Prediction of crack evolution and effective elastic behavior of damage-tolerant brittle composites☆

A constitutive model based on a combination of a fracture-mechanics based model and micromechanical formulations is developed to predict the crack evolution and effective mechanical behavior of damage-tolerant brittle composites. The constitutive model is cast in a rate form and considers microcrack nucleation rate and microcrack growth rate. The effective moduli of the composites containing different crack distributions are formulated using the self-consistent method and differential scheme. The constitutive model is then implemented into finite element codes to solve boundary value problems of the composites. Numerical simulations on a benchmark problem are carried out to illustrate the model features. Finally, to further assess the validity of the present framework, the present predictions are compared with experimental data on brittle composites. Published by Elsevier B.V.

[1]  N. Laws,et al.  Stiffness changes in unidirectional composites caused by crack systems , 1983 .

[2]  Bikas K. Chakrabarti,et al.  Book Review: Statistical Physics of Fracture and Breakdown in Disordered Systems , 1997 .

[3]  S. Šimunović,et al.  A computational approach for prediction of the damage evolution and crushing behavior of chopped random fiber composites , 2004 .

[4]  Brian Lawn,et al.  Fracture of brittle solids: Atomic aspects of fracture , 1993 .

[5]  George J. Dvorak,et al.  Analysis of Progressive Matrix Cracking in Composite Laminates I. Thermoelastic Properties of a Ply with Cracks , 1985 .

[6]  Milan Jirásek,et al.  Comparative study on finite elements with embedded discontinuities , 2000 .

[7]  Dusan Krajcinovic,et al.  Damage and Fracture of Disordered Materials , 2000 .

[8]  M. Benzeggagh,et al.  Micromechanical modelling of matrix degradation in randomly oriented discontinuous-fibre composites , 1995 .

[9]  R. Mclaughlin.  A study of the differential scheme for composite materials , 1977 .

[10]  Milena Vujosevic,et al.  Intrinsic failure modes of brittle materials , 1998 .

[11]  R. C. Crewdson,et al.  Dynamic Fracture Criteria of Homogeneous Materials. , 1970 .

[12]  B. Budiansky,et al.  Elastic moduli of a cracked solid , 1976 .

[13]  Karl S. Pister,et al.  Assessment of cap model: consistent return algorithms and rate-dependent extension , 1988 .

[14]  L. Keer.  A note on shear and combined loading for a penny-shaped crack☆ , 1966 .

[15]  R. Roscoe.  The viscosity of suspensions of rigid spheres , 1952 .

[16]  A. Huespe,et al.  From continuum mechanics to fracture mechanics: the strong discontinuity approach , 2002 .

[17]  Gilles Pijaudier-Cabot,et al.  Progressive damage in discrete models and consequences on continuum modelling , 1996 .

[18]  A. Hasegawa,et al.  Fracture Process and Bridging Zone Model and Influencing Factors in Fracture of Concrete , 1989 .

[19]  Mark Kachanov,et al.  Elastic Solids with Many Cracks and Related Problems , 1993 .

[20]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[21]  Leon Mishnaevsky,et al.  Methods of the theory of complex systems in modelling of fracture: A brief review , 1997 .

[22]  D. Krajcinovic,et al.  A Mesomechanical Model for Brittle Deformation Processes: Part II , 1989 .

[23]  Peter F. Arndt,et al.  Criterion for crack formation in disordered materials , 2001 .

[24]  P Meakin,et al.  Models for Material Failure and Deformation , 1991, Science.

[25]  Lynn Seaman,et al.  Computational models for ductile and brittle fracture , 1976 .

[26]  G. Dvorak,et al.  The effect of fiber breaks and aligned penny-shaped cracks on the stiffness and energy release rates in unidirectional composites , 1987 .

[27]  Jiann-Wen Ju,et al.  On two-dimensinal self-consistent micromechanical damage models for brittle solids , 1991 .

[28]  Sia Nemat-Nasser,et al.  Overall moduli of solids with microcracks: Load-induced anisotropy , 1983 .

[29]  Surendra P. Shah,et al.  Fracture of Concrete and Rock , 1989 .

[30]  Lynn Seaman,et al.  Dynamic fracture criteria for a polycarbonate , 1973 .

[31]  Mark Kachanov,et al.  Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts , 1992 .

[32]  Anand Jagota,et al.  Element breaking rules in computational models for brittle fracture , 1995 .

[33]  Stéphane Roux,et al.  Statistics Toolbox for Damage and Fracture , 2000 .

[34]  M. Ortiz,et al.  A finite element method for localized failure analysis , 1987 .

[35]  Zvi Hashin,et al.  The differential scheme and its application to cracked materials , 1988 .

[36]  H. Poincaré,et al.  Percolation ? , 1982 .

[37]  E. Garboczi,et al.  FRACTURE SIMULATIONS OF CONCRETE USING LATTICE MODELS : COMPUTATIONAL ASPECTS , 1997 .

[38]  John R. Rice,et al.  Fracture of Brittle Solids (Cambridge Solid State Science Series) , 1975 .

[39]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[40]  Z. Bažant,et al.  Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .

[41]  A. Hansen.  Statistical Models for the Fracture of Disordered Media , 1990 .

[42]  Michael Ortiz,et al.  Microcrack coalescence and macroscopic crack growth initiation in brittle solids , 1988 .

[43]  Bhushan Lal Karihaloo,et al.  Modelling of tension softening in quasi-brittle materials by an array of circular holes with edge cracks , 1991 .

[44]  J. N. Johnson,et al.  A constitutive model for the dynamic response of brittle materials , 1990 .

[45]  S. Kampe,et al.  Mechanical behavior of glass and blackglas® ceramic matrix composites , 1997 .

[46]  Muhammad Sahimi,et al.  Non-linear and non-local transport processes in heterogeneous media: from long-range correlated percolation to fracture and materials breakdown , 1998 .

[47]  B. Karihaloo,et al.  Tensile response of quasi-brittle materials , 1991 .

[48]  M. Isichenko.  Percolation, statistical topography, and transport in random media , 1992 .