Damage Coupled Viscoplastic Modeling of Particulate Composites With Imperfect Interphase

A micromechanical damage model is proposed to predict the overall viscoplastic behavior and damage evolution in particulate polymer composites with imperfect interfacial bonds. The constituents are treated as three distinct phases, consisting of agglomerate of particles, bulk matrix, and interfacial transition zone around the agglomerate. The influence of the interfacial transition zone on the overall mechanical behavior of composites is studied analytically and experimentally. Test data on particle-filled acrylic composites with three different interfacial properties are presented. The coefficient of thermal expansion (CTE) mismatch between the matrix and the filler particles is also introduced into the model. A damage evolution function based on irreversible thermodynamics is also introduced into the constitutive model to describe the degradation of the composite. The efficient general return-mapping algorithm is exploited to implement the proposed unified damage-coupled viscoplastic model into finite element formulation. Furthermore, the model predictions for uniaxial loading conditions are compared with the experimental data. Both the experimental results and analytical prediction show that interfacial conditions have great influence on the elastic properties of particle-filled acrylic composites. Keywords: micromechanics; particulate composite; interfaces; interfacial bond; damage

[1]  Zvi Hashin,et al.  Thermoelastic properties and conductivity of carbon/carbon fiber composites , 1990 .

[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]  S. Ahmed,et al.  A review of particulate reinforcement theories for polymer composites , 1990 .

[4]  Jiann-Wen Ju,et al.  A micromechanical damage model for effective elastoplastic behavior of partially debonded ductile matrix composites , 2001 .

[5]  E. H. Kerner.  The Elastic and Thermo-elastic Properties of Composite Media , 1956 .

[6]  Jiann-Wen Ju,et al.  Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities , 1994 .

[7]  A. Shapiro,et al.  Towards model-based engineering of underfill materials: CTE modeling , 2001 .

[8]  Zvi Hashin,et al.  Assessment of the Self Consistent Scheme Approximation: Conductivity of Particulate Composites , 1968 .

[9]  M. Taya.  Strengthening Mechanisms of Metal Matrix Composites , 1991 .

[10]  Cemal Basaran,et al.  A Damage Mechanics-Based Fatigue Life Prediction Model for Solder Joints , 2003 .

[11]  C. Basaran,et al.  An Irreversible Thermodynamics Theory for Damage Mechanics of Solids , 2004 .

[12]  Eun U. Lee.  Thermal stress and strain in a metal matrix , 1992, Metallurgical and Materials Transactions A.

[13]  J. Ju,et al.  A micromechanical damage model for effective elastoplastic behavior of ductile matrix composites considering evolutionary complete particle debonding , 2000 .

[14]  F. Ghahremani.  Effect of grain boundary sliding on anelasticity of polycrystals , 1980 .

[15]  G. Ravichandran,et al.  Modeling constitutive behavior of particulate composites undergoing damage , 1995 .

[16]  J. Móczó,et al.  The mechanism and kinetics of void formation and growth in particulate filled PE composites , 2007 .

[17]  Y. Benveniste,et al.  The effective mechanical behaviour of composite materials with imperfect contact between the constituents , 1985 .

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

[19]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[20]  G. Papanicolaou,et al.  The effect of the boundary interphase on the thermomechanical behaviour of composites reinforced with short fibres , 1979 .

[21]  Yu‐Lin Shen,et al.  Thermal expansion of particle-filled plastic encapsulant: a micromechanical characterization , 1998 .

[22]  Jiann-Wen Ju,et al.  Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation , 2001 .

[23]  Cemal Basaran,et al.  A thermodynamics based damage mechanics constitutive model for low cycle fatigue analysis of microelectronics solder joints incorporating size effects , 2005 .

[24]  George Z. Voyiadjis,et al.  A cyclic anisotropic-plasticity model for metal matrix composites , 1996 .

[25]  R. Christensen,et al.  Solutions for effective shear properties in three phase sphere and cylinder models , 1979 .

[26]  C. Basaran,et al.  A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds , 2005 .

[27]  A. A. Gusev,et al.  Loss Amplification Effect in Multiphase Materials with Viscoelastic Interfaces , 2009 .

[28]  Z. Di,et al.  Dimensioanl stability of TiC particle reinforced ZA43 matrix composite , 2001 .

[29]  Jiann-Wen Ju,et al.  Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities , 1994 .

[30]  Zvi Hashin,et al.  The Elastic Moduli of Heterogeneous Materials , 1962 .

[31]  J. Ju,et al.  Effective elastoplastic behavior of two-phase ductile matrix composites: A micromechanical framework , 1996 .

[32]  L. Walpole,et al.  A coated inclusion in an elastic medium , 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

[33]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[34]  J. Ju,et al.  Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal Inhomogeneities. Part II: applications , 2001 .

[35]  Sergey A. Lurie,et al.  Computational mechanics modelling of nanoparticle-reinforced composite materials across the length scales , 2006, Int. J. Comput. Sci. Eng..

[36]  C. Basaran,et al.  Influence of Interfacial Bond Strength on Fatigue Life and Thermo-Mechanical Behavior of a Particulate Composite: An Experimental Study , 2008 .

[37]  Zvi Hashin,et al.  The Spherical Inclusion With Imperfect Interface , 1991 .

[38]  L. Walpole.  On bounds for the overall elastic moduli of inhomogeneous systems—I , 1966 .

[39]  Jack C. Smith.  Simplification of van der Poel's Formula for the Shear Modulus of a Particulate Composite. , 1975, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[40]  J. Ju.  Consistent Tangent Moduli for a Class of Viscoplasticity , 1990 .

[41]  Hua Ye,et al.  A thermodynamic model for electrical current induced damage , 2003 .

[42]  G. Papanicolaou,et al.  Thermal properties and volume fraction of the boundary interphase in metal-filled epoxies , 1979 .

[43]  J. Willis,et al.  On methods for bounding the overall properties of nonlinear composites , 1991 .

[44]  A. Sundarrajan,et al.  Thermal expansion behavior of particulate metal-matrix composites , 1998 .

[45]  Cemal Basaran,et al.  A Thermodynamic Framework for Damage Mechanics of Solder Joints , 1998 .

[46]  Zvi Hashin,et al.  Thermoelastic properties of particulate composites with imperfect interface , 1991 .

[47]  Cemal Basaran,et al.  Implementation of a Thermodynamic Framework for Damage Mechanics of Solder Interconnects in Microelectronics Packaging , 2002 .

[48]  J. Ju,et al.  Effective Elastoplastic Algorithms for Ductile Matrix Composites , 1997 .

[49]  Toshio Mura,et al.  The stress field of a sliding inclusion , 1985 .

[50]  Jiann-Wen Ju,et al.  ISOTROPIC AND ANISOTROPIC DAMAGE VARIABLES IN CONTINUUM DAMAGE MECHANICS , 1990 .

[51]  Jack C. Smith.  Correction and Extension of van der Poel's Method for Calculating the Shear Modulus of a Particulate Composite. , 1974, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[52]  C. Liu,et al.  Damage growth in a particulate composite under a high strain rate loading , 1998 .

[53]  Jan Drewes Achenbach,et al.  Effect of interphases on micro and macromechanical behavior of hexagonal-array fiber composites , 1990 .

[54]  Jan Drewes Achenbach,et al.  Effect of interfacial zone on mechanical behavior and failure of fiber-reinforced composites , 1989 .

[55]  H. Choi,et al.  Analysis of the debonding process in polypropylene model composites , 2005 .

[56]  Z. Hashin,et al.  The Elastic Moduli of Fiber-Reinforced Materials , 1964 .

[57]  X. D. Liu,et al.  Finite element simulation of the thermal properties of particulate and continuous network-reinforced metal-matrix composites , 2005 .

[58]  C. Basaran,et al.  Failure Mechanisms in PMMA/ATH Acrylic Casting Dispersion , 2006 .

[59]  A. Ait-Kadi,et al.  Analysis of particulate composite behaviour based on non-linear elasticity and modulus degradation theory , 1997 .

[60]  C. Sun,et al.  Thermal residual stresses in co-continuous composites , 2003 .