynamic horizon based on a data point around a separating line between crack-type zones in the experimental phase diagram. Once the nonlocal size is smaller than the length-scale introduced by the thermal gradient, the computational results show that no fracture criterion is needed beyond Griffith’s criterion to capture the observed instabilities. The combination of thermal gradients and competing contraction forces on the two sides of the crack are behind the observed crack path instabilities. Elastic (velocity) vortices of material points show how and why the cracks develop along the observed paths. Our results demonstrate that thermally-driven fracture in brittle materials can be predicted with accuracy. We anticipate that this model will lead to design protocols for controlled fracture in brittle materials relevant in materials science and advanced manufacturing.


Peridynamics Crack growth Thermally-driven cracks Thermoelasticity Elastic vortices Quenched glass 



This work has been supported in part by grants from the AFOSR MURI Center for Material Failure Prediction Through Peridynamics, Grant Number FA9550-14-1-0073 (Program Managers Drs. James Fillerup, Ali Sayir, David Stargel, and Fariba Fahroo), and from the ONR Award #N00014-16-1-2173 (Program Manager William Nickerson). This work was completed utilizing the Holland Computing Center of the University of Nebraska, which receives support from the Nebraska Research Initiative.

Supplementary material

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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringUniversity of Nebraska-LincolnLincolnUSA
  2. 2.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina

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