Dynamic Mechanical Analysis Of Viscoelasticity Of Bituminous Mixtures

Bituminous binders and mixtures are the typical members in the group of viscoelastic materials of which the mechanical behavior strongly relates to temperature and time(or frequency).Linear viscoelasticity is usually described by empirical mathematical models or mechanical models,most of which are established from frequency domain.The 2S2P1 D model,an abbreviation of the combination of two springs,two parabolic creep elements(fractional derivative elements)and one dashpot,is so far recognized as a mechanical model which can best characterize the dynamic mechanical behavior.However,its dynamic response function is too complicated to deduce the transient function via integral transformations.Some other empirical mathematical models without phase angle function which can well describe experimental data are only formulas for the complex modulus magnitude.It seems incomplete for the description of viscoelasticity since the storage and loss functions cannot be obtained.Thus it is necessary to find a simplified model or an analytical expression to describe the transient and dynamic mechanical behavior of bituminous mixtures,and propose simple methods to determine model parameters.The main contents and results of this dissertation are as follows:We first analyze the characteristics of dynamic response functions of several linear viscoelastic models for bituminous binders and mixtures,and discuss the advantages and disadvantages of these models in describing mechanical behavior.Then,we review the constitutive equations,transient and dynamic response functions of simple mechanical models,generalized Maxwell and Kelvin–Voigt models,and fractional derivative models.The characteristics of dynamic response functions of mechanical models in the dynamic mechanical analysis(DMA)are discussed.In addition,exact interrelations among the viscoelastic functions are introduced,including the interrelation of a transient with the corresponding dynamic functions,the interrelation of the two transient functions,and interrelations between the components of a complex dynamic function,known as Kramers–Kronig integral relations.The main experiments and analysis methods are listed as follows.The classical physical properties and glass transition temperature of bituminous binders are measured.The dynamic mechanical analysis(DMA)is applied to characterize the dynamic mechanical behavior of bituminous binders and mixtures.The dynamic mechanical data are obtained with the aid of frequency sweep and the time-temperature superposition principle(TTSP).The static mechanical behavior of bituminous mixtures is measured by bending creep tests.Kramers–Kronig transforms are used to analyze dynamic response functions of an empirical mathematical model containing only complex modulus magnitude function and measured dynamic mechanical data.The relation between real and imaginary parts of complex dynamic function of a mechanical model has been established.For the simple mechanical models,including Maxwell,Kelvin–Voigt,and standard linear solid models,the complex plane plot of modulus or compliance is a full semicircle with its center on the real axis.For the fractional derivative models(Maxwell,Kelvin–Voigt,and standard linear solid models),the complex plane plot is a depressed or distorted semicircle with its center below the real axis.Only a part of the semicircle can be seen,since experimental data are collected over restricted frequency ranges due to the instrumental limitations in actual dynamic measurements.The model element parameters can be easily determined by the two intercepts of the extrapolated circular arc with the real axis and the displacement of the semicircle center(or radius of the circle)in the complex plane plot.Viscoelastic behavior of materials is usually characterized by a mechanical model composed of spring and dashpot or fractional derivative elements in series and parallel combination,which is only an ideal assumption method to simulate viscoelasticity.This dissertation attempts to discuss the nature of viscoelasticity with unknown factors in a system.A physical interpretation for the fractional derivative element is proposed from the view of the density gradient of a material produced by stress.We have established a general form of analytical expressions for complex dynamic functions of mechanical models.From a viewpoint of sinusoidal transfer function of a linear dynamic system in modern control engineering,viscoelasticity of materials can also be characterized by a sinusoidal transfer function,in which the gain,characteristic time constants and powers of the factors can be readily identified by the asymptotes of Bode plot(master curve)of complex modulus magnitude.In the frequency domain,the model parameters for bituminous mixtures are identified graphically via the complex plane plot and Bode plot of magnitude;in the time domain,the model parameters are determined by the bending creep compliance curve.Both the experimental results of dynamic and transient experiments show that the dynamic and static mechanical behavior of bituminous mixtures can be adequately described by the fractional derivative standard linear solid model.The real and imaginary parts in a complex dynamic function are not mathematically independent of each other,and its magnitude and phase angle are also not independent.They are connected by Kramers–Kronig transforms,which are expected to obtain other dynamic response functions of an empirical mathematical model containing only complex modulus magnitude function,complete measured dynamic mechanical data,and check the validity of dynamic mechanical data.