Stress time, creep

Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

Viscoelastic creep data are usually presented in one of two ways. In the first, the total strain experienced by the material under the applied stress is plotted as a function of time. Families of such curves may be presented at each temperature of interest, each curve representing the creep behavior of the material at a different level of applied stress. Below a critical stress, viscoelastic materials may exhibit linear viscoelasticity that is, the total strain at a given time is proportional to the applied stress. Above this critical stress, the creep rate becomes disproportionately faster. In the second, the apparent creep modulus is plotted as a function of time. 

Product performance data Products subjected to a given load develop a corresponding predictable deformation. If it continues to increase without any increase in load or stress, the material is said to be experiencing creep or cold flow. Creep in any product is defined as increasing strain over time in the presence of a constant stress (Figs. 2-25 and 26). The rate of creep for any given plastic, steel, wood, etc. material depends on the basic applied stress, time, and temperature. 

The strength of a fibre is not only a function of the test length, but also of the testing time and the temperature. It is shown that the introduction of a fracture criterion, which states that the total shear deformation in a creep experiment is bounded to a maximum value, explains the well-known Coleman relation as well as the relation between creep fracture stress and creep fracture strain. Moreover, it explains why highly oriented fibres have a longer lifetime than less oriented fibres of the same polymer, assuming that all other parameters stay the same. 

The creep modulus for a specified stress, time and temperature is the value of the stress divided by the strain measured after the selected time. 

PP bead foams of a range of densities were compressed using impact and creep loading in an Instron test machine. The stress-strain curves were analysed to determine the effective cell gas pressure as a function of time under load. Creep was controlled by the polymer linear viscoelastic response if the applied stress was low but, at stresses above the foam yield stress, the creep was more rapid until compressed cell gas took the majority of the load. Air was lost from the cells by diffusion through the cell faces, this creep mechanism being more rapid than in extruded foams, because of the small bead size and the open channels at the bead bonndaries. The foam permeability to air conld be related to the PP permeability and the foam density. 15 refs. 

The recommended maximum design stresses for a life of 5 to 10 years based on long-time creep tests are given in Table 3.24. 

Creep, stress relaxation and set are all methods of investigating the result of an applied stress or strain as a function of time. Creep is the measurement of the increase of strain with time under constant force stress relaxation is the measurement of change of stress with time under constant strain and set is the measurement of recovery after the removal of an applied stress or strain. It is important to appreciate that there are two distinct causes for the phenomena of creep, relaxation and set, the first physical and the second chemical. The physical effect is due to rubbers being viscoelastic, as discussed in Chapter 9, and the response to a stress or strain is not instantaneous but develops with time. The chemical effect is due to ageing of the rubber by oxidative chain scission, further crosslinking or other reaction. 

Fig. 13.84c, known as the Smith failure envelope, is of great importance because of its independence of the time scale. Moreover, investigations of Smith, and Landel and Fedors (1963,1967) proved that the failure envelope is independent of the path, so that the same envelope is generated in stress relaxation, creep and constant-rate experiments. As such it serves a very useful failure criterion. Landel and Fedors (1967) showed that a further generalisation is obtained if the data are reduced to ve, i.e. the number of elastically active network chains (EANCs). The latter is related to the modulus by... 

Figure 1.2 Highlighting load-time/viscoelasticity of plastics (1) stress-strain-time in creep and (2) strain-stress-time in stress relaxation.

In bodies showing retarded elasticity, the deformation is a function of time as well as stress. Such a stress-strain curve is shown in Figure 8-10. The upward part of the curve represents increasing values of stress when the stress is reduced, the corresponding strains are greater on the downward part of the curve. When the stress reaches 0, the strain has a finite value, which will slowly return to zero. There is no permanent deformation. The corresponding relaxation (stress-time) and creep (strain-time) curves... 

Fig. 5.1 Idealized representation of the transient change in fiber and matrix stress that occurs during the isothermal tensile creep and creep recovery of a fiber-reinforced ceramic (the loading and unloading transients have been exaggerated for clarity). It is assumed that the fibers have a much higher creep resistance than the matrix. The matrix stress reaches a maximum at the end of the initial loading transient. After full application of the creep load, the matrix stress relaxes and the fiber stress increases. Upon specimen unloading, elastic contraction of the composite occurs, followed by a time-dependent decrease in fiber stress and increase in matrix stress. Overall, creep tends to increase the difference in stress between constituents and recovery tends to minimize the difference in stress. After Wu and Holmes.15...

In both polymers, creep of compression-molded specimens is caused mainly by crazing, with shear processes accounting for less than 20% of the total time-dependent deformation. Crazing is associated with an increasing creep rate and a substantial drop in modulus. The effects of stress upon creep rates are described by the Eyring equation, which also offers an explanation for the effects of rubber content upon creep kinetics. Hot-drawing reduces creep rates parallel to the draw direction and increases the relative importance of shear mechanisms. 

A complete description of the viscoelastic properties of a material requires information over very long times. Creep and stress relaxation measurements are limited by inertial and experimental limitations at short times and by the patience of the investigator and structural changes in the lest material at very long times. To supplement these methods, the stress or the strain can be varied sinusoidally in a dynamic mechanical experiment. The frequency of this alternation is u cycles/s or m(= 27ri ) rad/s. An alternating experiment at frequency w is qualitatively equivalent to a creep or stress relaxation measurement at a time t = (I /w) sec. 

Rheological properties of mayonnaise have been studied using different rheological techniques steady shear rate-shear stress, time dependent shear rate-shear stress, stress growth and decay at a constant shear rate, dynamic viscoelastic behavior, and creep-compliance viscoelastic behavior. More studies have been devoted to the study of rheological properties of mayonnaise than of salad dressings, probably because the former is a more stable emulsion and exhibits complex viscous and viscoelastic rheological behavior. 

Two steady states are recognized for the long-time creep compliance of materials. Either the sample is a solid and the compliance becomes time independent or the sample is a liquid and the compliance becomes linear in -time. Once steady state has been achieved in creep, the stress can be removed (a = 0) and the elastic recoil, called creep recovery, can be measured. Recovery strain is defined as 7r(0 s 7(0) — 7(0 for t > 0, where t is defined to be zero at the start of recovery. The recoverable compliance is defined as the ratio of the time-dependent recovery strain 7r(0 and the initially applied stress a, where both 7r and t are now defined to be zero at the start of recovery ... 

Viscoelastic response At t = 0, J shows a sudden increase and this is followed by slower increase for the time apphed. When the stress is removed, J changes sign and shows an exponential decrease with increase of time (creep recovery), but it does not reach 0, as is the case for an elastic response. 

To gain a better understanding of the influence of fiber reinforcement on creep of RubCon, we investigated the relationship between values of compressive stresses and creep deformations that are damped out with time. The analysis of the result diagrams (Figures 2.54 and 2.55) shows linear stress-strain dependence of fiber-reinforced and plain RubCon samples at short-term compressive loading. However, creep deformations of these samples do not linearly depend on compressive stress value due to highly elastic deformation of the polybutadiene binder. 

Figure 3.78 Tensile creep of PVDF (MFR = 18 g/10 min) as a function of stress, time, and temperature...

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