One of the primary objectives in the design of composite structures is the prevention of premature bond failure. Therefore, the characterization of cohesive behavior is an important field of study in structural engineering. Using fracture mechanics principles, the cohesive behavior of an epoxy bonded coarse silica sand aggregate bond interface is studied in this paper, with a focus on finding a general analytical form of idealizing its behavior when used in a specimen possessing asymmetric and inhomogeneous qualities. Two series of small-scale specimens were experimentally tested under mixed-mode bending (MMB) conditions, where it was found that there was negligible influence exerted on the fracture energy of the interface due to changes in the mixed-mode ratio or initial crack length. Using finite element analysis (FEA) methods, an appropriate bilinear traction-separation model was developed to both validate as well as obtain a set of consistent parameters applicable to all tested specimens. Comparison of the Global Method and the Local Method, used to obtain partitioned Mode I and Mode II fracture energy values from MMB specimens, were made, with the conclusion that both methods are adequate in the calculation of the total fracture energy though the Local Method should be used to obtain accurate partitioned Mode I and Mode II fracture energy values. Idealization of the bond interface using the cohesive parameters derived can be accurately achieved by the use of both contact interactions and cohesive elements in two-dimensional and three-dimensional FE models, though the results obtained using contact interactions would be expected to exhibit greater global stiffness.
References
[1]
Inglis, G.R. Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 1957, 24, 361–364.
[2]
Griffith, A.A. The phenomenon of rupture and flow in solids. Philos. Trans. R. Soc. Lond. 1920, A221, 163–198.
[3]
Dugdale, D.S. Yielding of sheets containing slits. J. Mech. Phys. Solids 1960, 8, 100–104, doi:10.1016/0022-5096(60)90013-2.
[4]
Parmigiani, J.P.; Thouless, M.D. The effects of cohesive strength and toughness on mixed-mode delamination of beam-like geometries. Eng. Fract. Mech. 2007, 74, 2675–2699, doi:10.1016/j.engfracmech.2007.02.005.
[5]
Hashemi, S.; Kinloch, A.J.; Williams, J.G. Corrections needed in double-cantilever beam tests for assessing the interlaminar failure of fibre-composites. J. Mater. Sci. Lett. 1989, 8, 125–129, doi:10.1007/BF00730701.
[6]
Williams, J.G. End corrections for orthotropic DCB specimens. Compos. Sci. Technol. 1989, 35, 367–376, doi:10.1016/0266-3538(89)90058-4.
[7]
Williams, J.G. On the calculation of energy release rates for cracked laminates. Int. J. Fract. 1988, 36, 101–119, doi:10.1007/BF00017790.
[8]
Hutchinson, J.W.; Suo, Z. Mixed mode cracking in layered materials. Adv. Appl. Mech. 1992, 29, 63–191, doi:10.1016/S0065-2156(08)70164-9.
[9]
El-Hacha, R.; Chen, D. Behaviour of hybrid FRP-UHPC beams subjected to static flexural loading. Compos. Part B 2011, 43, 582–593, doi:10.1016/j.compositesb.2011.07.004.
[10]
S?rensen, B.F.; Jacobsen, T.K. Determination of cohesive laws by the J integral approach. Eng. Fract. Mech. 2003, 70, 1841–1858, doi:10.1016/S0013-7944(03)00127-9.
[11]
ASTM Standard D6671. Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites. In ASTM International; American Society for Testing and Materials: Philadelphia, PA, USA, 2006.
St-Cyr, D. Director of Research and Development. In Personal Communication; Pultrall Inc.: Thetford Mines, QC, Canada, 2013.
[14]
Graybeal, B.A. Material Property Characterization of Ultra-High Performance Concrete. Report No. FHWA-HRT-06–103; Federal Highway Administration: Washington, DC, USA. August, 2006.
[15]
Quispitupa, A.; Berggreen, C.; Carlsson, L.A. On the analysis of a mixed-mode bending sandwich specimen for debond fracture characteristics. Eng. Fract. Mech. 2009, 76, 597–613.
[16]
Da Silva, L.F.M.; Esteves, V.H.C.; Chaves, F.J.P. Fracture toughness of a structural adhesive under mixed mode loadings. Mater. Werkst. 2011, 42, 460–470, doi:10.1002/mawe.201100808.
[17]
Bui, Q.V. A modified Benzeggagh-Kenane fracture criterion for mixed-mode delamination. J. Compos. Mater. 2011, 45, 389–413, doi:10.1177/0021998310376105.
[18]
Harvey, C.M.; Wang, S. Experimental assessment of mixed-mode partition theories. Compos. Struct. 2012, 94, 2057–2067, doi:10.1016/j.compstruct.2012.02.007.
[19]
Bennati, S.; Fisicaro, P.; Valvo, P.S. An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model. Meccanica 2013, 48, 443–462, doi:10.1007/s11012-012-9686-3.
[20]
Wang, S.; Harvey, C.M.; Guan, L. Partition of mixed modes in layered isotropic double cantilever beams with non-rigid cohesive interfaces. Eng. Fract. Mech. 2013, 111, 1–25, doi:10.1016/j.engfracmech.2013.09.005.
Reeder, J.R.; Crews, J.R., Jr. Nonlinear analysis and redesign of the mixed-mode bending delamination test. NASA Tech. Memo. 1991, 14, doi:10.1520/CTR10078J.
[23]
Ducept, F.; Gamby, D.; Davies, P. A mixed-mode failure criterion derived from tests on symmetric and asymmetric specimens. Compos. Sci. Technol. 1999, 59, 609–619, doi:10.1016/S0266-3538(98)00105-5.
[24]
Kinloch, A.J.; Wang, Y.; William, J.G.; Yayla, P. The mixed-mode delamination of fibre composite materials. Compos. Sci. Technol. 1993, 47, 225–237, doi:10.1016/0266-3538(93)90031-B.
[25]
Schapery, R.A.; Davidson, B.D. Prediction of energy release rate for mixed-mode delamination using classical plate theory. Appl. Mech. Rev. 1990, 43, S281–S287, doi:10.1115/1.3120829.
[26]
Reeder, J.R.; Crew, J.R., Jr. Mixed-mode bending methods for delamination testing. Am. Inst. Aeronaut. Astronaut. 1990, 28, 1270–1276, doi:10.2514/3.25204.
[27]
De Moura, M.F.S.F.; Campilho, R.D.S.G.; Gon?alves, J.P.M. Pure mode II fracture characterization of composite bonded joints. Int. J. Adhes. Adhes. 2009, 46, 1589–1595.
[28]
Hashemi, S.; Kinloch, A.J.; Williams, J.G. The analysis of interlaminar fracture in uniaxial fibre-polymer composites. Proc. R. Soc. Lond. Ser. A 1990, 427, 173–199, doi:10.1098/rspa.1990.0007.
[29]
Benzeggagh, M.L.; Kenane, M. Measurement of mixed-mode delamination fracture toughness of uni-directional glass/epoxy composites with mixed-mode bending apparatus. Compos. Sci. Technol. 1996, 56, 439–449, doi:10.1016/0266-3538(96)00005-X.
[30]
Kanninen, M.F.; Popelar, C.H. Advanced Fracture Mechanics; Oxford University Press: New York, NY, USA, 1985.
[31]
Sills, R.B.; Thouless, M.D. The effect of cohesive-law parameters on mixed-mode fracture. Eng. Fract. Mech. 2012, 109, 353–368, doi:10.1016/j.engfracmech.2012.06.006.
[32]
Tvergaard, V.; Hutchinson, J.W. The influence of plasticity of mixed mode interface toughness. J. Mech. Phys. Solid 1993, 41, 110–135.
[33]
Tvergaard, V.; Hutchinson, J.W. On the toughness of ductile adhesive joints. J. Mech. Phys. Solid 1996, 44, 789–800, doi:10.1016/0022-5096(96)00011-7.
[34]
Campilho, R.D.S.G.; Banea, M.D.; Neto, J.A.B.P.; da Silva, L.F.M. Modelling adhesive joints with cohesive zone models: Effect of the cohesive law shape of the adhesive layer. Int. J. Adhes. Adhes. 2013, 44, 48–56.
[35]
Diehl, T. On using a penalty-based cohesive-zone finite element approach. Part I: Elastic solution benchmarks. Int. J. Adhes. Adhes. 2008, 28, 237–255, doi:10.1016/j.ijadhadh.2007.06.003.
[36]
Dassault Systèmes Simulia Corp. Abaqus Analysis User’s Manual. Version 6.9; Dassault Systemes Simulia Corporation: Providence, RI, USA, 2009.
[37]
Blackman, B.R.K.; Hadavinia, H.; Kinloch, A.J.; Williams, J.G. The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints. Int. J. Fract. 2003, 119, 25–46, doi:10.1023/A:1023998013255.
[38]
Chen, D.; El-Hacha, R. Bond strength between cast-in-place ultra-high-performance-concrete and glass fibre reinforced polymer plates using epoxy bonded coarse silica sand. J. ASTM Int. 2012, 9, doi:10.1520/JAI103836.
[39]
Chen, D.; El-Hacha, R. Characterization of Cohesive Bond Interfaces under Mode II Loading Using Finite Element Methods. In Proceedings of 4th Asia-Pacific Conference on FRP in Structures (APFIS 2013), Melbourne, Australia, 11–13 December 2013; p. 6.
Camanho, P.P.; Dávila, C.G. Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials; NASA/TM-2002-211737; National Aeronautics and Space Administration: Hampton, Virginia, USA.