留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

增材制造CFRP-II型层间断裂韧性的缺层置换测试法及其参数化分析

赵煜 熊家豪 药天运 贾梦怡 胡海洋 杨冰晨

赵煜, 熊家豪, 药天运, 等. 增材制造CFRP-II型层间断裂韧性的缺层置换测试法及其参数化分析[J]. 复合材料学报, 2024, 42(0): 1-16.
引用本文: 赵煜, 熊家豪, 药天运, 等. 增材制造CFRP-II型层间断裂韧性的缺层置换测试法及其参数化分析[J]. 复合材料学报, 2024, 42(0): 1-16.
ZHAO Yu, XIONG Jiahao, YAO Tianyun, et al. Missing layer replacement method and parameterized analysis of mode Ⅱ inter-layer fracture toughness of additive manufacturing CFRP[J]. Acta Materiae Compositae Sinica.
Citation: ZHAO Yu, XIONG Jiahao, YAO Tianyun, et al. Missing layer replacement method and parameterized analysis of mode Ⅱ inter-layer fracture toughness of additive manufacturing CFRP[J]. Acta Materiae Compositae Sinica.

增材制造CFRP-II型层间断裂韧性的缺层置换测试法及其参数化分析

基金项目: 国家重点研发计划项目(2021 YFB1600302);陕西省自然科学基础研究计划项目(2024 JC-YBQN-0387)
详细信息
    通讯作者:

    药天运,博士,讲师,研究方向为3D打印FRP技术在桥梁工程中的应用、混凝土桥梁损伤分析及服役状态评估、桥梁检/监测装备及平台开发 E-mail: yao_yao2021@chd.edu.cn

  • 中图分类号: TB332

Missing layer replacement method and parameterized analysis of mode Ⅱ inter-layer fracture toughness of additive manufacturing CFRP

Funds: National Key Research and Development Program of China (2021 YFB1600302); Natural Science Foundation Research Program of Shaanxi Province (2024 JC-YBQN-0387)
  • 摘要: 为实现增材制造碳纤维增强树脂基复合材料(Carbon fiber reinforced polymer-CFRP)Ⅱ型层间断裂韧性的测试分析,并量化打印参数对Ⅱ型层间断裂韧性的影响规律,推进增材制造CFRP技术在桥梁结构中的应用,本文分别从试验及仿真分析两方面展开了相关研究。首先,对打印工艺进行优化并提出了一种新型层间预制裂纹制备方法,即缺层置换法,并利用该方法探索了两类关键打印参数(打印温度、打印速度)对增材制造CFRP-Ⅱ型层间断裂韧性的影响规律。其次,基于内聚区理论建立了不同打印工况下预制裂纹试件端部缺口梁三点弯曲(End notched flexure-ENF)试验的仿真模型,并完成了仿真结果与试验数据的对比分析。结果表明:两类关键打印参数对增材制造CFRP-Ⅱ型层间断裂韧性的影响明显,且打印温度的影响更强。当打印温度从245℃提升至285℃,试验荷载峰值的变化幅度范围为18%~27%,层间断裂韧性的变化幅度范围为14%~32%;当打印速度从20 mm/s提升至60 mm/s,试验荷载峰值的变化幅度范围为4%~31%,层间断裂韧性的变化幅度范围为4%~16%。同时,仿真结果与试验数据的相对误差均控制在10%以内,表明本次所获试验数据合理且稳定,故缺层置换法可用于制备增材制造CFRP预制裂纹试件,且传统工艺复合材料仿真方法同样适用于增材制造CFRP的仿真分析。因此,本研究可为后续增材制造CFRP桥梁结构层间力学性能的量化分析提供技术支撑。

     

  • 图  1  增材制造碳纤维增强树脂基复合材料(Carbon fiber reinforced polymer-CFRP)试件的几何特征

    Figure  1.  Geometric characteristics of additive manufacturing carbon fiber reinforced polymer (CFRP)

    图  2  增材制造CFRP试件尺寸

    Figure  2.  Size of additive manufacturing CFRP specimen

    图  3  增材制造CFRP预制裂纹试件打印原理

    Figure  3.  Printing principles of additive manufacturing CFRP pre-crack specimen

    图  4  增材制造CFRP细观结构

    Figure  4.  Meso-structures of additive manufacturing CFRP

    图  5  增材制造CFRP细观结构几何模型

    Figure  5.  Meso-structures geometric model of additive manufacturing CFRP

    图  6  增材制造CFRP试件校准位置

    Figure  6.  Calibration locations of additive manufacturing CFRP specimen

    图  9  增材制造CFRP-Ⅱ型层间断裂加载过程

    Figure  9.  Mode Ⅱ inter-layer fracture loading process of additive manufacturing CFRP

    图  7  增材制造CFRP试件加载特征

    Figure  7.  Loading characteristics of additive manufacturing CFRP specimen

    图  8  增材制造CFRP试件柔度校准试验

    Figure  8.  Compliance calibration test of additive manufacturing CFRP specimen

    图  10  内聚区双线性本构模型

    Figure  10.  Bilinear constitutive model of cohesive zone

    图  11  增材制造CFRP预制裂纹试件ENF试验仿真模型

    Figure  11.  ENF experiment simulation model of additive manufacturing CFRP pre-crack specimen

    图  12  网格尺寸

    Figure  12.  Mesh size

    图  13  不同网格尺寸的计算结果对比

    Figure  13.  Comparison of calculation results with different mesh sizes

    图  14  打印速度40 mm/s下增材制造CFRP荷载-位移曲线:(a) 打印温度245℃;(b) 打印温度255℃;(c) 打印温度265℃;(d) 打印温度275℃;(e) 打印温度285℃

    Figure  14.  Load displacement curve of additive manufacturing CFRP with printing speed of 40 mm/s: (a) Printing temperature of 245℃; (b) Printing temperature of 255℃; (c) Printing temperature of 265℃; (d) Printing temperature of 275℃; (e) Printing temperature of 285℃

    图  15  打印速度40 mm/s下增材制造CFRP层间力学性能变化规律:(a) 荷载峰值;(b) 断裂韧性值

    Figure  15.  Variation of inter-layer mechanical properties of additive manufacturing CFRP with printing speed of 40 mm/s: (a) Peak load; (b) Fracture toughness

    图  16  打印速度40 mm/s下增材制造CFRP的细观结构

    Figure  16.  Meso-structures of additive manufacturing CFRP with printing speed of 40 mm/s

    图  17  打印温度275℃下增材制造CFRP荷载-位移曲线:(a) 打印速度20 mm/s;(b) 打印速度30 mm/s;(c) 打印速度40 mm/s;(d) 打印速度50 mm/s;(e) 打印速度60 mm/s

    Figure  17.  Load displacement curve of additive manufacturing CFRP with printing temperature of 275℃: (a) Printing speed of 20 mm/s; (b) Printing speed of 30 mm/s; (c) Printing speed of 40 mm/s; (d) Printing speed of 50 mm/s; (e) Printing speed of 60 mm/s

    图  18  打印温度275℃下增材制造CFRP层间力学性能变化规律:(a) 荷载峰值;(b) 断裂韧性值

    Figure  18.  Variation of inter-layer mechanical properties for additive manufacturing CFRP with printing temperature of 40 mm/s: (a) Peak load; (b) Fracture toughness

    图  19  打印温度275℃增材制造CFRP的细观结构

    Figure  19.  Meso-structures of additive manufacturing CFRP with printing temperature of 275℃

    图  20  打印速度40 mm/s下增材制造CFRP荷载-位移曲线仿真结果与试验数据对比:(a)打印温度245℃;(b)打印温度255℃;(c)打印温度265℃;(d) 打印温度275℃;(e) 打印温度285℃

    Figure  20.  Comparison between simulation results and test data of load displacement curve of additive manufacturing CFRP with printing speed of 40 mm/s: (a) Printing temperature of 245℃; (b) Printing temperature of 255℃; (c) Printing temperature of 265℃; (d) Printing temperature of 275℃; (e) Printing temperature of 285℃

    图  21  打印温度275℃下增材制造CFRP荷载-位移曲线仿真结果与试验数据对比:(a)打印速度20 mm/s;(b)打印速度30 mm/s;(c)打印速度40 mm/s;(d)打印速度50 mm/s;(e)打印速度60 mm/s

    Figure  21.  Comparison between simulation results and test data of load displacement curve of additive manufacturing CFRP with printing temperature of 275℃: (a) Printing speed of 20 mm/s; (b) Printing speed of 30 mm/s; (c) Printing speed of 40 mm/s; (d) Printing speed of 50 mm/s; (e) Printing speed of 60 mm/s

    表  1  增材制造碳纤维增强树脂基复合材料(Carbon fiber reinforced polymer-CFRP)的物理性能

    Table  1.   Physical properties of additive manufacturing carbon fiber reinforced polymer (CFRP)

    Test conditionPropertiesValues
    ASTM D792[20]Density /(g·cm−3)1.17
    DSC[21], 10℃/minVitrification temperature /℃56.6
    300℃, 2.16 kgMelt index /(g·min−1)205
    DSC[21], 10℃/minMelting point /℃220
    DSC[21], 10℃/minCrystallization temperature /℃186.6
    ISO 75[22] 1.8 MPaThermal deformation /℃196
    Notes: g/cm3 is a density unit and g/(10 min) is the unit of melt index.
    下载: 导出CSV

    表  2  增材制造CFRP固定打印参数

    Table  2.   Fixed printing parameters of additive manufacturing CFRP

    ParemetersValues
    Layer height /mm0.2
    Heated build platform temperature /℃90
    Filling rate /%99
    Filling shapeLinear
    Filling overlap rate /%5
    Nozzle diameter /mm0.4
    下载: 导出CSV

    表  3  增材制造CFRP变量打印参数

    Table  3.   Variable printing parameters of additive manufacturing CFRP

    Temperature /℃Speed /(mm/s)
    245/255/265/275/28520/30/40/50/60
    下载: 导出CSV

    表  4  不同工况下的界面刚度$ {K_0} $及界面强度$ {\sigma _0} $

    Table  4.   Interface stiffness $ {K_0} $ and interface strength $ {\sigma _0} $ with different working conditions

    Printing temperature /
    Printing speed /
    (mm·s−1)
    $ {K_0} $/
    (MPa·mm−1)
    $ {\sigma _0} $ /
    MPa
    Printing temperature /
    Printing speed /
    (mm·s−1)
    $ {K_0} $/
    (MPa·mm−1)
    $ {\sigma _0} $ /
    MPa
    245 40 1.8×103 16 275 20 1.7×103 17
    255 2.6×103 19 30 2.4×103 21
    265 2.7×103 22 50 3.3×103 26
    275 3.0×103 24 60 3.7×103 28
    285 3.3×103 28
    下载: 导出CSV

    表  5  不同网格尺寸下的计算用时及最大荷载对比

    Table  5.   Comparison of calculation time and maximum load with different mesh sizes

    Mesh size /mmNumber of unitsCPU calculation time /sMaximum load /N
    4347212181105.031
    3364013901111.864
    2768023341116.225
    下载: 导出CSV

    表  6  不同打印温度下试件荷载峰值

    Table  6.   Peak load of specimens with different printing temperatures

    Printing temperature /℃ Peak load /N
    245 255 265 275 285
    Specimen I 674.043 736.153 853.720 1083.141 1211.012
    Specimen Ⅱ 504.145 696.142 809.258 1044.133 1324.143
    Specimen Ⅲ 557.234 736.214 933.317 1207.024 1406.043
    Average value 578.474 722.836 865.432 1111.433 1313.733
    Standard deviation 70.968 18.876 50.220 69.444 79.961
    下载: 导出CSV

    表  7  不同打印温度下试件峰值力位移

    Table  7.   Peak load displacement of specimens with different printing temperatures

    Printing temperature /℃ Peak load displacement /mm
    245 255 265 275 285
    Specimen I 29.365 29.988 27.953 31.683 35.158
    Specimen Ⅱ 25.232 27.474 30.841 33.293 34.436
    Specimen Ⅲ 28.773 30.695 26.279 30.136 33.596
    Average value 27.790 29.284 28.358 31.704 34.397
    Standard deviation 1.825 1.429 1.675 1.289 0.638
    下载: 导出CSV

    表  8  不同打印温度下试件断裂韧性值

    Table  8.   Fracture toughness of specimens with different printing temperatures

    Printing temperature /℃ Fracture toughness /(mJ·mm−2)
    245 255 265 275 285
    Specimen I 0.983 1.086 1.459 1.850 2.098
    Specimen Ⅱ 0.814 1.041 1.287 1.876 2.138
    Specimen Ⅲ 0.772 1.250 1.518 1.905 2.231
    Average value 0.856 1.126 1.421 1.877 2.156
    Standard deviation 0.091 0.090 0.098 0.022 0.056
    下载: 导出CSV

    表  9  不同打印速度下试件荷载峰值

    Table  9.   Peak load of specimens with different printing speed

    Printing speed /(mm·s−1) Peak load /N
    20 30 40 50 60
    Specimen I 1045.134 868.359 1083.021 1167.156 1271.056
    Specimen Ⅱ 880.102 919.665 1044.359 1101.876 1378.168
    Specimen Ⅲ 784.413 751.864 1207.189 1206.341 1189.058
    Average value 903.216 846.629 1111.523 1158.458 1279.427
    Standard deviation 107.687 70.806 69.463 43.089 77.430
    下载: 导出CSV

    表  10  不同打印速度下试件峰值力位移

    Table  10.   Peak load displacement of specimens with different printing speed

    Printing speed /(mm·s−1) Peak load displacement /mm
    20 30 40 50 60
    Specimen I 31.302 31.711 31.683 31.899 34.281
    Specimen Ⅱ 26.290 30.126 33.293 33.451 32.507
    Specimen Ⅲ 29.075 32.883 30.136 30.541 35.929
    Average value 28.889 31.573 31.704 31.964 34.239
    Standard deviation 2.050 1.130 1.289 1.189 1.397
    下载: 导出CSV

    表  11  不同打印速度下试件断裂韧性值

    Table  11.   Fracture toughness of specimens with different printing speed

    Printing speed /(mm·s−1) Fracture toughness /(mJ·mm−2)
    20 30 40 50 60
    Specimen I 1.473 1.727 1.850 1.920 2.018
    Specimen Ⅱ 1.491 1.678 1.876 2.155 2.038
    Specimen Ⅲ 1.555 1.826 1.905 1.905 2.258
    Average value 1.506 1.744 1.877 1.993 2.105
    Standard deviation 0.035 0.062 0.022 0.114 0.109
    下载: 导出CSV

    表  12  变温度工况下增材制造CFRP力学性能仿真结果与试验数据的对比分析

    Table  12.   Comparison between simulation results and test data of additive manufacturing CFRP mechanical properties with variable temperature conditions

    Working conditions and parameters
    /(℃-mm/s)
    Peak load /N Relative errors /% Peak load displacement /mm Relative errors /%
    245-40 Test date 674.043 1.173 29.365 4.734
    Simulation result 685.920 27.975
    255-40 Test date 736.214 0.626 29.988 3.645
    Simulation result 740.854 28.895
    265-40 Test date 853.720 1.7145 27.953 8.664
    Simulation result 839.083 25.531
    275-40 Test date 1083.141 3.745 31.683 9.245
    Simulation result 1125.282 28.754
    285-40 Test date 1211.012 2.057 35.158 8.283
    Simulation result 1236.447 32.246
    下载: 导出CSV

    表  13  变速度工况下增材制造CFRP力学性能仿真结果与试验数据的对比分析

    Table  13.   Comparison between simulation results and test data of additive manufacturing CFRP mechanical properties with variable speed conditions

    Working conditions and parameters
    /(℃-mm/s)
    Peak load /N Relative errors /% Peak load displacement /mm Relative errors /%
    275-20 Test date 880.102 1.477 29.075 2.102
    Simulation result 893.294 28.464
    275-30 Test date 868.359 0.678 31.711 4.055
    Simulation result 874.284 30.425
    275-40 Test date 1083.021 3.756 31.683 9.245
    Simulation result 1125.282 28.754
    275-50 Test date 1167.156 2.895 31.899 8.483
    Simulation result 1201.949 29.193
    275-60 Test date 1271.056 3.095 34.281 6.677
    Simulation result 1311.648 31.992
    下载: 导出CSV
  • [1] 龙昱, 李岩, 付昆昆. 3D打印纤维增强复合材料工艺和力学性能研究进展[J]. 复合材料学报, 2022, 39(9): 4196-4212.

    LONG Yu, LI Yan, FU Kun-kun. Research progress in the process and mechanical properties of 3D printed fiber reinforced composite materials[J]. Acta Materiae Compositae Sinica, 2022, 39(9): 4196-4212(in Chinese).
    [2] 曹丰, 曾志勇, 黄建等. 连续纤维增强复合材料的3D打印工艺及应用进展[J]. 中国科学: 技术科学, 2023, 50(11): 1815-1833.

    CAO Feng, ZENG Zhi-yong, HUANG Jian, et al. Printing process and application progress of 3D printing continuous fiber reinforced composites[J]. Scientia Sinica (Technologica), 2023, 50(11): 1815-1833(in Chinese).
    [3] 张聘, 王奉晨, 李玥萱等. 连续纤维增强复合材料3D打印技术现状及展望[J]. 航空制造技术, 2023, 66(16): 76-87.

    ZHANG Pin, WANG Feng-chen, LI Yue-xuan, et al. Status and prospects of 3D printing for continuous fiber reinforced composites[J]. Aeronautical Manufacturing Technology, 2023, 66(16): 76-87(in Chinese).
    [4] 刘强, 马小康, 宗志坚. 斜纹机织碳纤维/环氧树脂复合材料性能及其在电动汽车轻量化设计中的应用[J]. 复合材料学报, 2011, 28(5): 83-88.

    LIU Qiang, MA Xiao-kang, ZONG Zhi-jian. Performance of twill woven carbon fiber/epoxy resin composite material and its application in lightweight design of electric vehicles[J]. Acta Materiae Compositae Sinica, 2011, 28(5): 83-88(in Chinese).
    [5] 车士俊, 张明睿. 复合材料在轨道交通中的应用综述[J]. 纤维复合材料, 2022, 39(2): 100-104. doi: 10.3969/j.issn.1003-6423.2022.02.019

    CHE Shi-jun, ZHANG Ming-rui. Overview of the application of composite materials in rail transit[J]. Fiber Composite Materials, 2022, 39(2): 100-104(in Chinese). doi: 10.3969/j.issn.1003-6423.2022.02.019
    [6] 赵丽滨, 龚愉, 张建宇. 纤维增强复合材料层合板分层扩展行为研究进展[J]. 航空学报, 2019, 40(1): 171-199.

    ZHAO Li-bin, GONG Yu, ZHANG Jian-yu. Research progress on delamination propagation behavior of fiber reinforced composite laminates[J]. Chinese Journal of Aeronautics, 2019, 40(1): 171-199(in Chinese).
    [7] LIU T F, TIAN X Y, ZHANG M Y, et al. Interfacial performance and fracture patterns of 3D printed continuous carbon fiber with sizing reinforced PA6 composites[J]. Composites Part A: Applied Science and Manufacturing, 2018, 114: 368-376. doi: 10.1016/j.compositesa.2018.09.001
    [8] LIU T F, TIAN X Y, ZHANG Y Y, et al. High-pressure interfacial impregnation by micro-screw in-situ extrusion for 3D printed continuous carbon fiber reinforced nylon composites[J]. Composites Part A: Applied Science and Manufacturing, 2020, 130: 105770. doi: 10.1016/j.compositesa.2020.105770
    [9] TIAN X Y, LIU T F, YANG C C, et al. Interface and performance of 3D printed continuous carbon fiber reinforced PLA composites[J]. Composites Part A: Applied Science and Manufacturing, 2016, 88: 198-205. doi: 10.1016/j.compositesa.2016.05.032
    [10] LUO M, TIAN X Y, SHANG J F, et al. Impregnation and interlayer bonding behaviours of 3D-printed continuous carbon-fiber-reinforced poly-ether-ether-ketone composites[J]. Composites Part A: Applied Science and Manufacturing, 2019, 121: 130-138. doi: 10.1016/j.compositesa.2019.03.020
    [11] LUO M, TIAN X Y, SHANG J F, et al. Bi-scale interfacial bond behaviors of CCF/PEEK composites by plasma-laser cooperatively assisted 3D printing process[J]. Composites Part A: Applied Science and Manufacturing, 2020, 131: 105812. doi: 10.1016/j.compositesa.2020.105812
    [12] IRAGI M, PASCUAL-GONZALEZ C, ESNAOLA A, et al. Ply and interlaminar behaviours of 3D printed continuous carbon fiber-reinforced thermoplastic laminates; effects of processing conditions and microstructure[J]. Additive Manufacturing, 2019, 30: 100884. doi: 10.1016/j.addma.2019.100884
    [13] CAMINERO M A, CHACON J M, GARCIA MOERNO I, et al. Interlaminar bonding performance of 3D printed continuous fiber reinforced thermoplastic composites using fused deposition modelling[J]. Polymer Testing, 2018, 68: 415-423. doi: 10.1016/j.polymertesting.2018.04.038
    [14] YAVAS D, ZHANG Z, LIU Q, et al. Interlaminar shear behavior of continuous and short carbon fiber reinforced polymer composites fabricated by additive manufacturing[J]. Composites Part B: Engineering, 2021, 204: 108460. doi: 10.1016/j.compositesb.2020.108460
    [15] SOMIREDDY M, SINGH C V, CZEKANSKI A. Mechanical behaviour of 3D printed composite parts with short carbon fiber reinforcements[J]. Engineering Failure Analysis, 2019, 107: 104232.
    [16] KONG X, LUO J, LUO Q, et al. Experimental study on interface failure behavior of 3D printed continuous fiber reinforced composites[J]. Additive Manufacturing, 2022, 59: 103077. doi: 10.1016/j.addma.2022.103077
    [17] CAI R, WEN W, WANG K, et al. Tailoring interfacial properties of 3D-printed continuous natural fiber reinforced polypropylene composites through parameter optimization using machine learning methods[J]. Materials Today Communications, 2022, 32: 103985. doi: 10.1016/j.mtcomm.2022.103985
    [18] TOUCHARD F, CHOCINSKI-ARNAULT L, FOURNIER T, et al. Interfacial adhesion quality in 3D printed continuous CF/PA6 composites at filament/matrix and interlaminar scales[J]. Composites Part B: Engineering, 2021, 218: 108891. doi: 10.1016/j.compositesb.2021.108891
    [19] DANG Z, CAO J, PAGANI A, et al. Fracture toughness determination and mechanism for mode-I interlaminar failure of 3D-printed carbon-Kevlar composites[J]. Composites Communications, 2023, 39: 101532. doi: 10.1016/j.coco.2023.101532
    [20] ASTM D792-2008, ASTM International. Standard Test Methods for Density and Specific Gravity (Relative Density) of Plastics by Displacement[S]. West Conshohocken, PA, USA: ASTM International, 2008.
    [21] Standardization Administration of the People's Republic of China, State Administration of Quality Supervision, Inspection and Quarantine. Plastic-Differential scanning calorimetry (DSC) -Part 3: Determination of temperature and enthalpy of melting and crystallization: GB /T 19466.3-2004[S]. Beijing: Standards Press of China, 2004.
    [22] International Organization for Standardization. Plastics- determination of temperature of deflection under load-Part 2: Plastics, ebonite and long-fibre-reinforced composite: ISO 75-2-2013[S]. Geneva: ISO copyright office, 2013.
    [23] ASTM D7905-19, ASTM International. Standard test method for mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites[S]. West Conshohocken, PA, USA: ASTM International, 2019.
    [24] 王雅娜, 赵魏. 复合材料Ⅱ型分层ENF试验数据处理方法对比分析[J]. 复合材料科学与工程, 2022, (7): 81-92.

    WANG Ya-na. ZHAO Wei. Comparative analysis of data processing methods for type II layered ENF testing of composite materials[J]. Composite Materials Science and Engineering, 2022, (7): 81-92(in Chinese).
    [25] BLACKMAN B R K, BRUNNER A J, WILLIAMS J G. Mode II fracture testing of composites: a new look at an old problem[J]. Engineering Fracture Mechanics, 2006, 73(16): 2443-2455. doi: 10.1016/j.engfracmech.2006.05.022
    [26] QIU Y, CRISFIELD M A, ALFANO G. An interface element formulation for the simulation of delamination with buckling[J]. Engineering Fracture Mechanics, 2001, 68(16): 1755-1776. doi: 10.1016/S0013-7944(01)00052-2
    [27] CAMANHO P, DáVILA C. Mixed-mode decohesion finite elements for the simulation of delamination in composite materials[R]. Hanover: NASA 2002.
    [28] TURON A, DAVILA C G, CAMANHO P P, et al. An engineering solution for using coarse meshes in the simulation of delamination with cohesive zone models[R]. Washington: NASA 2005.
    [29] BORG R, NILSSON L, SIMONSSON K. Simulation of low velocity impact on fiber laminates using a cohesive zone based delamination model[J]. Composites Science & Technology, 2004, 64(2): 279-288.
    [30] ALFANO G. On the influence of the shape of the interface law on the application of cohesive-zone models[J]. Composites Science and Technology, 2006, 66(6): 723-730. doi: 10.1016/j.compscitech.2004.12.024
    [31] ZHAO L B, GONG Y, QIN T L, et al. Failure prediction of out-of-plane woven composite joints using cohesive element[J]. Composite Structures, 2013, 106: 407-416. doi: 10.1016/j.compstruct.2013.06.017
  • 加载中
计量
  • 文章访问数:  30
  • HTML全文浏览量:  25
  • 被引次数: 0
出版历程
  • 收稿日期:  2024-03-19
  • 修回日期:  2023-05-07
  • 录用日期:  2023-05-17
  • 网络出版日期:  2024-06-14

目录

    /

    返回文章
    返回