Cyclic Deformations

We analyse the effect of a strain varying sinusoidally at an angular frequency (U 

For a linear viscoelastic material, the stress also varies sinusoidally, but leads in phase by an angle 8 

At higher strains, in the non-linear region, harmonics can be generated and more complex stress-strain responses occur. From these equations, the stress is croCOsS when the strain has its maximum value Bq (Fig. 7.11a). The energy input per unit volume of material in the first quarter of the strain cycle is 

Dynamic mechanical thermal analysers (DMTA) are semi-automated machines for determining the Young s or shear modulus of polymers as a 

If stress and strain in Eqs (7.16) and (7.17) are written in complex number form, they become 

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Fig. 14. Amplitude dependences (y0 is the amplitude of cyclic deformations) of the elastic modulus for frequency a) = 63 s 1 13% dispersion of acetylene carbon black in low- (/) and high-molecular (2) poly(isobutylene)s...

Under dynamic conditions, i.e., under cyclic deformations (stretching and compression), the physical methods to protect against ozone are no longer valid. 

Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or "creep" in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122], Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5] ... 

But contrary to HBIB polymers, they do not show any strain hardening and are very weak materials. The hysteresis behavior of HIBI and HBI polymers is also very different from that of the HBIB polymer. The former polymers show tremendously higher energy loss during cyclic deformations, and these differences are again inter-... 

The development of cardiac assist devices and other instrumentation and components which come in contact with the cardiovascular system requires materials which will perform in a physiological environment. One particularly difficult application is the diaphragm for blood pumps, which requires an elastomer to undergo cyclic deformation and/or flexing while in contact with blood. 

Dynamic properties Mechanical properties of polymeric materials exhibited under repeated cyclic deformation. 

The term dynamic test is used here to describe the type of mechanical test in which the rubber is subjected to a cyclic deformation pattern from which the stress strain behaviour is calculated. It does not include cyclic tests in which the main objective is to fatigue the rubber, as these are considered in Chapter 12. Dynamic properties are important in a large number of engineering applications of rubber including springs and dampers and are generally much more useful from a design point of view than the results of many of the simpler static tests considered in Chapter 8. Nevertheless, they are even today very much less used than the "static" tests, principally because of the increased complexity and apparatus cost. 

Most fatigue tests apply a fixed pre-stress or strain, partly because without bonding of the test piece it is necessary to hold the rubber in place. The amount of pre-stress or strain will affect the fatigue life in particular the fatigue life is appreciably shortened if the cyclic deformation passes near to or through zero strain. 

The contribution of the thermoelastic effect to energy dissipation in solids under transient or cyclic deformation was first studied by Zener and shown to account for mechanical relaxation peaks in some metals. 

These in situ generated silica fillers also give increased resistance to creep or compression set in cyclic deformations, as is illustrated in Figure 8.6.43 The in situ filled PDMS samples are seen to show very little compression set. They can also provide increased thermal stability, as demonstrated by the results presented in Figure 8.7. 44... 

The shear rate field that results from such cyclic deformation is... 

According to these considerations, we assume that for quasi-static, cyclic deformations of filler reinforced rubbers up to large strain the total free energy density consists of two contributions ... 

Precrack cyclic deformation that includes the formation of persistent slip bands, formation of extrusions and intrusions. 

Note that the loss tangent is also a measure of the ratio of energy lost to energy stored in a cyclic deformation. The energy loss density during one cycle of strain, AE, is given by... 

Damping and Dynamic Mechanical Spectroscopy. Dynamical mechanical spectroscopy means data taken with cyclical deformation of the sample. Often, the... 

Another important effect of Zr addition is the effect associated with vacancies, in particular it reduces the concentration of the free vacancies. The Zr modified ally result more resistant to cyclic deformation than the unmodified one the precipitation of trialuminades and the consequent more stable structure results in the increase of fatigue life of the material. 

Fracture surfaces of the cyclically deformed fatigue specimens were observed at low magnification in order to identify the zones of fatigue initiation and final failure, at higher magnifications in order to identify the regions of microscopic crack formation and growth and microscopic plastic mechanisms. 

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