Assessment of Existing Micro-mechanical Models for Asphalt Mastics Considering Viscoelastic Effects

ABSTRACT Micromechanical models have been directly used to predict the effective complex modulus of asphalt mastics from the mechanical properties of their constituents. Because the micromechanics models traditionally employed have been based on elastic theory, the viscoelastic effects of binders have not been considered. Moreover, due to the unique features of asphalt mastics such as high concentration and irregular shape of filler particles, some micromechanical models may not be suitable. A comprehensive investigation of four existing micromechanical methods is conducted considering viscoelastic effects. It is observed that the self-consistent model well predicts the experimental results without introducing any calibration; whereas the Mori-Tanaka model and the generalized self-consistent model, which have been widely used for asphalt materials, significantly underestimate the complex Young's modulus. Assuming binders to be incompressible and fillers to be rigid, the dilute model and the self-consistent model provide the same prediction, but they considerably overestimate the complex Young's modulus. The analyses suggest that these conventional assumptions are invalid for asphalt mastics at low temperatures and high frequencies. In addition, contradictory to the assumption of the previous elastic model, it is found that the phase angle of binders produces considerable effects on the absolute value of the complex modulus of mastics.

[1]  G. Weng,et al.  A unified approach from elasticity to viscoelasticity to viscoplasticity of particle-reinforced solids , 1998 .

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

[3]  Roman Lackner,et al.  Is Low-Temperature Creep of Asphalt Mastic Independent of Filler Shape and Mineralogy?—Arguments from Multiscale Analysis , 2005 .

[4]  A. T. Papagiannakis,et al.  LINEAR AND NONLINEAR VISCOELASTIC ANALYSIS OF THE MICROSTRUCTURE OF ASPHALT CONCRETES , 2004 .

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

[6]  Cédric Sauzéat,et al.  Three-Dimensional Linear Behavior of Bituminous Materials: Experiments and Modeling , 2007 .

[7]  L. Palade,et al.  Linear viscoelastic behavior of asphalt and asphalt based mastic , 2000 .

[8]  Glaucio H. Paulino,et al.  Micromechanics-based elastic model for functionally graded materials with particle interactions , 2004 .

[9]  Zvi Hashin,et al.  Complex moduli of viscoelastic composites—I. General theory and application to particulate composites , 1970 .

[10]  Graeme W. Milton,et al.  On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[11]  小林 昭一 "MICROMECHANICS: Overall Properties of Heterogeneous Materials", S.Nemat-Nasser & M.Hori(著), (1993年, North-Holland発行, B5判, 687ページ, DFL.260.00) , 1995 .

[12]  Eyad Masad,et al.  Internal Structure Characterization of Asphalt Concrete Using Image Analysis , 1999 .

[13]  William G. Buttlar,et al.  Understanding Asphalt Mastic Behavior Through Micromechanics , 1999 .

[14]  Y. Kim,et al.  Correspondence Principle for Characterization of Asphalt Concrete , 1995 .

[15]  Quanshui Zheng,et al.  An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution , 2001 .

[16]  M. M. Carroll,et al.  Foundations of Solid Mechanics , 1985 .

[17]  J. C. Petersen,et al.  Unique Effects of Hydrated Lime Filler on the Performance-Related Properties of Asphalt Cements: Physical and Chemical Interactions Revisited , 2005 .

[18]  Y R Kim,et al.  INTERCONVERSION BETWEEN RELAXATION MODULUS AND CREEP COMPLIANCE FOR VISCOELASTIC SOLIDS , 1999 .

[19]  Zvi Hashin,et al.  Viscoelastic Behavior of Heterogeneous Media , 1965 .

[20]  J. Berryman,et al.  On the effective viscoelastic moduli of two–phase media. II. Rigorous bounds on the complex shear modulus in three dimensions , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[21]  Richard M. Christensen,et al.  A critical evaluation for a class of micro-mechanics models , 1990 .

[22]  André Zaoui,et al.  n-Layered inclusion-based micromechanical modelling , 1993 .

[23]  R. D. Woods,et al.  Geophysical Characterization of Sites , 1994 .

[24]  Glaucio H. Paulino,et al.  The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited , 2003 .

[25]  H Di Benedetto,et al.  Micromechanics-Based Model for Asphalt Mastics Considering Viscoelastic Effects , 2006 .

[26]  D W Christensen,et al.  Interpretation of dynamic mechanical test data for paving grade asphalt cements , 1992 .

[27]  William G. Buttlar,et al.  Dynamic Modulus of Asphalt Concrete with a Hollow Cylinder Tensile Tester , 2002 .

[28]  William G. Buttlar,et al.  Discrete Element Modeling to Predict the Modulus of Asphalt Concrete Mixtures , 2004 .

[29]  B. Budiansky On the elastic moduli of some heterogeneous materials , 1965 .

[30]  N. Shashidhar,et al.  On using micromechanical models to describe dynamic mechanical behavior of asphalt mastics , 2002 .

[31]  F. D. Lydon,et al.  Effect of coarse aggregate on elastic modulus and compressive strength of high performance concrete , 1995 .

[32]  A. Collop,et al.  Linear Rheological Behavior of Bituminous Paving Materials , 2004 .

[33]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[34]  H. Yin,et al.  Elastic modelling of periodic composites with particle interactions , 2005 .

[35]  Dallas N. Little,et al.  Linear Viscoelastic Analysis of Asphalt Mastics , 2004 .

[36]  J. Ferry Viscoelastic properties of polymers , 1961 .

[37]  N. Laws,et al.  Self-consistent estimates for the viscoelastic creep compliances of composite materials , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[38]  G. Paulino,et al.  Correspondence Principle in Viscoelastic Functionally Graded Materials , 2001 .

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

[40]  Toshio Mura,et al.  The Elastic Field Outside an Ellipsoidal Inclusion , 1977 .

[41]  C. Sauzéat,et al.  Linear viscoelastic behaviour of bituminous materials: From binders to mixes , 2004 .

[42]  A. Muliana,et al.  A micromechanical constitutive framework for the nonlinear viscoelastic behavior of pultruded composite materials , 2003 .

[43]  L. C. Brinson,et al.  Comparison of micromechanics methods for effective properties of multiphase viscoelastic composites , 1998 .

[44]  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.

[45]  R. Christensen,et al.  Viscoelastic properties of heterogeneous media , 1969 .

[46]  F. Montheillet,et al.  Deformation of an inclusion in a viscous matrix and induced stress concentrations , 1986 .

[47]  R. Roque,et al.  EVALUATION OF EMPIRICAL AND THEORETICAL MODELS TO DETERMINE ASPHALT MIXTURE STIFFNESSES AT LOW TEMPERATURES (WITH DISCUSSION) , 1996 .

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

[49]  H. Yin,et al.  Magnetoelastic modelling of composites containing randomly dispersed ferromagnetic particles , 2006 .

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

[51]  Hershel Markovitz,et al.  Theory of viscoelasticity. An introduction , 1984 .