Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (3): 573-582    DOI: 10.3785/j.issn.1008-973X.2023.03.015
    
Finite element implementation and application of strength theory based cohesive zone model
Tian-xiang SHI1(),Xin ZHANG1,Yang-yang WANG1,Ke-hong ZHENG2,Yong-qiang ZHANG1,*()
1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. School of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China
Download: HTML     PDF(2243KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

The two-dimensional strength theory based cohesive zone model (ST-CZM) was extended to the three-dimensional case for a wider application. Furthermore, the finite element implementation of the ST-CZM was carried out using the Abaqus user element subroutine (UEL). The validity and accuracy of the ST-CZM were validated by several typical numerical benchmarks. On this basis, the ST-CZM finite element model was used to simulate the bond-slip behavior of the interface between fiber reinforced polymer (FRP) and concrete, which extended the application of the ST-CZM in complex working conditions. Compared to the traditional “traction laws” based cohesive zone model (CZM), the ST-CZM provides improved flexibility in mode mixity and allows independent selection of strength models in normal and tangent directions. In addition, the ST-CZM exhibits better convergence performance and more accurate strength predictions compared to “traction laws” based CZMs. All examples show that compared to the traditional “traction laws” based CZM, the ST-CZM finite element model can better predict the peak stress of the bonding interface and simulate the mixed-mode damage process, showing more realistic cracking process.

Key words： strength theory      cohesive zone model      Abaqus UEL      interface fracture     
Received: 29 March 2022      Published: 31 March 2023
CLC:  TB 121  
  O 346.5  
Fund:  国家自然科学基金资助项目(12172019, 52004245)
Corresponding Authors: Yong-qiang ZHANG     E-mail: stxzj@zju.edu.cn;cyqzhang@zju.edu.cn
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Tian-xiang SHI
Xin ZHANG
Yang-yang WANG
Ke-hong ZHENG
Yong-qiang ZHANG
Cite this article:

Tian-xiang SHI,Xin ZHANG,Yang-yang WANG,Ke-hong ZHENG,Yong-qiang ZHANG. Finite element implementation and application of strength theory based cohesive zone model. Journal of ZheJiang University (Engineering Science), 2023, 57(3): 573-582.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.03.015     OR     https://www.zjujournals.com/eng/Y2023/V57/I3/573


基于强度理论的内聚力模型的有限元实现及应用

在对基于强度理论的内聚力模型(ST-CZM)进行二维整理及三维拓展的基础上，使用Abaqus用户单元子程序(UEL)对该模型进行有限元实现. 通过经典界面破坏算例验证ST-CZM有限元模型的有效性和准确性，建立纤维增强复合材料(FRP)加固混凝土模型，采用ST-CZM模拟FRP与混凝土界面间的黏结破坏过程，实现ST-CZM在复杂工况下的应用. 相较于传统基于牵引力准则的内聚力模型，ST-CZM具有更灵活的混合模态耦合方式，且其切向和法向的强度模型相互独立，ST-CZM的收敛性更好，对强度的预测更准确. 所有算例表明，相较于传统基于牵引力准则的内聚力模型，ST-CZM有限元模型能够更好地实现黏结界面峰值应力的预测和损伤阶段的模拟.


关键词： 强度理论,  内聚力模型,  Abaqus UEL,  界面破坏 
Fig.1 Traction-separation relation of cohesive element under unidirectional load
Fig.2 Two-dimensional traction-failure surface
Fig.3 Three-dimensional traction-failure surface
模型 σI /MPa ueI/mm KI /(N·mm?3) GI/(N·mm?1) σII /MPa ueII /mm KII /(N·mm?3) GII /(N·mm?1)
双悬臂梁 30 3.0×10?4 1.0×105 0.26 60 6.0×10?4 1.0×105 1.002
固定比率混合 30 3.0×10?4 1.0×105 0.26 60 6.0×10?4 1.0×105 1.002
混合模态弯曲 100 4.0×10?4 2.5×105 0.50 100 4.0×10?4 2.5×105 0.500
Tab.1 Material parameters for cohesive elements in verification models for strength theory cohesive zone model[18]
模型 E11 /GPa E22, E33 /GPa G12, G13 /(N·mm?1) G23 /(N·mm?1) v12, v13 v23
双悬臂梁 120 10.5 5.25 3.48 0.30 0.51
固定比率混合 120 10.5 5.25 3.48 0.30 0.51
混合模态弯曲 122 122.0 — — 0.25 0.25
Tab.2 Material parameters of matrix in verification models for strength theory cohesive zone model
Fig.4 Geometry properties and boundary conditions of double cantilever beam specimen
Fig.5 Comparison of model test results and numerical simulation results of double cantilever beam
Fig.6 Boundary conditions of fixed ratio mixed mode
Fig.7 Comparison of numerical simulation results of fixed ratio hybrid model
Fig.8 Geometry properties of mixed mode bending specimen
Fig.9 Comparison of numerical values and analytical results of mixed mode bending model
试验数值模型 σI /MPa ueI/mm KI /（N·mm?3） GI/（N·mm?1） σII /MPa ueII /mm KII /（N·mm?3） GII /（N·mm?1）
单剪 8.77 0.019 1 459.160 0.494 8.77 0.019 1 459.160 0.494
四点弯曲梁 12.00 0.029 0 0.297 0.891 12.00 0.029 0 0.297 0.891
Tab.3 Material parameters of cohesive element in practical models for strength theory cohesive zone model
Fig.10 Geometry properties of single-shear specimen
Fig.11 Comparison results of simple shear model test and numerical simulation
Fig.12 Damage propagation of single shear model
Fig.13 Geometry properties of four-point bending beam
Fig.14 Experimental crack patterns of L2D1250[24]
Fig.15 Local debonding positions plot of L2D1250[24]
Fig.16 Tensile damage contour L2D1250
Fig.17 Comparison of L2D1250 test and numerical simulation results
Fig.18 Experimental crack patterns of L2D1750[24]
Fig.19 Local debonding positions plot of L2D1750[24]
Fig.20 Tensile damage contour of L2D1750
Fig.21 Comparison of L2D1750 test and numerical simulation results
[1]   KO H, MATTHYS S, PALMIERI A, et al Development of a simplified bond stress–slip model for bonded FRP–concrete interfaces[J]. Construction and Building Materials, 2014, 68: 142- 157
doi: 10.1016/j.conbuildmat.2014.06.037
[2]   EBADI-RAJOLI J, AKHAVAN-SAFAR A, HOSSEINI-TOUDESHKY H, et al Progressive damage modeling of composite materials subjected to mixed mode cyclic loading using cohesive zone model[J]. Mechanics of Materials, 2020, 143: 103322
doi: 10.1016/j.mechmat.2020.103322
[3]   WONG R S Y, VECCHIO F J Towards modeling of reinforced concrete members with externally bonded fiber-reinforced polymer composites[J]. ACI Structural Journal, 2003, 100 (1): 47- 55
[4]   WU Z, YUAN H, NIU H Stress transfer and fracture propagation in different kinds of adhesive joints[J]. Journal of Engineering Mechanics, 2002, 128 (5): 562- 573
doi: 10.1061/(ASCE)0733-9399(2002)128:5(562)
[5]   WU Z, YIN J Fracturing behaviors of FRP-strengthened concrete structures[J]. Engineering Fracture Mechanics, 2003, 70 (10): 1339- 1355
doi: 10.1016/S0013-7944(02)00100-5
[6]   XU Y, GUO Y, LIANG L, et al A unified cohesive zone model for simulating adhesive failure of composite structures and its parameter identification[J]. Composite Structures, 2017, 182: 555- 565
doi: 10.1016/j.compstruct.2017.09.012
[7]   LI S, THOULESS M D, WAAS A M, et al Mixed-mode cohesive-zone models for fracture of an adhesively bonded polymer–matrix composite[J]. Engineering Fracture Mechanics, 2006, 73 (1): 64- 78
doi: 10.1016/j.engfracmech.2005.07.004
[8]   NEEDLEMAN A A continuum model for void nucleation by inclusion debonding[J]. Journal of Applied Mechanics, 1987, 54 (3): 525- 531
doi: 10.1115/1.3173064
[9]   XU X P, NEEDLEMAN A Void nucleation by inclusion debonding in a crystal matrix[J]. Modelling and Simulation in Materials Science and Engineering, 1999, 1 (2): 111
[10]   DIMITRI R, TRULLO M, DE LORENZIS L, et al Coupled cohesive zone models for mixed-mode fracture: a comparative study[J]. Engineering Fracture Mechanics, 2015, 148: 145- 179
doi: 10.1016/j.engfracmech.2015.09.029
[11]   YANG Q D, THOULESS M D Mixed-mode fracture analyses of plastically-deforming adhesive joints[J]. International Journal of Fracture, 2001, 110: 175- 187
doi: 10.1023/A:1010869706996
[12]   ZANI M, FANTERIA D, CATAPANO A, et al A consistent energy-based cohesive zone model to simulate delamination between differently oriented plies[J]. Composite Structures, 2022, 282: 115042
doi: 10.1016/j.compstruct.2021.115042
[13]   NAIRN J A, AIMENE Y E A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws[J]. Engineering Fracture Mechanics, 2021, 248: 107704
doi: 10.1016/j.engfracmech.2021.107704
[14]   刘敏, 李旭 基于内聚力理论的二维二次界面单元在ABAQUS中的UEL程序实现[J]. 计算力学学报, 2019, 36 (5): 693- 698
LIU Min, LI Xu The finite element formulation for a 2D quadratic cohesive element and its program implementation of UEL in ABAQUS[J]. Chinese Journal of Computational Mechanics, 2019, 36 (5): 693- 698
doi: 10.7511/jslx20180805001
[15]   刘国威, 李庆斌, 左正 相场断裂模型分步算法在ABAQUS中的实现[J]. 岩石力学与工程学报, 2016, 35 (5): 1019- 1030
LIU Guo-wei, LI Qing-bin, ZUO Zheng Implementation of a staggered algorithm for a phase field model in ABAQUS[J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35 (5): 1019- 1030
[16]   GARG N, PRUSTY B G, OOI E T, et al Application of scaled boundary finite element method for delamination analysis of composite laminates using cohesive zone modelling[J]. Composite Structures, 2020, 253: 112773
doi: 10.1016/j.compstruct.2020.112773
[17]   PARK K, PAULINO G H Computational implementation of the PPR potential-based cohesive model in ABAQUS: educational perspective[J]. Engineering Fracture Mechanics, 2012, 93: 239- 262
doi: 10.1016/j.engfracmech.2012.02.007
[18]   REEDER J R, CREWS J H Mixed-mode bending method for delamination testing[J]. AIAA Journal, 1990, 28 (7): 1270- 1276
doi: 10.2514/3.25204
[19]   HARPER P W, HALLETT S R Cohesive zone length in numerical simulations of composite delamination[J]. Engineering Fracture Mechanics, 2008, 75 (16): 4774- 4792
doi: 10.1016/j.engfracmech.2008.06.004
[20]   CAMANHO P P, DÁVILA C G. Mixed-mode decohesion finite elements for the simulation of delamination in composite materials [R]. [S. l.]: NASA, 2002.
[21]   SEPASDAR R, SHAKIBA M Overcoming the convergence difficulty of cohesive zone models through a Newton-Raphson modification technique[J]. Engineering Fracture Mechanics, 2020, 233: 107046
doi: 10.1016/j.engfracmech.2020.107046
[22]   WANG Z, XIAN G Cohesive zone model prediction of debonding failure in CFRP-to-steel bonded interface with a ductile adhesive[J]. Composites Science and Technology, 2022, 230: 109315
doi: 10.1016/j.compscitech.2022.109315
[23]   ZHANG P, LEI D, REN Q, et al Experimental and numerical investigation of debonding process of the FRP plate-concrete interface[J]. Construction and Building Materials, 2019, 235: 117457
[24]   FU B, TENG J G, CHEN G M, et al Effect of load distribution on IC debonding in FRP-strengthened RC beams: full-scale experiments[J]. Composite Structures, 2018, 188: 483- 496
doi: 10.1016/j.compstruct.2018.01.026
[25]   ABDALLA J A, ABU-OBEIDAH A S, HAWILEH R A, et al Shear strengthening of reinforced concrete beams using externally-bonded aluminum alloy plates: an experimental study[J]. Construction and Building Materials, 2016, 128: 24- 37
doi: 10.1016/j.conbuildmat.2016.10.071
[26]   MAZZOTTI C, SAVOIA M, FERRACUTI B A new single-shear set-up for stable debonding of FRP–concrete joints[J]. Construction and Building Materials, 2009, 23 (4): 1529- 1537
doi: 10.1016/j.conbuildmat.2008.04.003
[27]   LI W, CHEN W, TANG L, et al A general strength model for fiber bundle composites under transverse tension or interlaminar shear[J]. Composites Part A: Applied Science and Manufacturing, 2019, 121: 45- 55
doi: 10.1016/j.compositesa.2019.03.009
[28]   齐虎, 李云贵, 吕西林 混凝土弹塑性损伤本构模型参数及其工程应用[J]. 浙江大学学报: 工学版, 2015, 49 (3): 547- 554
QI Hu, LI Yun-gui, LV Xi-lin Study of variables of elastic plastic damage model and its engineering application[J]. Journal of Zhejiang University: Engineering Science, 2015, 49 (3): 547- 554
[29]   方恩权, 石国柱 碳纤维增强塑料布与混凝土基层粘结行为研究[J]. 建筑材料学报, 2007, 10 (4): 412- 417
FANG En-quan, SHI Guo-zhu Study of bonding behavior between CFRP sheet and concrete[J]. Journal of Building Materials, 2007, 10 (4): 412- 417
[30]   TENG J G, SMITH S T, YAO J, et al Intermediate crack-induced debonding in RC beams and slabs[J]. Construction and Building Materials, 2003, 17 (6/7): 447- 462
[31]   TENG J G, CHEN J F. Mechanics of debonding in FRP-plated RC beams [J]. Structures and Buildings. 2009, 162(5): 335-345.
[1] Jian ZHOU,Gang MA,Wei ZHOU,Yong-gang CHENG,Quan-shui HUANG,Xue-xing CAO. Statistical analysis of fragment shape of rock grain after crushing based on FDEM[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(2): 348-357.
[2] Bi-sheng WANG,Yi-bo LI,Shun YUAN,Jian LI. Parameter identification of cohesive zone model for Al-Li alloy/FM94 bonded joints[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(2): 365-373.
[3] QIAN Zhi-hong, TAO Wei-ming, YANG Xing-wang. Modeling and influences of imperfect interfaces
in multiferroic composites[J]. Journal of ZheJiang University (Engineering Science), 2012, 46(5): 935-940.