Elasticity, delayed

Elastic modulus Up to the fracture stress, glass behaves, for most practical purposes, as an elastic solid at ordinary temperatures. Most silicate-based commercial glasses display an elastic modulus of about 70GNm", i.e. about 1/3 the value for steel. If stress is applied at temperatures near the annealing range, then delayed elastic effects will be observed and viscous flow may lead to permanent deformation. 

The extension of an amorphous material under a tensile force can be resolved into three parts first, an immediate elastic extension. Which is immediately recoverable on removing the tensile force Mcondly, a delayed elastic extension which is recoverable slowly and thirdly, a plastic extension, viscous flow, or creep, which cannot be glteovered. With glass at ordinary temperatures, this plastic exten- ion is practically absent. A very slow delayed elastic extension OOCUrs. This effect can be troublesome in work with torsion fibres. The delayed elastic effect in vitreous silica fibres is 100 times less than in other glass fibres, and viscous flow of silica is negligible below OO C (N. J. Tighe, 1956). For exact work vitreous sihea torsion flbres are therefore used. 

The measurements reported by Bach (56) apparently were not under constant temperature conditions. Strain recovery after loading in the plasticized state is small. The longer the loading period the smaller the recoverable strain. This suggests plastic flow under load and a conversion of delayed elastic strain into an irreversible deformation. 

Experimentally, as indicated in Fig. 12.13, we find that D/Dq depends on the shear stress at the wall xw (a flow variable) and the molecular weight distribution (MWD) (a structural variable) (22). The length-to-diameter ratio of the capillary (a geometric variable) also influences D/Dq. The swelling ratio at constant xw decreases exponentially with increasing L/Dq and becomes constant for L/Dq > 30. The reason for this decrease can be explained qualitatively as follows. Extrudate swelling is related to the ability of polymer melts and solutions to undergo delayed elastic strain recovery, as discussed in... 

The usual way in which the deformation changes with time, has been dealt with in 6.1. The best representation appeared to be a Maxwell element with a Kelvin-Voigt element in series the deformation is then composed of three components an immediate elastic strain, which recovers spontaneously after removal of the load, a delayed elastic strain which gradually recovers, and a permanent strain. Moreover, we noticed that a single retardation time (a single Kelvin-Voigt element) is not sufficient we need to introduce a spectrum ... 

If the creep experiment is extended to infinite times, the strain in this element does not grow indefinitely but approaches an asymptotic value equal to tq/G. This is almost the behavior of an ideal elastic solid as described in Eq. (11 -6) or (11 -27). The difference is that the strain does not assume its final value immediately on imposition of the stress but approaches its limiting value gradually. This mechanical model exhibits delayed elasticity and is sometimes known as a Kelvin solid. Similarly, in creep recovery the Maxwell body will retract instantaneously, but not completely, whereas the Voigt model recovery is gradual but complete. 

Curve 1 in Fig. 1 under low rotor r.p.m. corresponds to the case when the rate of the stress buildup under the effect of deformation is commensurate with the rate of their relaxation. The development of time-delayed elastic deformations determines the final rate of attainment of the steady-state regime of viscous flow, under which the stationary value of the shear stress is recorded. Starting with the moment of time t, the stress will increase and the period of the viscous-plastic state comes to an end. 

The same parameters can also be determined by applying a constant shear stress to the interface and measuring the resulting shear strain as a function of time (see fig. 3.40), so-called interfacial creep tests. At t = 0, a shear stress is suddenly applied, and kept constant thereafter. For ideally viscous monolayers a steady increase of the shear strain with t will be observed, while for an elastic material the observed strain will be instantaneous and constcmt in time. For a viscoelastic material, as in fig. 3.40, there is first am Instantaneous increase AB in the strain, the elastic response followed by a delayed elastic response BC and a viscous... 

In a Voigt (or Kelvin) element tlie spring and dashpot are parallel. If a stress is suddenly applied the spring cannot respond immediately because of the resistance caused by the viscous flow (delayed elasticity). Monolayers with a two-dimensional network and viscous material between the cross-links will display such behaviour. So, the increase of the strain is retarded. Eventually the maximum strain / K° is attained, see fig. 3.52a. After cessation of the strain the energy stored in the spring relaxes, again with a rate determined by the parallel viscosity, till AA— 0. Behaviour like this is semi-solid. In the limit of r] - 0 the block diagram of fig. 3.49b is retrieved. 

Even at room temperature, long-term measurements have proved the existence of slow irreversible deformations in glasses which, however, are accompanied by delayed elastic effects on loading. The viscosity of glass and its viscous flow is usually conside-... 

When attempting to describe more accurately the rheological behaviour of ceramic plastic mixes, one should also take into account the elastic behaviour above the yield point. If a plastic body is abruptly stressed by a constant load, there first occurs rapid clastic deformation followed by delayed elastic deformation and irreversible flow. Similarly, instant as well as delayed relaxation take place after stress relief. If a formed product has only a limited possibility to relax, it retains some interna stress w hich may be the cause of drying defects. 

In Figure 5.8d an intermediate behavior, called viscoelastic, is depicted such a relation is often called a creep curve, and the time-dependent value of the strain over the stress applied is called creep compliance. On application of the stress, the material at first deforms elastically, i.e., instantaneously, but then it starts to deform with time. After some time the material thus exhibits flow for some materials, the strain can even linearly increase with time (as depicted). When the stress is released, the material instantaneously loses some of it deformation (which is called elastic recovery), and then the deformation decreases ever slower (delayed elasticity), until a constant value is obtained. Part of the deformation is thus permanent and viscous. The material has some memory of its original shape but tends to forget more of it as time passes. 

Samples of bulk polymers respond to applied stresses in several ways some materials behave as elastic solids, some as viscous liquids, and stiU others exhibit viscous as well as elastic properties. The latter are called viscoelastic solids. If a constant force is applied to a viscoelastic sample, the extension of this solid may be divided into three parts (1) an instantaneous elastic deformation, (2) a delayed elasticity or creep, and (3) a viscous flow. This may be seen best by referring to Fig. 15-17 which illustrates an example of a tensile force Fo applied at zero time, maintained until... 

Immediate elastic recovery (ASTM D 4848), Recoverable deformation that is essentially independent of time, that is, occurring in (a time approaching) zero time after removal of the applied force. (See Delayed deformation and compare with (delayed) elastic recovery.)... 

The early work on viscoelasticity was performed on silk, mbber, and glass, and it was concluded that these materials exhibited a delayed elasticity manifest in the observation that the imposition of a stress resulted in an instantaneous strain, which continued to increase more slowly with time. It is this delay betweai cause and effect that is fundamental to the observed viscoelastic response, and the three major examples of this hysteresis effect are (1) creep, where there is a delayed strain response afto the rapid application of a stress, (2) stress-relaxation (Section 13.15), in which the material is quickly subjected to a strain and a subsequent decay of stress is observed, and (3) dynamic response (Section 13.17) of a body to the imposition of a steady sinusoidal stress. This produces a strain oscillating with the same frequeney as, but out of phase with, the stress. For maximum usefulness, these measurements must be carried out over a wide range of temperature. 

By stressing a viscoelastic plastic material there are three deformation behaviors to be observed. They are an initial elastic response, followed by a time-dependent delayed elasticity that may also be fully recoverable, and the last observation is a viscous, non-recoverable, flow component. Most... 

In many materials, the mechanical response can show both elastic and viscous types of behavior the combination is known as viscoelasticity. In elastic solids, the strain and stress are considered to occur simultaneously, whereas viscosity leads to time-dependent strain effects. Viscoelastic effects are exhibited in many different forms and for a variety of structural reasons. For example, the thermoelastic effect was shown earlier to give rise to a delayed strain, though recovery of the strain was complete on unloading. This delayed elasticity is termed anelastic-ity and can result from various time-dependent mechanisms (internal friction). Figure 5.9 shows an example of the behavior that occurs for a material that has a combination of elastic and anelastic behavior. The material is subjected to a constant stress for a time, t. The elastic strain occurs instantaneously but, then, an additional time-dependent strain appears. On unloading, the elastic strain is recovered immediately but the anelastic strain takes some time before it disappears. Viscoelasticity is also important in creep but, in this case, the time-dependent strain becomes permanent (Fig. 5.10). In other cases, a strain can be applied to a material and a viscous flow process allows stress relaxation (Fig. 5.11). 

Fig. 1.13 Normalized distribution of activation energies for delayed elastic shear relaxations in two binary metallic glass alloys (a) Cu4oZr6o and (b) PdsoSi2o (from Argon and Kuo (1980) courtesy of North-Holland).

Argon, A. S. (1968) Delayed elasticity in inorganic glasses, /. Appl. Phys., 39, 4080-4086. 

It is also essential to take into account delayed elastic effects, specially in the neighborhood of Tg. In this case, one has to wait for the relaxation of elastic response before the glass enters into Newtonian behavior. For polymers, which are not Newtonian, one has to determine the viscosity as a function of shear rate. In some instances, the zero shear viscosity is reported, where one extrapolates the viscosity value to zero shear rate. 

Yarn elasticity. After strong degradation no elasticity tests were possible to be performed because the strong degradation decreases breaking load under 5 N. Hie mean values of the initial deformation at 5 N and the immediate elasticity, the delayed elasticity and the permanent set in % of warp and weft samples are reported in Table 3. 

Reference Initial strain at 5N Immediate Elasticitv Delayed Elasticity Permanent set... 

Delayed elasticity is a property that is characteristic of a disorderly molecular arrangement in amorphous material or of disordered regions in crystalline material [190]. It is caused by thermally activated processes and may therefore involve entropy-elastic forces. Two observations suggest that the time-dependent elasticity... 

Creep describes time-dependent permanent deformation of materials resulting from constant structural stress. The creep of polymers can be divided into two main stages primary creep and steady-state creep. The creep strain rate decreases with time in the primary creep and is constant in the steady-state creep. Strain recovery occurs with the removal of external load after a creep time. Therefore, the total strain (e) consists of three separate parts el, e2, and e3. The el and e2 are the immediate elastic deformation and delayed elastic deformation, respectively. The e3 is the Newtonian flow. It was found that the el and e2 decreased with increasing clay contenf indicating lower creep recovery with the addition of C20A. The creep compHance J, the ratio of strain and applied load, can be expressed as... 

A long delayed elastic recovery viscoelasticity). The residual indentation should be measured immediately after load release in order to minimize the viscoelastic recovery of the material. 

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