Document Type : Research Paper

Authors

School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

In this study, delamination growth in mode I loading of unidirectional laminated composites with R-curve effect was investigated. To this end, a finite element simulation of delamination growth in double cantilever beam (DCB) performed using the cohesive zone model (CZM) based on traction-separation laws. By increasing the delamination length in DCB specimens, the strain energy release rate increases and for this reason the simple traction-separation law such as bilinear are not capable to predict the load-displacement curve of this specimens accurately. To solve this shortcoming, cohesive zone models with multi-linear traction-separation laws were proposed to predict delamination behavior of the DCB specimens numerically. Afterwards, by minimizing the difference between experimental and numerical load-displacement curves using optimization method based on genetic algorithm, cohesive zone parameters are characterized. A comparison of the results obtained by cohesive laws with experimental data show that four-linear cohesive law can predict the maximum bridging stress as well as the experimental load-displacement curve accurately.

Keywords

[1] ASTM Standard D5528-94a, Standard Test Method for Mode Inter-Laminar Fracture Toughness of Unidirectional Continuous Fiber Reinforced Polymer Matrix Composites, Philadelphia, PA, 1994.
[2] Rybicki, E. F. and Kanninen, M. F., “A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral,” Eng. Fract. Mech., Vol. 9, No. 4, pp. 931–938, Jan. 1977.
[3] Nairn, J. A., “Analytical and Numerical Modeling of R -Curves for Cracks With Bridging Zones,” Int. J. Fract., vol. 155, No. 2, pp. 167–181, 2009.
[4] Williams, J. G. Hadavinia, H. and Kinloch, A. J., “Cohesive Zone Models in The Characterisation of Toughness,” Compos. Sci. Technol., Vol. 3, 2005.
[5] Alfano, G., “On The Influence of The Shape of The Interface Law on The Application of Cohesive-Zone Models,” Compos. Sci. Technol., Vol. 66, No. 6, pp. 723–730, May 2006.
[6] Dugdale, D. S., “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids, Vol. 8, No. 2, pp. 100–104, May 1960.
[7] Barenblatt, G. I., “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Compos. Sci. Technol, Vol. 3, pp. 55–129, 1962.
[8] Camanho, P. P. Davila, C. G. and De Moura, M. F., “Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials,” J. Compos. Mater., Vol. 37, No. 16, pp. 1415–1438, 2003.
[9] Turon, A. Dávila, C. G. Camanho, P. P. and Costa, J., “An Engineering Solution for Mesh Size Effects in The Simulation of Delamination Using Cohesive Zone Models,” Eng. Fract. Mech., Vol. 74, No. 10, pp. 1665–1682, 2007.
[10] Dávila, C. G. Rose, C. A. and Camanho, P. P., “A Procedure for Superposinglinear Cohesive Laws to Represent Multiple Damage Mechanisms in The Fracture Of Composites,” Int. J. Fract., Vol. 158, No. 2, pp. 211–223, 2009.
[11] Heidari-Rarani, M. Shokrieh, M. M. and Camanho, P. P., “Finite Element Modeling of Mode I Delamination Growth in Laminated DCB Specimens With R-curve Effects,” Compos. Part B Eng., Vol. 45, No. 1, pp. 897–903, 2013.
[12] Sorensen, B. F. and Jacobsen, T. K., “Large-Scale Bridging in Composites: R-Curves and Bridging Laws,” Compos. Part A Appl. Sci. Manuf., Vol. 29, No. 11, pp. 1443–1451, 1998.
[13] Shokrieh, M. M. Salamat-talab, M. and Heidari-Rarani, M., “Effect of Initial Crack Length on The Measured Bridging Law of Unidirectional E-Glass/Epoxy Double Cantilever Beam Specimens,” Mater. Des., Vol. 55, pp. 605–611, 2014.
[14] Farmand-Ashtiani, E. Cugnoni, J. and Botsis, J., “Specimen Thickness Dependence of Large Scale Fiber Bridging in Mode I Interlaminar Fracture of Carbon Epoxy Composite,” Int. J. Solids Struct. Vol. 55, pp. 58–65, 2014.
[15] Manshadi, B. D. Vassilopoulos, A. P. and Botsis, J., “A Combined Experimental/Numerical Study of The Scaling Effects on Mode I Delamination of GFRP,” Compos. Sci. Technol., Vol. 83, pp. 32–39, 2013.
[16] Manshadi, B. D. Farmand-Ashtiani, E. Botsis, J. and Vassilopoulos, A. P., “An Iterative Analytical/Experimental Study of Bridging in Delamination of The Double Cantilever Beam Specimen,” Compos. Part A Appl. Sci. Manuf., Vol. 61, pp. 43–50, Jun. 2014.
[17] Dourado, N. De Moura, M. F. S. F. De Morais, A. B. and Pereira, A. B., “Bilinear Approximations to The Mode II Delamination Cohesive Law Using an Inverse Method,” Mech. Mater, Vol. 49, pp. 42–50, 2012.
[18] de Morais, A.B. Pereira, A.B. de Moura, M.F.S.F. Silva, F.G.A. Silva Dourado, N., “Bilinear Approximations to the Mixed-Mode I–II Delamination Cohesive Law Using an Inverse Method,” Compos. Struct., Vol. 122, pp. 361–366, 2015.
[19] Blackman, B. R. K. Hadavinia, H. Kinloch, A. J. and Williams, J. G., “The Use of a Cohesive Zone Model to Study The Fracture of Fibre Composites and Adhesively-Bonded Joints,” Compos. Sci. Technol., Vol. 1, pp. 25–46, 2003.
[20] Salamat-talab, M., “Simulation Of Delamination Growth In Double Cantilever Beam Specimen Made Of Laminated Composites” MSc Thesis, Department of Mechanical Engineering, Iran university of Science and Technology, 2011.