Principles Of Linear Viscoelasticity Research Articles

Using the Dynamic Shear Rheometer for Low-Temperature Grading of Asphalt Binders

Abstract The Superpave Performance Grading (PG) framework or a variation of this framework is often used as a purchase specification in the United States and as a tool to evaluate the expected performance of modified and unmodified asphalt binders in many countries around the world. A cornerstone of the PG framework is the low-temperature grade of the asphalt binder that is assessed using a bending beam rheometer (BBR) using maximum stiffness and a minimum rate of deformation as criteria. Several previous studies from other researchers have demonstrated the feasibility of using the dynamic shear rheometer (DSR) with a 4-mm parallel plate geometry to measure the rheological properties of asphalt binders at low temperatures. This article builds on these studies to evaluate the feasibility of using a DSR to replace the use of a BBR for low-temperature grading of the asphalt binder using two different approaches. The first approach was to measure complex shear modulus of different asphalt binders using the DSR, convert these measurements to BBR equivalent stiffness and m-value using principles of linear viscoelasticity, and compare the two pairs of parameters from each method. The second approach was to use the complex shear modulus and phase angle measured using the DSR in lieu of using the stiffness and m-value measured using the BBR. Although the results from both methods show feasibility of using the 4-mm plate with the DSR to estimate low-temperature properties, the second approach of measuring and using the DSR-based complex shear moduli and phase angle is a more viable alternative for routine use.

An approach for dynamic stiffness evaluation in asphalt concrete

Stiffness modulus is a fundamental parameter for fatigue evaluation in asphalt concrete (AC). It is evaluated with different considerations like static or dynamic loading, elastic or visco-elastic material etc. Asphalt being visco-elastic and fatigue being due to dynamic loading, the modulus parameter happens to be time dependent complex variable. This is named as complex modulus (E∗) and the absolute value of E∗ is known as dynamic stiffness modulus (|E∗|). The present paper focuses on the development of a theoretical approach for E∗ and |E∗| based on principles of linear visco-elasticity. The expression of |E∗| and phase angle (ψ) for generalized Maxwell model under constant strain amplitude sinusoidal loading has been derived. It is seen that both |E∗| and ψ as function of time (t) follow cyclic variation with exponential decay due to viscous effect. Numerical analysis has been performed using Maxwell parameters (under relaxation condition) of AC at 10°C and -20°C. It is observed that |E∗| and ψ variations with time are significantly different at different temperatures. Their rate of decay depends upon the relaxation time of mix. The present work also explores the evaluation of dynamic modulus, while considering decay due to material damage.

Validation of Effective Time Translational Invariance and Linear Viscoelasticity of Polymer Undergoing Cross-linking Reaction

In polymeric liquids undergoing cross-linking reactions, rheological properties continuously change as a function of time. Consequently, the materials do not obey the time translational invariance and therefore the principles of linear viscoelasticity. In this work, we propose a methodology in which principles of linear viscoelasticity are transformed from the real time domain to the effective time domain. In the latter, the readjustment of the material clock, which accounts for the time dependency, facilitates validation of the effective time translational invariance. By carrying out experiments on cross-linking PDMS, we show that material that is undergoing time evolution in the real time domain indeed validates the Boltzmann superposition principle and convolution relation relating creep compliance and relaxation modulus in the effective time domain.

Modulus Testing in Indirect Tension Mode

ABSTRACT In 2004, a new European standard (NF EN 12697-26), the object of which is the measurement of stiffness modulus, appeared. It includes five annexes corresponding to five different testing methods, in particular modulus testing in indirect tension (IDT) mode. Given that a typical asphalt layer thickness is about a few centimeters and that coring is the most effective method for obtaining specimens from actual pavements, the IDT testing of cores is bound to become very practical for routine use. Notwithstanding this fact, IDT testing is still of little use in French public and private sector laboratories and, moreover, little information is available in the technical literature concerning the comparison between stiffness modulus data obtained in uniaxial direct tension or tension-compression and in biaxial indirect tension. This paper provides rational understanding, based on principles of linear viscoelasticity in particular, of the moduli commonly used for structural evaluation of asphalt mixtures: complex, secant and resilient moduli. The assumptions and limitations of these moduli are discussed. The pros and cons of the adopted testing and analysis methods are evaluated. A simple and direct relationship was found and exemplified between stiffness moduli obtained either in uniaxial direct tension/tension-compression mode or in biaxial indirect tension mode.

An introduction to the mechanical properties of solid polymers

Preface. 1 Structure of Polymers. 2 The Deformation of an Elastic Solid. 3 Rubber-like Elasticity. 4 Principles of Linear Viscoelasticity. 5 The Measurement of Viscoelastic Behaviour. 6 Experimental Studies of Linear Viscoelastic Behaviour as a Function of Frequency and Temperature: Time-Temperature Equivalence. 7 Anisotropic Mechanical Behaviour. 8 Polymer Composites: Macroscale and Microscale. 9 Relaxation Transitions: Experimental Behaviour and Molecular Interpretation. 10 Creep, Stress Relaxation and Non-linear Viscoelasticity. 11 Yielding and Instability in Polymers. 12 Breaking Phenomena. Appendix 1. Appendix 2. Answers to Problems. Index.

Viscoelastic behavior of crumb rubber modified asphalt binders

ABSTRACT The Superpave binder specification characterizes asphalt binders using dynamic mechanical analysis based on the principles of linear viscoelasticity. Dynamic mechanical analysis of crumb rubber modified binders showed that the time-temperature superposition principle is applicable to the crumb rubber modified binders included in this study and the master curves for these binders can be analytically represented using various techniques applicable to unmodified binders. It was observed that the unmodified and crumb rubber modified binders with the same high temperature performance grading show different viscoelastic behavior over a range of frequencies.

Microindentation hardness and dynamic mechanical moduli in polypropylene near the glass transition

The microindentation hardness studies of crystalline polymers carried out in the last few years have aimed to detect the textural and morphological changes in these polymers [1]. As plastic straining produced by microindentation measurements is confined to a few micrometres at the polymeric surface, this nondestructive technique is a powerful tool to study surface modifications [2] as well as structural changes in the whole mass of a homogeneous polymer [1]. On the other hand, the determination of storage and loss parts of the complex moduli of polymers by means of dynamic mechanical analysis is a wellestablished approach to the understanding of viscoelastic properties of polymers [3]. The results of dynamic mechanical measurements allow one to locate the viscoelastic relaxations of polymers, to study the influence on them of many structural parameters (crystallinity, crosslinking, orientation, plastification) and to provide an alternative route for research on technological topics such as composite structure, adhesion and peeling, friction, acoustic damping and impact strength [4]. The variation of this last property as a function of temperature has been correlated with dynamic mechanical results. In some polymers such as polytetrafluoroethylene, the trends in the plots of impact strength and loss factor against temperature are quite similar [5]. The theoretical explanation of this remarkable parallelism is, however, rather elusive, because dynamic mechanical measurements are founded on principles of linear viscoelasticity whereas impact strength determinations are clearly based on nonlinear phenomena. Notwithstanding this, both measurements deal with dissipation of elastic energy, thus justifying the phenomenological parallelism. Microindentation hardness values are related to deformation and recovery of a material under load. This load can be considered as a microimpact and the results of the microindentation should correlate with the values of dynamic moduli. The apparent absence of studies of this correlation, prompted us to measure the microindentation hardness and the dynamic moduli of polypropylene in the temperature range between 20 ° and 20 ° C, in which the glass transition of this polymer takes place. Microhardness measurements have been performed by a Vickers indentor attached to a Universal research

A Model for Predicting Set in Helices

A model is developed to calculate the residual set in a helical fiber axis after it has been wrapped around a mandrel, set into this shape, and released. The theory used is linear viscoelasticity in conjunction with the bending and twisting equations for thin rods. The model may be applied equally well to calculate the snarling behavior of twisted yams. An example of this is presented to confirm predictions made by the model. Two cases in the setting of helices are analyzed. In the first case the released helix is not in contact with the mandrel. In this case the bending and torsional set in the helical fiber axis follows quite simply from principles of linear viscoelasticity. In the second case, the released helix is constrained to lie on the surface of the mandrel. Results of this second case are more complex, but have been computed and presented in tabular form.