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Title: A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains

Abstract

Summary The discrete crack mechanics (DCM) method is a dislocation‐based crack modeling technique where cracks are constructed using Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite‐medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi‐static growth problems. Convergence and accuracy of the DCM method are verified with two‐ and three‐dimensional problems with well‐known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation ismore » accommodated.« less

Authors:
ORCiD logo [1];  [1];  [2];  [1]
  1. Univ. of California, Los Angeles, CA (United States)
  2. Alberta Innovates Technology Futures, Edmonton, AB (Canada)
Publication Date:
Research Org.:
Univ. of California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)
OSTI Identifier:
1612979
Alternate Identifier(s):
OSTI ID: 1472170
Grant/Contract Number:  
SC0018410; FA9550-16-1-0444; 1563427
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 117; Journal Issue: 1; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Engineering; Mathematics

Citation Formats

Sheng, A., Ghoniem, N. M., Crosby, T., and Po, G. A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains. United States: N. p., 2018. Web. doi:10.1002/nme.5946.
Sheng, A., Ghoniem, N. M., Crosby, T., & Po, G. A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains. United States. https://doi.org/10.1002/nme.5946
Sheng, A., Ghoniem, N. M., Crosby, T., and Po, G. Fri . "A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains". United States. https://doi.org/10.1002/nme.5946. https://www.osti.gov/servlets/purl/1612979.
@article{osti_1612979,
title = {A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains},
author = {Sheng, A. and Ghoniem, N. M. and Crosby, T. and Po, G.},
abstractNote = {Summary The discrete crack mechanics (DCM) method is a dislocation‐based crack modeling technique where cracks are constructed using Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite‐medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi‐static growth problems. Convergence and accuracy of the DCM method are verified with two‐ and three‐dimensional problems with well‐known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated.},
doi = {10.1002/nme.5946},
journal = {International Journal for Numerical Methods in Engineering},
number = 1,
volume = 117,
place = {United States},
year = {Fri Sep 21 00:00:00 EDT 2018},
month = {Fri Sep 21 00:00:00 EDT 2018}
}

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