A non-local fracture model for composite laminates and numerical simulations by using the FFT method

Abstract In this paper, we present a fracture model for composite laminates and its numerical solution by using the Fast Fourier Transforms (FFTs). The FFT-based formulation initially proposed for seeking the average behaviour of linear and non-linear composites by means of the homogenisation procedures [1,2] was adapted to evaluate the damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed to assess the failure in the matrix and the fibres. This non-local model was then connected to the Griffith–Irwin criterion in the aim of predicting crack growth. In order to assess the matrix/fibre interface delamination, we have adapted the cohesive model developed by Li [3] for accounting the mixed-mode dependent interface failure. To this end, the interfaces between the matrix and the fibres are replaced by a thin layer of interphase with the purpose of facilitating the FFT simulations. By using the proposed model, we carried out several numerical simulations on fracture process in different specimens. From these studies, we can conclude that the present FFT-based analysis is capable to deal with crack initiation and crack growth in composite laminates with high accuracy and efficiency, especially in the cases of matrix/fibre interface debonding and of multi-crack growth.

[1]  Paolo Lonetti,et al.  An Inelastic Damage Model for Fiber Reinforced Laminates , 2002 .

[2]  Hervé Moulinec,et al.  A Computational Method Based on Augmented Lagrangians and Fast Fourier Transforms for Composites with High Contrast , 2000 .

[3]  Radhi Abdelmoula,et al.  A damage model for crack prediction in brittle and quasi-brittle materials solved by the FFT method , 2012, International Journal of Fracture.

[4]  Pedro P. Camanho,et al.  A continuum damage model for composite laminates: Part I - Constitutive model , 2007 .

[5]  Jia Li,et al.  Debonding of the interface as 'crack arrestor' , 2000 .

[6]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[7]  Craig S. Collier,et al.  Progressive damage and failure modeling in notched laminated fiber reinforced composites , 2009 .

[8]  Qingda Yang,et al.  Cohesive models for damage evolution in laminated composites , 2005 .

[10]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[11]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[12]  M. Williams.  The Bending Stress Distribution at the Base of a Stationary Crack , 1961 .

[13]  R. Salganik,et al.  The strength of adhesive joints using the theory of cracks , 1965 .

[14]  Jia Li,et al.  A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials , 2006 .

[15]  De Xie,et al.  Discrete cohesive zone model for mixed-mode fracture using finite element analysis , 2006 .

[16]  Hsuan-Teh Hu,et al.  Nonlinear Analysis of Fiber-Reinforced Composite Laminates Subjected to Uniaxial Tensile Load , 2002 .

[17]  Rami Haj-Ali,et al.  Cohesive Micromechanics: A New Approach for Progressive Damage Modeling in Laminated Composites , 2009 .

[18]  S. E. Yamada,et al.  Analysis of Laminate Strength and Its Distribution , 1978 .

[19]  Ireneusz Lapczyk,et al.  Progressive damage modeling in fiber-reinforced materials , 2007 .

[20]  Z. Hashin.  Failure Criteria for Unidirectional Fiber Composites , 1980 .

[21]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[22]  John R. Rice,et al.  The Bending of Plates of Dissimilar Materials With Cracks , 1964 .

[23]  Anthony M. Waas,et al.  Prediction of progressive failure in multidirectional composite laminated panels , 2007 .

[24]  A. G. Evans,et al.  An experimental study of the fracture resistance of bimaterial interfaces , 1989 .

[25]  A. A. Griffith.  The Phenomena of Rupture and Flow in Solids , 1921 .

[26]  Leslie Banks-Sills,et al.  A new cohesive zone model for mixed mode interface fracture in bimaterials , 2008 .

[27]  John W. Hutchinson,et al.  Crack Paralleling an Interface Between Dissimilar Materials , 1987 .

[28]  K. Liechti,et al.  Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear , 1992 .

[29]  O. Hoffman.  The Brittle Strength of Orthotropic Materials , 1967 .

[30]  Robert L. Taylor,et al.  A constitutive model for anisotropic damage in fiber-composites , 1995 .

[31]  Dominique Leguillon,et al.  Strength or toughness? A criterion for crack onset at a notch , 2002 .

[32]  Bernard Peseux,et al.  A new modeling of plasticity coupled with the damage and identification for carbon fibre composite laminates , 2006 .

[33]  C. Sun,et al.  Modeling of composite fracture using cohesive zone and bridging models , 2006 .

[34]  Z. Suo,et al.  Mixed mode cracking in layered materials , 1991 .

[35]  G. R. Irwin,et al.  Linear fracture mechanics, fracture transition, and fracture control , 1968 .