ÇENTİKLİ ELEMANLARIN KIRILMASININ BİR KONTROL ALGORİTMASI KULLANILARAK STABİLİZASYONU

Öz

Çatlak yayılımı, yük etkisine maruz yarı-gevrek malzemelerin davranışını belirleyen önemli bir mekanizmadır. Çatlak yayılımı çok aniden ortaya çıkabilmekte ve bu da bazı problemlerin analizinde sayısal dengesizliklere ve kusurlara neden olabilmektedir. Bu davranış kendini sayısal sonucun ıraksaması yani bütün yük yerdeğiştirme eğrisinin elde edilememesi olarak veya yük-yerdeğiştirme eğrisinde sıçrama şeklinde gösterir. Bu çalışmada çatlak yayılmasının bütün yük-yer değiştirme eğrisinin elde edilmesinde sayısal sorunlar yarattığı, snap-back (geri tepme) davranışında olduğu gibi, durumlar için bir kontrol algoritması uygulanması verilmiştir. Kontrol tekniğinin performansı tek çentikli levhaya uygulanan doğrudan çekme deneyi, çentikli kirişlerde üç noktalı eğilme deneyi ve iki çentikli levhaların karışık kırılma modu testi simüle edilerek gösterilmiştir. Bu çalışma, kontrol algoritmasının bu tür problemler için kararlı bir çözüm yolu üretebildiğini göstermiştir. Bu yöntem herhangi bir kullanıcı tanımlı alt rutine ihtiyaç duymadan mevcut ticari sonlu eleman kodlarında kolayca uygulanabilir.

Anahtar Kelimeler

• Kontrol algoritması
• Kırılma
• Sonlu Elemanlar Yöntemi
• Yarı-gevrek
• Snap-back (geri tepme).

STABILIZATION OF NOTCHED ELEMENTS' FRACTURE BY USING A CONTROL ALGORITHM

Öz

Crack propagation is a significant mechanism for quasi-brittle materials under applied loading. It can occur very suddenly and causes numerical instabilities and deficiencies in some problems. This behavior manifest itself as non-convergence solutions i.e. the inability to obtain the entire load-displacement curve or jumps in the load displacement curve. In this study, a control technique is implemented to obtain the whole load–displacement curve when crack propagation causes severe numerical instabilities such as snap-back behavior. The performance of the control technique was demonstrated by simulating uniaxial tension test of pre-notched plate, three-point bending test of a notched beam and mixed-mode test of a notched plate. This study shows that the control algorithm is able to produce a stable solution path for these kinds of problems. This method can be easily implemented in available commercial finite element codes without the need for any user defined subroutines.

Anahtar Kelimeler

• Control algorithm
• Fracture
• Finite Element Method
• Quasi-brittle
• Snap-back.

Kaynakça

1. Abaqus. (2011). Providence, RI, USA.: Dassault Systemes Simulia Corporation.
2. Ayhan, B., Lale, E. & Celik, N., 2021. Size effect analysis of concrete beams under bending using crack-band approach.. Journal of Polytechnic, pp. 1-1.
3. Biolzi, L., 1990. Mixed mode fracture in concrete beams. Engineering Fracture Mechanics, 35(1-3), pp. 187-193.
4. Biolzi, L., Cangiano, S., Tognon, G. & Carpinteri, A., 1989. Snap-back softening instability in high-strength concrete beams.. Materials and Structures, 22(6), pp. 429-436.
5. Bocca, P., Carpinteri, A. & Valente, S., 1990. Size effects in the mixed mode crack propagation: softening and snap-back analysis. Engineering Fracture Mechanics, 35(1-3), pp. 159-170.
6. Carpinteri, A., 1989. Post-peak and post-bifurcation analysis of cohesive crack propagation. Engineering Fracture Mechanics, 32(2), pp. 265-278.
7. Carpinteri, A., 1989. Softening and snap‐back instability in cohesive solids. International Journal for Numerical Methods in Engineering, 28(7), pp. 1521-1537.
8. Carpinteri, A. & Colombo, G., 1989. Numerical analysis of catastrophic softening behavior (snap-back instability). Computers & Structures, Volume 31, pp. 607-636.

9. Crisfield, M., 1981. A fast incremental/iterative solution procedure that handles "snap-through". Computational methods in nonlinear structural and solid mechanics, pp. 55-62.
10. Crisfield, M., 1983. An arc‐length method including line searches and accelerations. International journal for numerical methods in engineering, pp. 1269-1289.
11. De Borst, R., 1988. Bifurcations in finite element models with a non‐associated flow law. International Journal for Numerical and Analytical Methods in Geomechanics, 12(1), pp. 99-116.
12. De Borst, R., 1989. Numerical methods for bifurcation analysis in geomechanics. Ingenieur-Archiv., 59(2), pp. 160-174.
13. Hoover, C. G. et al., 2013. Comprehensive concrete fracture tests: Description and results. Engineering Fracture Mechanics, Volume 114, pp. 92-103.
14. Lale, E. & Gianluca, C., 2021. Symmetric high order microplane model for damage localization and size effect in quasi‐brittle materials. International Journal for Numerical and Analytical Methods in Geomechanics, 45(10), pp. 1458-1476.
15. Lee, J. & Fenves, G. L., 1998. Plastic-Damage Model for Cyclic Loading of Concrete Structures. Journal of Engineering Mechanics, Volume 124(8), pp. 892-900.
16. Lubliner, J., Oliver, J., Oller, S. & Oñate, E., 1989. A Plastic-Damage Model for Concrete. International Journal of Solids and Structures, Volume 25, pp. 299-329.
17. Martínez-Pañeda, E., del Busto, S. & Betegón, C., 2017. Non-local plasticity effects on notch fracture mechanics. Theoretical and Applied Fracture Mechanics, Volume 92, pp. 276-287.
18. Martínez-Pañeda, E. & Fleck, N. A., 2018. Crack growth resistance in metallic alloys: the role of isotropic versus kinematic hardening. Journal of Applied Mechanics, 85(11), p. 111002.
19. Nooru-Mohamed, M. B., 1993. Mixed-mode fracture of concrete: An experimental approach. The Netherlands: Delft University of Technology.
20. Ramm, E., 1981. Strategies for Tracing the Nonlinear Response Near Limit. Berlin: Springer.
21. Riks, E., 1972. The application of Newton’s method to the problem of elastic stability.. Journal of Applied Mechanics., pp. 1060-1066.
22. Riks, E., 1979. An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures, pp. 529-551.
23. Segurado, J. & LLorca, J., 2004. A new three-dimensional interface finite element to simulate fracture in composites. İnternational Journal of Solids and Stuctures, 41(11-12), pp. 2977-2993.
24. Tvergaard, V., 1976. Effect of thickness inhomogeneities in internally pressurized elastic-plastic spherical shells.. Journal of the Mechanics and Physics of Solids, 24(5), pp. 291-304.
25. Wempner, G. A., 1971. Discrete approximations related to non-linear theories of solids. International Journal of Solids and Structures, pp. 1581-1599.