Comparison of calculations of energy release rates for DCB multi-directional laminate specimens
Source abstract
Abstract
The double cantilever beam (DCB) specimen has been used extensively to measure the mode I fracture toughness of laminate composites. There are standards which were developed for testing unidirectional (UD) material. In addition, this specimen has been used extensively for multi-directional laminates. Typically, fracture resistance curves are presented. To this end, calculation of the energy release rate is required. For UD specimens, there are expressions for this parameter given in the standards. They depend upon the applied load, the crack opening displacement, specimen dimensions and the axial Young’s modulus or specimen compliance. For multi-directional composites, the specimen arms may not be symmetric. In this case, the arm heights differ, as well as their effective moduli. In this study, expressions are presented for all cases. That is, expressions for the energy release rate are presented in which the specimen arms are symmetric and in which their heights differ; these are found in the literature. In addition, new expressions for which the axial moduli also differ are developed. Calculations are made with these equations and compared to results obtained elsewhere using the finite element method and the conservative J-integral. It is seen that excellent agreement is achieved when both the different heights and moduli are accounted for, as well as a delamination length correction. The purpose of this investigation is to examine expressions for calculating the energy release rate in comparison to finite element analyses and to show that by taking into consideration the different specimen arm heights and stiffnesses, simple formulas may be used instead of the more complicated finite element analyses.
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Research context
OpenAlex topics: Mechanical Behavior of Composites · Composite Structure Analysis and Optimization · Fatigue and fracture mechanics
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References (45)
Show source-provided references
1. Aboudi J, Arnold SM, Bednarcyk BA (2012) Micromechanics of composite materials: a generalized multiscale analysis approach. Butterworth-Heinemann, Amsterdam
2. Alif N, Carlsson LA, Boogh L (1998) The effect of weave pattern and crack propagation direction on mode I delamination resistance of woven glass and carbon composites. Composites Part B 29(5):603–61110.1016/S1359-8368(98)00014-6 ↗
3. Andersons J, König M (2004) Dependence of fracture toughness of composite laminates on interface ply orientations and delamination growth direction. Compos Sci Technol 64(13–14):2139–215210.1016/j.compscitech.2004.03.007 ↗
4. ASTM D5528-13 (2013) Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. Space simulation; aerospace and aircraft; composite materials, vol 15.03, West Conshohocken, PA
5. ASTM D6671M-13 (2014) Standard test method for mixed mode I—mode II interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. Space simulation; aerospace and aircraft; composite materials, vol 15.03, West Conshohocken, PA
6. ASTM D7905/D7905M-14 (2014) Standard test method for determination of the mode II interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. Space simulation; aerospace and aircraft; composite materials, vol 15.03, West Conshohocken, PA
7. Banks-Sills L, Ishbir C, Fourman V, Rogel L, Eliasi R (2013) Interface fracture toughness of a multi-directional woven composite. Int J Fract 182(2):187–20710.1007/s10704-013-9868-6 ↗
8. Bathe KJ (2009) ADINA-Automatic Dynamic Incremental Nonlinear Analysis, version 8.6.0. ADINA R&D, Inc., Watertown
9. Bennati S, Colleluori M, Corigliano D, Valvo PS (2009) An enhanced beam-theory model of the asymmetric double cantilever beam (ADCB) test for composite laminates. Compos Sci Technol 69(11–12):1735–174510.1016/j.compscitech.2009.01.019 ↗
10. Bin Mohamed Rehan MS, Rousseau J, Fontaine S, Gong XJ (2017) Experimental study of the influence of ply orientation on DCB mode-I delamination behavior by using multidirectional fully isotropic carbon/epoxy laminates. Compos Struct 161:1–710.1016/j.compstruct.2016.11.036 ↗
11. Blake SP, Berube KA, Lopez-Anido RA (2012) Interlaminar fracture toughness of woven E-glass fabric composites. J Compos Mater 46(13):1583–159210.1177/0021998311421221 ↗
12. Brugo T, Palazzetti R (2016) The effect of thickness of Nylon 6.6 nanofibrous mat on Modes I-II fracture mechanics of UD and woven composite laminates. Compos Struct 154:172–17810.1016/j.compstruct.2016.07.034 ↗
13. Brunner AJ (2000) Experimental aspects of Mode I and Mode II fracture toughness testing of fibre-reinforced polymer-matrix composites. Comput Method Appl Mech Eng 185(2–4):161–17210.1016/S0045-7825(99)00257-1 ↗
14. Chocron T, Banks-Sills L (2019) Nearly mode I fracture toughness and fatigue delamination propagation in a multidirectional laminate fabricated by a wet-layup. Phys Mesomech 22(2):107–14010.1134/S1029959919020036 ↗
15. Choi NS, Kinloch AJ, Williams JG (1999) Delamination fracture of multidirectional carbon-fiber/epoxy composites under mode I, mode II and mixed-mode I/II loading. J Compos Mater 33(1):73–10010.1177/002199839903300105 ↗
16. Davidson BD, Schapery RA (1988) Effect of finite width on deflection and energy release rate of an orthotropic double cantilever specimen. J Compos Mater 22(7):640–65610.1177/002199838802200704 ↗
17. Davidson BD, Krüger R, König M (1996) Effect of stacking sequence on energy release rate distributions in multidirectional DCB and ENF specimens. Eng Fract Mech 55(4):557–56910.1016/S0013-7944(96)00037-9 ↗
18. Davies P, Moulin C, Kausch HH, Fischer M (1990) Measurement of ${G}Ic$ and ${G}I\!Ic$ in carbon/epoxy composites. Compos Sci Technol 39(3):193–20510.1016/0266-3538(90)90041-3 ↗
19. de Morais AB (2011) A new fibre bridging based analysis of the Double Cantilever Beam (DCB) test. Composites Part A 42(10):1361–136810.1016/j.compositesa.2011.05.019 ↗
20. de Morais AB, de Moura MF, Marques AT, de Castro PT (2002) Mode-I interlaminar fracture of carbon/epoxy cross-ply composites. Compos Sci Technol 62(5):679–68610.1016/S0266-3538(01)00223-8 ↗
21. Frossard G, Cugnoni J, Gmür T, Botsis J (2016) Mode I interlaminar fracture of carbon epoxy laminates: effects of ply thickness. Composites Part A 91:1–810.1016/j.compositesa.2016.09.009 ↗
22. Garulli T, Catapano A, Fanteria D, Jumel J, Martin E (2020) Design and finite element assessment of fully uncoupled multi-directional layups for delamination tests. J Compos Mater 54(6):773–79010.1177/0021998319868293 ↗
23. Gill AF, Robinson P, Pinho S (2009) Effect of variation in fibre volume fraction on modes I and II delamination behaviour of 5HS woven composites manufactured by RTM. Compos Sci Technol 69(14):2368–237510.1016/j.compscitech.2009.02.008 ↗
24. Gong XJ, Hurez A, Verchery G (2010) On the determination of delamination toughness by using multidirectional DCB specimens. Polym Test 29(6):658–66610.1016/j.polymertesting.2010.04.007 ↗
25. Gong Y, Zhang B, Zhao L, Zhang J, Hu N, Zhang C (2019) R-curve behaviour of the mixed-mode I/II delamination in carbon/epoxy laminates with unidirectional and multidirectional interfaces. Compos Struct 223:11094910.1016/j.compstruct.2019.110949 ↗
26. Hashemi S, Kinloch AJ, Williams JG (1990) The analysis of interlaminar fracture in uniaxial fibre-polymer composites. Proc R Soc Lond A 427(1872):173–19910.1098/rspa.1990.0007 ↗
27. ISO 15024:2001(E) (2001) Fiber reinforced plastic composites—determination of mode I interlaminar fracture toughness, $GIC$, for unidirectional reinforced materials. International Organization for Standardization, Geneva
28. ISO 15114:2014(E) (2014) Fiber reinforced plastic composites—determination of mode II fracture resistance for unidirectionally reinforced materials using the calibrated end-loaded split (C-ELS) test and an effective crack length approach. International Organization for Standardization, Geneva
29. Naik NK, Reddy KS, Meduri S, Raju NB, Prasad PD, Azad SNM, Ogde PA, Reddy BCK (2002) Interlaminar fracture characterization for plain weave fabric composites. J Mater Sci 37(14):2983–298710.1023/A:1016025232102 ↗
30. Pereira AB, de Morais AB, de Moura MFSF, Magalhães AG (2005) Mode I interlaminar fracture of woven glass/epoxy multidirectional laminates. Composites Part A 36(8):1119–112710.1016/j.compositesa.2005.01.006 ↗
31. Rajendran TS, Johar M, Low KO, Abu Hassan S, Wong KJ (2019) Interlaminar fracture toughness of a plain weave flax/epoxy composite. Plastics Rubber Compos 48(2):74–8110.1080/14658011.2018.1550235 ↗
32. Robinson P, Foster S, Hodgkinson JM (1996) The effects of starter film thickness, residual stresses and layup on ${G}Ic$ of a $0\circ /0\circ $ interface. Adv Compos Lett 5(6):159–16310.1177/096369359600500601 ↗
33. Rzeczkowski J, Samborski S, de Moura M (2020) Experimental investigation of delamination in composite continuous fiber-reinforced plastic laminates with elastic couplings. Materials 13(22):514610.3390/ma13225146 ↗
34. Sebaey TA, Blanco N, Costa J, Lopes CS (2012) Characterization of crack propagation in mode I delamination of multidirectional CFRP laminates. Compos Sci Technol 72(11):1251–125610.1016/j.compscitech.2012.04.011 ↗
35. Shokrieh MM, Zeinedini A (2014) A novel method for calculation of strain energy release rate of asymmetric double cantilever laminated composite beams. Appl Compos Mater 21(3):399–41510.1007/s10443-013-9328-5 ↗
36. Shokrieh MM, Heidari-Rarani M (2011) Effect of stacking sequence on R-curve behavior of glass/epoxy DCB laminates with $0\circ //0\circ $ crack interface. Mater Sci Eng A 529:265–26910.1016/j.msea.2011.09.027 ↗
37. Simon I, Banks-Sills L, Fourman V (2017) Mode I delamination propagation and R-ratio effects in woven composite DCB specimens for a multi-directional layup. Int J Fatigue 96:237–25110.1016/j.ijfatigue.2016.12.005 ↗
38. Sørensen BF, Jacobsen TK (1998) Large-scale bridging in composites: R-curves and bridging laws. Composites Part A 29(11):1443–145110.1016/S1359-835X(98)00025-6 ↗
39. Sørensen BF, Jacobsen TK (2000) Crack growth in composites applicability of R-curves and bridging laws. Plastics Rubber Compos 29(3):119–13310.1179/146580100101540879 ↗
40. Williams JG (1988) On the calculation of energy release rates for cracked laminates. Int J Fract 36(2):101–11910.1007/BF00017790 ↗
41. Williams JG (1989a) End corrections for orthotropic DCB specimens. Compos Sci Technol 35(4):367–37610.1016/0266-3538(89)90058-4 ↗
42. Williams JG (1989b) The fracture mechanics of delamination tests. J Strain Anal Eng 24(4):207–21410.1243/03093247V244207 ↗
43. Xiao F, Hui CY, Kramer EJ (1993) Analysis of a mixed mode fracture specimen: the asymmetric double cantilever beam. J Mater Sci 28(20):5620–562910.1007/BF00367838 ↗
44. Zhao L, Wang Y, Zhang J, Gong Y, Lu Z, Hu N, Xu J (2017) An interface-dependent model of plateau fracture toughness in multidirectional CFRP laminates under mode I loading. Composites Part B 131:196–20810.1016/j.compositesb.2017.07.077 ↗
45. Zhao Y, Cao M, Lum WP, Tan VBC, Tay TE (2018) Interlaminar fracture toughness of hybrid woven carbon-Dyneema composites. Composites Part A 114:377–38710.1016/j.compositesa.2018.08.035 ↗