Limit analyses for surface crack instantaneous propagation angles in elastic hertzian field

Xin Sun, Mohammad A. Khaleel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents the limit analyses of instantaneous crack propagation angle in the classical linear-elastic Hertzian field. The formation and propagation of Hertzian cone crack have been studied extensively in the open literature. Many experiments have been carried out on soda-lime glass under static loading. The observed final Hertzian cone angle is usually around 22°, and it tends to increase with increasing indentation velocity, The goal of this paper is to use the crack tip stress field derived in linear elastic fracture mechanics (LEFM) to bound the instantaneous surface ring crack extension angles in the Hertzian field. The upper and lower bounds for the instantaneous crack extension angle are expressed in terms of the ratios of the mode I and mode II stress intensity factors at the crack tip field. It is shown that under a pure mode I dominant stress field, instantaneous crack growth would follow the original surface crack direction; and under a perfect mode II stress field, the instantaneous crack extension angle has a limiting angle of 19.5°. The actual instantaneous crack extension angle will fall between these two limit states depending on the ratio of KI/KII at the crack tip.

Original languageEnglish
Title of host publicationCeramic Engineering and Science Proceedings
Pages93-102
Number of pages10
Volume28
Edition5
Publication statusPublished - 23 Dec 2008
Externally publishedYes
Event31st International Conference on Advanced Ceramics and Composites - Daytona Beach, FL, United States
Duration: 21 Jan 200726 Jan 2007

Other

Other31st International Conference on Advanced Ceramics and Composites
CountryUnited States
CityDaytona Beach, FL
Period21/1/0726/1/07

Fingerprint

Crack propagation
Cracks
Crack tips
Cones
Indentation
Fracture mechanics
Lime
Stress intensity factors
Glass
Experiments

ASJC Scopus subject areas

  • Ceramics and Composites
  • Materials Chemistry

Cite this

Sun, X., & Khaleel, M. A. (2008). Limit analyses for surface crack instantaneous propagation angles in elastic hertzian field. In Ceramic Engineering and Science Proceedings (5 ed., Vol. 28, pp. 93-102)

Limit analyses for surface crack instantaneous propagation angles in elastic hertzian field. / Sun, Xin; Khaleel, Mohammad A.

Ceramic Engineering and Science Proceedings. Vol. 28 5. ed. 2008. p. 93-102.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sun, X & Khaleel, MA 2008, Limit analyses for surface crack instantaneous propagation angles in elastic hertzian field. in Ceramic Engineering and Science Proceedings. 5 edn, vol. 28, pp. 93-102, 31st International Conference on Advanced Ceramics and Composites, Daytona Beach, FL, United States, 21/1/07.
Sun X, Khaleel MA. Limit analyses for surface crack instantaneous propagation angles in elastic hertzian field. In Ceramic Engineering and Science Proceedings. 5 ed. Vol. 28. 2008. p. 93-102
Sun, Xin ; Khaleel, Mohammad A. / Limit analyses for surface crack instantaneous propagation angles in elastic hertzian field. Ceramic Engineering and Science Proceedings. Vol. 28 5. ed. 2008. pp. 93-102
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