In this paper, the debonding of a single fiber-matrix system of carbon fiber reinforced composite (CFRP) AS4/Epson 828 material is studied using Cohesive Zone Model (CZM). The effect of parameters namely, maximum tangential contact stress, tangential slip distance and artificial damping coefficient on the debonding length at the interface of the fiber-matrix is analyzed. Contact elements used in the CZM are coupled based on a bilinear stress-strain curve. Load is applied on the matrix, tangential to the interface. Hence, debonding is observed primarily in Mode II. Wide range of values are considered to study the inter-dependency of the parameters and its effect on debonding length. Out of the three parameters mentioned, artificial damping coefficient and tangential slip distance significantly affect debonding length. A thorough investigation is recommended for case wise interface debonding analysis, to estimate the optimal parametric values while using CZM.
tangential slip distance at the maximum tangential contact stress (unc)
0.1
maximum tangential contact stress (τmax)
500 MPa
tangential slip distance at the completion of debonding (utc)
0.001
artificial damping coefficient (μ)
0.001
tangential slip under normal compression (β)
1
Tab.2
No. of elements
% deviation debonding length (%)
3400
2.40
2725
1.37
2166
0.0
2052
−3.21
1632
−4.01
Tab.3
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
Fig.9
1
Pattabhi Ramaiah B, Rammohan B, Vijay Kumar S, Satish Babu D, Raghuatnhan R. Aero-elastic analysis of stiffened composite wing structure. Advances in Vibration Engineering, 2009, 8(3): 255–264
2
Sudhir Sastry Y B, Budarapu P R, Madhavi N, Krishna Y. Buckling analysis of thin wall stiffened composite panels. Computational Materials Science, 2015, 96(B): 459–471
3
Frolov V A. Strength of a composite material for structural applications. Mechanics of Composite Materials, 1987, 23(2): 148–154
4
Sudhir Sastry Y B, Budarapu P R, Krishna Y, Devaraj S. Studies on ballistic impact of the composite panels. Theoretical and Applied Fracture Mechanics, 2014, 72: 2–12
5
BP O'Rourke. The uses of composite materials in the design and manufacture of formula 1 racing cars. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 1990, 204: 41–48
6
Parga-Landa B, Hernández-Olivares F. Analytical model to predict behaviour of soft armours. International Journal of Impact Engineering, 1995, 16(3): 455–466
7
Anderson C E Jr, Bodner S R. Ballistic impact: The status of analytical and material modeling. International Journal of Impact Engineering, 1988, 7(1): 9–35
8
Naik N K, Shrirao P. Composite structures under ballistic impact. Composite Structures, 2004, 66(1-4): 579–590
9
James C. Leslie, The use of composite material increase the availability of oil and gas and reduce the cost of drilling and production operations. Proc. SPIE 6531, Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security, 65310E, 2007
https://doi.org/10.1117/12.716157
10
Anderson C E Jr, Bodner S R. Ballistic impact: The status of analytical and material modeling. International Journal of Impact Engineering, 1988, 7(1): 9–35
11
Naik N K, Shrirao P. Composite structures under ballistic impact. Composite Structures, 2004, 66(1−4): 579–590
12
Katz S, Grossman E, Gouzman I, Murat M, Wiesel E, Wagner H D. Response of composite materials to hypervelocity impact. International Journal of Impact Engineering, 2008, 35(12): 1606–1611
13
Budarapu P R, Narayana T S S, Rammohan B, Rabczuk T. Directionality of sound radiation from rectangular panels. Applied Acoustics, 2015, 89: 128–140
14
Scoutis C. Carbon fiber reinforced plastics in aircraft construction. Materials Science and Engineering: A, 2005, 412(1−2): 171–176
15
Paipetis A S. Room vs. temperature studies of model composites: modes of failure of carbon fibre/epoxy interfaces. Composite Interfaces, 2012, 19(2): 135–158
16
Xu Z, Li J, Wu X, Huang Y, Chen L, Zhang G. Effect of kidney-type and circular cross sections on carbon fiber surface and composite interface. Composites. Part A, Applied Science and Manufacturing, 2008, 39(2): 301–307
17
Zhao J, Ho K K C, Shamsuddin S R, Bismarck A, Dutschk V. A comparative study of fibre/matrix interface in glass fibre reinforced polyvinylidene fluoride composites. Colloids Surfaces A Physicochem, Eng Asp, 2012, 413: 58–64
18
Nath R B, Fenner D N, Galiotis C. Progressional approach to interfacial failure in carbon reinforced composites: Elasto-plastic finite element modelling of interface cracks. Composites. Part A, Applied Science and Manufacturing, 2000, 31(9): 929–943
19
Kim B W, Nairn J A. Observations of fiber fracture and interfacial debonding phenomena using the fragmentation test in single fiber composites. Journal of Composite Materials, 2002, 36(15): 1825–1858
20
Ho H, Drzal L T. Non-linear numerical study of the single-fiber fragmentation test Part I: Test mechanics. Composites Engineering, 1995, 5(10−11): 1231–1244
21
Yang S W, Budarapu P R, Roy Mahapatra D, Bordas S, Rabczuk T. A meshless adaptive multiscale method for fracture. Computational Materials Science, 2015, 96(B): 382–395
22
Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modelling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143
23
Budarapu P R, Gracie R, Bordas S P A, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
24
Sudhir Sastry Y B, Krishna Y, Budarapu P R. Parametric studies on buckling of thin walled channel beams. Computational Materials Science, 2015, 96(B): 416–424
25
Budarapu P R, Yb S S, Javvaji B, Mahapatra D R. Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium. Frontiers of Structural and Civil Engineering, 2014, 8(2): 151–159
26
Xiao S P, Belytschko T. A bridging domain method for coupling continua with molecular dynamics. Computer Methods in Applied Mechanics and Engineering, 2004, 193(17−20): 1645–1669
27
Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2008, 197(6−8): 641–658
28
Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid−structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
29
Robert G, Belytschko T. Concurrently coupled atomistic and XFEM models for dislocations and cracks. International Journal for Numerical Methods in Engineering, 2008, 78: 354–378
30
Rabczuk T, Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760
31
Rabczuk T, Bordas S P, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495
32
Bordas S P, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, 2008, 75(5): 943–960
33
Gracie R, Belytschko T. Adaptive continuum-atomistic simulations of dislocation dynamics. International Journal for Numerical Methods in Engineering, 2011, 86(4−5): 575–597
34
Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29−30): 2777–2799
35
Rabczuk T, Areias P M A, Belytschko T. A simplified meshfree method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering, 2007, 69(5): 993–1021
36
Rabczuk T, Song J H, Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Engineering Fracture Mechanics, 2009, 76(6): 730–741
37
Rabczuk T, Zi G, Bordas S P, Nguyen-Xuan H. A simple and robust threedimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37−40): 2437–2455
38
Turon A, Camanho P P, Costa J, Dávila C G. A damage model for the simulation of delamination in advanced composites under variable-mode loading, Mechanics of Materials, 2006, 38(11): 1072–1089
39
Irwin G R. Fracture. Handbuch der Physik. Flugge S, ed. Berlin: Springer, 1958, VI: 551–590
40
Rybicki E F, Kanninen M F. A finite element calculation of stress intensity factors by a modified crack closure integral. Engineering Fracture Mechanics, 1977, 9(4): 931–938
41
Shivakumar K N. Tan,PW. Newman, JC. A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies. International Journal of Fracture, 1988, 36: R43–R50
42
Krueger R. Virtual crack closure technique: History, approach, and applications. Applied Mechanics Reviews, 2004, 57(2): 109–143
43
Raju I S. Calculation of strain-energy release rates with higher order and singular finite elements. Engineering Fracture Mechanics, 1987, 28(3): 251–274
44
Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, 1968, 35(2): 379–386
45
Hellen T K. On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering, 1975, 9(1): 187–207
46
Parks D M. A stiffness derivative finite element technique of crack tip stress intensity factors. International Journal of Fracture, 1974, 10(4): 487–502
47
Griffith A A. The phenomenon of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1921, 221(582−593): 163–198
48
Turon A, Costa J, Camanho P P, Davila, C G. Simulation of delamination propagation in composites under high-cycle fatigue by means of cohesive-zone models, NASA/TM 214532 1− 28, 2006
49
Turon A, Camanho P P, Costa J, Dávila C G. Mechanics of Materials, 2006, 38: 1072–1089
50
Turon A, Costa J, Camanho P P, Dávila C G. Composites. Part A, Applied science and manufacturing, 2008, 38: 2270–2282
51
Kumar S, Singh I V, Mishra B K. A homogenized XFEM approach to simulate fatigue crack growth problems. Computers & Structures, 2015, 150: 1–22
52
Kumar S, Singh I V, Mishra B K, Rabczuk T. Modeling and simulation of kinked cracks by virtual node XFEM. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 1425–1466
53
Kumar S, Singh I V, Mishra B K. A multigrid coupled (FE-EFG) approach to simulate fatigue crack growth in heterogeneous materials. Theoretical and Applied Fracture Mechanics, 2014, 72: 121–135
54
Agarwal A, Singh I V, Mishra B K. Numerical prediction of elasto-plastic behaviour of interpenetrating phase composites by EFGM. Composites. Part B, Engineering, 2013, 51: 327–336
55
Bhardwaj G, Singh I V, Mishra B K, Bui T Q. Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions. Composite Structures, 2015, 126: 347–359
56
Bhardwaj G, Singh I V, Mishra B K. Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 186–229
57
Dugdale D S. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8(2): 100–104
58
Barenblatt G I. The mathematical theory of equilibrium cracks in brittle f<?Pub Caret?>racture. Advances in Applied Mechanics, 1962, 7(C): 55–129
59
Bažant Z P, Jirásek M. Nonlocal integral formulations of plasticity and damage: Survey of progress. Journal of Engineering Mechanics, 2002, 128(11): 1119–1149
60
Alfano G, Crisfield M A. Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. International Journal for Numerical Methods in Engineering, 2001, 50(7): 1701–1736
https://doi.org/10.1002/nme.93vol50(7)
61
Fujimoto T, Kagami J, Kawaguchi T, Hatazawa T. Micro-displacement characteristics under tangential force. Wear, 2000, 241(2): 136–142
62
Grzemba B, Pohrt R, Teidelt E, Popov V L. Maximum micro-slip in tangential contact of randomly rough self-affine surfaces. Wear, 2014, 309(1−2): 256–258
63
Design M, Section C S, Technical N, Introduction I. An artificial damping method for the harmonically excited non-linear systems. 1988, 120: 597–608
64
Kim S. Artificial damping in multigrid methods. Applied Mathematics Letters, 2001, 14(3): 359–364
