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Viscoelastic Behaviour
Published in B. R. Gupta, Rheology Applied in Polymer Processing, 2023
From Table 6.4 it can be seen that the stress decays exponentially with time. The relaxation time represents the time required to relax the stress by a constant factor of e between the successive relaxation time intervals. It characterizes the rate of approach to the equilibrium when the stresses disappear. The rate of relaxation of stress depends on the magnitude of the relaxation time. For small value of 0 the rate of relaxation is high and for high values it is low. It is important to note that the fraction of stress relaxed is very high in the beginning and then reduces progressively to become insignificant. As a result of this mechanism of relaxation the stress reduces to zero after a very long time. Some materials retain some stress, which is known as the residual or the equilibrium stress.
Overview of pavement vehicle interaction research at the MIT concrete sustainability hub
Published in A. Kumar, A.T. Papagiannakis, A. Bhasin, D. Little, Advances in Materials and Pavement Performance Prediction II, 2020
J. Mack, M. Akbarian, F. J. Ulm, Randolph Kirchain, Jeremy Gregory, A. Louhghalam
In total, MIT ran nearly 200 experimental configurations, equivalent to 290 km (180 miles) of road testing, to investigate the impact of key PVI parameters on excess energy dissipation with varying loads, speeds, pavement modulus values, pavement thicknesses and viscoelasticities (relaxation time). Once the testing was completed, the scaling relationship between the theoretical deflection-induced PVI model were compared to the scaling of the dissipation forces from PVI desk-top model and the results were found to be consistent. This confirmed the contribution of pavement structure to EFC and that an increase in pavement stiffness minimizes the impact of deflection-induced PVI. It also verified that deflection-induced PVI impacts can be captured and can have a significant impact on life cycle energy use and emissions. (Mack et al. 2018)
Linear Viscoelasticity
Published in Timothy P. Lodge, Paul C. Hiemenz, Polymer Chemistry, 2020
Timothy P. Lodge, Paul C. Hiemenz
where the dot denotes the time derivative. We have defined a relaxation time, τ≡η^/G^, and from Equation 11.2.1 it is clear that this ratio has the correct units: η^/G^=(σ/γ˙)/(σ/γ)=(γ/γ˙)=t. The concept of relaxation time is central to the material in this chapter. In essence, the relaxation time is a measure of the time required for a system to return to equilibrium after any kind of disturbance.
Highly stable surfactant-crumb rubber-modified bitumen: NMR and rheological investigation
Published in Road Materials and Pavement Design, 2018
Elisabeta I. Szerb, Isabella Nicotera, Bagdat Teltayev, Rosolino Vaiana, Cesare Oliviero Rossi
The P(T2) times distribution can be used as a measure of the softness of a given material. The relaxation process, in fact, is more efficient when the material is more rigid, that corresponds to shorter relaxation times. As matter of fact, higher temperatures correspond to longer T2 times, bitumen is not an exception. The T2 time is usually extracted from an exponential decay which is the envelope of the recorded echo signals. When the material is not homogeneous, the measured T2 is averaged over all of the contributions of the different macro-structures. Considering bitumen models, one can roughly distinguish between a rigid (asphaltenes) and a soft fraction (maltenes) inside the substance. Consequently, the T2 distributions can be considered a fingerprint of structure of the system.
Using combined Avrami-Ozawa method to evaluate low-temperature reversible aging in asphalt binders
Published in Road Materials and Pavement Design, 2020
Yanjun Qiu, Haibo Ding, Ali Rahman, Enhui Yang
Four Burgers parameters and derived parameters (relaxation time and delay time) of asphalt binders in all measured conditioning times and types of asphalt binders are presented in Table 2. Among which, the relaxation time is of paramount importance for the characterisation of asphalt binder at low temperature. The physical meaning of relaxation time is the characteristic time for a system to reach an equilibrium condition after a disturbance. The longer relaxation time of asphalt binder at low-temperature means longer time is required for an asphalt system to dissipate accumulated stress. Figure 10 shows the relaxation time of different asphalt binders with extended conditioning time. As expected, relaxation time extended with extended conditioning time. It should be noted that longer relaxation time which is undesirable according to the current specification because of lower m-values, resulted in the slower development of thermal stresses, which is a desirable property (Marasteanu & Basu, 2004). Consequently, the longer relaxation time is not necessarily detrimental to the low-temperature performance. For instance, for climates characterised by extremely cold temperatures, it is not apparent that shorter relaxation time leads to better performance since thermal stresses may develop faster and can result in cracking occurrence before relaxation can occur. However, for climates in which the temperature stays at reasonable low values for prolonged periods time, the binders with shorter relaxation time hold better performance since they can dissipate stress promptly (Marasteanu, 2004).
Low-temperature rheological properties and micro-mechanism of DIBCH plasticizer modified bitumen
Published in International Journal of Pavement Engineering, 2021
Zhen Fu, Songran Liu, Feng Ma, Xinglong Guo, Chen Li, Jiasheng Dai, Menglei Lin
The relaxation time (λ=η1/E1) of bitumen was calculated using the viscoelastic parameters. The relaxation time is characteristic of the stress-relaxation ability of materials. A smaller λ corresponds to a higher stress-relaxation velocity and faster stress dissipation, which contributes to improving the low-temperature properties of materials (Ashish et al.2020). The relaxation times of the different specimens at the three test temperatures are shown in Figure 7.