Incremental mean-fields micromechanics scheme for non-linear response of ductile damaged composite materials

Abstract This work is concerned with the modeling of ductile damage behavior in composite materials by the means of the Incremental Micromechanics Scheme (IMS) as Mean-Fields Homogenization (MFH) technique. Indeed, IMS is known for its capability to overcome the well-known accuracy restrictions of the Mori–Tanaka (MT) and Self-Consistent (SC) schemes when a high volume fraction of heterogeneities or/and a high contrast between phases properties is reached. This micromechanics formalism is based on the Eshelby’s inclusion concept. The kinematic equation of Dederichs and Zeller (1973) is used as formal solution of the heterogeneous material problem. The nonlinear behavior of the composite is addressed in a general framework based on the kinematic hardening of Lemaiˆtre–Chaboche’s ductile damage model. Thus a classical J 2 plasticity that accounts for the damage evolution within the microstructure is implemented. The time discretization of all rate relations is solved through a generalized mid-point rule that yields to an anisotropic consistent (algorithmic) tangent modulus. To avoid a stiffer macroscopic stress–strain response, an isotropization procedure is adopted during the computation of the Eshelby tensor involved in the IMS modeling. From a computational aspect, the non linear response of the composite is obtained through two interdependent loops: inner and outer. In the inner loop, the IMS determines the global strain concentration tensor that is passed to the outer loop. Then, the macroscopic stress–strain response is derived using an iterative algorithm based on the Hill-type incremental formulation. Numerical results are obtained considering several heterogeneous materials such as Metal Matrix Composites (MMCs) as well as Carbon fibers reinforced Epoxy Matrix Composites. The model’s predictions are compared in most of the cases, with experimental data and predictions obtained from MT-based modeling in the open literature.

[1]  O. Fassi-Fehri.  Le problème de la paire d'inclusions plastiques et hétérogènes dans une matrice anisotrope : application à l'étude du comportement des matériaux composites et de la plasticité , 1985 .

[2]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  G. P. Tandon,et al.  A Theory of Particle-Reinforced Plasticity , 1988 .

[4]  E. Kröner.  Effective moduli of random elastic media-unified calculation of bounds and self-consistent values , 1977 .

[5]  I. Bernstein,et al.  Proposed failure mechanism in a discontinuously reinforced aluminum alloy , 1987 .

[6]  Andreas Menzel,et al.  A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials , 2014 .

[7]  E. Kröner.  Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[8]  John K. Tien,et al.  SiC-reinforced aluminium metal matrix composites , 1985 .

[9]  I. Doghri,et al.  A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites , 2013 .

[10]  S. Suresh,et al.  Effects of SiC reinforcement and aging treatment on fatigue crack growth in an AlSiC composite , 1988 .

[11]  Jean-Louis Chaboche,et al.  On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites , 2005 .

[12]  I. Doghri.  Mechanics of Deformable Solids , 2000 .

[13]  S. Mccarthy,et al.  Fiber reinforced nylon‐6 composites produced by the reaction injection pultrusion process , 1996 .

[14]  P. H. Dederichs,et al.  Variational treatment of the elastic constants of disordered materials , 1973 .

[15]  E. S. Perdahcıoğlu,et al.  Constitutive modeling of two phase materials using the mean field method for homogenization , 2011 .

[16]  P. Lipinski,et al.  Prediction of mechanical behaviour of inhomogeneous and anisotropic materials using an incremental scheme , 2000 .

[17]  Subra Suresh,et al.  An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites , 1991 .

[18]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .

[19]  Dimitris C. Lagoudas,et al.  Elastoplastic behavior of metal matrix composites based on incremental plasticity and the Mori-Tanaka averaging scheme , 1991 .

[20]  Wiyao Azoti,et al.  Mean-field constitutive modeling of elasto-plastic composites using two (2) incremental formulations , 2013 .

[21]  R. M. Natal Jorge,et al.  Numerical modelling of ductile plastic damage in bulk metal forming , 2003 .

[22]  P. Viéville,et al.  Modelling effective properties of composite materials using the inclusion concept. General considerations , 2006 .

[23]  K. Han,et al.  Preparation and Mechanical Properties of Long Glass Fiber Reinforced PA6 Composites Prepared by a Novel Process , 2005 .

[24]  Ludovic Noels,et al.  A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models , 2012 .

[25]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[26]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[27]  E. Kröner.  Bounds for effective elastic moduli of disordered materials , 1977 .

[28]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[29]  D. Chandrasekharaiah,et al.  Mechanics of Deformable Solids: Linear, Nonlinear, Analytical and Computational Aspects , 2000 .

[30]  I. Doghri,et al.  Study of various estimates of the macroscopic tangent operator in the incremental homogenization of elastoplastic composites , 2006 .

[31]  Subra Suresh,et al.  An experimental and numerical study of deformation in metal-ceramic composites , 1989 .

[32]  A. Zaoui,et al.  A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization , 2005 .

[33]  J. Willis,et al.  Variational and Related Methods for the Overall Properties of Composites , 1981 .

[34]  Amine Ouaar,et al.  Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms , 2003 .

[35]  John W. Hutchinson,et al.  Elastic-plastic behaviour of polycrystalline metals and composites , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.