Interconversion of Frequency Domain Complex Modulus to Time Domain Modulus and Compliance of Asphalt Concrete: Numerical Modeling and Laboratory Validation

2016 ◽  
Author(s):  
A. S. M. Asifur Rahman ◽  
Rafiqul A. Tarefder
Keyword(s):  
Viscoelastic Material ◽  
Asphalt Concrete ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Modulus Function ◽  
Approximate Methods ◽  
Material Functions ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic

Viscoelastic material functions such as time domain functions, such as, relaxation modulus and creep compliance, or frequency domain function, such as, complex modulus can be used to characterize the linear viscoelastic behavior of asphalt concrete in modeling and analysis of pavement structure. Among these, the complex modulus has been adopted in the recent pavement Mechanistic-Empirical (M-E) design software AASHTOWare-ME. However, for advanced analysis of pavement, such as, use of finite element method requires that the complex modulus function to be converted into relaxation modulus or creep compliance functions. There are a number of exact or approximate methods available in the literature to convert complex modulus function to relaxation modulus or creep compliance functions. All these methods (i.e. exact or approximate methods) are applicable for any linear viscoelastic material up to a certain level of accuracy. However, the applicability and accuracy of these interconversion methods for asphalt concrete material were not studied very much in the past and thus question arises if these methods are even applicable in case of asphalt concrete, and if so, what is the precision level of the interconversion method being used. Therefore, to investigate these facts, this study undertaken an effort to validate a numerical interconversion technique by conducting representative laboratory tests. Cylindrical specimens of asphalt concrete were prepared in the laboratory for conducting complex modulus, relaxation modulus, and creep compliance tests at different test temperatures and loading rates. The time-temperature superposition principle was applied to develop broadband linear viscoelastic material functions. A numerical interconversion technique was used to convert complex modulus function to relaxation modulus and creep compliance functions, and hence, the converted relaxation modulus and creep compliance are compared to the laboratory tested relaxation modulus and creep compliance functions. The comparison showed good agreement with the laboratory test data. Toward the end, a statistical evaluation was conducted to determine if the interconverted material functions are similar to the laboratory tested material functions.

Effect of Progressive Aging on the Viscoelastic Material Functions of Asphalt Concrete and its Binder

2017 ◽  
Author(s):  
A. S. M. Asifur Rahman ◽  
Hasan M. Faisal ◽  
Rafiqul A. Tarefder
Keyword(s):  
Shear Modulus ◽  
Viscoelastic Material ◽  
Asphalt Concrete ◽  
Complex Modulus ◽  
Superposition Principle ◽  
Asphalt Binder ◽  
Relaxation Modulus ◽  
Concrete Specimen ◽  
Material Functions ◽  
Four Levels

In this study, field collected loose asphalt-aggregate mixtures were used to prepare cylindrical asphalt concrete specimen using a Superpave gyratory compactor and samples were subjected to four levels of aging. Unaged and aged samples were then tested for complex modulus, relaxation modulus, and creep compliance in the laboratory at different temperatures and loading conditions. To determine broadband characteristics, mastercurves of related viscoelastic material functions were determined by applying time-temperature superposition principle. A comparison study showed that increasing levels of aging have significant effect on viscoelastic functions of asphalt concrete. In addition, liquid asphalt binder corresponding to the asphalt-aggregate mixture was tested for complex shear modulus at various levels of aged conditions, using a dynamic shear rheometer. Results showed that even though the binder shear modulus increases significantly with aging, asphalt concrete modulus does not necessarily show similar increment.

Relationships Among Rate-Dependent Stiffnesses of Asphalt Concrete Using Laboratory and Field Test Methods

1998 ◽  
Vol 1630 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Jo Sias Daniel ◽  
Y. Richard Kim
Keyword(s):  
Asphalt Concrete ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Test Methods ◽  
Rate Dependent ◽  
Creep Stiffness ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Theory ◽  
Falling Weight

As the application of nondestructive testing on pavements in service becomes more frequent, it is increasingly important to relate the resulting stiffnesses to those from laboratory test methods. The relationship among stiffnesses measured from five test methods currently used for asphalt concrete is addressed: creep compliance, complex modulus, impact resonance, falling weight deflectometer, and surface wave. Established relationships from linear viscoelastic theory are used to relate stiffnesses, including a comparison of creep stiffness, S( t), and relaxation modulus, E( t), calculated from creep compliance, D( t). Using laboratory and field measured stiffnesses, a linear relationship was discovered between stiffness and frequency on a log-log scale.

scholarly journals THE EXACT SOLUTION FOR STRAINS AND STRESSES IN A HOLLOW CYLINDER OF NON-LINEAR VISCOELASTIC MATERIAL SUBJECT TO INTERNAL AND EXTERNAL PRESSURES IN THE CASE OF POWER MATERIAL FUNCTION GOVERNING NON-LINEARITY

2020 ◽  
Vol 82 (2) ◽  
pp. 225-243
Author(s):  
A.V. Khokhlov
Keyword(s):  
Exact Solution ◽  
Creep Compliance ◽  
Stress Fields ◽  
Loading History ◽  
Material Function ◽  
Material Functions ◽  
External Pressures ◽  
Linear Viscoelastic Material ◽  
Non Linear ◽  
Linear Viscoelastic

We study analytically the exact solution of the quasi-static problem for a thick-walled tube of physically non-linear viscoelastic material obeying the Rabotnov constitutive equation with two arbitrary material functions (a creep compliance and a function which governs physical non-linearity). We suppose that a material is homogeneous, isotropic and incompressible and that a tube is loaded with time-dependent internal and external pressures (varying slowly enough to neglect inertia terms in the equilibrium equations) and that a plain strain state is realized, i.e. zero axial displacements are given on the edge cross sections of the tube. We previously have obtained the closed form expressions for displacement, strain and stress fields via the single unknown function of time and integral operators involving this function, two arbitrary material functions of the constitutive relation, preset pressure values and radii of the tube and derive functional equation to determine this unknown resolving function. Assuming creep complience is arbitrary and choosing the material function governing non-linearity to be power function with a positive exponent, we construct exact solution of the resolving non-linear functional equation, calculate all the convolution integrals involved in the general representation for strain and stress fields and reduce it to simple algebraic formulas convenient for analysis and use. Strains evolution in time is characterized by creep compliance function and loading history. The stresses in this case depend on the current magnitudes of pressures only, they don't depend on creep compliance (i.e. viscoelastic properties of a material) and on loading history. The stress field coincides with classical solution for non-linear elastic material or elastoplastic material with power hardening (for non-decreasing pressure difference). We obtain criteria for increase, decrease or constancy of stresses with respect to radial coordinate in form of inequalities for the exponent value and for difference of pressures. Assuming creep compliance is arbitrary, we study analytically properties of strain and stress fields in a tube under internal pressure growing with constant rate and properties of corresponding stress-strain curves implying measurement of strains at a surface point of a tubular specimen.

Solution of Viscoelastic Stress Analysis Problems Using Measured Creep or Relaxation Functions

1963 ◽  
Vol 30 (1) ◽  
pp. 127-133 ◽  
Author(s):  
E. H. Lee ◽  
T. G. Rogers
Keyword(s):  
Stress Analysis ◽  
Integral Equations ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Material Behavior ◽  
Relaxation Functions ◽  
Analysis Theory ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Improved Technique

Stress analysis problems for linear viscoelastic material behavior are solved on the basis of integral operator stress-strain relations. These characterize the material by relaxation modulus functions or creep compliances which are directly measurable over finite time ranges, and completely describe material behavior for stress determinations for the same duration. The stress analysis theory can lead to integral equations which are shown to be soluble with high accuracy by simple finite-difference numerical integration procedures. Examples are presented and compared with solutions obtained by other methods. A possible improved technique for relaxation modulus and creep compliance measurements is suggested, based on the method presented for numerical solution of the integral equations.

Indentation Creep and Relaxation Measurements of Polymers

2004 ◽  
Vol 841 ◽  
Author(s):  
Mark R. VanLandingham ◽  
Peter L. Drzal ◽  
Christopher C. White
Keyword(s):  
Stress Relaxation ◽  
Mechanical Response ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Polymeric Materials ◽  
Indentation Creep ◽  
Dimethyl Siloxane ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Creep And Stress Relaxation

ABSTRACTInstrumented indentation was used to characterize the mechanical response of polymeric materials. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for creep compliance and stress relaxation modulus for epoxy, poly(methyl methacrylate) (PMMA), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison to the indentation creep and stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than rheometry values. Additional study of the deformation remaining in epoxy after creep testing revealed that a large portion of the creep displacement measured was due to post-yield flow. Indentation creep measurements of the epoxy using a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the PDMS were mainly linear elastic, but the filled PDMS exhibited some time-dependence and nonlinearity in both rheometry and indentation measurements.

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