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Published in: Mechanics of Composite Materials 5/2016

01-11-2016

Revisiting the Numerical Convergence of Cohesive-Zone Models in Simulating the Delamination of Composite Adhesive Joints by Using the Finite-Element Analysis

Authors: P. F. Liu, Z. P. Gu, Z. H. Hu

Published in: Mechanics of Composite Materials | Issue 5/2016

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Abstract

Delamination is the dominating failure mechanism in composite adhesive joints. A deep insight into the delamination failure mechanism requires advanced numerical methods. Currently, cohesive-zone models (CZMs), in combination with the finite-element analysis (FEA), have become powerful tools for modeling the initiation and growth of delaminations in composites. However, ensuring the numerical convergence in the CZMs used for a delamination analysis of three-dimensional (3D) composite structures is always a challenging issue due to the “snap-back” instability in the nonlinear implicit FEA, which arises mainly from the cohesive softening behavior. Based on the midplane interpolation technique, first numerical techniques for implementing 3D bilinear and exponential CZMs by using ABAQUS-UEL (user element subroutine) are developed in this paper. In particular, a viscous regularization by introducing the damping effect into the stiffness equation is used to improve the convergence. Two examples, a single-lap composite joint and a composite skin/stiffener panel under tension, demonstrate the numerical technique developed. Then, the effect of cohesion parameters on the numerical convergence based on the viscous regularization is studied.

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Literature
1.
go back to reference S. E. Stapleton, E. J. Pineda, T. Gries, and A.M., Waas, “Adaptive shape functions and internal mesh adaptation for modeling progressive failure in adhesively bonded joints,” Int. J. Solids Struct., 51, No. 18, 3252-3264 (2014). S. E. Stapleton, E. J. Pineda, T. Gries, and A.M., Waas, “Adaptive shape functions and internal mesh adaptation for modeling progressive failure in adhesively bonded joints,” Int. J. Solids Struct., 51, No. 18, 3252-3264 (2014).
2.
go back to reference D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids, 8, No. 2, 100-104 (1960).CrossRef D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids, 8, No. 2, 100-104 (1960).CrossRef
3.
go back to reference G. I. Barenblatt, “The mathematical theory of equilibrium cracks in brittle fracture,” Adv. Appl. Mech., 7, No. 1, 55-129 (1962).CrossRef G. I. Barenblatt, “The mathematical theory of equilibrium cracks in brittle fracture,” Adv. Appl. Mech., 7, No. 1, 55-129 (1962).CrossRef
4.
go back to reference Y. Mi, M. A. Crisfield, G. Davies, and H. Hellweg, “Progressive delamination using interface elements,” J. Compos. Mater., 32, No. 14, 1246-1272 (1998).CrossRef Y. Mi, M. A. Crisfield, G. Davies, and H. Hellweg, “Progressive delamination using interface elements,” J. Compos. Mater., 32, No. 14, 1246-1272 (1998).CrossRef
5.
go back to reference G. Alfano, and M. A. Crisfield, “Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues,” Int. J. Numer. Meth. Eng., 50, No. 7, 1701-1736 (2001).CrossRef G. Alfano, and M. A. Crisfield, “Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues,” Int. J. Numer. Meth. Eng., 50, No. 7, 1701-1736 (2001).CrossRef
6.
go back to reference P. P. Camanho, C. G. Davila, and M. F. de Moura, “Numerical simulation of mixed-mode progressive delamination in composite materials,” J. Compos. Mater., 37, No. 16, 1415-1438 (2003).CrossRef P. P. Camanho, C. G. Davila, and M. F. de Moura, “Numerical simulation of mixed-mode progressive delamination in composite materials,” J. Compos. Mater., 37, No. 16, 1415-1438 (2003).CrossRef
7.
go back to reference A. Turon, P. P. Camanho, J. Costa, and C. G. Dávila, “A damage model for the simulation of delamination in advanced composites under variable-mode loading,” Mech. Mater., 38, No. 11, 1072-1089 (2006).CrossRef A. Turon, P. P. Camanho, J. Costa, and C. G. Dávila, “A damage model for the simulation of delamination in advanced composites under variable-mode loading,” Mech. Mater., 38, No. 11, 1072-1089 (2006).CrossRef
8.
go back to reference D. Xie and A. M. Waas, “Discrete cohesive zone model for mixed-mode fracture using finite element analysis,” Eng. Fract. Mech., 73, No. 13, 1783-1796 (2006).CrossRef D. Xie and A. M. Waas, “Discrete cohesive zone model for mixed-mode fracture using finite element analysis,” Eng. Fract. Mech., 73, No. 13, 1783-1796 (2006).CrossRef
9.
go back to reference V. Tvergaard, “Model studies of fibre breakage and debonding in a metal reinforced by short fibres,” J. Mech. Phys. Solids, 41, No. 8, 1309-1326 (1993).CrossRef V. Tvergaard, “Model studies of fibre breakage and debonding in a metal reinforced by short fibres,” J. Mech. Phys. Solids, 41, No. 8, 1309-1326 (1993).CrossRef
10.
go back to reference V. Tvergaard and J. W. Hutchinson, “Effect of strain-dependent cohesive zone model on predictions of crack growth resistance,” Int. J. Solids Struct., 33, No. 20, 3297-3308 (1996).CrossRef V. Tvergaard and J. W. Hutchinson, “Effect of strain-dependent cohesive zone model on predictions of crack growth resistance,” Int. J. Solids Struct., 33, No. 20, 3297-3308 (1996).CrossRef
11.
go back to reference X. P. Xu and A. Needleman, “Numerical simulations of fast crack growth in brittle solids,” J. Mech. Phys. Solids, 42, No. 9, 1397-1434 (1994).CrossRef X. P. Xu and A. Needleman, “Numerical simulations of fast crack growth in brittle solids,” J. Mech. Phys. Solids, 42, No. 9, 1397-1434 (1994).CrossRef
12.
go back to reference V. K. Goyal, E. R. Johnson, and C. G Dávila, “Irreversible constitutive law for modeling the delamination process using interfacial surface discontinuities,” Compos. Struct., 65, No. 3, 289-305 (2004).CrossRef V. K. Goyal, E. R. Johnson, and C. G Dávila, “Irreversible constitutive law for modeling the delamination process using interfacial surface discontinuities,” Compos. Struct., 65, No. 3, 289-305 (2004).CrossRef
13.
go back to reference K. Park, G. H. Paulino, and J. R. Roesler, “A unified potential-based cohesive model of mixed-mode fracture,” J. Mech. Phys. Solids, 57, No. 6, 891-908 (2009).CrossRef K. Park, G. H. Paulino, and J. R. Roesler, “A unified potential-based cohesive model of mixed-mode fracture,” J. Mech. Phys. Solids, 57, No. 6, 891-908 (2009).CrossRef
14.
go back to reference P. F. Liu, and M. M. Islam, “A nonlinear cohesive model for mixed-mode delamination of composite laminates,” Compos. Struct., 106, 47-56 (2013).CrossRef P. F. Liu, and M. M. Islam, “A nonlinear cohesive model for mixed-mode delamination of composite laminates,” Compos. Struct., 106, 47-56 (2013).CrossRef
15.
go back to reference E. Riks, “An incremental approach to the solution of snapping and buckling problems,” Int. J. Solids Struct., 15, 529-551 (1979).CrossRef E. Riks, “An incremental approach to the solution of snapping and buckling problems,” Int. J. Solids Struct., 15, 529-551 (1979).CrossRef
16.
go back to reference J. L. Chaboche, F. Feyel, and Y. Monerie, “Interface debonding models: a viscous regularization with a limited rate dependency,” Int. J. Solids Struct., 38, No. 18:3127-3160(2001). J. L. Chaboche, F. Feyel, and Y. Monerie, “Interface debonding models: a viscous regularization with a limited rate dependency,” Int. J. Solids Struct., 38, No. 18:3127-3160(2001).
17.
go back to reference L. Hamitouche, M. Tarfaoui, and A. Vautrin, “An interface debonding law subject to viscous regularization for avoiding instability: application to the delamination problems,” Eng. Fract. Mech., 75, No. 10, 3084-3100 (2008).CrossRef L. Hamitouche, M. Tarfaoui, and A. Vautrin, “An interface debonding law subject to viscous regularization for avoiding instability: application to the delamination problems,” Eng. Fract. Mech., 75, No. 10, 3084-3100 (2008).CrossRef
18.
go back to reference Y. F. Gao and A. F. Bower, “A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces,” Model. Simul. Mater. Sci. Eng., 12, No. 3, 453 (2004).CrossRef Y. F. Gao and A. F. Bower, “A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces,” Model. Simul. Mater. Sci. Eng., 12, No. 3, 453 (2004).CrossRef
19.
go back to reference N. Hu, Y., Zemba, T. Okabe, C. Yan, H. Fukunaga, and A. Elmarakbi, “A new cohesive model for simulating delamination propagation in composite laminates under transverse loads,” Mech. Mater., 40, No. 11, 920-935 (2008). N. Hu, Y., Zemba, T. Okabe, C. Yan, H. Fukunaga, and A. Elmarakbi, “A new cohesive model for simulating delamination propagation in composite laminates under transverse loads,” Mech. Mater., 40, No. 11, 920-935 (2008).
20.
go back to reference M. L. Benzeggagh and M. Kenane, “Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus,” Compos. Sci. Technol., 56, No. 4, 439-449 (1996).CrossRef M. L. Benzeggagh and M. Kenane, “Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus,” Compos. Sci. Technol., 56, No. 4, 439-449 (1996).CrossRef
21.
go back to reference J. Segurado and J. LLorca, “A new three-dimensional interface finite element to simulate fracture in composites,” Int. J. Solids Struct., 41, No. 11, 2977-2993 (2004).CrossRef J. Segurado and J. LLorca, “A new three-dimensional interface finite element to simulate fracture in composites,” Int. J. Solids Struct., 41, No. 11, 2977-2993 (2004).CrossRef
22.
go back to reference A. Turon, C. G. Dávila, P. P. Camanho, and J. Costa, “An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models,” Eng. Fract. Mech. 74, No. 10, 1665-1682 (2007).CrossRef A. Turon, C. G. Dávila, P. P. Camanho, and J. Costa, “An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models,” Eng. Fract. Mech. 74, No. 10, 1665-1682 (2007).CrossRef
23.
go back to reference P. W. Harper and S. R. Hallett, “Cohesive zone length in numerical simulations of composite delamination,” Eng. Fract. Mech., 75, No. 16, 4774-4792 (2008).CrossRef P. W. Harper and S. R. Hallett, “Cohesive zone length in numerical simulations of composite delamination,” Eng. Fract. Mech., 75, No. 16, 4774-4792 (2008).CrossRef
24.
go back to reference Abaqus-Abaqus Version 6.12 Documentation-Abaqus Analysis Users Manual. Abaqus-Abaqus Version 6.12 Documentation-Abaqus Analysis Users Manual.
25.
go back to reference K. Y. Volokh, “Comparison between cohesive zone models,” Commun. Numer. Meth. Eng. 20, No. 11, 845-856 (2004).CrossRef K. Y. Volokh, “Comparison between cohesive zone models,” Commun. Numer. Meth. Eng. 20, No. 11, 845-856 (2004).CrossRef
26.
go back to reference G. Alfano, “On the influence of the shape of the interface law on the application of cohesive-zone models,” Compos. Sci. Technol., 66, No. 6, 723-730 (2006).CrossRef G. Alfano, “On the influence of the shape of the interface law on the application of cohesive-zone models,” Compos. Sci. Technol., 66, No. 6, 723-730 (2006).CrossRef
27.
go back to reference Q. D. Yang, M. D. Thouless, and S. M. Ward, “Elastic-plastic mode-II fracture of adhesive joints,” Inter. J. Solids Struct., 38, No. 18, 3251-3262 (2001).CrossRef Q. D. Yang, M. D. Thouless, and S. M. Ward, “Elastic-plastic mode-II fracture of adhesive joints,” Inter. J. Solids Struct., 38, No. 18, 3251-3262 (2001).CrossRef
28.
go back to reference S. K. Panigrahi, “Damage analyses of adhesively bonded single lap joints due to delaminated FRP composite adherends,” Appl. Compos. Mater., 16, No. 4, 211-223 (2009).CrossRef S. K. Panigrahi, “Damage analyses of adhesively bonded single lap joints due to delaminated FRP composite adherends,” Appl. Compos. Mater., 16, No. 4, 211-223 (2009).CrossRef
29.
go back to reference R. D. S. G. Campilho, M. D. Banea, J. A. B. P. Neto, and L. F. da Silva, “Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer,” Int. J. Adhes. Adhes., 44, 48-56 (2013).CrossRef R. D. S. G. Campilho, M. D. Banea, J. A. B. P. Neto, and L. F. da Silva, “Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer,” Int. J. Adhes. Adhes., 44, 48-56 (2013).CrossRef
30.
go back to reference R. Krueger, and T. K. O’Brien, “A shell/3D modeling technique for the analysis of delaminated composite laminates,” Compos. Part A, 32, No. 1, 25-44 (2001).CrossRef R. Krueger, and T. K. O’Brien, “A shell/3D modeling technique for the analysis of delaminated composite laminates,” Compos. Part A, 32, No. 1, 25-44 (2001).CrossRef
31.
go back to reference B. Dattaguru, K. Venkatesha, T. Ramamurthy, and F. Buchholz, “Finite element estimates of strain energy release rate components at the tip of an interface crack under mode I loading,” Eng. Fract. Mech., 49, No. 3, 451-463 (1994).CrossRef B. Dattaguru, K. Venkatesha, T. Ramamurthy, and F. Buchholz, “Finite element estimates of strain energy release rate components at the tip of an interface crack under mode I loading,” Eng. Fract. Mech., 49, No. 3, 451-463 (1994).CrossRef
32.
go back to reference B. Pradhan and S. K. Panda, “Effect of material anisotropy and curing stresses on interface delamination propagation characteristics in multiply laminated FRP composites,” ASME J. Eng. Mater. Tchnol., 128, No. 3, 383-392 (2006).CrossRef B. Pradhan and S. K. Panda, “Effect of material anisotropy and curing stresses on interface delamination propagation characteristics in multiply laminated FRP composites,” ASME J. Eng. Mater. Tchnol., 128, No. 3, 383-392 (2006).CrossRef
33.
go back to reference F. Hu and C. Soutis, “Strength prediction of patch-repaired CFRP laminates loaded in compression,” Compos. Sci. Technol., 60(7), 1103-1114 (2000).CrossRef F. Hu and C. Soutis, “Strength prediction of patch-repaired CFRP laminates loaded in compression,” Compos. Sci. Technol., 60(7), 1103-1114 (2000).CrossRef
34.
go back to reference K. S. Kim, J. S. Yoo, Y. M. Yi, and C. G. Kim, “Failure mode and strength of uni-directional composite single lap bonded joints with different bonding methods,” Compos. Struct., 72, No. 4, 477-485 (2006).CrossRef K. S. Kim, J. S. Yoo, Y. M. Yi, and C. G. Kim, “Failure mode and strength of uni-directional composite single lap bonded joints with different bonding methods,” Compos. Struct., 72, No. 4, 477-485 (2006).CrossRef
35.
go back to reference C. D. M. Liljedahl, A. D. Crocombe, M. A. Wahab, and I. A. Ashcroft, “Damage modelling of adhesively bonded joints,” Int. J. Fract., 141,141-161(2006).CrossRef C. D. M. Liljedahl, A. D. Crocombe, M. A. Wahab, and I. A. Ashcroft, “Damage modelling of adhesively bonded joints,” Int. J. Fract., 141,141-161(2006).CrossRef
36.
go back to reference A. C. Orifici, R. S. Thomson, R. Degenhardt, C. Bisagni, and J. Bayandor, “Development of a finite-element analysis methodology for the propagation of delaminations in composite structures,” Mech. Compos. Mater., 43, No. 1, 9-28 (2007).CrossRef A. C. Orifici, R. S. Thomson, R. Degenhardt, C. Bisagni, and J. Bayandor, “Development of a finite-element analysis methodology for the propagation of delaminations in composite structures,” Mech. Compos. Mater., 43, No. 1, 9-28 (2007).CrossRef
37.
go back to reference E. F. Rybicki and M. F. Kanninen, “A finite element calculation of stress intensity factors by a modified crack closure integral,” Eng. Fract. Mech., 9, 931-938(1977).CrossRef E. F. Rybicki and M. F. Kanninen, “A finite element calculation of stress intensity factors by a modified crack closure integral,” Eng. Fract. Mech., 9, 931-938(1977).CrossRef
38.
go back to reference N. Chandra, H. Li, C. Shet, and H. Ghonem, “Some issues in the application of cohesive zone models for metal-ceramic interfaces,” Int. J. Solids Struct., 39, No. 10, 2827-2855 (2002).CrossRef N. Chandra, H. Li, C. Shet, and H. Ghonem, “Some issues in the application of cohesive zone models for metal-ceramic interfaces,” Int. J. Solids Struct., 39, No. 10, 2827-2855 (2002).CrossRef
Metadata
Title
Revisiting the Numerical Convergence of Cohesive-Zone Models in Simulating the Delamination of Composite Adhesive Joints by Using the Finite-Element Analysis
Authors
P. F. Liu
Z. P. Gu
Z. H. Hu
Publication date
01-11-2016
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 5/2016
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-016-9614-z

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