Eğilme Altındaki Beton Kirişlerin Çatlak-Bant Genişliği Yaklaşımı ile Boyut Etkisinin Analizi

Year 2022, , 605 - 613, 01.06.2022

Bahar Ayhan , Erol Lale Nilay Çelik

https://doi.org/10.2339/politeknik.762634

Cited By: 1

Abstract

Bu araştırmada, yarı gevrek malzemelerdeki boyut etkisinin hasar-plastisite modeli kullanılarak çözümlemesi sunulmuştur. Çentikli ve çentiksiz üç noktalı eğilme deneyleri üç boyutlu (3D) sonlu eleman modeli ile analiz edilmiştir. Bu amaçla, Abaqus yazılımı kullanılmıştır. Beton elemanların gerçekçi bir şekilde analizinde, özellikle boyut etkisinin dikkate alınmasında, çatlak bant genişliği yaklaşımı uygulanmış, hasar-plastisite modelinin etkinliği araştırılmıştır. Kırılma mekaniği parametrelerinin bulunması amacıyla, açıklık-yükseklik oranı, L/D=2.176, olan üç noktalı eğilme deneyine ait 2D sonlu eleman modeli, her bir çentik derinliği için oluşturulmuştur. Bu modelde, kiriş 8-düğüm noktalı dörtgen düzlem gerilme elemanları ile modellenmiş ve çatlak uç noktasındaki tekillik “quarter point” tekniği kullanılarak oluşturulmuştur. Bu analizler sonucunda, J-integral bulunmuş ve enerji salınım oranı hesaplanmıştır. Elde edilen sonuçlar literatürde verilmiş olan deney sonuçları ve ayrıca Bazant’ ın boyut etkisi eğrisi ile karşılaştırılmıştır. Bu çalışma, çatlak bant genişliği yaklaşımı uygulanmış hasar-plastisite modelinin, beton gibi malzemelerde, boyut etkisini yakalamak için uygun olduğunu göstermiştir.

Keywords

sonlu eleman modeli, Çatlak analizi, ağ boyutu bağımsızlığı, çentik boyu

Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach

Abstract

Analysis of size effect phenomenon in quasi-brittle materials is presented in this research using damage plasticity model. Notched and unnotched specimens under three-point bending fracture test are analyzed by setting a 3D finite element model. For this purpose, Abaqus software is utilized. Concrete damage-plasticity model (CDPM) enhanced with crack band approach is used to conduct simulations of concrete specimens. The efficiency of this model is investigated especially for size effect phenomenon. 2D finite element model is setup for three-point bending beams in order to estimate fracture parameters for specific span to depth ratio, L/D=2.176. The simulations are conducted for each different notch depths. 8-node quadratic plane stress elements are used to define 2D domain and singularity field at the notch tip is modeled using quarter point technique. Energy release rate is calculated using J-integral approach. Obtained results are compared to experimental ones reported in literature and are also compared to the Bazant’s size effect law. This study shows that concrete damage-plasticity model enhanced with crack band approach can capture size effect observed in concrete-like materials’ fracture. 

Keywords

Size effect, crack band approach, mesh size independency, notch length, finite element analysis

References

• [1] Hillerborg A., Modeer M. and Phtersson P.E., Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements, Cement and Concrete Research, 6(6): 773-781, (1976).
• [2] Bažant Z.P. and Pang S.D., Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture, Journal of the Mechanics and Physics of Solids, 55(1): 91-131, (2007).
• [3] Ballarini R., Pisano G. and Royer-Carfagni G., The Lower Bound for Glass Strength and Its Interpretation with Generalized Weibull Statistics for Structural Applications, Journal of Engineering Mechanics, 142(12): (2016).
• [4] Gonzalez K., Xue J., Chu A. and Kirane K., Fracture and Energetic Strength Scaling of Soft, Brittle, and Weakly Nonlinear Elastomers, Journal of Applied Mechanics, 87:, (2020).
• [5] Bažant Z.P. and Kazemi M.T., Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete, International Journal of Fracture, 44: 111-131, (1990).
• [6] Bazant Z.P. and Oh B.H., Crack band theory for fracture of concrete, Matériaux et Constructions, 16: 155-177, (1983).
• [7] Jirásek M. ve Bauer M., Numerical aspects of the crack band approach, Computers and Structures, 110-111: 60-78, (2012).
• [8] Barbat G.B., Cervera M., Chiumenti M. and Espinoza E., Structural size effect: Experimental, theoretical and accurate computational assessment, Engineering Structures, 213: , 110555, (2020).
• [9] Havlásek P., Grassl P. and Jirásek M., Analysis of size effect on strength of quasi-brittle materials using integral-type nonlocal models, Engineering Fracture Mechanics, 157: 72-85, (2016).
• [10] Grégoire D.,  Rojas‐Solano L.B. and Pijaudier‐Cabot G., Failure and size effect for notched and unnotched concrete beams, Int. J. Numer. Anal. Meth. Geomech., 37: 1434-1452, (2013).
• [11] Cusatis G. and Zhou X., High-order microplane theory for quasi-brittle materials with multiple characteristic lengths., Journal of Engineering Mechanics, 140(7): 04014046, (2014).
• [12] Lale E., Xinwei Z. and Cusatis G., Isogeometric Implementation of High-Order Microplane Model for the Simulation of High-Order Elasticity, Softening, and Localization, Journal of Applied Mechanics, 84(1): 011005, 2017.
• [13] Simulia, ABAQUS User’s Manual, Providence, RI: Dassault Systemes Simulia Corp., (2017).
• [14] Lubliner J., Oliver J., Oller S. and Oñate E., A Plastic-Damage Model for Concrete, International Journal of Solids and Structures, 25: 299-329, (1989).
• [15] Lee J. and Fenves G.L., Plastic-Damage Model for Cyclic Loading of Concrete Structures, Journal of Engineering Mechanics, 124(8): 892-900, (1998).
• [16] Bažant Z.P. and Yu Q., Universal size effect law and effect of crack depth on quasi-brittle structure strength, Journal of engineering mechanics, 135(2): 78-84, (2009).
• [17] Tada H., Paris P.C. and Irwin G.R., The stress analysis of cracks handbook, New York: ASME Press, (2000).
• [18] Hoover C.G., Bažant Z.P., Vorel J., Wendner R. and Hubler M.H., Comprehensive concrete fracture tests: description and results., Engineering fracture mechanics, 114: 92-103, (2013).
• [19] Cornelissen H., Hordijk D. and Reinhardt H., Experimental determination of crack softening characteristics of normalweight and lightweight, Heron, 31(2): 45-46, (1986).
• [20] Hordijk D. , Local Approach to Fatigue of Concrete, PhD Thesis: Delft University of Technology, (1991).