Time-dependent properties materials

In this method appropriate values of such time-dependent properties as the modulus are selected and substituted into the standard equations. It has been found that this approach is sufficiently accurate if the value chosen for the modulus takes into account the projected service life of the product and/or the limiting strain of the plastic, assuming that the limiting strain for the material is known. Unfortunately, this is not just a straightforward value applicable to all plastics or even to one plastic in all its applications. This type of evaluation takes into consideration the value to use as a safety factor. If no history exist a high value will be required. In time with service condition inputs, the SF can be reduced if justified. 

Actually, some fluids and solids have both elastic (solid) properties and viscous (fluid) properties. These are said to be viscoelastic and are most notably materials composed of high polymers. The complete description of the rheological properties of these materials may involve a function relating the stress and strain as well as derivatives or integrals of these with respect to time. Because the elastic properties of these materials (both fluids and solids) impart memory to the material (as described previously), which results in a tendency to recover to a preferred state upon the removal of the force (stress), they are often termed memory materials and exhibit time-dependent properties. 

All thermoplastics are known as viscoelastic materials and hence exhibit time dependent properties. It is known that during crack propagation the influence of time is also involved such that slow crack speeds correspond to long times and high crack speeds to short times. In the following we will be concerned with this problem in more detail. 

The time-dependent properties of the molecular dynamics simulation are characteristic of a material element flowing through the shock wave, within the approximations made in the derivation of the method. Therefore, the spatial profile of the simulated shock wave can be reconstructed by calculating the position of a material element x at time t,... 

The time-temperature superimposition technique allows the prediction of material properties that normally would require measurements over many months or years. To collect the necessary data, measurements of a time-dependent variable are made at a number of temperatures. The curves are shifted mathematically along the time axis until some overlap occurs and a continuous curve is formed covering several decades of time this curve is called a master curve. A master curve can be used to determine the time-dependent property as a function of time. Figure 10.30c shows total strain as a function of time and temperature for PTFE. 

These assumptions are not always justifiable when applied to plastics unless modification has occurred. The classical equations cannot be used indiscriminately. Each case must be considered on its own merits, with account being taken of such factors as the mode of deformation, the service temperature and environment, the fabrication method, and so on. In particular, it should be noted that the past traditional equations that have been developed for other materials, principally steel, use the relationship that stress equals the modulus times strain, where the modulus is constant. Except for thermoset reinforced plastics and certain engineering plastics, many plastics do not generally have a constant modulus. Different approaches have been used for the nonconstant situation some are quite accurate. The drawback is that most of these methods are quite complex, involving numerical techniques that are not attractive to designers. One method that has been widely accepted is this so-called pseudoelastic design method. In this method appropriate values of such time-dependent properties as the modulus are selected and substituted into the standard equations. 

Vegetable fibers also show time-dependent properties associated with other polymeric materials. There is, however, only limited data available, which analyzes creep, relaxation, or strain-rate behavior of vegetable fibers. 

Thus, the distribution of free volume, or the LL environments, and the distributed material property affected, such as the local fluidity or relaxation behavior, reflects the variations in the local atomic packing discussed in Section 1.3. Such property variations have long been of interest (Scherer 1990). For the case presented above, in which the viscosity at T2 needs a certain relaxation time from that of Ti, the change in the time-dependent property, p (e.g., viscosity), is given by a relaxation function Mp(t),... 

Zilch, H., Rohimann, A., Bergmarm, G., and KolbeL R. (1980), Material properties of fenaoral cancellous bone in axial loading n. Time dependent properties. Arch. Orthop. Trauma Surg. 97(4) 257-262. 

All polymer materials used in reinforced plastics display some viscoelastic or time-dependent properties. The origins of creep in composites stem from the behaviour of polymers under load together with local stress redistributions between fibre and matrix as a function of time. There is little creep at normal temperatures in the reinforcing fibres. The origin of the creep mechanisms is related to the nature and levels of internal bonding forces between the chains of the polymer, which are influenced by temperature and moisture. 

Viscoeiasticity. As already noted, the time-dependent properties of polymer-based materials are due to the phenomenon of viscoelasticity (qv), a combination of solid-like elastic behavior with liquid-like flow behavior. During deformation, equations 3 and 6 above applied to an isotropic, perfectly elastic solid. The work done on such a solid is stored as the energy of deformation that energy is released completely when the stresses are removed and the original shape is restored. A metal spring approximates this behavior. 

Finally, the power of finite elasticity theory is that once the material properties [Wi and W2 or are known, the stresses in any deformation field can be calculated. There is an extensive literature on ways to represent the material functions and, in fact, commercial finite element codes use finite elasticity theory in calculations that can be important in applications that range from the stresses in automobile tires (105) to those in earthquake bearings for large buildings (106). One feature of the K-BKZ theory to be discussed next is that it retains the structure of finite elasticity theory and includes time-dependent properties of the viscoelastic materials that were discussed in the earlier sections of this article. 

Polymers have viscoelastic properties they contain both elastic and viscous components. When the solicitation submitted to polymeric materials is mechanical, their time-dependent properties can be examined by creep, stress relaxation, and DMA. In DMA, a sample is subjected to a sinusoidal load (stress or strain), with the... 

Viscoelasticity or Rheology The study of materials whose mechanical properties have characteristics of both solid and fluid materials. Viscoelasticity is a term often used by those whose primary interest is solid mechanics while rheology is a term often used by those whose primary interest is fluid mechanics. The term also implies that mechanical properties are a function of time due to the intrinsic nature of a material and that the material possesses a memory (fading) of past events. The latter separates such materials from those with time dependent properties due primarily to changing environments or corrosion. All polymers (fluid or solid) have time or temperature domains in which they are viscoelastic. 

Thus, if the time dependent creep or relaxation properties of a material are known, the complex moduli and compliances can be calculated simply via Fourier transforms (Eqs. 6.49-6.50). Comparison back to the Laplace transforms (Eq. 6.44), we see that s or ioi times the Laplace or Fourier transform, respectively, of the time dependent properties provide the transformed properties which can be used in the correspondence principle forms Eqs. 6.43 and 6.46. 

For an isotropic viscoelastic material only two time dependent properties are independent and it is clear from the correspondence principle that similar relationships to Eqs. 9.15 hold for the Laplace transformed moduli such that. 

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