赵丽滨1, 龚愉2, 张建宇2
收稿日期:
2018-07-03
修回日期:
2018-08-09
出版日期:
2019-01-15
发布日期:
2018-10-10
通讯作者:
赵丽滨
E-mail:lbzhao@buaa.edu.cn
基金资助:
ZHAO Libin1, GONG Yu2, ZHANG Jianyu2
Received:
2018-07-03
Revised:
2018-08-09
Online:
2019-01-15
Published:
2018-10-10
Supported by:
摘要: 纤维增强复合材料层合板在航空航天等领域被广泛应用,分层损伤是层合板主要的损伤形式,一直是复合材料力学研究的焦点问题之一。本文从试验研究、理论分析和数值模拟3个方面对国内外在纤维增强复合材料分层问题所取得的研究成果进行了系统综述,重点介绍了单向复合材料I型、Ⅱ型和I/Ⅱ复合型层间断裂韧性测试方法和原理以及多向层合板分层扩展行为的试验研究。得到了表征和评价分层失效机理和扩展行为的纤维桥接模型、静力分层扩展准则和疲劳分层模型,并详细阐述了采用内聚力模型(CZM)、虚拟裂纹闭合技术(VCCT)和扩展有限元方法(XFEM)等先进数值方法模拟分层扩展的研究现状。最后,对复合材料层合板分层扩展研究的发展方向进行了展望。
中图分类号:
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): 522509-522509.
ZHAO Libin, GONG Yu, ZHANG Jianyu. A survey on delamination growth behavior in fiber reinforced composite laminates[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(1): 522509-522509.
[1] 杜善义, 关志东. 我国大型客机先进复合材料技术应对策略思考[J]. 复合材料学报, 2008, 25(1):1-10. DU S Y,GUAN Z D. Strategic considerations for development of advanced composite technology for large commercial aircraft in China[J]. Acta Materiae Compositae Sinica, 2008, 25(1):1-10(in Chinese). [2] 董慧民, 益小苏, 安学峰. 复合材料热固性聚合物基复合材料层间增韧研究进展[J]. 复合材料学报, 2014, 31(2):273-285. DONG H M, YI X S, AN X F. Development of interleaved fibre-reinforced thermoset polymer matrix composites[J]. Acta Materiae Compositae Sinica, 2014, 31(2):273-285(in Chinese). [3] 杨乃宾, 章怡宁. 复合材料飞机结构设计[M]. 北京:航空工业出版社, 2002. YANG N B, ZHANG Y N. Structural design of composite aircraft[M]. Beijing:Aviation Industry Press, 2002(in Chinese). [4] 中国航空研究院. 复合材料飞机结构耐久性/损伤容限设计指南[M]. 北京:航空工业出版社, 1995. Chinese Aeronautical Establishment. Guide for durability/damage tolerance design of composite aircraft structures[M]. Beijing:Aviation Industry Press, 1995(in Chinese). [5] Federal Aviation Administration. Composite aircraft structures:AC20-107B[S]. Washington, D.C.:Federal Aviation Administration, 2009. [6] CANTURRI C, GREENHALGH E S, PINHO S T, et al. Delamination growth directionality and the subsequent migration processes-The key to damage tolerant design[J]. Composites Part A:Applied Science and Manufacturing, 2013, 54:79-87. [7] ISO. Fibre-reinforced plastic composites-determination of mode I interlaminar fracture toughness GIC, for unidirectionally reinforced materials:ISO 15024[S]. Geneva:ISO, 2001. [8] ASTM International. Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites:ASTM D5528-13[S]. West Conshohocken, PA:ASTM International, 2013. [9] 中国航空工业总公司. 碳纤维复合材料层合板Ⅰ型层间断裂韧性GIC试验方法:HB 7402-1996[S]. 北京:中国航空工业总公司, 1996. Aviation Industry Corporation of China. Test method for mode I interlaminar fracture toughness GIC of CFRP laminates:HB 7402-1996[S]. Beijing:Aviation Industry Corporation of China, 1996(in Chinese). [10] HASHEMI S, KINLOCH A J, WILLIAMS J G. Mechanics and mechanisms of delamination in a poly (ether sulphone)-Fibre composite[J]. Composites Science and Technology, 1990, 37(4):429-462. [11] WILLIAMS J G. End corrections for orthotropic DCB specimens[J]. Composites Science and Technology, 1989, 35(4):367-376. [12] HASHEMI S, KINLOCH A J, WILLIAMS J G. Corrections needed in double-cantilever beam tests for assessing the interlaminar failure of fibre-composites[J]. Journal of Materials Science Letters, 1989, 8(2):125-129. [13] PENG L, ZHANG J Y, ZHAO L B, et al. Mode I delamination growth of multidirectional composite laminates under fatigue loading[J]. Journal of Composite Materials, 2011, 45(10):1077-1090. [14] DAVIES P, CASARI P, CARLSSON L A. Influence of fibre volume fraction on mode Ⅱ interlaminar fracture toughness of glass/epoxy using the 4ENF specimen[J]. Composites Science and Technology, 2005, 65(2):295-300. [15] BARRETT J D, FOSCHI R O. Mode Ⅱ stress-intensity factors for cracked wood beams[J]. Engineering Fracture Mechanics, 1977, 9(2):371-378. [16] RUSSELL A J, STREET K N. Factors affecting the interlaminar fracture energy of graphite/epoxy laminates[C]//HAYASHI T, KAWATA K, UMEKAWAS. Progress in Science and Engineering of Composites:Proceedings of the Fourth International Conference on Composite Material, 1982:279-286. [17] ASTM International. Standard test method for determination of the mode Ⅱ interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites:ASTM D7905/D7905M-14[S]. West Conshohocken, PA:ASTM International, 2014. [18] Japanese Standards Association. Testing methods for interlaminar fracture toughness of carbon fibre reinforced plastics:JSA K7086[S]. Tokyo:Japanese Standards Association, 1993. [19] 中国航空工业总公司. 碳纤维复合材料层合板Ⅱ型层间断裂韧性GⅡC试验方法:HB7403-1996[S]. 北京:中国航空工业总公司, 1996. Aviation Industry Corporation of China. Test method for mode Ⅱ interlaminar fracture toughness GⅡC of CFRP laminates:HB7403-1996[S]. Beijing:Aviation Industry Corporation of China, 1996(in Chinese). [20] TANAKA K, KAGEYAMA K, HOJO M. Prestandardization study on mode Ⅱ interlaminar fracture toughness test for CFRP in Japan[J]. Composites, 1995, 26(4):257-267. [21] RUSSELL A, STREET K. The effect of matrix toughness on delamination:Static and fatigue fracture under mode Ⅱ shear loading of graphite fiber composites[M]. West Conshohocken, PA:ASTM International, 1987. [22] MARTIN R H, DAVIDSOM B D. Mode Ⅱ fracture toughness evaluation using a 4-point bend end notched flexure test[C]//4th International Conference on Deformation and Fracture of Composites, 1997. [23] MARTIN R H, ELMS T, BOWRON S. Characterization of mode Ⅱ delamination using the 4ENF[C]//Fourth European Conference on Composite Materials:Testing and Standardization, 1998. [24] 李玉龙, 刘会芳. 加载速率对层间断裂韧性的影响[J]. 航空学报, 2015, 36(8):2620-2650. LI Y L, LIU H F. Loading rate effect on interlaminar fracture toughness[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(8):2620-2650(in Chinese). [25] GUSTAFSON C, HOJO M, HOLM D. A nonlinear analysis of the CLS specimen[J]. Journal of Composite Materials, 1989, 23(2):146-162. [26] TRACY G D, FERABOLI P, KEDWARD K T. A new mixed mode test for carbon/epoxy composite systems[J]. Composites Part A:Applied Science and Manufacturing, 2003, 34(11):1125-1131. [27] ARCAN M, HASHIN Z, VOLOSHIN A. A method to produce uniform plane-stress states with applications to fiber-reinforced materials[J]. Experimental Mechanics, 1978, 18(4):141-146. [28] DA SILVA L F M, ESTEVES V H C, CHAVES F J P. Fracture toughness of a structural adhesive under mixed mode loadings[J]. Materials Science and Engineering Technology, 2011, 42(5):460-470. [29] CREWS J H, REEDER J R. A mixed-mode bending apparatus for delamination testing:NASA TM-100662[R]. Washington, D.C.:NASA, 1988. [30] REEDER J R, CREWS J H. Nonlinear analysis and redesign of the mixed-mode bending delamination test[R]. Hampton, VA:NASA Langley Research Center, 1991. [31] ASTM International. Standard test method for mixed mode I-mode Ⅱ interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites:ASTM D6671/D6671M-13e1[S]. West Conshohocken, PA:ASTM International, 2013. [32] ZHANG J Y, PENG L, ZHAO L B, et al. Fatigue delamination growth rates and thresholds of composite laminates under mixed mode loading[J]. International Journal of Fatigue, 2012, 40:7-15. [33] LAKSIMI A, AHMED BENYAHIA A, BENZEGGAGH M L, et al. Initiation and bifurcation mechanisms of cracks in multi-directional laminates[J]. Composites Science and Technology, 2000, 60(4):597-604. [34] BIN MOHAMED REHAN MS, ROUSSEAU J, FONTAINE S, et al. Experimental study of the influence of ply orientation on DCB mode-I delamination behavior by using multidirectional fully isotropic carbon/epoxy laminates[J]. Composite Structures, 2017, 161:1-7. [35] DAVIDSON B D, KRUGER R, KOING M. Effect of stacking sequence on energy release rate distributions in multidirectional DCB and ENF specimens[J]. Engineering Fracture Mechanics, 1996, 55(4):557-569. [36] DAVIDSON B D, SCHAPERY R A. Effect of finite width on deflection and energy release rate of an orthotropic double cantilever specimen[J]. Journal of Composite Materials, 1988, 22(7):640-656. [37] BRUNNER A J, BLACKMAN B, DAVIES P. A status report on delamination resistance testing of polymer-matrix composites[J]. Engineering Fracture Mechanics, 2008, 75(9):2779-2794. [38] OZDIL F, CARLSSON L A, DAVIES P. Beam analysis of angle-ply laminate end-notched flexure specimens[J]. Composites Science and Technology, 1998, 58(12):1929-1938. [39] CHOI N S, KINLOCH A J, WILLIAMS J G. Delamination fracture of multidirectional carbon-fiber/epoxy composites under mode I, mode Ⅱ and mixed-mode I/Ⅱ loading[J]. Journal of Composite Materials, 1999, 33(1):73-100. [40] PEREIRA A B, DE MORAIS A B, MARQUES A T, et al. Mode Ⅱ interlaminar fracture of carbon/epoxy multidirectional laminates[J]. Composites Science and Technology, 2004, 64(10):1653-1659. [41] SHI Y B, HULL D, PRICE J N. Mode Ⅱ fracture of +θ/-θ angled laminate interfaces[J]. Composites Science and Technology, 1993, 47(2):173-184. [42] GONG Y, ZHANG B, HALLETT S R. Delamination migration in multidirectional composite laminates under mode I quasi-static and fatigue loading[J]. Composite Structures, 2018, 189:160-176. [43] GONG Y, ZHANG B, MUKHOPADHYAY S, et al. Experimental study on delamination migration in multidirectional laminates under mode Ⅱ static and fatigue loading, with comparison to mode I[J]. Composite Structures, 2018, 201:683-698. [44] BRUNNER A J, BLACKMAN B. Delamination fracture in cross-ply laminates:What can be learned from experiment?[J]. European Structural Integrity Society, 2003, 32:433-444. [45] PEREIRA A B, DE MORAIS A B. Mode I interlaminar fracture of carbon/epoxy multidirectional laminates[J]. Composites Science and Technology, 2004, 64(13):2261-2270. [46] ZHAO L B, WANG Y N, ZHANG J Y, et al. An interface-dependent model of plateau fracture toughness in multidirectional CFRP laminates under mode I loading[J]. Composites Part B:Engineering, 2017, 131:196-208. [47] LAKSIMI A, BENZEGGAGH M L, JING G, et al. Mode I interlaminar fracture of symmetrical cross-ply composites[J]. Composites Science and Technology, 1991, 41(2):147-164. [48] DE MORAIS A B, DE MOURA M F, MARQUES A T, et al. Mode-I interlaminar fracture of carbon/epoxy cross-ply composites[J]. Composites Science and Technology, 2002, 62(5):679-686. [49] OZDIL F, CARLSSON L A. Beam analysis of angle-ply laminate DCB specimens[J]. Composites Science and Technology, 1999, 59(2):305-315. [50] ROBINSON P, SONG D Q. A modified DCB specimen for mode I testing of multidirectional laminates[J]. Journal of Composite Materials, 1992, 26(11):1554-1577. [51] ROBINSON P, JAVIDRAD F, HITCHINGS D. Finite element modelling of delamination growth in the DCB and edge delaminated DCB specimens[J]. Composite Structures, 1995, 32(1):275-285. [52] PEREIRA A B, DE MORAIS A B, DE MOURA M, et al. Mode I interlaminar fracture of woven glass/epoxy multidirectional laminates[J]. Composites Part A:Applied Science and Manufacturing, 2005, 36(8):1119-1127. [53] PEREIRA A B, DE MORAIS A B. Mode Ⅱ interlaminar fracture of glass/epoxy multidirectional laminates[J]. Composites Part A:Applied Science and Manufacturing, 2004, 35(2):265-272. [54] CHOU I, KIMPARA I, KAGEYAMA K, et al. Mode I and mode Ⅱ fracture toughness measured between differently oriented plies in graphite/epoxy composites[J]. ASTM Special Technical Publication, 1995, 1230:132-151. [55] OZDIL F, CARLSSON L A. Beam analysis of angle-ply laminate mixed-mode bending specimens[J]. Composites Science and Technology, 1999, 59(6):937-945. [56] KIM B W, MAYER A H. Influence of fiber direction and mixed-mode ratio on delamination fracture toughness of carbon/epoxy laminates[J]. Composites Science and Technology, 2003, 63(5):695-713. [57] REHAN M S, ROUSSEAU J, GONG X J, et al. Effects of fiber orientation of adjacent plies on the mode I crack propagation in a carbon-epoxy laminates[J]. Procedia Engineering, 2011, 10:3179-3184. [58] NEMAT-NASSER S, NI L. A fiber-bridged crack with rate-dependent bridging forces[J]. Journal of the Mechanics and Physics of Solids, 2001, 49(11):2635-2650. [59] YAO L, ALDERLIESTEN R C, BENEDICTUS R. The effect of fibre bridging on the Paris relation for mode I fatigue delamination growth in composites[J]. Composite Structures, 2016, 140:125-135. [60] DE MOURA M, CAMPILHO R, AMARO A M, et al. Interlaminar and intralaminar fracture characterization of composites under mode I loading[J]. Composite Structures, 2010, 92(1):144-149. [61] SHOKRIEH M M, HEIDARI-RARANI M. Effect of stacking sequence on R-curve behavior of glass/epoxy DCB laminates with 0°//0° crack interface[J]. Materials Science and Engineering:A, 2011, 529:265-269. [62] SPEARING S M, EVANS A G. The role of fiber bridging in the delamination resistance of fiber-reinforced composites[J]. Acta Metallurgica et Materialia, 1992, 40(9):2191-2199. [63] TAMUZS V, TARASOVS S, VILKS U. Progressive delamination and fiber bridging modeling in double cantilever beam composite specimens[J]. Engineering Fracture Mechanics, 2001, 68(5):513-525. [64] DAVIES P, SIMS G D, BLACKMAN B, et al. Comparison of test configurations for the determination of GⅡC:Results from an international round robin[J]. Plastics, Rubber and Composites, 1999, 28(9):432-437. [65] IVENS J, ALBERTSEN H, WEVERS M, et al. Interlaminar fracture toughness of CFRP influenced by fibre surface treatment:Part 2. Modelling of the interface effect[J]. Composites Science and Technology, 1995, 54(2):147-159. [66] SHOKRIEH M M, ZEINEDINI A, GHOREISHI S M. On the mixed mode I/Ⅱ delamination R-curve of E-glass/epoxy laminated composites[J]. Composite Structures, 2017, 171:19-31. [67] DáVILA C G, ROSE C A, CAMANHO P P. A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites[J]. International Journal of Fracture, 2009, 158(2):211-223. [68] FOOTE R M, MAI Y, COTTERELL B. Crack growth resistance curves in strain-softening materials[J]. Journal of the Mechanics and Physics of Solids, 1986, 34(6):593-607. [69] COX B N, MARSHALL D B. The determination of crack bridging forces[J]. International Journal of Fracture, 1991, 49(3):159-176. [70] SUO Z, BAO G, FAN B. Delamination R-curve phenomena due to damage[J]. Journal of the Mechanics and Physics of Solids, 1992, 40(1):1-16. [71] ZOK F, HOM C L. Large scale bridging in brittle matrix composites[J]. Acta Metallurgica et Materialia, 1990, 38(10):1895-1904. [72] LINDHAGEN J E, BERGLUND L A. Application of bridging-law concepts to short-fibre composites Part 1:DCB test procedures for bridging law and fracture energy[J]. Composites Science and Technology, 2000, 60(6):871-883. [73] FERNBERG S P, BERGLUND L A. Bridging law and toughness characterisation of CSM and SMC composites[J]. Composites Science and Technology, 2001, 61(16):2445-2454. [74] FROSSARD G, CUGNONI J, GMVR T, et al. An efficient method for fiber bridging traction identification based on the R-Curve:Formulation and experimental validation[J]. Composite Structures, 2017, 175:135-144. [75] MANSHADI B D, FARMAND-ASHTIANI E, BOTSIS J, et al. An iterative analytical/experimental study of bridging in delamination of the double cantilever beam specimen[J]. Composites Part A:Applied Science and Manufacturing, 2014, 61:43-50. [76] SORENSEN L, BOTSIS J, GMVR T, et al. Delamination detection and characterisation of bridging tractions using long FBG optical sensors[J]. Composites Part A:Applied Science and Manufacturing, 2007, 38(10):2087-2096. [77] MANSHADI B D, VASSILOPOULOS A P, BOTSIS J. A combined experimental/numerical study of the scaling effects on mode I delamination of GFRP[J]. Composites Science and Technology, 2013, 83:32-39. [78] STUTZ S, CUGNONI J, BOTSIS J. Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing and numerical analysis[J]. Composites Science and Technology, 2011, 71(4):443-449. [79] FARMAND-ASHTIANI E, ALANIS D, CUGNONI J, et al. Delamination in cross-ply laminates:Identification of traction-separation relations and cohesive zone modeling[J]. Composites Science and Technology, 2015, 119:85-92. [80] FROSSARD G, CUGNONI J, GMVR T, et al. Mode I interlaminar fracture of carbon epoxy laminates:Effects of ply thickness[J]. Composites Part A:Applied Science and Manufacturing, 2016, 91:1-8. [81] SHOKRIEH M M, SALAMAT-TALAB M, HEIDARI-RARANI M. Effect of initial crack length on the measured bridging law of unidirectional E-glass/epoxy double cantilever beam specimens[J]. Materials & Design, 2014, 55:605-611. [82] SØRENSEN L, BOTSIS J, GMVR T, et al. Bridging tractions in mode I delamination:Measurements and simulations[J]. Composites Science and Technology, 2008, 68(12):2350-2358. [83] SØRENSEN B F, JACOBSEN T K. Large-scale bridging in composites:R-curves and bridging laws[J]. Composites Part A:Applied Science and Manufacturing, 1998, 29(11):1443-1451. [84] GUTKIN R, LAFFAN M L, PINHO S T, et al. Modelling the R-curve effect and its specimen-dependence[J]. International Journal of Solids and Structures, 2011, 48(11):1767-1777. [85] SHOKRIEH M M, HEIDARI-RARANI M, AYATOLLAHI M R. Delamination R-curve as a material property of unidirectional glass/epoxy composites[J]. Materials & Design, 2012, 34:211-218. [86] DUCEPT F, DAVIES P, GAMBY D. An experimental study to validate tests used to determine mixed mode failure criteria of glass/epoxy composites[J]. Composites Part A:Applied Science and Manufacturing, 1997, 28(8):719-729. [87] LIU Y, ZHANG C, XIANG Y. A critical plane-based fracture criterion for mixed-mode delamination in composite materials[J]. Composites Part B:Engineering, 2015, 82:212-220. [88] GREENHALGH E, SINGH S. The effect of moisture, matrix and ply orientation on delamination resistance, failure criteria and fracture morphology in CFRP[M]. West Conshohocken, PA:ASTM International, 2002. [89] ASP L E, SJÖGREN A, GREENHALGH E S. Delamination growth and thresholds in a carbon/epoxy composite under fatigue loading[J]. Journal of Composites, Technology and Research, 2001, 23(2):55-68. [90] WILLIAMS J G. The fracture mechanics of delamination tests[J]. The Journal of Strain Analysis for Engineering Design, 1989, 24(4):207-214. [91] HASHEMI S, KINLOCH A, WILLIAMS G. Mixed-mode fracture in fiber-polymer composite laminates[M]. West Conshohocken, PA:ASTM International, 1991. [92] DAVIDSON B D, ZHAO W. An accurate mixed-mode delamination failure criterion for laminated fibrous composites requiring limited experimental input[J]. Journal of Composite Materials, 2006, 41(6):679-702. [93] TURON A, CAMANHO P P, COSTA J, et al. A damage model for the simulation of delamination in advanced composites under variable-mode loading[J]. Mechanics of Materials, 2006, 38(11):1072-1089. [94] GONG Y, ZHAO L, ZHANG J, et al. Delamination propagation criterion including the effect of fiber bridging for mixed-mode I/Ⅱ delamination in CFRP multidirectional laminates[J]. Composites Science and Technology, 2017, 151:302-309. [95] LEBLANC L R, LAPLANTE G. Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon/epoxy composite[J]. Composites Part A:Applied Science and Manufacturing, 2016, 81:202-213. [96] MARAT-MENDES R M, FREITAS M M. Failure criteria for mixed mode delamination in glass fibre epoxy composites[J]. Composite Structures, 2010, 92(9):2292-2298. [97] GONG Y, ZHAO L, ZHANG J, et al. An improved power law criterion for the delamination propagation with the effect of large-scale fiber bridging in composite multidirectional laminates[J]. Composite Structures, 2018, 184:961-968. [98] WANG A S D, SLOMIANA M, BUCINELL R B. Delamination crack growth in composite laminates[M]. West Conshohocken, PA:ASTM International, 1985. [99] HOJO M, TANAKA M, GUSTAFSON C, et al. Effect of stress ratio on near-threshold propagation of delamination fatigue cracks in unidirectional CFRP[J]. Composites Science and Technology, 1987, 29(4):273-292. [100] O'BRIEN K. Generic aspects of delamination in fatigue of composites[J]. Journal of the American Helicopter Society, 1987, 32:13-18. [101] GUSTAFSON C, HOJO M. Delamination fatigue crack growth in unidirectional graphite/epoxy laminates[J]. Journal of Reinforced Plastics and Composites, 1987, 6(1):36-52. [102] HOJO M, GUSTAFSON C, TANAKA K, et al. Mode I propagation of delamination fatigue cracks in CFRP[J] Transactions of the Japan Society of Mechanical Engineers, Part A, 1987, 54(499):455-460 [103] WHITCOMB J D. Strain-energy release rate analysis of cyclic delamination growth in compressively loaded laminates[M]. West Conshohocken, PA:ASTM International, 1984. [104] ROUNDI W, EL MAHI A, EL GHARAD A, et al. Experimental and numerical investigation of the effects of stacking sequence and stress ratio on fatigue damage of glass/epoxy composites[J]. Composites Part B:Engineering, 2017, 109:64-71. [105] PASCOE J A, ALDERLIESTEN R C, BENEDICTUS R. Methods for the prediction of fatigue delamination growth in composites and adhesive bonds-A critical review[J]. Engineering Fracture Mechanics, 2013, 112:72-96. [106] HOJO M, ANDO T, TANAKA M, et al. Mode I and Ⅱ interlaminar fracture toughness and fatigue delamination of CF/epoxy laminates with self-same epoxy interleaf[J]. International Journal of Fatigue, 2006, 28(10):1154-1165. [107] HOJO M, NAKASHIMA K, KUSAKA T, et al. Mode I fatigue delamination of Zanchor-reinforced CF/epoxy laminates[J]. International Journal of Fatigue, 2010, 32(1):37-45. [108] ALLEGRI G, WISNOM M R, HALLETT S R. A new semi-empirical law for variable stress-ratio and mixed-mode fatigue delamination growth[J]. Composites Part A:Applied Science and Manufacturing, 2013, 48:192-200. [109] STELZER S, BRUNNER A J, ARGVELLES A, et al. Mode I delamination fatigue crack growth in unidirectional fiber reinforced composites:Results from ESIS TC4 round-robins[J]. Engineering Fracture Mechanics, 2014, 116:92-107. [110] SHAHVERDI M, VASSILOPOULOS A P, KELLER T. Experimental investigation of R-ratio effects on fatigue crack growth of adhesively-bonded pultruded GFRP DCB joints under CA loading[J]. Composites Part A:Applied Science and Manufacturing, 2012, 43(10):1689-1697. [111] MOHLIN T, BLOM A F, CARLSSON L A, et al. Delamination growth in a notched graphite/epoxy laminate under compression fatigue loading[M]. West Conshohocken, PA:ASTM International, 1985. [112] RANS C, ALDERLIESTEN R, BENEDICTUS R. Misinterpreting the results:How similitude can improve our understanding of fatigue delamination growth[J]. Composites Science and Technology, 2011, 71(2):230-238. [113] HWANG W, HAN K S. Interlaminar fracture behavior and fiber bridging of glass-epoxy composite under mode I static and cyclic loadings[J]. Journal of Composite Materials, 1989, 23(4):396-430. [114] KHAN R, ALDERLIESTEN R, YAO L, et al. Crack closure and fibre bridging during delamination growth in carbon fibre/epoxy laminates under mode I fatigue loading[J]. Composites Part A:Applied Science and Manufacturing, 2014, 67:201-211. [115] GREGORY J R, SPEARING S M. A fiber bridging model for fatigue delamination in composite materials[J]. Acta Materialia, 2004, 52(19):5493-5502. [116] ALLEGRI G, JONES M I, WISNOM M R, et al. A new semi-empirical model for stress ratio effect on mode Ⅱ fatigue delamination growth[J]. Composites Part A:Applied Science and Manufacturing, 2011, 42(7):733-740. [117] BLANCO N, GAMSTEDT E K, ASP L E, et al. Mixed-mode delamination growth in carbon-fibre composite laminates under cyclic loading[J]. International Journal of Solids and Structures, 2004, 41(15):4219-4235. [118] WANG A, SLOMIANA M, BUCINELL R B. Delamination crack growth in composite laminates[M]. West Conshohocken, PA:ASTM International, 1985. [119] RAMKUMAR R L, WHITCOMB J D. Characterization of mode I and mixed-mode delamination growth in T300/5208 graphite/epoxy[J]. Delamination and Debonding of Materials, 1985, 876(985):315-335. [120] RUSSELL A J, STREET K N. Predicting interlaminar fatigue crack growth rates in compressively loaded laminates[J]. Composite Materials:Fatigue and Fracture, 1989, 1012:162-178. [121] ALLEGRI G, WISNOM M R. A non-linear damage evolution model for mode Ⅱ fatigue delamination onset and growth[J]. International Journal of Fatigue, 2012, 43:226-234. [122] POURSARTIP A. The characterization of edge delamination growth in laminates under fatigue loading[M]. West Conshohocken, PA:ASTM International, 1985. [123] SHIVAKUMAR K, CHEN H, ABALI F, et al. A total fatigue life model for mode I delaminated composite laminates[J]. International Journal of Fatigue, 2006, 28(1):33-42. [124] CHEN H, SHIVAKUMAR K, ABALI F. A comparison of total fatigue life models for composite laminates[J]. Fatigue & Fracture of Engineering Materials & Structures, 2006, 29(1):31-39. [125] MURRI G B. Evaluation of delamination growth characterization methods under mode I fatigue loading[C]//15th US-Japan Conference on Composites, 2012. [126] KRUZIC J J, CANNON R M, Ⅲ J W A, et al. Fatigue threshold R-curves for predicting reliability of ceramics under cyclic loading[J]. Acta Materialia, 2005, 53:2595-2605. [127] YAO L, ALDERLIESTEN R C, ZHAO M, et al. Discussion on the use of the strain energy release rate for fatigue delamination characterization[J]. Composites Part A:Applied Science and Manufacturing, 2014, 66:65-72. [128] YAO L, ALDERLIESTEN R, ZHAO M, et al. Bridging effect on mode I fatigue delamination behavior in composite laminates[J]. Composites Part A:Applied Science and Manufacturing, 2014, 63:103-109. [129] PENG L, XU J, ZHANG J, et al. Mixed mode delamination growth of multidirectional composite laminates under fatigue loading[J]. Engineering Fracture Mechanics, 2012, 96:676-686. [130] ZHAO L B, GONG Y, ZHANG J Y, et al. A novel interpretation of fatigue delamination growth behavior in CFRP multidirectional laminates[J]. Composites Science and Technology, 2016, 133:79-88. [131] GONG Y, ZHAO L B, ZHANG J Y, et al. A novel model for determining the fatigue delamination resistance in composite laminates from a viewpoint of energy[J]. Composites Science and Technology, 2018, 167:489-496. [132] BRUSSAT T R, CHIU S T, MOSTOVOY S. Fracture mechanics for structural adhesive bonds:LR-28196[R]. Montgomery County, MD:Lockheed Coperation, 1977. [133] KARDOMATEAS G A, PELEGRI A A, MALIK B. Growth of internal delaminations under cyclic compression in composite plates[J]. Journal of the Mechanics and Physics of Solids, 1995, 43(6):847-868. [134] KENANE M, BENZEGGAGH M L. Mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites under fatigue loading[J]. Composites Science and Technology, 1997, 57(5):597-605. [135] ELBERT W. The significance of fatigue crack closure[C]//Seventy-third Annual Meeting American Society for Testing and Materials. West Conshohocken, PA:ASTM International, 1971. [136] JABLONSKI D A. Fatigue crack growth in structural adhesives[J]. The Journal of Adhesion, 1980, 11(2):125-143. [137] FAWAZ S A. Application of the virtual crack closure technique to calculate stress intensity factors for through cracks with an elliptical crack front[J]. Engineering Fracture Mechanics, 1998, 59(3):327-342. [138] XIE D, BIGGERS JR S B. Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I:Formulation and validation[J]. Engineering Fracture Mechanics, 2006, 73(6):771-785. [139] XIE D, BIGGERS JR S B. Progressive crack growth analysis using interface element based on the virtual crack closure technique[J]. Finite Elements in Analysis and Design, 2006, 42(11):977-984. [140] KRUEGER R. Virtual crack closure technique:History, approach, and applications[J]. Applied Mechanics Reviews, 2004, 57(2):109-143. [141] LI H C H, DHARMAWAN F, HERSZBERG I, et al. Fracture behaviour of composite maritime T-joints[J]. Composite Structures, 2006, 75(1):339-350. [142] 孟令兵, 陈普会. 层压复合材料分层扩展分析的虚拟裂纹闭合技术及其应用[J]. 复合材料学报, 2010, 27(1):190-195. MENG L B. CHEN P H. Virtual crack closure technique for delamination growth analysis of laminated composites and its application[J]. Acta Materiae Compositae Sinica, 2010, 27(1):190-195(in Chinese). [143] 肖涛, 左正兴. 虚拟裂纹闭合法在结构断裂分析中的应用[J]. 计算力学学报, 2008, 25:16-19. XIAO T, ZUO Z X. Application of virtual crack closure technique in structure fracture analysis[J]. Chinese Journal of Computational Mechanics, 2008, 25:16-19(in Chinese). [144] MARJANOVIĆ M, MESCHKE G, VUKSANOVIĆ D. A finite element model for propagating delamination in laminated composite plates based on the virtual crack closure method[J]. Composite Structures, 2016, 150:8-19. [145] 赵丽滨, 徐吉峰. 先进复合材料连接结构分析方法[M]. 北京:北京航空航天大学出版社, 2015. ZHAO L B, XU J F. Analysis method for connecting structure of advanced composite materials[M]. Beijing:Beihang University Press, 2015(in Chinese). [146] XU X P, NEEDLEMAN A. Void nucleation by inclusion debonding in a crystal matrix[J]. Modelling and Simulation in Materials Science and Engineering, 1993, 1(2):111-132. [147] TVERGAARD V, HUTCHINSON J W. The relation between crack growth resistance and fracture process parameters in elastic-plastic solids[J]. Journal of the Mechanics and Physics of Solids, 1992, 40(6):1377-1397. [148] CAMANHO P P, DAVILA C G, DE MOURA M F. Numerical simulation of mixed-mode progressive delamination in composite materials[J]. Journal of Composite Materials, 2003, 37(16):1415-1438. [149] REEDY E D, MELLO F J, GUESS T R. Modeling the initiation and growth of delaminations in composite structures[J]. Journal of Composite Materials, 1997, 31(8):812-831. [150] TURON A, VILA C G D, 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, 74:1665-1682. [151] ZOU Z, REID S R, LI S, et al. Modelling interlaminar and intralaminar damage in filament-wound pipes under quasi-static indentation[J]. Journal of Composite Materials, 2002, 36(4):477-499. [152] HILLERBORG A, MODEER M, PETERSSON P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J]. Cement and Concrete Research, 1976, 6(6):773-781. [153] DUGDALE D S. Yielding of steel sheets containing slits[J]. Journal of Mechanics and Physics of Solids, 1960, 8(2):100-104. [154] BARENBLATT G. The mathematical theory of equilibrium cracks in brittle fracture[J]. Advances in Applied Mechanics, 1962, 7:55-129. [155] RICE J R. The mechanics of earthquake rupture[D]. Providence:Brown University, 1979. [156] FALK M L, NEEDLEMAN A, RICE J R. A critical evaluation of cohesive zone models of dynamic fracture[C]//5th European Mechanics of Materials Conference, 2001. [157] HUI C, JAGOTA A, BENNISON S, et al. Crack blunting and the strength of soft elastic solids[J]. Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 2003, 459:1489-1516. [158] IRWIN G R. Plastic zone near a crack and fracture toughness[D]. New York:Syracuse University, 1960. [159] NEKKANTY S, WALTER M E, SHIVPURI R. A cohesive zone finite element approach to model tensile cracks in thin film coatings[J]. Journal of Mechanics of Materials & Structures, 2007, 2(7):1231-1247. [160] ALFANO G, CRISFIELD M A. Solution strategies for the delamination analysis based on a combination of local-control arc-length and line searches[J]. International Journal for Numerical Methods in Engineering, 2003, 58(7):999-1048. [161] LIU P F, ZHENG J Y. Recent developments on damage modeling and finite element analysis for composite laminates:A review[J]. Materials & Design, 2010, 31(8):3825-3834. [162] HAMITOUCHE L, TARFAOUI M, VAUTRIN A. An interface debonding law subject to viscous regularization for avoiding instability:Application to the delamination problems[J]. Engineering Fracture Mechanics, 2008, 75(10):3084-3100. [163] SIMONOVSKI I, CIZELJ L. Cohesive element approach to grain level modelling of intergranular cracking[J]. Engineering Fracture Mechanics, 2013, 110:364-377. [164] PEZZOTTA M, ZHANG Z L. Effect of thermal mismatch induced residual stresses on grain boundary microcracking of titanium diboride ceramics[J]. Journal of Materials Science, 2010, 45(2):382-391. [165] RANATUNGA V. Finite element modeling of delamination crack propagation in laminated composites[C]//Wor-ld Congress on Engineering, 2011. [166] CHEN J, RAVEY E, HALLETT S, et al. Prediction of delamination in braided composite T-piece specimens[J]. Composites Science and Technology, 2009, 69(14):2363-2367. [167] KRUEGER R. Development of benchmark examples for delamination onset and fatigue growth prediction[C]//the NAFEMS World Congress, 2011. [168] JIANG H, GAO X, SRIVATSAN T S. Predicting the influence of overload and loading mode on fatigue crack growth:A numerical approach using irreversible cohesive elements[J]. Finite Elements in Analysis and Design, 2009, 45(10):675-685. [169] WILLIAMSON R L, KNOLL D A. Simulating dynamic fracture in oxide fuel pellets using cohesive zone models[C]//20th International Conference on Structural Mech-anics in Reactor Technology, 2009. [170] TURON A, CAMANHO P P, COSTA J, et al. An interface damage model for the simulation of delamination under variable-mode ratio in composite materials:NASA/TM-2004-213277[R]. Washington, D.C.:NASA, 2004. [171] YE Q, CHEN P. Prediction of the cohesive strength for numerically simulating composite delamination via CZM-based FEM[J]. Composites Part B:Engineering, 2011, 42(5):1076-1083. [172] BORG R, NILSSON L, SIMONSSON K. Simulating DCB, ENF and MMB experiments using shell elements and a cohesive zone model[J]. Composites Science and Technology, 2004, 64(2):269-278. [173] BORG R, NILSSON L, SIMONSSON K. Modeling of delamination using a discretized cohesive zone and damage formulation[J]. Composites Science and Technology, 2002, 62(10):1299-1314. [174] BORG R, NILSSON L, SIMONSSON K. Simulation of low velocity impact on fiber laminates using a cohesive zone based delamination model[J]. Composites Science and Technology, 2004, 64(2):279-288. [175] YANG Q, COX B. Cohesive models for damage evolution in laminated composites[J]. International Journal of Fracture, 2005, 133(2):107-137. [176] DáVILA C G, CAMANHO P P, TURON TRAVESA A. Cohesive elements for shells:NASA/TP-2007-214869[R]. Washington, D.C.:NASA, 2007. [177] CAMANHO P P, DAVILA C G, AMBUR D R. Numerical simulation of delamination growth in composite materials:NASA/TP-2001-211041[R]. Washington, D.C.:NASA, 2001. [178] SCHÖN J, NYMAN T, BLOM A, et al. A numerical and experimental investigation of delamination behaviour in the DCB specimen[J]. Composites Science and Technology, 2000, 60(2):173-184. [179] NAGHIPOUR P, BARTSCH M, CHERNOVA L, et al. Effect of fiber angle orientation and stacking sequence on mixed mode fracture toughness of carbon fiber reinforced plastics:Numerical and experimental investigations[J]. Materials Science and Engineering:A, 2010, 527(3):509-517. [180] 林国伟, 陈普会. 胶接修补复合材料层合板失效分析的PDA-CZM方法[J]. 航空学报, 2009, 30(10):1877-1882. LIN G W, CHEN P H. PDA-CZM method for failure analysis of bonded repair of composite laminates[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(10):1877-1882(in Chinese). [181] WU H, XIAO J, XING S, et al. Numerical and experimental investigation into failure of T700/bismaleimide composite T-joints under tensile loading[J]. Composite Structures, 2015, 130:63-74. [182] 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. [183] AYMERICH F, DORE F, PRIOLO P. Prediction of impact-induced delamination in cross-ply composite laminates using cohesive interface elements[J]. Composites Science and Technology, 2008, 68(12):2383-2390. [184] SUN X C, HALLETT S R. Failure mechanisms and damage evolution of laminated composites under Compression After Impact (CAI):Experimental and numerical study[J]. Composites Part A:Applied Science and Manufacturing, 2018, 104(Supplement C):41-59. [185] WANG K, ZHAO L, HONG H, et al. A strain-rate-dependent damage model for evaluating the low velocity impact induced damage of composite laminates[J]. Composite Structures, 2018, 201:995-1003. [186] DE MOURA M F S F, MORAIS J J L, DOURADO N. A new data reduction scheme for mode I wood fracture characterization using the double cantilever beam test[J]. Engineering Fracture Mechanics, 2008, 75(13):3852-3865. [187] SZEKRéNYES A, UJ J. Advanced beam model for fiber-bridging in unidirectional composite double-cantilever beam specimens[J]. Engineering Fracture Mechanics, 2005, 72(17):2686-2702. [188] AIROLDI A, DáVILA C G. Identification of material parameters for modelling delamination in the presence of fibre bridging[J]. Composite Structures, 2012, 94(11):3240-3249. [189] SØRENSEN B F, GOUTIANOS S, JACOBSEN T K. Strength scaling of adhesive joints in polymer-matrix composites[J]. International Journal of Solids and Structures, 2009, 46(3):741-761. [190] BARSOUM R S. On the use of isoparametric finite elements in linear fracture mechanics[J]. International Journal for Numerical Methods in Engineering, 1976, 10(1):25-37. [191] ASHARI S E, MOHAMMADI S. Delamination analysis of composites by new orthotropic bimaterial extended finite element method[J]. International Journal for Numerical Methods in Engineering, 2011, 86(13):1507-1543. [192] ESNA ASHARI S, MOHAMMADI S. Fracture analysis of FRP-reinforced beams by orthotropic XFEM[J]. Journal of Composite Materials, 2012, 46(11):1367-1389. [193] BOUHALA L, MAKRADI A, BELOUETTAR S, et al. Modelling of failure in long fibres reinforced composites by X-FEM and cohesive zone model[J]. Composites Part B:Engineering, 2013, 55:352-361. [194] WELLS G N, SLUYS L J. A new method for modelling cohesive cracks using finite elements[J]. International Journal for Numerical Methods in Engineering, 2001, 50(12):2667-2682. [195] WELLS G N, DE BORST R, SLUYS L J. A consistent geometrically non-linear approach for delamination[J]. International Journal for Numerical Methods in Engineering, 2002, 54(9):1333-1355. [196] HUYNH D, BELYTSCHKO T. The extended finite element method for fracture in composite materials[J]. International Journal for Numerical Methods in Engineering, 2009, 77(2):214-239. [197] SUKUMAR N, HUANG Z Y, PRЁVOST J H, et al. Partition of unity enrichment for bimaterial interface cracks[J]. International Journal for Numerical Methods in Engineering, 2004, 59(8):1075-1102. [198] REMMERS J J, WELLS G N, BORST R D. A solid-like shell element allowing for arbitrary delaminations[J]. International Journal for Numerical Methods in Engineering, 2003, 58(13):2013-2040. [199] SAMIMI M, VAN DOMMELEN J, GEERS M. An enriched cohesive zone model for delamination in brittle interfaces[J]. International Journal for Numerical Methods in Engineering, 2009, 80(5):609-630. [200] GUIAMATSIA I, ANKERSEN J K, DAVIES G, et al. Decohesion finite element with enriched basis functions for delamination[J]. Composites Science and Technology, 2009, 69(15-16):2616-2624. [201] VAN DER MEER F P, MOЁS N, SLUYS L J. A level set model for delamination-Modeling crack growth without cohesive zone or stress singularity[J]. Engineering Fracture Mechanics, 2012, 79:191-212. [202] AFSHAR A, DANESHYAR A, MOHAMMADI S. XFEM analysis of fiber bridging in mixed-mode crack propagation in composites[J]. Composite Structures, 2015, 125:314-327. [203] YAZDANI S, RUST W J H, WRIGGERS P. An XFEM approach for modelling delamination in composite laminates[J]. Composite Structures, 2016, 135:353-364. [204] ZHAO L B, ZHI J, ZHANG J Y, et al. XFEM simulation of delamination in composite laminates[J]. Composites Part A:Applied Science and Manufacturing, 2016, 80:61-71. [205] ZHAO L B, WANG Y N, ZHANG J Y, et al. XFEM-based model for simulating zigzag delamination growth in laminated composites under mode I loading[J]. Composite Structures, 2017, 160:1155-1162. [206] GROGAN D M, BRÁDAIGH C Í, LEEN S B. A combined XFEM and cohesive zone model for composite laminate microcracking and permeability[J]. Composite Structures, 2015, 120:246-261. [207] GROGAN D M, Í BRÁDAIGH C M, MCGARRY J P, et al. Damage and permeability in tape-laid thermoplastic composite cryogenic tanks[J]. Composites Part A:Applied Science and Manufacturing, 2015, 78:390-402. [208] SONG J H, AREIAS P, BELYTSCHKO T. A method for dynamic crack and shear band propagation with phantom nodes[J]. International Journal for Numerical Methods in Engineering, 2006, 67(6):868-893. [209] REMMERS J J C, DE BORST R, NEEDLEMAN A. The simulation of dynamic crack propagation using the cohesive segments method[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(1):70-92. |
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