Deformation time dependent

An important aspect of the mechanical properties of fibers concerns their response to time dependent deformations. Fibers are frequently subjected to conditions of loading and unloading at various frequencies and strains, and it is important to know their response to these dynamic conditions. In this connection the fatigue properties of textile fibers are of particular importance, and have been studied extensively in cycHc tension (23). The results have been interpreted in terms of molecular processes. The mechanical and other properties of fibers have been reviewed extensively (20,24—27). 

Creep. The phenomenon of creep refers to time-dependent deformation. In practice, at least for most metals and ceramics, the creep behavior becomes important at high temperatures and thus sets a limit on the maximum appHcation temperature. In general, this limit increases with the melting point of a material. An approximate limit can be estimated to He at about half of the Kelvin melting temperature. The basic governing equation of steady-state creep can be written as foUows ... 

This is the governing equation for the Kelvin (or Voigt) Model and it is interesting to consider its predictions for the common time dependent deformations. 

Fatigue is an example of the influence of time on the mechanical properties of a material. Another example of a time-dependent mechanical property is creep. Creep, sometimes called viscoplasticity, is defined as time-dependent deformation nnder constant stress, usually at elevated temperatures. Elevated temperatures are necessary because creep is typically important only above Tmp % where T p is the absolute melting point of the material. 

Creep, Stress Relaxation, Elastic Recovery. Olefin fibers exhibit creep, or time-dependent deformation under load, and undergo stress relaxation, or the spontaneous relief of internal stress. High molecular weight and high orientation reduce creep. 

Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long-term stress. Creep deformation is time-dependent deformation. 

Rees, J. E., and Rue, P. J. (1978), Time-dependent deformation of some direct compression excipients,/. Pharm. Pharmacol, 30, 601-607. 

Based upon results obtained from monotonic tensile experiments conducted with 0° SCS-6 SiCf/HPSN, 0790° Q/SiC, and 0° Nicalon SiCf/CAS-II composites, Shuler and Holmes38 have recommended a loading rate of 20-100 MPa/s to minimize time-dependent deformation during room temperature and elevated temperature monotonic tensile or flexural testing. Equivalent times-to-failure should be used in displacement controlled tests. 

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. 

If the solid does not shows time-dependent behavior, that is, it deforms instantaneously, one has an ideal elastic body or a Hookean solid. The symbol E for the modulus is used when the applied strain is extension or compression, while the symbol G is used when the modulus is determined using shear strain. The conduct of experiment such that a linear relationship is obtained between stress and strain should be noted. In addition, for an ideal Hookean solid, the deformation is instantaneous. In contrast, all real materials are either viscoplastic or viscoelastic in nature and, in particular, the latter exhibit time-dependent deformations. The rheological behavior of many foods may be described as viscoplastic and the applicable equations are discussed in Chapter 2. 

Many powders, especially with viscoelastic compaction mechanism, such as starch or avicel, exhibit large degree of stress relaxation (with time-dependent deformation). 

Creep. One of the most remarkable aspects of the deformation of polydiacetylenes is that it is not possible to measure any time-dependent deformation or creep when crystals are deformed in tension parallel to the chain direction (14,24). This behviour is demonstrated in Figure 3 for a polyDCHD crystal held at constant stress at room temperature and the indications are that creep does not take place at temperatures of up to at least 100 C (24). Creep and time-dependent deformation are normally a serious draw-back in the use of conventional high-modulus polymer fibres such as polyethylenes (28). Defects such as loops and chain-ends allow the translation of molecules parallel to the chain direction in polyethylene fibres. In contrast since polydiacetylene single crystal fibres contain perfectly-aligned long polymer molecules (cf Figure lb) there is no mechanism whereby creep can take place even at high temperatures. 

The above modulus definition does not take time into account. For materials that exhibit time-dependent deformation, such as polymers, the reported modulus must include, to be valid, a time factor. This... 

For studying the viscous deformation caused by the creep of dam and its base rock under time-dependent loading, different visco-elastic constitutive models are developed to identify the most suitable models and parameters for more accurate simulation of the time-dependent deformation of the dam-foundation system. 

The creep of dam concrete includes two parts instantaneous elastic deformation and viscous deformation. A generalized Kelvin model consisting of two standard Kelvin model in series is used to describe the time-dependent deformation of the dam concrete as shown in Figure 1. 

The time-dependent deformation of the foundation rock, caused by loadings, is described by a Burgers model, which is composed of a Kelvin model and Maxwell model in series, as showed in Figure 2, The partial strain expression of Burgers model is... 

Soft mode operation requires additional circuitry to apply a constant force to the specimen. The specifications for the tensilometer are given in Table I. For the position sensor used the precision is 0.1 nm, and the accuracy is 0.1% over the range 1-10 jw,m. The equivalent noise generated by the servocontrol is less than 10" N. The accuracy of the force output depends on the scale and the previous time-dependent deformation of the platforms and is approximately 2%. In practice values of the cross-sectional area and length of the specimen are the limiting features in transforming the data to stress-strain curves. 

The most characteristics features of viscoelastic materials are that they exhibit time-dependent deformation or strain when subjected to a constant stress (creep) and a time-dependent stress when... 

In the SSRT testing, creep stands for time-dependent deformation of the sample after the load application. Maximum load is defined as the load that results in the failure of one component. The strain rate is the initial rate of increase of the gage length of an initial... 

Different sediments exhibit varying amounts of time-dependent deformations and stress variation with time. The effect can result in either an increase or a decrease in shear strength (S J compared to the behavior at a standard strain loading rate (e) of 1% per hour. 

A plot of the logarithm of strain rate decreases as a function of the logarithm of time and is linear. The same behavior has been observed for undisturbed and remolded wet or dry clay, NC and OC clay, and sand (Singh and Mitchell, 1968). In general, different soil types exhibit varying amounts of time-dependent deformations and stress variations with time. These variations are also exhibited by their secondary compression and creep characteristics. 

A number of viscoelastic (i.e., rheological) models have been proposed to model steady-state creep in soils. A selection of fom of these models is presented in Figure 8.47. A model incorporating spring constants, and E2 a slider element of resistance x and a dash-pot with viscosity, v, was proposed by Murayama and Shibata (1964), which is shown in Figure 8.47a. The time-dependent deformation is controlled by the slider element Xq. Deformation will only occur for applied stresses in excess of Xq. 

An empirical method is the third approach used to describe time-dependent deformations in soils. This approach involves modeling the behavior of the material under controlled conditions. Attempts are then made to develop mathematical relationships between the system parameters to obtain equations that both describe and predict the material... 

Selecting ceramics for use at high temperatures or under applied load requires consideration of their long-term stability. Time dependent deformation is known as creep, and creep resistance is a critical design parameter. Even if creep does not lead to failure, a change in shape or size may render a component useless. The mechanism responsible for creep depends on temperature, stress, and the microstructure of the ceramic. 

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. 

The long-term behavior of plastics must, in other words, be investigated using static methods. The best-known method is the time-to-mpture or creep test, whereby a workpiece is subjected to stress CTq at time t = 0 and the stress parameter is maintained at a constant level for the entire duration of the test Time-dependent deformation is then measured. Fig. 26. If the elongation is constant, the stress parameter drops off in time with plastics. This is known as relaxation. This knowledge has applications related, for instance, to screw cmmections (plastic... 

So far the parameters defined, compliances, moduli and contraction ratios, are in forms which can be rigorously interpreted for infinitesimal time dependent deformation under constant stress, thus creep moduli E 9, r) are functions of angle and time. Extension to accommodate nonlinear behaviour at finite strain is obtained by allowing the quantities to become also functions of stress or strain. Thus modulus has the form E 6,t,%) and compliance functions Si/t.t). Such an extension is not rigorous but is useful. 

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