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Speed Effects on Moving Cracks in Nonlinear/Ductile materials Open Access


Other title
Moving Cracks
Ductile fracture
Speed Effect
Type of item
Degree grantor
University of Alberta
Author or creator
Wu, Jian
Supervisor and department
Ru, Chongqing (Department of Mechanical Engineering)
Examining committee member and department
Ru, Chongqing (Department of Mechanical Engineering)
Wang, Xiaodong (Department of Mechanical Engineering)
Chen, Zengtao (Department of Mechanical Engineering)
Schiavnone, Peter (Department of Mechanical Engineering)
Chen, Weixing (Department of Chemical and Materials Engineering)
Department of Mechanical Engineering

Date accepted
Graduation date
Doctor of Philosophy
Degree level
Speed effects on moving cracks in ductile or nonlinear materials are studied with newly developed theoretical models in the present thesis. Speed-dependent stress field, traction distribution and fracture energy are discussed in detail in four chapters. 1) An asymptotic analysis near the tip of a steady-state moving crack in a compressible hyperelastic material is given based on a finite plane strain model. The crack tip deformation and stress fields are derived up to the third order which meets the strict positivity of Jacobian determinant in the vicinity of the moving crack tip. Comparison with the experimental data shows that the crack-face profile and the energy release rate predicted by the present model are in reasonable agreement with experiments and several recent nonlinear elastic models. In addition, the crack branching angle predicted by the present model also agrees well with some known experimental data. 2) Steady-state moving crack under mode-I loading is studied with a modified cohesive zone model which addresses speed-dependent role of the normal stress parallel to the crack axis and the non-uniformity of traction force in cohesive zone. Unlike the classical Dugdale model which predicts independence of the cohesive zone length on crack speed, the present modified model predicts that the cohesive zone length strongly depends on crack speed. Comparison with some known experimental data suggests that the present modified model has the potential to capture the speed effects on moving cracks in ductile materials especially at high crack speed. 3) The modified cohesive zone model is then applied to a self-similar high-speed expanding crack problem. Numerical results show that the normal stress parallel to the crack face increases with increasing crack speed and can be even larger than the normal traction in the cohesive zone, which justifies the necessity of including the normal stress parallel to the crack faces in the yielding condition at high crack speed. Strain hardening effect is also examined based on a non-uniform traction distribution given by a polynomial whose coefficients are to be determined as part of the solution. 4) A simple mass-spring model is presented to study inertia effect of cohesive zone for a Yoffe-type mode-I steady-state moving crack of constant length. Traction distribution surrounding the cohesive zone and fracture energy at high crack speed are solved numerically by a proposed numerical method. Results show that fracture energy predicted by the present model increases significantly at high crack speed, which defines a limiting crack speed above that fracture energy tends to infinity. Reasonable agreement with some known experimental data suggests that the present model has the potential to catch inertia effect of cohesive zone of a high-speed moving crack which has not been considered by existing cohesive zone models. The theoretical models and numerical results achieved in this thesis contribute new ideas and insights into the study of high-speed dynamic fracture of nonlinear and ductile materials, and some results predicted by the present models provide plausible explanations for a few important phenomena of moving cracks at high crack speed which have not been well explained by the existing models.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
J. Wu and C.Q. Ru, Speed-dependent tip fields of a moving crack in a hyperelastic material, Mathematic and Mechanics of Solids, 2013 (18):285-300.J. Wu and C.Q. Ru, A speed-dependent cohesive zone model for moving cracks with non-uniform traction force, Engineering Fracture Mechanics, 2014(117):12-27.J. Wu and C.Q. Ru, A modified cohesive zone model for a high-speed expanding crack, Fatigue & Fracture of Engineering Materials & Structures, 2014 (online available).

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