## __2016-Sustainable Industrial Processing Summit__

SIPS 2016 Volume 7: Yang Intl. Symp. / Multiscale Material Mechanics

Editors: | Kongoli F, Aifantis E, Wang H, Zhu T |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2016 |

Pages: | 190 pages |

ISBN: | 978-1-987820-48-5 |

ISSN: | 2291-1227 (**Metals and Materials Processing in a Clean Environment Series**) |

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## Experimentally Derived Constitutive Laws Governing Dynamic Fracture Propagation

**kaiwen
xia**^{1};

^{1}UNIVERSITY OF TORONTO, Toronto, Canada;

**Type of Paper:** Regular

**Id Paper:** 475

**Topic:** 1## Abstract:

By now fracture mechanics has been considered as a mature branch of mechanics. However, there are still many outstanding questions in this branch that have not yet been answered. One such question for dynamic fracture propagation is the relation between fracture toughness and fracture velocity. Theoretically, there are two models proposed for solving dynamic fracture propagation problems: steady-state model and self-similar model. Using either model, the three independent variables in the mathematical formulation can be reduced into two. However, constant fracture velocity assumption has to be made in both models. To verify these theoretical models, researchers have been conducting controlled laboratory dynamic fracture experiments. Earlier laboratory experiments by Ravi-Chandar and Knauss showed that there is no clear relation between the fracture toughness and fracture velocity. Later Shukla et al. showed similar results. Another set of classical experiment by Rosakis showed the observation of limiting fracture velocity and suggested a relation between the toughness and fracture velocity, which has been adopted by the fracture textbook by Anderson. Spontaneous fracture tests by Xia et al. observed constant fracture velocity that is independent of fracture toughness, supporting the self-similar fracture propagation model. Recent dynamic fracture tests by Xia on brittle solids showed similar dependence of fracture toughness on the fracture velocity as that observed by Rosakis. Based on the available experimental data, two constitutive models governing the dynamic fracture propagation is proposed: 1. Self-similar model where fracture velocity is independent of fracture toughness and 2. Limiting fracture velocity model where the fracture toughness approaches infinite as the fracture velocity approaches the limiting velocity. The conditions where these models are applicable are discussed.

## Keywords:

Dynamics; Materials; Mechanics; Rocks; Solids; Technology;

## Cite this article as:

xia k. Experimentally Derived Constitutive Laws Governing Dynamic Fracture Propagation. In: Kongoli F, Aifantis E, Wang H, Zhu T, editors. Sustainable Industrial Processing Summit SIPS 2016 Volume 7: Yang Intl. Symp. / Multiscale Material Mechanics. Volume 7. Montreal(Canada): FLOGEN Star Outreach. 2016. p. 161-162.