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Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

Javier Bonet, Antonio Gil Orcid Logo

International Journal of Fracture, Volume: 229, Pages: 55 - 75

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1007/s10704-021-00541-y

Abstract

This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous so...

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Published in: International Journal of Fracture
ISSN: 0376-9429 1573-2673
Published: Springer Science and Business Media LLC 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56695
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spelling 2021-11-10T11:27:12.2286234 v2 56695 2021-04-19 Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2021-04-19 CIVL This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory. Journal Article International Journal of Fracture 229 55 75 Springer Science and Business Media LLC 0376-9429 1573-2673 Dynamic crack propagation; Supersonic crack speed; Linear elastodynamics; Shocks; Hyperbolic equations 11 5 2021 2021-05-11 10.1007/s10704-021-00541-y https://link.springer.com/article/10.1007/s10704-021-00541-y#Abs1 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2021-11-10T11:27:12.2286234 2021-04-19T15:21:36.3290776 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Javier Bonet 1 Antonio Gil 0000-0001-7753-1414 2 56695__19956__7a2a5bd5a7134bc191a64d339157e517.pdf 56695.pdf 2021-05-21T09:28:30.6562482 Output 1648338 application/pdf Version of Record true © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License true eng https://creativecommons.org/licenses/by/4.0/
title Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
spellingShingle Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
Antonio Gil
title_short Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
title_full Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
title_fullStr Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
title_full_unstemmed Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
title_sort Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 Javier Bonet
Antonio Gil
format Journal article
container_title International Journal of Fracture
container_volume 229
container_start_page 55
publishDate 2021
institution Swansea University
issn 0376-9429
1573-2673
doi_str_mv 10.1007/s10704-021-00541-y
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.
published_date 2021-05-11T04:11:50Z
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score 11.017797

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