Quasi-static measurements

Flinn et al. [30] describes an experimental impact technique in which <100)-oriented LiF single crystals ( 8 ppm Mg) are loaded in a controlled manner and the multiplication of screw dislocations is measured. The peak shear stress in this relatively soft material is 0.01 GPa. For shear impulses exceeding approximately 40 dyne s/cm, dislocation multiplication is adequately described by the multiple-cross-glide mechanism [(7.24)] with m = l/bL = (2-4) X 10 m, in reasonable agreement with quasi-static measurement [2]. 

Quasi-static measurements force-distance curves and adhesion... 

Prrei+ positive state of relaxed remanent polarization, relaxed for one second in the Pr+ state. Equal to the positive state of remanent polarization of the quasi statically measured loop (see Section 3.3.4)... 

Besides impact testing, quasi-static measurements are carried out to assess the Young modulus, E, the yield stress, cry, and the elongation at break, break> as the most current parameters. They follow international standards (e.g. ISO 527 for tensile tests, ISO 178 for bending measurements). 

It is interesting to compare the softening of the material near Tg measured by H, as a function of temperature, with the corresponding DSC traces for amorphous PET and PMMA (Fig. 3.3). These experiments demonstrate that both methods, H and DSC, yield a similar measure of Tg. The apparent difference in the Tg values obtained ( 10°C) is a result of the fast heating rate used in the DSC determination in contrast to the quasi-static measurement in the case of H. 

The quantities E and G refer to quasi-static measurements. When cyclic motions of stress and strain are involved, it is more convenient to use dynamical mechanical moduli. The complex Young s modulus is then defined as = " + iE", where E is the storage modulus and " the loss modulus. The storage modulus is a measure of the energy stored elastically during deformation the loss modulus is a measure of the energy converted to heat. Similar definitions hold for G, J, and other mechanical properties. 

Before entering into a detailed discussion of the glass transition, the five regions of viscoelastic behavior are briefly discussed to provide a broader picture of the temperature dependence of polymer properties. In the following, quasi-static measurements of the modulus at constant time, perhaps 10 or 100 s, and the temperature being raised l°C/min will be assumed. 

For quasi-static measurements such as illustrated in Figure 8.2, the glass transition temperature, Tg, is often taken at the maximum rate of turndown of the modulus at the elbow, where E = lO Pa. Often the glass transition temperature is defined as the temperature where the thermal expansion coefficient (Section 8.3) undergoes a discontinuity. (Enthalpic and dynamic definitions are given in Section 8.2.9. Other, more precise definitions are given in Section 8.5.)... 

However, it was found that the obtained values are lower than the modulus obtained from quasi-static measurements, indicating that a direct comparison between the results from both techniques is not straightforward. A weak tendency of increasing E with increasing HA content is seen up to 20% ceramic content. As observed before, this formulation also optimised the ultimate strength, being in principle the material with better mechanical performance. 

While the uniaxial tensile test may be considered as a quasi-static measure of the fracture resistance of materials. 

In practice, change caimot be effected reversibly, since a system at equilibrium will remain at equihbrium unless disturbed and, when disturbed, can reach a new equilibrimn state only by evolving through a series of non-equilibrium states. What is usually done in the measurement of heat capacities (heat absorbed per Kelvin), from which entropy changes are computed, is to keep the system as close to equilibrimn as possible by minimizing the temperature difference between the system and the surroundings. These are called quasi-static measurements, the closest we can get to reversible measurements. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

Using physical properties relating to performance parameters leads to the development of algorithms for predicting performance for laboratory screening of potential improvements. Many of these algorithms have been estabUshed. The two main categories of measurement criteria are quasi static and dynamic mechanical properties. 

To illustrate the effect of radial release interactions on the structure/ property relationships in shock-loaded materials, experiments were conducted on copper shock loaded using several shock-recovery designs that yielded differences in es but all having been subjected to a 10 GPa, 1 fis pulse duration, shock process [13]. Compression specimens were sectioned from these soft recovery samples to measure the reload yield behavior, and examined in the transmission electron microscope (TEM) to study the substructure evolution. The substructure and yield strength of the bulk shock-loaded copper samples were found to depend on the amount of e, in the shock-recovered sample at a constant peak pressure and pulse duration. In Fig. 6.8 the quasi-static reload yield strength of the 10 GPa shock-loaded copper is observed to increase with increasing residual sample strain. 

In this chapter, we overview basic techniques for making nanoscale adhesion and mechanical property measurements. Both quasi-static and dynamic measurements are addressed. In Section 2 of this chapter, we overview basic AFM instrumentation and techniques, while depth-sensing nanoindentation is overviewed in Section 3. Section 4 addresses recent advances in instrumentation and techniques... 

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

Dynamic properties are more relevant than the more usual quasi-static stress-strain tests for any application where the dynamic response is important. For example, the dynamic modulus at low strain may not undergo the same proportionate change as the quasi-static tensile modulus. Dynamic properties are not measured as frequently as they should be simply because of high apparatus costs. However, the introduction of dynamic thermomechanical analysis (DMTA) has greatly widened the availability of dynamic property measurement. 

When the Pecet number, the measure of the relative importance of advection to diffusion, is small, which is the case for high viscosity magmas, the temporal derivation of concentration and the advection term in Eq. (13.31) may be ignored, and quasi-static approximation may be developed. In this case, Eq. (13.31) reduces to... 

M. Kuhn, A quasi-static technique for MOS C-V and surface state measurements, Solid-State Electron, 13(6) (1970) 873-885. 

SFM s can be also classified according to static and dynamic operating modes. Under quasi-static conditions, the microscope measures the instantaneous response of the cantilever when it interacts with the sample. Dynamic SFM enables separation of the elastic and inelastic component in the cantilever deflection when the sample surface is exposed to a periodically varying stress field. The dynamic modes are useful for investigation of viscoelastic materials such as polymers and results in additional improvements in the signal-to-noise ratio. 

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