Viscoelastic materials relaxation

Whether a viscoelastic material behaves as a viscous Hquid or an elastic soHd depends on the relation between the time scale of the experiment and the time required for the system to respond to stress or deformation. Although the concept of a single relaxation time is generally inappHcable to real materials, a mean characteristic time can be defined as the time required for a stress to decay to 1/ of its elastic response to a step change in strain. The... 

The most characteristic features of viscoelastic materials are that they exhibit a time dependent strain response to a constant stress (creep) and a time dependent stress response to a constant strain (relaxation). In addition when the... 

When a viscoelastic material is subjected to a constant strain, the stress initially induced within it decays in a time-dependent manner. This behavior is called stress relaxation. The viscoelastic stress relaxation behavior is typical of many TPs. The material specimen is a system to which a strain-versus-time profile is applied as input and from which a stress-versus-time profile is obtained as an output. Initially the material is subjected to a constant strain that is maintained for a long period of time. An immediate initial stress gradually approaches zero as time passes. The material responds with an immediate initial stress that decreases with time. When the applied strain is removed, the material responds with an immediate decrease in stress that may result in a change from tensile to compressive stress. The residual stress then gradually approaches zero. 

In computing ordinary short-term characteristics of plastics, the standard stress analysis formulas may be used. For predicting creep and stress-rupture behavior, the method will vary according to circumstances. In viscoelastic materials, relaxation data can be used in Eqs. 2-16 to 2-20 to predict creep deformations. In other cases the rate theory may be used. 

Unfortunately, this group Db depends on the assignment of a single characteristic time to the fluid (perhaps a relaxation time). While this has led to some success, it appears to be inadequate for many viscoelastic materials which show different relaxation behaviour under differing conditions. 

Most pigmented systems are considered viscoelastic. At low shear rates and slow deformation, these systems are largely viscous. As the rate of deformation or shear rate increases, however, the viscous response cannot keep up, and the elasticity of the material increases. There is a certain amount of emphasis on viscoelastic behavior in connection with pigment dispersion as well as ink transportation and transformation processes in high-speed printing machines (see below). Under periodic strain, a viscoelastic material will behave as an elastic solid if the time scale of the experiment approaches the time required for the system to respond, i.e., the relaxation time. Elastic response can be visualized as a failure of the material to flow quickly enough to keep up with extremely short and fast stress/strain periods. 

We have developed the idea that we can describe linear viscoelastic materials by a sum of Maxwell models. These models are the most appropriate for describing the response of a body to an applied strain. The same ideas apply to a sum of Kelvin models, which are more appropriately applied to stress controlled experiments. A combination of these models enables us to predict the results of different experiments. If we were able to predict the form of the model from the chemical constituents of the system we could predict all the viscoelastic responses in shear. We know that when a strain is applied to a viscoelastic material the molecules and particles that form the system gradual diffuse to relax the applied strain. For example, consider a solution of polymer... 

The other mechanism responsible for unstable spinning is the mechanical resistance of a viscoelastic material to rapid deformation. It is a well-known fact that increased yam breaks can be a consequence of spinning speed, which relates to prolonged relaxation time and therefore to break. The fracture can be observed at a maximum extent of deformation under distortion of the covalent bonds. 

Note 5 The standard linear viscoelastic solid can be used to represent both creep and stress relaxation in materials in terms of single retardation and relaxation times, respectively. 

We can get a first approximation of the physical nature of a material from its response time. For a Maxwell element, the relaxation time is the time required for the stress in a stress-strain experiment to decay to 1/e or 0.37 of its initial value. A material with a low relaxation time flows easily so it shows relatively rapid stress decay. Thus, whether a viscoelastic material behaves as a solid or fluid is indicated by its response time and the experimental timescale or observation time. This observation was first made by Marcus Reiner who defined the ratio of the material response time to the experimental timescale as the Deborah Number, Dn-Presumably the name was derived by Reiner from the Biblical quote in Judges 5, Song of Deborah, where it says The mountains flowed before the Lord. ... 

The difference between solids and liquids is found in the magnitude of D. Liquids, which relax in small fractions of a second, have small D. Solids have a large D. A sufficient lime span can reduce the Deborah number of a solid to unity, and impact loading can increase D of a liquid. Viscoelastic materials are best characterized under conditions in which D lies within a few decades of unity. 

The creep of a viscoelastic body or the stress relaxation of an elasacoviscous one is employed in the evaluation of T] and G. In such studies, the long-time behavior of a material at low temperatures resembles the short-time response at high temperatures. A means of superimposing data over a wide range of temperatures has resulted which permits the mechanical behavior of viscoelastic materials to be expressed as a master curve over a reduced time scale covering as much as twenty decades (powers of ten). 

The sample must have reached steady state before cessation of the test or the application of a second step. Steady state in a creep test is seen as a constant slope in the strain curve. A constant slope in the stress curve may also be seen in a stress relaxation test, but often the signal is lost in the noise. A material that is liquid-like in real time will need a test period of 5 to 10 min. A stress relaxation test is likely to be somewhat shorter than a creep test since the signal inevitably decays into the noise at some point. A creep test will last indefinitely but will probably reach steady state within an hour. For a material that is a solid in real time, all experiments should be longer as molecular motion is, by definition, slower. Viscoelastic materials will lie in between these extremes. Polymer melts can take 1 hr or more to respond in a creep test, but somewhat less time in a stress relaxation test. 

Real (viscoelastic) materials give an intermediate response that is an exponential curve. The exponential time constants associated with the curve are used to approximate the relaxation times of the material itself. Thus, the shape of the output curve is analyzed to give viscoelastic information, although this model fitting is only strictly legitimate in the linear viscoelastic region. Workers have shown that the mechanical parts of the models (springs and dashpots) can be associated with specific parts of a food s makeup. 

Thus, we may give a good description of a linear viscoelastic material in terms of relaxed, and unrelaxed elastic constants and a distribution of relaxation times (- this is not necessarily the same distribution for each elastic constant ). These all have to be found from experiments. In general it is possible to find some of the relaxed and unrelaxed elastic constants and to estimate the distribution of relaxation times. 

The exact solutions of the linear elasticity theory only apply for small strains, and under idealised loading conditions, so that they should at best only be treated as approximations to the real behaviour of materials under test conditions. In order to describe a material fully we need to know all the elastic constants and, in the case of linear viscoelastic materials, relaxed and unrelaxed values of each, a distribution of relaxation times and an activation energy. While for non-linear viscoelastic materials we cannot obtain a full description of the mechanical properties. 

The most obvious problem of non-linearity is the definition of a modulus. For a linear viscoelastic material we need to define not only a real and an imaginary modulus but also a spectrum of relaxation times if we are fully to describe the material - although it is more usual to quote either an isochronous modulus or a modulus at a fixed frequency. We must, for a full description of a non-linear material give the moduli (and relaxation times) as a function of strain as well this will not usually be practicable so we satisfy ourselves by quoting the modulus at a given strain. The question then arises as to whether this... 

Viscoelastic hysteresis. Relaxation processes within the materials can contribute to rolling friction especially in the case of viscoelastic materials. 

According to the change of strain rate versus stress the response of the material can be categorized as linear, non-linear, or plastic. When linear response take place the material is categorized as a Newtonian. When the material is considered as Newtonian, the stress is linearly proportional to the strain rate. Then the material exhibits a non-linear response to the strain rate, it is categorized as Non Newtonian material. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. This kind of materials are known as thixotropic deformation is observed when the stress is independent of the strain rate [2,3], In some cases viscoelastic materials behave as rubbers. In fact, in the case of many polymers specially those with crosslinking, rubber elasticity is observed. In these systems hysteresis, stress relaxation and creep take place. 

A viscoelastic material is characterized by at least three phenomena the presence of hysteresis, which is observed on stress-strain curves, stress relaxation which take place where step constant strain causes decreasing stress and creep occurs where step constant stress causes increasing strain. 

K. Onaram, W.H. Findley, Creep and Relaxation of Nonlinear Viscoelastic Materials , Dover Publications, New York (1989). 

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