Finite Element Analysis of a Dynamic Linear Crack Problem
Abstract
This work investigates the problem of a linear crack in the middle of a uniform elastic medium under normal tension-compression loading. The direct Finite Element numerical procedure is used to solve the fractured media deformation problem, which also includes an examination of the dynamic field variables of the problem. A Finite Element algorithm that satisfies the unilateral Signorini contact constraint is also described for solving the crack faces' contact interaction, as well as how this affects the qualitative and quantitative numerical results while calculating the dynamic fracture parameter.
Downloads
References
A.A. Griffith, “The phenomena of rupture and flow in solids,” Philosophical Transactions of the Royal Society of London, Series A, 221, 163-198 (1921).
T.L. Anderson, Fracture Mechanics. Fundamentals and Applications,” 2nd edition, (CRC Press, Boca Raton, 1995).
O.V. Menshykov, and I.A. Guz, “Effect of Contact Interaction of the Crack Faces for a Crack under Harmonic Loading,” International Applied Mechanics, 43, 809-815 (2007). https://doi.org/10.1007/s10778-007-0082-y
A.N. Guz, and V.V. Zozulya, “Contact interaction between crack edges under a dynamic load,” Int. Appl. Mech,” 28, 407–414 (1992). https://doi.org/10.1007/BF00847122
L. Zhang, Z. Zhang, Y. Chen, B. Dai, and B. Wang, “Crack development and damage patterns under combined dynamic-static loading of parallel double fractured rocks based on DIC technique,” Acta Geotech, 18, 877–901 (2023). https://doi.org/10.1007/s11440-022-01595-5
S. Abu-Qbeitah, M. Jabareen, and K. Y. Volokh, “Dynamic Versus Quasi-Static Analysis of Crack Propagation in Soft Materials,” ASME. J. Appl. Mech. 89, 121008 (2022). https://doi.org/10.1115/1.4055670
P. Wriggers, “Finite Element Algorithms for Contact Problems. Archives of Computational Methods in Engineering,” State-of-the-art reviews, 2, 1–49 (1995). https://doi.org/10.1007/BF02736195
M. Schäfer, Computational Engineering – Introduction to Numerical Methods, (Springer Berlin Heidelberg, New York, 2006).
K.H. Huebner, D.L. Dewhirst, D.E. Smith, and J.G. Byron, The Finite Element for Engineers, (Wiley-interscience, New York, 2001).
Q. Han, Y. Wang, Y. Yin, and D. Wang, “Determination of stress intensity factor for mode I fatigue crack based on finite element analysis,” Engineering Fracture Mechanics, 138, 118–126 (2015). https://doi.org/10.1016/j.engfracmech.2015.02.019
O.V. Menshykov, M.V. Menshykova, I.A. Guz, and V.A. Mikucka, “Contact Problems for Interface Cracks under Harmonic Loading,” Appl. Math. 10, 127–128 (2010). https://doi.org/10.1002/pamm.201010056
S.M. Walley, and J.E. Field, Elastic Wave Propagation in Materials, (Cavendish Laboratory, Cambridge, UK, 2016). https://doi.org/10.1016/B978-0-12-803581-8.02945-3
O.V. Menshykov, V.A. Menshykov, and I.A. Guz, “The contact problem for an open penny-shaped crack under normally incident tension-compression wave,” Engineering Fracture Mechanic, 75, 1114–1126 (2008). https://doi.org/10.1016/j.engfracmech.2007.04.017
M.V. Menshykova, O.V. Menshykov, and I.A. Guz, “Modelling crack closure for an interface crack under harmonic loading,” Int. J. Fracture, 165, 127–134 (2010). https://doi.org/10.1007/s10704-010-9492-7
M.V. Menshykova, O.V. Menshykov, V.A. Mikucka, and I.A. Guz, “Interface cracks with initial opening under harmonic loading,” Composites Science and Technology, 72, 1057-1063 (2012). https://doi.org/10.1016/j.compscitech.2011.10.010
B.E. Usibe, and O.V. Menshykov, “Evaluation of Dynamic Stress Intensity Factor of Griffith Crack Using the Finite Element Method,” International Journal of Mechanics and Applications, 10, 1-10 (2021). https://doi.org/10.5923/j.mechanics.20211001.01
S.K. Chan, L.S. Tuba, and W.K. Wilson, “On the Finite Element Method in Linear Fracture Mechanics,” Engineering Fracture Mechanics, 2, 1-17 (1970). https://doi.org/10.1016/0013-7944(70)90026-3
B. Zafošnik, and G. Fajdiga, “Determining Stress Intensity Factor KI with Extrapolation Method,” Technical Gazette, 23, 1673 1678 (2016). http://dx.doi.org/10.17559/TV-20150424160509
ABAQUS/CAE User's Manual, Version 6.14-1
C. Obbink-Huizer, Modelling a crack using Abaqus: Simuleon FEA, Accessed 16 December 2022. https://info.simuleon.com/blog/modelling-a-crack-using-abaqus
D. Gross, and T. Seelig, Fracture Mechanics with an Introduction to Micromechanics, (Springer Heidelberg Dordrecht, New York, 2011).
A.N. Guz, and V.V. Zozulya, “Elastodynamic unilateral contact problems with friction for bodies with cracks,” International Applied Mechanics, 38, 895–932 (2002). https://doi.org/10.1023/A:1021266113662
O.V. Menshykov, M.V. Menshykova, and I.A. Guz, “3-D elastodynamic contact problem for an interface crack under harmonic loading,” Engineering Fracture Mechanics, 80, 52– 59 (2012). https://doi.org/10.1016/j.engfracmech.2010.12.010
O.V. Menshykov, M.V. Menshykova, and I.A. Guz, “Effects of crack closure and friction for linear crack under normal impact,” Eng. Anal. Bound. Elem. 115, 1–9 (2020). https://doi.org/10.1016/j.enganabound.2020.02.013
O.V. Menshykov, V.A. Menshykov, and I.A. Guz, “The effect of frequency in the problem of interface crack under harmonic loading,” Int. J. Fract. 146, 197-202 (2007). https://doi.org/10.1007/s10704-007-9157-3
V.A. Mikucka, O.V. Menshykov, and M.V. Menshykova, “Elastodynamic Contact Problems for Interface Cracks under Harmonic Loading,” Proceedings in Applied Mathematics and Mechanics, 11, 165-166 (2011). https://doi.org/10.1002/pamm.201110074
Copyright (c) 2024 Brian E. Usibe, Williams E. Azogor, Prince C. Iwuji, Joseph Amajama, Nkoyo A. Nkang, Oruk O. Egbai, Alexander I. Ikeuba
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
