Young’s

Restored parameters for the evaluation of PDSM, may be different PMF of material tensor of stresses or its invariants, spatial gradients of elastic features (in particular. Young s modulus E and shear modulus G), strong, technological ( hardness HRC, plasticity ), physical (density) and others. 

Fig.2. Tomographic (a) and graphic (b, for depth 13 mm) images of relative change of Young s modulus 5E% (average on volume Eo=218,310 Pa) of material in section perpendicular to surface of thick-sheet sample (thickness 26 mm).

Equation X-17 was stated in qualitative form by Young in 1805 [30], and we will follow its designation as Young s equation. The equivalent equation, Eq. X-19, was stated in algebraic form by Dupre in 1869 [31], along with the definition of work of adhesion. An alternative designation for both equations, which are really the same, is that of the Young and Dupre equation (see Ref. 32 for an emphatic dissent). 

The preceding definitions have been directed toward the treatment of the solid-liquid-gas contact angle. It is also quite possible to have a solid-liquid-liquid contact angle where two mutually immiscible liquids are involved. The same relationships apply, only now more care must be taken to specify the extent of mutual saturations. Thus for a solid and liquids A and B, Young s equation becomes... 

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

Fig. 6. The calculated Young s modulus as a function of cut-off energy (basis set size). Convergence is basically reached for a cut-off of 54 Ry.

Regarding mechanical properties of polymers, the efficiency of the Car-Parrinello approach has enabled us to evaluate the ultimate Young s modulus of orthorhombic polyethylene, and demonstrate basis set convergence for that property. 

Comparing this result with Eq. (3.1) shows that the quantity in brackets equals Young s modulus for an ideal elastomer in a perfect network. Since the number of subchains per unit volume, i /V, is also equal to pN /Mj, where M, is the molecular weight of the subchain, the modulus may be written as... 

Over the range of fit, matching the dependence of Oj on a produces only a numerical coefficient and does not constitute a test of the predicted dependence of the modulus on either T or Mj,. We have already confirmed that Young s modulus actually does increase with temperature for elastomers. Next let us... 

A general relationship between Young s modulus and the shear modulus is E... 

Young s modulus for [CERAMICS - TffiCHANICAL PROPERTIES AND BEHAVIOR] (Vol 5)... 

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

---