Temperature-dependent compressive response

Figure 15. Temperature-dependent compressive response of [0] composite laminates. (Reproduced from reference 13.)...

Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response fiinctions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where A is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothemial compressibility iCp which is another response fiinction. Temperature-dependent fluctuations characterize the dynamic equilibrium of themiodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

Finally, we note that in a very recent work Heuberger et al. investigated protein-resistant copolymer monolayers of PEG grafted to poly(L-lysine) (PLL) (PLL-g-PEG) in terms of the role of water in surface grafted PEG layers [159], interaction forces and morphology [160], compressibility, temperature dependence and molecular architecture [161], PEG is often used in biomedical applications in order to create protein-resistant surfaces but the mechanisms responsible for the protein-repelling properties of PEG are not fully understood. 

Temperature-dependant material property models were implemented into stmc-tural theory to establish a mechanical response model for FRP composites under elevated temperatures and fire in this chapter. On the basis of the finite difference method, the modeling mechanical responses were calculated and further vaUdated through experimental results obtained from the exposure of full-scale FRP beam and column elements to mechanical loading and fire for up to 2 h. Because of the revealed vulnerabihty of thermal exposed FRP components in compression, compact and slender specimens were further examined and their mechanical responses and time-to-failure were well predicted by the proposed models. 

Sanchez et al. re-examined polymer bulk data in a rigorous classical thermodynamic analysis (7,8). A new principle of temperature-pressure (T-P) superposition of compression response was foimd. Stated briefly, a dimensionless pressure variable is used to superpose compression data as a function of temperature into a universal curve. The governing parameter of compression is the first pressure coefficient B (= CiB/QP)p, of the bulk modulus B. It is related to the asymmetry of the free energy aroimd its minimum, between dilation and compression. For polymers, Bi is aroimd 10, and universal. A new isothermal equation of state was formulated through a Fade analysis of the pressure dependence of the bulk modulus (8). Both the Tait and the Fade equations describe almost perfectly the isothermal pressure dependence of volume. Both can be used to smoothen experimental PVT data. 

The behaviour of linear polymers depends largely on the temperature and the stress state e.g. the response in tension may differ markedly from that in compression. 

We present a constitutive model for amorphous polymers in their glassy state (T < Tg) when no crazing takes place (like in shear or in compression). The formulation is supplemented with a simple description of the material response when the temperature gets higher than Tg, as found experimentally to occur at sufficiently high loading rates [2,3]. Therefore, two descriptions of the viscoplastic response of amorphous polymers are used, depending on the... 

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