Dynamic mechanical transient

The mechanism of these transitions is nontrivial and has been discussed in detail elsewhere Q, 12) it involves the development of a homoclinic tangencv and subsequently of a homoclinic tangle between the stable and unstable manifolds of the saddle-type periodic solution S. This tangle is accompanied by nontrivial dynamics (chaotic transients, large multiplicity of solutions etc.). It is impossible to locate and analyze these phenomena without computing the unstable, saddle-tvpe periodic frequency locked solution as well as its stable and unstable manifolds. It is precisely the interactions of such manifolds that are termed global bifurcations and cause in this case the loss of the quasiperiodic solution. 

Fig. 4 Schematic illustrating the dynamic mechanism of metal atom penetration into a SAM by means of transient opening of holes by lateral motion of the adsorbate molecules...

Numerous efforts have focused upon the nature of moisture transport of epoxy systems. Previous-sorption desorption work demonstrated that equilibrium moisture levels In an epoxy system can be related to thermodynamic states (1,2,3). Transient and equilibrium dynamic mechanical experiments are performed In this work with two epoxy systems TGEBA-TETA and N-5208. These experiments provide Insight Into the nature and extent that network changes have on the dynamic mechanical properties as a result of hygrothermal cycling. 

The second type of dynamic mechanical experiment involved collection of "transient" -Rheovibron data at a fix frequency as a function of time after a change in either the moisture or thermal environment. The experimental apparatus designed for this purpose is depicted in Figure 1. 

There are two basic types of transient dynamic mechanical experiments which were performed In this study. The first type Involves Isothermal cycling of an epoxy sample between a dry and wet environment. The second type of experiment Involves cycling the epoxy sample between two different temperatures under a liquid water environment. In each case, the transient and equilibrium values of dynamic mechanical properties change In a unique manner. 

Isothermal Moisture Transients Isothermal experiments will first be discussed for the DGEBA-TETA systems. Film samples from this system were equilibrated In a desiccated environment and subsequently exposed to liquid water environment In the Rheovlbron apparatus. Figure 5 summarizes typical results of these dynamic mechanical experiment. In addition to the... 

Figure 5. Dynamic mechanical and swelling behavior for a transient moisture sorption experiment on DGEBA-TETA.

Figure 6 plots transient Isothermal tan 6 dynamic mechanical data for a 25 PHR-DDS N-5208 epoxy sample. This sample was Initially exposed to a dry 50 C environment. This temperature was selected since It coincides with the vicinity of the dynamic mechanical u transition. Hence, differences between properties In the dry and wet states could be maximized. Behavior of the Initial dry to wet state transient cycle was previously discussed for DGEBA-TETA epoxy sample of Figure 5. Similar behavior Is noted for this N-5208 epoxy sample. There Is an Initial rise In the tan 5 followed by a "blocking" and gradual reduction. After the tan 6 appeared to approach a stable value, the environment In the sample chamber was switched from one of a 50 C liquid environment to a 50°C desiccated environment. Once again, a rapid Increase In the mobility of the system occurred. After the sharp Increase In tan 5, a gradual decrease followed.

Tan 5, storage compliance, and loss compliance values for these experiments are plotted as a function of time in Figure 8. This transient temperature cycle data illustrates interactions between the dynamic mechanical plasticization and blocking behavior just discussed as well as the epoxy s equilibrium moisture uptake behavior (3), and the temperature behavior of dynamic mechanical properties observed for this epoxy in Figure 2a. Perhaps the easiest comparison to consider involves the relationship between transient temperature cycling data of Figure 8 and the thermal behavior observed for N-5208 epoxy tan 6 data of Figure 2a. 

Based on "equilibrium" dynamic mechanical results of Figure 2a, tan 6 properties associated with network thermal behavior at 20 C should be greater than comparable behavior at the 50 C thermal state. The difference in relative magnitudes stems from the relative positions of the 20 C and 50 C thermal states with respect to the low temperature 8 transition for this epoxy. This difference for the transient data is best observed in Figure 8. Equilibrated 20°C tan 5 and loss property values for the 20°C hygrothermal state are greater than the subsequent 50°C hygrothermal state measurements. 

Figure 8. Transient dynamic mechanical properties of 25 PHR-DDS N-5208 epoxy sample during liquid water thermal cycling between 20 C and 50 C.

Transient dynamic mechanical data on the DGEBA-TETA and high performance M-5208 epoxy based systems have been obtained and compared with "equilibrium" data.. The transient data have demonstrated that moisture can act not only to plasticize an epoxy network but also to restrict and stiffen molecular chain movement. The behavior observed was explained by examining the synergistic effects that moisture and temperature have on the particular epoxy network structure. 

Glass transition temperature, Tg, and storage modulus, E , were measured to explore how the pigment dispersion affects the material (i.e. cross-link density) and mechanical properties. Both Tg and E were determined from dynamic mechanical analysis method using a dynamic mechanical thermal analyzer (DMTA, TA Instruments RSA III) equipped with transient testing capability. A minimum of 3 to 4 specimens were analyzed from each sample. The estimated uncertainties of data are one-standard deviation. 

We have already referred to various kinds of data on mechanical behavior of polymers. We are now going to consider methods of acquisition of such information. The most fi equently used are the so-called quasistatic methods which involve relatively slow loading. Tension, compression, and flexure belong here. The quasistatic methods have to be distinguished from so-called transient tests which include stress relaxation and creep. There are also impact tests and dynamic mechanical procedures which will be defined later. 

Two manifestations of linear viscoelasticity are creep and stress relaxation-, the respective two testing methods are known as transient tests. One can also apply sinusoidal load, an increasingly more used method of study of viscoelasticity by dynamic mechanical analysis (qv) (DMA). We shall now briefly discuss each of these three approaches. 

C. Khoo and R. Normandin, The mechanism and dynamics of transient thermal grating diffraction in nematic liquid crystal Aims, IEEE J. Quantum Electron., vol. QE-21, pp. 329-335, 1985 I. C Khoo and S. Shepard, ""Submillisecond grating diffractions in ne matic liquid crystal films, J. Appl. Phvs., vol. 54. pp. 5491-5494 1983. 

FIGURE 7.21. (a) When subjected to an intense light for a period of 30 min, a giant vesicle is placed under mechanical stress. Transient pores open up, close down, and are reborn every 3 rnin. (b) Closure of a hole in a vesicle. (From Dynamics of Transient Pores in Stretched Vesicles. by O. Sandre, L. Moreaux, and F. Brochard. In Proceedings of the National Academy, of Sciences, (c) 2001 National Academy of Sciences, USA. Reproduced by perrni.ssion.)... 

In a very extensive study of both stress relaxation and dynamic mechanical properties in simple extension, on single crystal mats of fractions of linear polyethylene, Takayanagi and collaborators were able to combine data at different temperatures by reduced variables over most of the range from 16°C up to the temperature of crystallization and also to show that the dynamic and transient data corresponded fairly closely, provided the latter were corrected for nonlinear behavior by an extrapolation procedure to zero strain. It is characteristic of crystalline polymers that departures from linear viscoelastic behavior appear at very small strains, and are sometimes significant in stress relaxation even at a tensile strain of = 0.001. In dynamic measurements, the strains are usually small enough to fall within the linear range. 

The mechanical behavior of DEs depends on the type of stimulation. For static stimuli the final deformation will be reached depending on the compliance of the elastomer. In case of dynamic stimulation, transient effects leading to more complex models have to be considered. 

Dynamic experiments. Often a viscoelastic material is subjected to stresses or strains, which change over time. When experiments are set up to mimic such conditions, they are referred to as dynamic experiments or dynamic mechanical analysis. For transient experiments, the time scale is qualitatively proportional to the inverse of the test frequency used for dynamic experiments-We will consider the above equations with respect to a simple sinusoidal stress as is often imposed by common commercial test machines. 

In a previous paper presented by Dr, Leborgne and Spassky, from the Universite Pierre et Marie Curie, in Paris, it has been shown that it is now possible to prepare optically active polylactones by a "stereoelective" polymerization process. It is the purpose of the present paper to indicate important differences in properties between the optically active and the racemic poly(a-methyl-a-n-propyl-3-propiolactone) (PMPPL). Results will be presented concerning the crystallization and melting properties, as well as the dynamic and transient mechanical properties of these polymers. 

Khoo, I. C., and R. Normandin. 1985. The mechanism and dynamics of transient thermal grating diffraction in nematic liquid crystal film. IEEE J. Quantum Electron. QE21 329. 

The measurement of the dynamic-mechanical properties of polymers requires the separation of the response of the material to cyclic or transient loading into two components an elastic response and an inelastic response. Frequently, these two are best resolved experimentally as a complex response and a damping. Whilst the complex or total reponse is familiar to most experimentalists, damping frequently poses a conceptual problem. However, the effect of damping is manifested in many ways. For example (i) the phase lag between stress and strain (Le. load and displacement) (ii) the decrease with time of the amplitude of stress and strain in a freely vibrating system and (iii) the limited amplitude of a system excited at resonance. 

In this regard perturbation analysis like step analysis and electrochemical impedance spectroscopy (EIS) can show the way (Choudhury et al., 2005, Jenseit et al., 1993). The popular trend of using transmission line model for EIS analysis may not be sufficient to diagnose the dynamic mechanisms. Thus to understand and decouple the effects, there is a need to develop and validate comprehensive transient models based on first principles. With the availability of increased computational power it may be possible to develop online fault diagnosis analyzer systems for the actual field units. 

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