Stress relaxation relationship with creep

We will first consider the parameters we are trying to model. Let us start with stress relaxation, where it is usual to describe properties in terms of a relaxation modulus, defined in Table 13-5 for tensile [ (r)] and shear [G(r)] experiments. The parameter used to describe the equivalent creep experiments are the tensile creep compliance [D(r)] and shear creep compliance [7(0]. It is important to realize that the modulus and the compliance are inversely related to one another for linear, tune-independent behavior, but this relationship no longer holds if the parameters depend on time. 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

One of the direct consequences of the Boltzmann superposition principle is that there is a relationship between the stress relaxation modulus and the creep compliance. We have already seen that when dealing with time-independent... 

The measurement of rheological properties for non-Newtonian, lipid-based food systems, such as dilatant, pseudoplastic, and plastic, as depicted in Figure 4.1, are much more difficult. There are several measurement methods that may involve the ratio of shear stress and rate of shear, and also the relationship of stress to time under constant strain (i.e., relaxation) and the relationship of strain to time under constant stress (i.e., creep). In relaxation measurements, a material, by principle, is subjected to a sudden deformation, which is held constant and in many food systems structure, the stress will decay with time. The point at which the stress has decayed to some percentage of the original value is called the relaxation time. When the strain is removed at time tg, the stress returns to zero (Figure 4.8). In creep experi-... 

If we consider the case of tests at ambient temperatures and moderate times, then the elTects measured are principally physical. Creep and stress relaxation tests under these conditions may need extrapolating to longer times. Ignoring any possible degradation effects, it is commonly found with rubbers that a plot of modulus against log of time will yield a linear relationship, which makes extrapolation very easy. With plastics, the log... 

At intermediate times it will be seen that, in creep, the compliance passes from /u to /r with time constant r . In stress relaxation the modulus passes from G to Gr with time constant r. Thus, at very short and very long times the stress and strain are Hookean, but at intermediate times when the time t is of the order of the relaxation times this k not true and it in this region that we see viscoelastic effects. The relationship between theory (Figure 4.15) and experiment (Figures 4.4 and 4.7, for e mple) will be explored later the reader may well however compare these figmres now and see in outline how theory is in broad agreement with eqieriment... 

Human AM has been widely applied in the repair of peripheral nerve injury. This application and research verifies that human AM has a similar tendency for stress relaxation and creep properties compared with sciatic nerve, indicating that it has good stress relaxation and aeep properties for transplantation applications. The stress relaxation curves of human AM and sciatic nerve have a logarithmic relationship, while the aeep curves have an exponential relationship. ... 

Blood and lymphatic vessels are soft tissues with densities which exhibit nonlinear stress-strain relationships [1]. The walls of blood and lymphatic vessels show not only elastic [2, 3] or pseudoelastic [4] behavior, but also possess distinctive inelastic character [5, 6] as well, including viscosity, creep, stress relaxation and pressure-diameter hysteresis. The mechanical properties of these vessels depend largely on the constituents of their walls, especially the collagen, elastin, and vascular smooth muscle content. In general, the walls of blood and lymphatic vessels are anisotropic. Moreover, their properties are affected by age and disease state. This section presents the data concerning the characteristic dimensions of arterial tree and venous system the constituents and mechanical properties of the vessel walls. Water permeability or hydraulic conductivity of blood vessel walls have been also included, because this transport property of blood vessel wall is believed to be important both in nourishing the vessel walls and in affecting development of atherosclerosis [7-9]. 

Macroscopic properties, alternatively referred to as bulk properties or simply performance , are of the utmost importance in material selection. For any application it is essential that the material provides the properties desired, under the conditions of use. In addition, it is wise to characterise the material more fully in order to understand what the effect might be, for example, of changing the temperature. Consideration should also be given to time-related phenomena, such as creep or stress relaxation. What are the consequences of dimensional instability Techniques that can provide this type of information directly include mechanical testing, rheology and thermal analysis. In cases where knowledge of the relationship between structure and properties is desirable, then obviously the techniques described here must be used in combination with those which follow. 

Clearly some simple method must he devised to characterize the mecheuiical response as a function of time (and of course temperature). Creep tests were a possibility hut the continued strain with time wo ild cause changes in structure and thereby make the structure-property relationship difficult to interpret. Stress relaxation was also a possibility but at that point there were instrumentation difficulties in obtaining short time measurements. What was needed was some simple method that wo ild cover a wide range of time scale of loading in which the applied strain magnitude was a controlled variable. This line of thought led to the development of the rotating beam dynamic tester ... 

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