Viscoelasticity creep

DavkJ Ford Sims, Viscoelastic Creep and Relaxation Behavior of Laminated Composite Plates, Ph.O. dissertation. Department of Mechanical Engineering and Solid Mechanics Center, Institute of Technology, Southern Methodist University, Dallas, Texas, 1972. (Also available from Xerox University Microfilms as Order 72-27,298.)... 

Long time dynamic load involves behaviors such as creep, fatigue, and impact. T vo of the most important types of long-term material behavior are more specifically viscoelastic creep and stress relaxation. Whereas stress-strain behavior usually occurs in less than one or two hours, creep and stress relaxation may continue over the entire life of the structure such as 100,000 hours or more. 

When a viscoelastic material is subjected to a constant stress, it undergoes a time-dependent increase in strain. This behavior is called creep. The viscoelastic creep behavior typical of many TPs is illustrated in Figs. 2-22 and 2-23. At time to the material is suddenly subjected to a constant stress that is main-... 

Fig. 2-22 Viscoelastic creep behavior typical of many TPs under long-term stress to rupture (a) input stress vs. time profile and (b) output strain vs. time profile.

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. 

The viscoelastic creep modulus may be determined at a given temperature by dividing the constant applied stress by the total strain prevailing at a particular time. Since the creep strain increases with time, the viscoelastic creep modulus must decrease with time (Fig. 2-23). Below its critical stress for linear viscoelasticity, the viscoelastic creep modulus versus time curve for a material is independent of the applied stress. In other words, the family of strain versus time curves for a material at a given temperature and several levels of applied stress may be collapsed to a single viscoelastic creep-modulus-time-curve if the highest applied stress is less than the critical value. 

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 rate of creep and stress relaxation of TPs increases considerably with temperature those of the TSs (thermoset plastics) remain relatively unaffected up to fairly high temperatures. The rate of viscoelastic creep and stress relaxation at a given temperature may also vary significantly from one TP to an-... 

Laws and McLaughlin30 discuss viscoelastic creep compliances of composite materials using another approach to the problem of the elastic properties of heterogeneous materials - the self-consistent method. 

When subjected to a step constant stress, viscoelastic materials experience a time-dependent increase in strain. This phenomenon is known as viscoelastic creep. 

Viscoelastic creep data can be presented by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time [23-26], Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material s critical stress value. 

Viscoelastic creep is important when considering long-term structural design. Given loading and temperature conditions, designers can choose materials that best suit component lifetimes. 

The polymeric materials are viscoelastic (creep) and this property is very important in corrosion applications. The temperature limit is 260°C and most of the applications are below 150°C. The tanks and piping are used below 100°C. The mechanical properties of... 

Fig. 35a-c. Mechanical models of creep and recovery, (d) Modified model for viscoelastic creep... 

C is the so-called plane-strain viscoelastic creep compliance. It is connected to the relaxation modulus E(t) and Poisson s ratio v(t) by... 

Just as linear viscoelastic behaviour with full recovery of strain is an idealisation of the behaviour of some real polymers under suitable conditions, so ideal yield behaviour may be imagined to conform to the following for stresses and strains below the yield point the material has time-indepen-dent linear elastic behaviour with a very low compliance and with full recovery of strain on removal of stress at a certain stress level, called the yield stress, the strain increases without further increase in the stress if the material has been strained beyond the yield stress there is no recovery of strain. This ideal behaviour is illustrated in fig. 8.1 and the differences between ideal viscoelastic creep and ideal yield behaviour are shown in table 8.1. 

Viscoelastic creep manifests itself in the time-dependent deformation of a material. Experimental data obtained from a laboratory creep test under constant applied stress for a viscoelastic solid is shown in Fig. 12.1. Traditionally, a creep curve consists of three stages. In the first stage, also known as primary creep, the creep strain rate decreases with time until it reaches a constant value. The second stage, known as steady state creep, is defined as the region where the slope of the creep strain is a constant with respect to time. In the third and final stage, termed tertiary creep, the creep strain rate increases with time through progressive failure and terminates with the rupture of the specimen. 

A sample subjected to tensile or compressive stress (Figure 40.27) exhibits the instantaneous deformation (elastic part) at first, which then increases with time (viscoelastic creep). After cycling the moisture content to and from a higher moisture content, the creep has been significantly greater due to mechanosorptive action. 

Retaining important possibilities of viscoelastic creep (mechanosorptive creep is always a source of stress reversal) such an effect is obtained at high temperatures, provided the moisture content is sufficiently high (Irvine, 1984)... 

In addition, this condition imposes a relatively high value of EMC (only one part of shrinkage is effected and the influence of temperature on the viscoelastic creep is not inhibited by a relatively low moisture content level). However, a high relative humidity value can activate the development of fungi. 

Rule 2 High temperature. A high value of temperature is most often a positive factor. This accelerates the internal moisture transfer and activates the viscoelastic creep. However, care should be taken with sensitive species high temperature levels can increase the risk of collapse, problems of color, or even thermal degradation of the wood constituents. 

The long delayed responses of the fuel cell to changes in load have been attributed to mechanical property changes in the polymer. We have initiated measurements of polymer stress relaxation. The stress relaxation and viscoelastic creep of Nafion is both temperature and water concentration dependent. Response times vary from 1 s to 10 s, which can give a wide range of characteristic response times for PEM fuel cells. 

Polymers exhibit this property of linear viscoelastic creep at low stresses (stresses sufficiently low that the strains are below 0.005). In a creep experiment, the plot of strain against stress at a specific time is known as an isochronal. 

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