Simulation of the Griffith's Crack Using Own Method of Predicting the Crack Propagation

• Autorzy: Podgórski Jerzy , Gontarz Jakub

Identyfikatory

DOI

10.12913/22998624/141908

• Języki publikacji: EN

Abstrakty

EN

The paper presents the results of numerical simulation of brittle material fracture initiated by Griffith's crack situated at any angle with respect to the load direction. The simulations were performed with the Simulia Abaqus FEA system using the X-FEM method. The direction of the crack propagation was determined using the user's subroutine written in Fortran, implemented in the Abaqus system. The authors programmed several conditions for the direction of the fracture propagation: maximum principal stress criterion, Ottosen-Podgórski criterion, three criteria based on displacements around the crack tip, and the MTS criterion, which is based on stress intensity factors. For the purposes of this study, two shapes of the crack tip were analyzed - sharp and blunted. The relationship between the direction of the initial fracture and the direction of crack propagation was found. The simulations were carried out for the angles of the initial crack from 0° to 90°, every 10°. A theoretical analysis of the implemented criteria was also carried out and compared to numerical results. The influence of the shape of the crack tip on the simulation result was analyzed. It was shown that the simulation results closest to the theoretical results were obtained for the own implementation of the stress-based criteria. It has also been proven that the shape of the crack tip has little effect on the result if the finite element mesh is properly densified. However, the sharp crack has a disadvantage for small initial crack angles. The Author’s method of predicting the crack propagation has been proven correct and effective. This work is also the basis for the further development of the described method.

Słowa kluczowe

EN

fracture mechanics; X-FEM; Abaqus user subroutine; UDMGINI; griffith’s crack

PL

mechanika pęknięć; X-FEM; podprogramy użytkownika abaqus; UDMGINI; pęknięcie Griffitha

• Wydawca: Lublin University of Technology ; Polish Society of Ecological Engineering (PTIE), Branch of PTIE in Lublin
• Czasopismo: Advances in Science and Technology. Research Journal
• Rocznik: 2021
• Tom: Vol. 15, no 4
• Strony: 1--13
• Opis fizyczny: Bibliogr. 19 poz., fig.

Twórcy

autor

Podgórski Jerzy

• Faculty of Civil Engineering and Architecture, Lublin University of Technology, Poland

• https://orcid.org/0000-0003-4745-7705

autor

Gontarz Jakub

• Faculty of Civil Engineering and Architecture, Lublin University of Technology, Poland

Bibliografia

• 1. Gontarz J. & Podgórski J. Comparison of Various Criteria Determining the Direction of Crack Propa- gation Using the UDMGINI User Procedure Imple- mented in Abaqus. Materials. 2021;14(12):3382.
• 2. Moës N., Dolbow J., Belytschko T. A Finite Ele- ment Method for Crack Growth without Remesh- ing. International Journal for Numerical Methods in Engineering. 1999;46(1):131–150.
• 3. Xin H. & Veljkovic M. Fatigue Crack Initiation Pre- diction Using Phantom Nodes-Based Extended Finite Element Method for S355 and S690 Steel Grades. Engineering Fracture Mechanics. 2019;214:164–176.
• 4. Wang X., Guan Z., Du S., Han G., Li Z. An Accu- rate and Easy to Implement Method for Predicting Matrix Crack and Plasticity of Composites with an Efficient Search Algorithm for LaRC05 Criterion. Composites Part A: Applied Science and Manufac- turing. 2020;131:105808.
• 5. Zhao L., Wang Y., Zhang J., Gong Y., Hu N., Li N. XFEM-Based Model for Simulating Zigzag Delami- nation Growth in Laminated Composites under Mode I Loading. Composite Structures. 2017;160:1155–1162.
• 6. van Dongen B., van Oostrum A., Zarouchas D. A Blended Continuum Damage and Fracture Me- chanics Method for Progressive Damage Analysis of Composite Structures Using XFEM. Composite Structures. 2018;184:512–522.
• 7. Elruby A.Y. & Nakhla S. Strain Energy Density Based Damage Initiation in Heavily Cross-Linked Epoxy Using XFEM. Theoretical and Applied Fracture Mechanics. 2019;103:1–13.
• 8. Yin H., Qi H.J., Fan F., Zhu T., Wang B., Wei Y. Griffith Criterion for Brittle Fracture in Graphene. Nano Letters. 2015;15(3):1918–1924.
• 9. Dewapriya M.A.N. & Meguid S.A. Atomistic Mod- eling of Out-of-Plane Deformation of a Propagat- ing Griffith Crack in Graphene. Acta Mechanica. 2017;228(9):3063–3075.
• 10. Wang S., Tan F., You M., Jiao Y.Y., Tu F. Discrete Element Modeling of Crack Initiation Stress of Marble Based on Griffith’s Strength Theory. Ad - vances in Civil Engineering. 2020;2020.
• 11. Erdogan F. & Sih G.C. On the Crack Extension in Plates under Plane Loading and Transverse Shear. Journal of Basic Engineering. 1963;85(4):519–525.
• 12. Williams J.G., Ewing P.D. Fracture under Complex Stress — The Angled Crack Problem. International Journal of Fracture. 1984;26(4):346–351.
• 13. Anderson T.L. Fracture Mechanics. Fundamentals and Applications, 3-Re Ed. CRC Press: 2005.
• 14. Podgórski J. General Failure Criterion for Isotropic Media. Journ Eng Mech ASCE. 1985;111(2):188–201.
• 15. Podgórski J. Criterion for Angle Prediction for the Crack in Materials with Random Structure. Me- chanics and Control. 2011;30(4):229–233.
• 16. Podgórski J. The Criterion for Determining the Di- rection of Crack Propagation in a Random Pattern Composites. Meccanica. 2017;52(8):1923–1934.
• 17. Hussain M.A., Pu S.L., Underwood J.H. Strain Energy Release Rate for a Crack under Combined Mode I and Mode II. American Society for Testing & Materials (STP). 1974;560:2–28.
• 18. Wu C.H. Fracture under Combined Loads by Maximum-Energy-Release-Rate Criterion. Jour- nal of Applied Mechanics, Transactions ASME. 1978;45(3):553–558.
• 19. Zhen-zhong Du. eXtended Finite Element Method (XFEM) in Abaqus, Dassault Systemes, https:// www.simulia.com/download/rum11/UK/Ad- vanced-XFEM-Analysis.pdf, accessed August 2021

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).