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

Year 2022, Volume 25, Issue 2, 605 - 613, 01.06.2022
https://doi.org/10.2339/politeknik.762634

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.

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).

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

Year 2022, Volume 25, Issue 2, 605 - 613, 01.06.2022
https://doi.org/10.2339/politeknik.762634

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. 

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).

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Bahar AYHAN> (Primary Author)
İSTANBUL TEKNİK ÜNİVERSİTESİ, İNŞAAT FAKÜLTESİ
0000-0001-9809-097X
Türkiye


Erol LALE This is me
İSTANBUL TEKNİK ÜNİVERSİTESİ, İNŞAAT FAKÜLTESİ
0000-0003-4895-5239
Türkiye


Nilay ÇELİK This is me
İSTANBUL TEKNİK ÜNİVERSİTESİ, İNŞAAT FAKÜLTESİ
0000-0002-7914-0086
Türkiye

Publication Date June 1, 2022
Submission Date July 2, 2020
Published in Issue Year 2022, Volume 25, Issue 2

Cite

Bibtex @research article { politeknik762634, journal = {Politeknik Dergisi}, issn = {}, eissn = {2147-9429}, address = {Gazi Üniversitesi Teknoloji Fakültesi 06500 Teknikokullar - ANKARA}, publisher = {Gazi University}, year = {2022}, pages = {605 - 613}, doi = {10.2339/politeknik.762634}, title = {Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach}, key = {cite}, author = {Ayhan, Bahar and Lale, Erol and Çelik, Nilay} }
APA Ayhan, B. , Lale, E. & Çelik, N. (2022). Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach . Politeknik Dergisi , 25 (2) , 605-613 . DOI: 10.2339/politeknik.762634
MLA Ayhan, B. , Lale, E. , Çelik, N. "Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach" . Politeknik Dergisi 25 (2022 ): 605-613 <https://dergipark.org.tr/en/pub/politeknik/article/762634>
Chicago Ayhan, B. , Lale, E. , Çelik, N. "Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach". Politeknik Dergisi 25 (2022 ): 605-613
RIS TY - JOUR T1 - Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach AU - BaharAyhan, ErolLale, NilayÇelik Y1 - 2022 PY - 2022 N1 - doi: 10.2339/politeknik.762634 DO - 10.2339/politeknik.762634 T2 - Politeknik Dergisi JF - Journal JO - JOR SP - 605 EP - 613 VL - 25 IS - 2 SN - -2147-9429 M3 - doi: 10.2339/politeknik.762634 UR - https://doi.org/10.2339/politeknik.762634 Y2 - 2020 ER -
EndNote %0 Politeknik Dergisi Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach %A Bahar Ayhan , Erol Lale , Nilay Çelik %T Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach %D 2022 %J Politeknik Dergisi %P -2147-9429 %V 25 %N 2 %R doi: 10.2339/politeknik.762634 %U 10.2339/politeknik.762634
ISNAD Ayhan, Bahar , Lale, Erol , Çelik, Nilay . "Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach". Politeknik Dergisi 25 / 2 (June 2022): 605-613 . https://doi.org/10.2339/politeknik.762634
AMA Ayhan B. , Lale E. , Çelik N. Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach. Politeknik Dergisi. 2022; 25(2): 605-613.
Vancouver Ayhan B. , Lale E. , Çelik N. Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach. Politeknik Dergisi. 2022; 25(2): 605-613.
IEEE B. Ayhan , E. Lale and N. Çelik , "Size Effect Analysis of Concrete Beams Under Bending Using Crack-Band Approach", Politeknik Dergisi, vol. 25, no. 2, pp. 605-613, Jun. 2022, doi:10.2339/politeknik.762634
 
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