Comparative analysis of data reduction method of ENF test of mode Ⅱ delamination

doi:10.19936/j.cnki.2096-8000.20220728.013

Abstract

Abstract: Mode Ⅱ delamination is a common failure mode in composite laminate structures, so the mode Ⅱ interlaminar fracture toughness is the important mechanical property parameter needed for characterizing the interlaminar properties of composites, and required by composite structure design. There are several test methods for mode Ⅱ interlaminar fracture toughness, among which the end notched flexure (ENF) test is widely adopted in engineer practice. As for the complex driving mechanism and lots of influence factors of mode Ⅱ delamination in ENF test, researchers have proposed many data reduction methods for mode Ⅱ fracture toughness, and the obtained data would be diverse when different data reduction methods were adopted. In order to help engineers to learn deeply the differences of various data reduction methods for mode Ⅱ fracture toughness, this paper firstly systematically reviewed the mechanics, simplification conditions, derivation process and precision of different data reduction methods of mode Ⅱ interlaminar fracture toughness in ENF test, for the purpose of offering useful guidance for engineers in the field of composite materials development, testing and design.

Key words: composite, laminate, delamination, fracture toughness, data reduction

CLC Number:

TB332

WANG Ya-na, ZHAO Wei. Comparative analysis of data reduction method of ENF test of mode Ⅱ delamination[J]. COMPOSITES SCIENCE AND ENGINEERING, 2022, 0(7): 81-92.

References

[1] 沈军, 谢怀勤. 先进复合材料在航空航天领域的研发与应用[J]. 材料科学与工艺, 2008, 16(5): 737-740.
[2] 诸强, 杨智春, 张开达. 一种计及分层效应的复合材料层合板疲劳寿命计算方法[J]. 西北工业大学学报, 2005, 23(6): 708-712.
[3] WILLIAMS J G. Fracture mechanics testing methods for polymers, adhesives and composites[J]. Polymer Testing, 2002, 21(3): 363-363.
[4] 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.
[5] SIEGFRIED M J C, TOLA C, CLAES M, et al. Impact and residual after impact properties of carbon fiber/epoxy composites modified with carbon nanotubes[J]. Composite Structures, 2014, 111(11): 488-496.
[6] 刘伟先, 周光明, 王新峰. 复合材料ENF试件裂纹扩展理论分析[J]. 航空学报, 2014, 35(1): 187-194.
[7] KAGEYAMA K, KIKUCHI M, YANAGISAWA N. Stabilized end notched flexure test: Characterization of Mode Ⅱ interlaminar crack growth[C]//In:O'Brien TK, editor. STP1110:Composite materials: Fatigue and fracture (third volume). West Conshohocken, PA: ASTM International, 1991: 210-225.
[8] MARTIN R H, DAVIDSON B D. Mode Ⅱ fracture toughness evaluation using four point bend, end notched flexure test[J]. Plastics, Rubber and Composites, 1999, 28(8): 401-406.
[9] WANG W X, NAKATA M, TAKAO Y, et al. Experimental investigation on test methods for mode Ⅱ inter-laminar fracture testing of carbon fiber reinforced composites[J]. Composites Part A Applied Science & Manufacturing, 2009, 40(9): 1447-1455.
[10] British Standards Institution. Fibre-reinforced plastic composites. Determination of the mode Ⅱ fracture resistance for unidirectionally reinforced materials using the calibrated end-loaded split (C-ELS) test and an effective crack length approach: ISO 15114[S]. London: 2014.
[11] ARRESE A, BOYANO A I, DE GRACIA J et al. A novel procedure to determine the cohesive law in DCB tests[J]. Composites Science and Technology, 2017, 152(10): 76-84.
[12] KOLOOR S S R, TAMIN M N. Mode-Ⅱ interlaminar fracture and crack-jump phenomenon in CFRP composite laminate materials[J]. Composite Structures, 2018, 204: 594-606.
[13] VINCIQUERRA A J, DAVIDSON B D. Effect of crack length measurement technique and data reduction procedures on the perceived toughness from four-point bend end-notched flexure tests[J]. Journal of Reinforced Plastics and Composites, 2004, 23(10): 1051-1062.
[14] MIYAGAWA H, SATO C, IKEGAMI K. Mode Ⅱ inter-laminar fracture toughness of multidirectional carbon fiber reinforced plastics cracking on 0//0 interface by Raman spectroscopy[J]. Materials Science & Engineering A, 2001, 308(1-2): 200-208.
[15] 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: 1653-1659.
[16] 碳纤维复合材料层合板 Ⅱ 型层间断裂韧性G_ⅠC试验方法: HB 7402[S]. 中国: 中国人民共和国航空工业标准, 1996.
[17] Standard test method for determination of the mode Ⅱ interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites: ASTM D7905/D7905M—14[S]. American: American Society for Testing and Materials, 2014.
[18] Testing methods for interlaminar fracture toughness of carbon fiber reinforced plastics: JIS K 7086[S]. Japanese Standards Association,
1993.
[19] DAVIDSON B D, SUN X. Geometry and data reduction recommendations for a standardized end notched flexure test for unidirectional composites[J]. Journal of ASTM International, 2006, 3(9): 19.
[20] 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.
[21] JR J W G, CARLSSON L A, PIPES R B. Finite element analysis of the end notched flexure specimen for measuring mode Ⅱ fracture toughness[J]. Composites Science & Technology, 1986, 27(3): 177-197.
[22] 尹凯, 于志成, 矫桂琼. 一种减小复合材料层板Ⅱ型层间断裂韧性测试值离散度的改进方法[C]//第十一届全国复合材料学术会议. 合肥: 中国复合材料学会, 2000: 568-572.
[23] LYASHENKO T, LERMAN N, WOLF A et al. Improved mode Ⅱ delamination fracture toughness of composite materials by selective placement of protein-surface treated CNT[J]. Composites Science and Technology, 2013, 85: 29-35.
[24] DAVIES P, KAUSCH H H, WILLIAMS J G, et al, Round-robin interlaminar fracture testing of carbon-fibre-reinforced epoxy and PEEK composites[J]. Composites Science and Technology, 1992, 43: 129-136.
[25] CARLSSON L A, GILLESPIE J W, PIPES R B. On the analysis and design of the end notched flexure (ENF) specimen for mode Ⅱ testing[J]. Journal of Composite Materials, 1986, 20(6): 594-604.
[26] Timoshenko S P. Strength of Materials, Part Ⅰ[M]. Kneger Publishing, 1984: 121-151.
[27] DAVIES P, SIMS G D, BLACKMAN B R K, et al. Comparison of test configurations for determination of mode Ⅱ interlaminar fracture toughness results from international collaborative test programme[J]. Plastics, Rubber and Composites, 1999, 28(9): 432-437.
[28] 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.
[29] WILLIAMS J G. End corrections for orthotropic DCB specimens[J]. Composites Science & Technology, 1989, 35(4): 367-376.
[30] WANG Y, WILLIAMS J G. Corrections for mode-Ⅱ fracture-toughness specimens of composites materials[J]. Composites Science & Technology, 1992, 43(3): 251-256.
[31] PENG L, XU J, ZHANG J Y, et al. Mixed mode delamination growth of multidirectional composite laminates under fatigue loading[J]. Engineering Fracture Mechanics, 2012, 96: 676-686.
[32] HASHEMI S, KINLOCH A J, WILLIAMS J G. The analysis of interlaminar fracture in uniaxial fibre-polymer composites[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1990, 427(1872): 173-199.
[33] BHASHYAM S, DAVIDSON B. Evaluation of data reduction methods for the mixed-mode bending test[J]. AIAA Journal, 1997, 35(3): 546-552.
[34] MORAIS A B D, PEREIRA A B. Application of the effective crack method to mode Ⅰ and mode Ⅱ interlaminar fracture of carbon/epoxy unidirectional laminates[J]. Composites Part A, 2007, 38(3): 785-794.
[35] MOURA M F S F D, SILVA M A L, MORAIS A B D, et al. Equivalent crack based mode Ⅱ fracture characterization of wood[J]. Engineering Fracture Mechanics, 2006, 73(8): 978-993.
[36] WILLIAMS J G, BLACKMAN B R K, BRUNNER A J . Mode Ⅱ fracture testing of composites: A new look at an old problem[J]. Engineering Fracture Mechanics, 2006, 73(16): 2443-2455.
[37] 于志成. 复合材料Ⅱ型层间断裂韧性试验方法研究[J]. 航空材料学报, 1997, 17(4): 54-61.
[38] CARLSSON L A, GILLESPIE J W, TRETHEWEY B R. Mode Ⅱ interlaminar fracture of graphite/epoxy and graphite/PEEK[J]. Journal of Reinforced Plastics and Composites, 1986, 5(3): 170-187.
[39] JR J W G, CARLSSON L A, PIPES R B. Finite element analysis of the end notched flexure specimen for measuring mode Ⅱ fracture toughness[J]. Composites Science & Technology, 1986, 27(3): 177-197.
[40] PEREIRA A B, DE MORAIS A B. Mode Ⅱ inter-laminar fracture of glass/epoxy multidirectional laminates[J]. Composites Part A: Applied Science and Manu-facturing, 2004, 35(2): 265-272.
[41] DAVIDSON B D, ALTONEN C S, POLAHA J J. Effect of stacking sequence on delamination toughness and delamination growth behavior in composite end-notched flexure specimens[C]//In: R. Deo and C. Saff, editor. ASTM STP 1274: Composite Materials: Testing and Design(twelfth Volume). West Conshohocken: ASTM International, 1996: 393-413.
[42] SCHUECKER C, DAVIDSON B D. Evaluation of the accuracy of the four-point bend end-notched flexure test for mode Ⅱ delamination toughness determination[J]. Composites Science & Technology, 2000, 60(11): 2137-2146.
[43] RICE J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks[J]. Journal of Applied Mechanics, 1968, 35(2): 379-386.
[44] SARRADO C, TURON A, RENART J, et al. An experimental data reduction method for the mixed mode bending test based on the J-integral approach[J]. Composites Science & Technology, 2015, 117: 85-91.
[45] ZHAO Y, SEAH L K, CHAI G B. Measurement of interlaminar fracture properties of composites using the J-integral method[J]. Journal of Reinforced Plasticsand Composites, 2016, 1-12.
[46] WHITNEY J M, BROWNING C E, HOOGSTEDEN W. A double cantilever beam test for characterizing Mode Ⅰ delamination of composite materials[J]. Journal of Reinforced Plastics and Composites, 1982, 1(4): 297-313.
[47] GRADY J E. Fracture toughness testing of polymer matrix composites: NASA technical paper 3199[R]. 1992.
[48] WHITNEY J M. Analysis of interlaminar mode Ⅱ bending specimens using a higher order beam theory[J]. Journal of Reinforced Plastics & Composites, 1990, 9(6): 522-536.
[49] REISSNER E. On a variational theorem in elasticity[J]. Studies in Applied Mathematics, 1950, 29(1-4): 90-95.
[50] SHI Y B, HULL D, PRICE J N. Mode Ⅱ fracture of +θ/-θ angled laminate interfaces[J]. Composites Science & Technology, 1993, 47(2): 173-184.
[51] VAN D M F P, SLUYS L J. A numerical investigation into the size effect in the transverse crack tension test for mode Ⅱ delamination[J]. Composites Part A: Applied Science and Manufacturing, 2013, 54: 145-152.
[52] CARLSSON L A, JR J W G. Chapter 4-mode-Ⅱ interlaminar fracture of composites[J]. Composite Materials, 1989, 6(2): 113-157.
[53] 矫桂琼, 李健为, 贾普荣. 热塑性复合材料的Ⅰ型层间断裂韧性[J]. 航空学报, 1993, 14(6): 242-247.
[54] BHASHYAM S, DAVIDSON B. An evaluation of data reduction methods for the mixed mode bending test[J]. AIAA Journal, 2006, 35(3): 546-552.
[55] SCHÖN N J, NYMAN T, BLOM A,et al. Numerical and experimental investigation of a composite ENF-specimen[J]. Engineering Fracture Mechanics, 2000, 65(4): 405-433.
[56] SALPEKAR S A, RAJU I S, O'BRIEN T K. Strain energy release rate analysis of the end-notched flexure specimen using the finite-element method[J]. Journal of Composites Technology & Research, 1988, 10(4): 133-139.
[57] MALL S, KOCHHAR N K. Finite element analysis of end notch flexure specimen[J]. Journal of Composites Technology & Research, 1986, 8(2): 54-57.
[58] DAVIDSON B D, KRUGER R, KÖNIG M. Three dimensional analysis and resulting design recommendations for unidirectional and multidirectional end-notched flexure tests[J]. Journal of Composite Materials, 1995, 29(16): 2108-2133.
[59] DAVIDSON B D. Standardization of the end-notched flexure test for mode Ⅱ interlaminar fracture toughness determination of unidirectional laminated composites[J]. Journal of Testing & Evaluation, 2015, 43(6): 1540-1553.
[60] DAVIDSON B D, GHARIBIAN S J, YU L J. Evaluation of energy release rate-based approaches for predicting delamination growth in laminated composites[J]. International Journal of Fracture, 2000, 105(4): 343-365.
[61] DAVIDSON B D, BIALASZEWSKI R D, SAINATH S S. A non-classical, energy release rate based approach for predicting delamination growth in graphite reinforced laminated polymericcomposites[J]. Composites Science & Technology, 2006, 66(10): 1479-1496.