Creep effect viscoelastic behavior

Maxwell model A mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus E) in series with a dashpot of coefficient of viscosity (ri). It is an isostress model (with stress 8), the strain (e) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as stress relaxation and creep with Newtonian flow analysis. Also called Maxwell fluid model. See stress relaxation viscoelasticity. Maxwell-Wagner efifect See dielectric, Maxwell-Wagner effect. 

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). 

J(A.,T, ) has known the meaning of the creep function at constant temperature as a function of the effective time A.. All these results may be transferred immediately to the problem of viscoelastic behavior under the influence of aging at constant temperature [9,15]. The temperature history has to be replaced by the degree of aging. A, of the sample and the time-temperature shift function, a(T,T ), by the time-age shift function, b (A,A ). The degree of aging, also called the age of the sample, defines the time elapsed from the last quench from the equilibrium state down to the aging temperature so far A, can then be expressed ... 

When a plastics (polymer) is subjected to stress, the structure can react in a number of ways. In the first reaction the bonds are stressed by stretching or bending which is the elastic response. Unlike the more ordered structures, adjustment of the strain in the materials is hindered by the interference between molecules so that all but the very initial response is hindered by frictional effects and the material shows a delay between the application of the stress and the resulting strain. This behavior is referred to as viscoelastic behavior. From Fig. 1-9 it can be seen how the molecules slide past each other to increase spacings and reduce the elastic load on the bonds. Sustained stress causes actual displacement of the molecular chains with extensive movement of the chains past each other and results in flow-like behavior which is referred to as creep or cold flow. At constant initial strain the slippage of the molecules and the adjustment of position lead to another condition which is called stress relaxation. The level of the resistance of the structure to applied deformation drops and the material assumes a lower energy configuration. 

In linear viscoelasticity, the creep function and the relaxation function are interrelated and each would permit the derivation of the viscoelastic constitutive relation under the condition that the principle of time invariance can be applied, meaning that the material is influenced only by a t) and s(f) and no other influencing variables are being effective. In summary, in the idealized case of the isothermal linear viscoelasticity under the conditions of static stress or strain, the linear viscoelastic behavior of a material may adequately be described by the creep function F t), the relaxation function R t), the retardation spectrum or the relaxation spectrum. 

Different viscoelastic materials may have considerably different creep behavior at the same temperature. A given viscoelastic material may have considerably different creep behavior at different temperatures. Viscoelastic creep data are necessary and extremely important in designing products that must bear long-term loads. It is inappropriate to use an instantaneous (short load) modulus of elasticity to design such structures because they do not reflect the effects of creep. Viscoelastic creep modulus, on the other hand, allows one to estimate the total material strain that will result from a given applied stress acting for a given time at the anticipated use temperature of the structure. 

The mechanical behavior of plastics on time-dependent applied loading can cause different important effects on materials viscoelasticity. Loads applied for short times and at normal rates (Chapter 2) causes material response that is essentially elastic in character. However, under sustained load plastics, particularly TPs, tend to creep, a factor that is included in the design analysis. 

Researchers have examined the creep and creep recovery of textile fibers extensively (13-21). For example, Hunt and Darlington (16, 17) studied the effects of temperature, humidity, and previous thermal history on the creep properties of Nylon 6,6. They were able to explain the shift in creep curves with changes in temperature and humidity. Lead-erman (19) studied the time dependence of creep at different temperatures and humidities. Shifts in creep curves due to changes in temperature and humidity were explained with simple equations and convenient shift factors. Morton and Hearle (21) also examined the dependence of fiber creep on temperature and humidity. Meredith (20) studied many mechanical properties, including creep of several generic fiber types. Phenomenological theory of linear viscoelasticity of semicrystalline polymers has been tested with creep measurements performed on textile fibers (18). From these works one can readily appreciate that creep behavior is affected by many factors on both practical and theoretical levels. 

Craze growth at the crack tip has been qualitatively interpreted as a cooperative effect between the inhomogeneous stress field at the crack tip and the viscoelastic material behavior of PMMA, the latter leading to a decrease of creep modulus and yield stress with loading time. If a constant stress on the whole craze is assumed then time dependent material parameters can be derived by the aid of the Dugdale model. An averaged curve of the creep modulus E(t) is shown in Fig. 13 as a function of time, whilst the craze stress is shown in Fig. 24. 

Viscoelastic Effects. Time plays a very Important role in the properties of polymers. For metals, creep is generally significant only at relatively high temperatures, typically greater than half their absolute melting temperature. However, many polymers demonstrate time dependent behavior not only at room temperature but even at cryogenic temperatures (38). 

A comprehensive analytical model for predicting long term durability of resins and of fibre reinforced plastics (FRP) taking into account viscoelastic/viscoplastic creep, hygrothermal effects and the effects of physical and chemical aging on polymer response has been presented. An analytical tool consisting of a specialized test-bed finite element code, NOVA-3D, was used for the solution of complex stress analysis problems, including interactions between non-linear material constitutive behavior and environmental effects. 

Viscoelastic phenomena may be described through three aspects, namely stress relaxation, creep and recovery. Stress relaxation is the decline in stress with time in response to a constant applied strain, at a constant temperature. Creep is the increase in strain with time in response to a constant applied stress, at a constant temperature. Recovery is the tendency of the material to return partially to its previous state upon removal of an applied load. The material is said to have memory as if it remembers where it came from. Because of the memory effect, in transient flows the behavior of viscoelastic fluids wUl be dramatically different from that of Newtonian fluids. Viseoelastie fluids are fiiU of instabilities. Some examples inelude instabilities in Taylor-Couette flow, in eone-and-plate and plate-and-plate flows (Larson 1992). The extrudate distortion, commonly called melt fraeture, is a notorious example of viscoelastic instability in polymer processing. The viseoelastie instability in injection molding can result in specific surface defects such as tiger stripes (Bogaerds et al. 2004). 

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