Axial elastic modulus

Among the basic mechanical properties of fibers are their deformability and tenacity. When an axial stretching force is applied to the fiber, the principal quantitative indices of deformability are the axial elastic modulus (E)... 

The axial elastic modulus of PET fibers E) depends, as with other kinds of fibers, on the value of the elastic modulus of crystalline material ) and amorphous fiber... 

Draw ratio Density of the amorphous material da) (g/cm-" ) Amorphous orientation function fa) Crystallite length Oc) (nm) Long period (L) (nm) Degree of crystallinity (X=>) Substructure parameter (A) Axial elastic modulus ... 

The Halpin-Tsai equations represent a semiempirical approach to the problem of the significant separation between the upper and lower bounds of elastic properties observed when the fiber and matrix elastic constants differ significantly. The equations employ the rule-of-mixture approximations for axial elastic modulus and Poisson s ratio [Equations. (5.119) and (5.120), respectively]. The expressions for the transverse elastic modulus, Et, and the axial and transverse shear moduli, Ga and Gf, are assumed to be of the general form... 

Axial elasticity modulus ( (GPa) ASTM D 638, ASTM D7565 1155-165 210-300 400... 

CNTs have extraordinary mechanical properties [40-42], It is the stiffest (highest modulus) and strongest (tensile specific) material known to men. The rupture tension measured for MWNTs is 63 GPa [4], while the axial elasticity modulus is ITPa, what make them around five times tougher than steel. Therefore, a breakthrough is anticipated for the manufacture of a reinforced and light fiber that can... 

E ( denotes the axial elastic modulus of the fiber, where as V)2f is the longitudinal Poisson s ratio of the fiber, determined by measuring the radial contraction under an axial tensile load in the fiber axis direction and Gm denotes the matrix shear modulus. It should be noted that the negative sign in the expression for the shear stress is introduced to be consistent with the definition of an interfacial shear stress in classical theory of elasticity. The radial stress at the interface is given by ... 

The high axial elastic modulus of polyethylene and polyamide 6 is due to the fact that these polymers have a preferred conformation that is fully extended, i.e. all-trans. The elastic deformation is caused by the deformation of bond angles and by bond stretching, both showing high elastic constants. Isotactic polypropylene and polyoxymethylene crystallize in helical conformations and therefore exhibit a maximum stiffness which is only 20% of the maximum stiffness of the all-trans polymers. The elastic deformation of a helical chain involves, in addition to the deformation of bond angles and bond stretching, deformation by torsion about the G bonds. The latter... 

Their tautness is responsible for the high axial elastic modulus which may reach 80 GPa. Annealing reduces the... 

Figure 14.2 The compositional change at tendon-to-bone insertion site and the corresponding change of mechanical properties, (a) Relative mineral content evaluated from confocal Raman microprobe spectroscopy measurements, showing the ratio of the areas of the 960 Acm" PO4 peak to the 2940Acm collagen peak, across the tendon-to-bone insertion, (b) Bounds and estimates for the axial elastic modulus ( ) of a partially mineralized fiber. Mineral stiffens fibers dramatically at volume fraction above the percolation threshold = 0.5), indicated by the arrows. Percolation occurs at lower volume fraction for regions of enhanced mineralization elongated parallel to the fiber axis.

Upper and lower bounds on the elastic constants of transversely isotropic unidirectional composites involve only the elastic constants of the two phases and the fiber volume fraction, Vf. The following symbols and conventions are used in expressions for mechanical properties Superscript plus and minus signs denote upper and lower bounds, and subscripts / and m indicate fiber and matrix properties, as previously. Upper and lower bounds on the composite axial tensile modulus, Ea, are given by the following expressions ... 

For most materials, the bonnds on axial tensile modnlns tend to be reasonably close together, and the rule-of-mixtures prediction given by Eq. (5.82) is generally accurate enough for practical purposes for both the elastic modulus... 

Assume that the conductivity of a undirectional, continuous fiber-reinforced composite is a summation effect just like elastic modulus and tensile strength that is, an equation analogous to Eq. (5.88) can be used to describe the conductivity in the axial direction, and one analogous to (5.92) can be used for the transverse direction, where the modulus is replaced with the corresponding conductivity of the fiber and matrix phase. Perform the following calculations for an aluminum matrix composite reinforced with 40 vol% continuous, unidirectional AI2O3 fibers. Use average conductivity values from Appendix 8. 

Here, and Ey are the axial and transverse elastic modulus of the driveshaft material, and Vxy and Vy are the axial and transverse Poisson s ratios, respectively (see Section 5.4.3.1 for more information). 

E Elastic modulus, Ib/sq in k Thermal conductivity, Btu/ft -hr-°F q Swelling coefficient, dimensionless 0 Coefficient of thermal expansion, in/in- F fl Poisson s Ratio, dimensionless h Film heat transfer coefficient, Btu/ft -hr-°F N Number of layers in the lining R Thermal resistance, per axial foot T Temperature... 

Here is the elastic modulus tensor. It has 3 = 81 elements, however since the stress and strain are represented by symmetric matrices with six independent elements each, the number of independent modulus tensor elements is reduced to 36. An additional reduction to 21 is achieved by considering elastic materials for which a strain energy function exists. Physically, C2323 represents a shear modulus since it couples a shear stress with a shear strain. Cim couples axial stress and strain in the 1 or x direction,... 

Mechanical Properties of Various Nanocelluloses Obtained from Different Sources Elastic Modulus in Axial Direction (GPa) Elastic Modulus in Transverse Direction (GPa) Tensile Strength (Tensile Testing) (GPa)... 

Hence, to define the elastic properties of the fiber, five independent components of elastic modulus are required—Axial Young s modulus En or ii ) Shear modulus (Gn or G ) Transverse Young s modulus (ii22 or Transverse Shear modulus (G22 or G ) and the Axial Poisson ratio (vi2 or v ). 

Where a is the longitudinal stress, e is corresponding strain, and E is called Young s modulus (or the modulus of elasticity). Similarly, in shear deformation, the modulus is called the shear modulus or the modulus of rigidity (G). When a hydrostatic force is applied, a third elastic modulus is used the modulus of compressibility or bulk modulus (K). It is defined as the ratio of hydrostatic pressure to volume strain. A deformation (elongation or compression) caused by an axial force is always associated with an opposite deformation (contraction or expansion) in the lateral direction. The ratio of the lateral strain to the longitudinal strain is the fourth elastic constant called Poisson s ratio (v). For a small deformation, elastic parameters can be correlated in the following way ... 

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