Semi-elliptical Surface Crack Propagation of PMMA Based on Cohesive Zone Model

doi:10.3901/JME.2025.24.158

Abstract

Abstract: The study of crack initiation and propagation in polymethyl methacrylate (PMMA) is of great significance to the structural integrity analysis and life prediction of its engineering components. The semi-elliptical surface crack propagation of PMMA is investigated by using the cohesive zone model. Firstly, the cohesive zone model parameters of PMMA are determined by using the standard fracture toughness test and the finite element inversion method. Then the tensile test and finite element simulation of wide plate with a semi-elliptical surface crack are carried out, and the experimental and simulated results are compared. Finally, the crack propagation behavior of the semi-elliptical surface crack with various shapes is studied by using the cohesive zone model. The results show that the peak load and quasi-static crack growth morphology of the simulation and experiment are in good agreement, which proves the validity of the cohesive zone model and parameters. When the initial crack depth is the same, the peak load decreases with the increase of the initial crack length. At the initial stage of crack propagation, long cracks expand more in the depth direction and less in the length direction, while short cracks are the opposite. However, their shape ratios in the depth and length direction tend to a constant with the crack propagation.

Key words: PMMA, cohesive zone model, semi-elliptical surface crack, crack propagation

CLC Number:

O346

ZHANG Shun, XUE He, ZHANG Jiaqing, WU Jun. Semi-elliptical Surface Crack Propagation of PMMA Based on Cohesive Zone Model[J]. Journal of Mechanical Engineering, 2025, 61(24): 158-167.

References

[1] 王元清,孙洲,王综轶,等. 结构有机玻璃的工程应用与研究进展[J]. 工程力学,2022,39(4):1-14. WANG Yuanqing,SUN Zhou,WANG Zongyi,et al. Engineering application and research progress of structural acryli[J]. Engineering Mechanics,2022,39(4):1-14.
[2] 王旋,徐金瑾,侯乃丹,等. 高速水射流冲击下航空有机玻璃(PMMA)损伤行为[J]. 航空学报,2022,43(12):340-352. WANG Xuan,XU Jinjin,HOU Naidan,et al. Damage behavior of aeronaut perspex (PMMA) under high-velocity water jet impact[J]. Acta Aeronautica et Astronautica Sinica,2022,43(12):340-352.
[3] 高成君,姜磊,刘帅,等. 大尺寸球冠形观察窗的结构强度研究[J]. 中国造船,2022,63(6):152-160. GAO Chengjun,JIANG Lei,LIU Shuai,et al. Study on structural strength of large-size spherical sector window[J]. Shipbuilding of China,2022,63(6):152-160.
[4] 杨莎,蔡振兵,沈明学,等. 有机玻璃扭动微动磨损的实时观测与摩擦振动分析[J]. 机械工程学报,2013,49(9):69-74. YANG Sha,CAI Zhenbing,SHEN Mingxue,et al. Real time observation and friction vibration analysis of torsional fretting wear of polymethylmethacrylate[J]. Journal of Mechanical Engineering,2013,49(9):69-74.
[5] WANG Z Y,WANG Y Q,DU X X,et al. Study on the fracture properties of the PMMA structure for the JUNO central detector[J]. KSCE Journal of Civil Engineering,2019,23(6):2584-2597.
[6] 杨晓宇,衡月昆,何伟,等. 江门中微子实验中心探测器小模型的结构设计[C]//第29届全国结构工程学术会议,中国,武汉,2020:204-214. YANG Xiaoyu,HENG Yuekun,HE Wei,et al. Structure design of the small prototype for JUNO central detector[C]//The 29th National Structural Engineering Conference,Wuhan,China,2020:204-214.
[7] 郑梦瑶,姜旭胤,吴国庆,等. 深海潜水器观察窗玻璃损伤缺陷研究[J]. 船舶工程,2022,44(11):8-13. ZHENG Mengyao,JIANG Xuyin,WU Guoqing,et al. Research on damage and defects of deep-sea submersible acrylic windows[J]. Ship Engineering,2022,44(11):8-13.
[8] 郑梦瑶,吴国庆,姜旭胤,等. 潜水器观察窗用有机玻璃的损伤与破坏行为[J]. 工程塑料应用,2023,51(2):126-132. ZHENG Mengyao,WU Guoqing,JIANG Xuyin,et al. Damage and failure behaviors of PMMA used in deep-sea submersible observation windows[J]. Engineering Plastics Application,2023,51(2):126-132.
[9] 朱婷,胡德安,王毅刚. PMMA材料裂纹动态扩展及止裂研究[J]. 应用力学学报,2017,34(2):230-236. ZHU Ting,HU De'an,WANG Yigang. Study on dynamic crack propagation and arrest of PMMA materials[J]. Chinese Journal of Applied Mechanics,2017,34(2):230-236.
[10] 代晓瑛,雷兴平,靳耿栓. 航空有机玻璃应用性能研究[J]. 塑料工业,2020,48(S1):125-127. DAI Xiaoying,LEI Xingping,JIN Gengshuan. Study on the application performance of aviation plexglass[J]. China Plastics Industry,2020,48(S1):125-127.
[11] 张小丽,陈雪峰,李兵,等. 机械重大装备寿命预测综述[J]. 机械工程学报,2011,47(11):100-116. ZHANG Xiaoli,CHEN Xuefeng,LI Bing,et al. Review of life prediction for mechanical major equipments[J],Journal of Mechanical Engineering,2011,47(11):100-116.
[12] 于培师,赵军华,郭万林. 三维损伤容限设计:离面约束理论与疲劳断裂准则[J]. 机械工程学报,2021,57(16):87-105. YU Peishi,ZHAO Junhua,GUO Wanlin. Three-dimensional damage tolerance design:out-of-plane constraint theory and fatigue/fracture criteria[J]. Journal of Mechanical Engineering,2021,57(16):87-105.
[13] 王综轶,王元清,杜新喜,等. 不同温度下有机玻璃厚板的平面应变断裂韧性试验[J]. 东南大学学报(自然科学版),2018,48(5):864-870. WANG Zongyi,WANG Yuanqing,DU Xinxi,et al. Plain-strain fracture toughness tests of thick acrylic sheets at different temperatures[J]. Journal of Southeast University(Natural Science Edition),2018,48(5):864-870.
[14] 车福炎,耿黎明. 基于APDL和UIDL联合技术计算三维表面裂纹应力强度因子[J]. 机械强度,2020,42(5):1223-1229. CHE Fuyan,GENG Liming. Calculation of 3-D surface crack stress intensity factor based on APDL and UIDL[J]. Journal of Mechanical Strength,2020,42(5):1223-1229.
[15] ZHOU X P,LONG Y D,YE W. Experimental investigations on the cracking and mechanical responses of PMMA samples with two 3D embedded elliptic flaws under uniaxial compression[J]. Geohazard Mechanics,2023,1(1):77-85.
[16] ZHOU X P,FU L,JU W,et al. An experimental study of the mechanical and fracturing behavior in PMMA specimen containing multiple 3D embedded flaws under uniaxial compression[J]. Theoretical and Applied Fracture Mechanics,2019,101:207-216.
[17] 黄如旭,万正权. 三维裂纹扩展数值预报方法研究[J]. 中国造船,2019,60(1):11-21. HUANG Ruxu,WAN Zhengquan. Numerical prediction method for 3D crack growth[J]. Shipbuilding of China,2019,60(1):11-21.
[18] 高潮,伍黎明,何宇廷,等. 基于能量模型的三维穿透裂纹扩展研究[J]. 航空动力学报,2015,30(3):639-648. GAO Chao,WU Liming,HE Yuting,et al. Study on three-dimensional through-thickness crack growth based on energy model[J]. Journal of Aerospace Power,2015,30(3):639-648.
[19] COHEN G,FINEBERG J,BERMAN N. Dynamics and properties of the cohesive zone in rapid fracture and friction[J]. Physical Review Letters,2020,125(12):125503.
[20] DUGDALE D S. Yielding of steel sheets containing slits[J]. Journal of the Mechanics and Physics of Solids,1960,8(2):100-104.
[21] BARENBLATT G I. The mathematical theory of equilibrium cracks in brittle fracture[J]. Advances in Applied Mechanics. Elsevier,1962,7:55-129.
[22] SCHEEL J,SCHLOSSER A,RICOEUR A. The J-integral for mixed-mode loaded cracks with cohesive zones[J]. International Journal of Fracture,2021,227(1):79-94.
[23] 赵文滔,杨颜志,王长焕,等. 基于贝叶斯推断的复合材料层间内聚力模型参数反演[J]. 机械工程学报,2022,58(6):110-118. ZHAO Wentao,YANG Yanzhi,WANG Changhuan,et al. Parameter inversion for composite interlayer cohesive zone model based on Bayesian inference[J]. Journal of Mechanical Engineering,2022,58(6):110-118.
[24] 林德佳,臧孟炎. 基于内聚力模型的夹层玻璃冲击破坏仿真分析[J]. 机械工程学报,2017,53(22):176-181. LIN Dejia,ZANG Mengyan. Research on impact fracture behavior of the laminated glass based on cohesive zone model[J]. Journal of Mechanical Engineering,2017,53(22):176-181.
[25] OH J C,KIM H G. Inverse estimation of cohesive zone laws from experimentally measured displacements for the quasi-static mode I fracture of PMMA[J]. Engineering Fracture Mechanics,2013,99:118-131.
[26] LIN L Q,DHANAWADE R,ZENG X W. Numerical simulations of dynamic fracture growth based on a cohesive zone model with microcracks[J]. Journal of Nanomechanics and Micromechanics,2014,4(3):B4014003.
[27] XIE Z X,WU X G,LONG T D,et al. Visualization of hydraulic fracture interacting with pre-existing fracture[J]. Petroleum Science,2023,20(6):3723-3735.
[28] CAMPOS T D,BARBOSA M L S,MARTINS M,et al. On the evaluation of strain energy release rate of cement-bone bonded joints under mode II loading[J]. Theoretical and Applied Fracture Mechanics,2023,124:103793.
[29] DOITRAND A,ESTEVEZ R,LEGUILLON D. Experimental characterization and numerical modeling of crack initiation in rhombus hole PMMA specimens under compression[J]. European Journal of Mechanics- A/Solids,2019,76:290-299.
[30] ZHANG T L,YUAN H,YANG S. Fracture energy and tensile strength depending on stress triaxiality along a running crack front in three-dimensional cohesive modeling[J]. Engineering Fracture Mechanics,2020,227:106919.
[31] HUTCHINSON J W,EVANS A G. Mechanics of materials:top-down approaches to fracture[J]. Acta Materialia,2000,48(1):125-135.
[32] SORENSEN B F,JACOBSEN T K. Determination of cohesive laws by the J integral approach[J]. Engineering Fracture Mechanics,2003,70(14):1841-1858.
[33] CORNEC A,SCHEIDER I,SCHWALBE K H. On the practical application of the cohesive model[J]. Engineering Fracture Mechanics,2003,70(14):1963-1987.
[34] MI Y,CRISFIELD M A,DAVIES G A O,et al. Progressive delamination using interface elements[J]. Journal of Composite Materials,1998,32(14):1246-1272.
[35] GEE B,PARCHEI-ESFAHANI M,GRACIE R. XFEM simulation of a mixed-mode fracture experiment in PMMA[J]. Engineering Fracture Mechanics,2020,229:106945.
[36] ELICES M,GUINEA G V,GOMEZ J,et al. The cohesive zone model:advantages,limitations and challenges[J]. Engineering Fracture Mechanics,2002,69(2):137-163.
[37] FAYE A,PARAMESWARAN V,BASU S. Dynamic fracture initiation toughness of PMMA:A critical evaluation[J]. Mechanics of Materials,2016,94:156-169.
[38] 王元清,郑宝锋,舒赣平,等. 结构用有机玻璃的力学性能及其工程应用[J]. 建筑结构,2023,53(8):1-6. WANG Yuanqging,ZHENG Baofeng,SHU Ganping,et al. Mechanical properties and engineering application of structural acrylic[J]. Building Structure,2023,53(8):1-6.
[39] 国家市场监督管理总局,国家标准化管理委员会. GB/T 1040.2-2022塑料拉伸性能的测定第2部分:模塑和挤塑塑料的试验条件[S]. 北京:中国标准出版社,2022. General Administration of Market Supervision and Administration of the People's Republic of China,Standardization Administration of the People's Republic of China. GB/T 1040.2-2022 Plastics-Determination of tensile properties-Part 2:Test conditions for moulding and extrusion plastics[S]. Beijing:Standards Press of China,2022.
[40] 薛河,张永刚,侯成,等. 基于数字图像相关方法的L450管线钢单轴拉伸变形研究[J]. 压力容器,2021,38(9):27-33. XUE He,ZHANG Yonggang,HOU Cheng,et al. Study on uniaxial tensile deformation of L450 pipeline steel using DIC method[J]. Pressure Vessel Technology,2021,38(9):27-33.
[41] YUAN H,LI X. Effects of the cohesive law on ductile crack propagation simulation by using cohesive zone models[J]. Engineering Fracture Mechanics,2014,126:1-11.
[42] UNGER J F,ECKARDT S,KONKE C. Modelling of cohesive crack growth in concrete structures with the extended finite element method[J]. Computer Methods in Applied Mechanics and Engineering,2007,196(41):4087-4100.
[43] 国家市场监督管理总局,国家标准化管理委员会. GB/T 41932-2022塑料断裂韧性(GIC和KIC)的测定线弹性断裂力学(LEFM)法[S]. 北京:中国标准出版社,2022. General Administration of Market Supervision and Administration of the People's Republic of China,Standardization Administration of the People's Republic of China. GB/T 41932-2022 Plastics-Determination of fracture toughness(GIC and KIC)-Linear elastic fracture mechanics (LEFM) approach[S]. Beijing:Standards Press of China,2022.
[44] TURON A,DAVILA C G,CAMANHO P P,et al. An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models[J]. Engineering Fracture Mechanics,2007,74(10):1665-1682.
[45] HEIDARI-RARANI M,SAYEDAIN M. Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT,CZM and XFEM approaches[J]. Theoretical and Applied Fracture Mechanics,2019,103:102246.
[46] HUO X T,LUO Q T,LI Q,et al. On characterization of cohesive zone model (CZM) based upon digital image correlation (DIC) method[J]. International Journal of Mechanical Sciences,2022,215:106921.
[47] NEWMAN J C,RAJU I S. An empirical stress-intensity factor equation for the surface crack[J]. Engineering Fracture Mechanics,1981,15(1):185-192.
[48] WANG S,WANG B,JANIN Y J,et al. Effects of the surface crack shape on J values along the front of an elliptical crack[J]. Fatigue & Fracture of Engineering Materials & Structures,2021,44(11):2944-2961.