Longitudinal elastic modulus

Measurements of heat capacity jumps at the glass-transition temperatures, Tg, in the matrix material and the composites, carried out from heat-capacity experiments, were intimately related to the extent of the mesophase thickness. Further accurate measurements of the overall longitudinal elastic modulus of the composites and the... 

Knowing the mass density p of the sample, the longitudinal elastic modulus c, related to the wave vector q, can be calculated according to Eq. (18). This equation is most important since it provides the key for the determination of the mechanical properties of materials at hypersonic frequencies from BriUouin spectra in a nondestructive manner. 

Fig. 9 Effect of draw ratio on the longitudinal elastic modulus of PET/PHB60 fibers (o) experimantal values, — theoretical.

The CNT aspect ratio is one of the main effective parameters on the longitudinal elastic modulus. Generally, the CNTs have a high aspect ratio, but their ultimate performance in a polymer composite is different. Stress transfer from the pol5mier matrix to the dispersed CNTs increases with increase in the aspect ratio of CNT [116]. However, the aggregation of CNTs could lead to a decrease in the effective aspect ratio of the CNTs. 

TABLE 10.2. Theoretical Values of the Longitudinal Elastic Modulus of Polyethylene Obtained by Various Methods Using the Molecular Orbital (MO) Approach to Clusters or the Crystal Orbital (CO) Approach to Infinite Periodic Polymers ... 

TABLE 10.3. Experimental Values of the Longitudinal Elastic Modulus of Polyethylene Obtained with Different Types of Measurements... 

Finally, we note that the longitudinal elastic modulus computed or measured in PE represents only an upper bound for the values which are measured in macroscopic samples. The reason is that both the calculated and measured moduli refer to a single PE chain (in Table 10.3, only the results of such experiments are given). In reality, however, due to impurities, chain breakages, and distortions, interactions between chains... 

Figure 14-11. Evolution of the longitudinal elastic modulus H, as a function of the bulk density, for sintered and compressed gels.

Moreover the longitudinal elastic modulus or Young s modulus of polyethylene has also been investigated. We compare the computed value with experimental results in table 4. 

The microscopic longitudinal elastic modulus, deviations from Hooke s law, the maximum of the retractive force and tensil strength are calculated for single infinite polyethylene chains using a first principle crystal orbital method and including electron correlation effects by perturbation theory. The ultraviolet spectrum of polyethylene is interpreted in terms of singlet charge transfer excitons. 

Different experimental and theoretical procedures for the investigation of the deformation properties of PE have been discussed in a recent paper (13) in more detail In this contribution, we present shortly only those new theoretical results which throw som more light for the role of various electronic effects in determining the longitudinal elastic modulus and the deviations from Hooke s law in PE. 

From the total energy of the polymer per elementary cell as a function of the stretch we can extract the longitudinal elastic modulus given by Y=(1/A)9F /Sl, where 1 is the length and A the effective cross-sectional area of a monomer unit and F is the force per monomer acting along the polymer axis z The values... 

TABLE 1. Theoretical values of the longitudinal elastic modulus of PE obtained with the HF and HF+MP methods using different atomic basis sets (in GPa units). 

CFRP composite Longitudinal elastic modulus Efrpl 128,093 MPa... 

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