Young elasticity modulus

The mechanical properties can be studied by stretching a polymer specimen at constant rate and monitoring the stress produced. The Young (elastic) modulus is determined from the initial linear portion of the stress-strain curve, and other mechanical parameters of interest include the yield and break stresses and the corresponding strain (draw ratio) values. Some of these parameters will be reported in the following paragraphs, referred to as results on thermotropic polybibenzoates with different spacers. The stress-strain plots were obtained at various drawing temperatures and rates. 

The classic Griffith-Orowan theory describes the relationship between strength and toughness of brittle materials such as ceramics (Griffith, 1920 Orowan, 1949). In the simple basic equation of the theory, the stress to fracture <7f is related to Youngs elastic modulus E, the fracture energy y and the critical crack length c by... 

The oil droplets or discontinuities usually induce a loss of mechanical properties, such as a decrease of the tensile strength and Young (elastic) modulus as given in Table 38.4. 

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. 

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. 

Elasticity. Glasses, like other britde materials, deform elastically until they break in direct proportion to the appHed stress. The Young s modulus E is the constant of proportionaUty between the appHed stress and the resulting strain. It is about 70 GPa (10 psi) [(0.07 MPa stress per )Tm/m strain = (0.07 MPa-m) / Tm)] for a typical glass. 

Magnesium alloys have a Young s modulus of elasticity of approximately 45 GPa (6.5 x 10 psi). The modulus of rigidity or modulus of shear is 17 GPa (2.4 X 10 psi) and Poisson s ratio is 0.35. Poisson s ratio is the ratio of transverse contracting strain to the elongation strain when a rod is stretched by forces at its ends parallel to the rod s axis. 

Fig. 7. Relations between elastic constants and ultrasonic wave velocities, (a) Young s modulus (b) shear modulus (c) Poisson s ratio and (d) bulk...

Moduli and Poisson s Ratio. The Young s modulus of vitreous sihca at 25°C is 73 GPa (<1.06 x 10 psi), the shear modulus is 31 GPa (<4.5 X 10 psi), and the Poisson s ratio is 0.17. Minor differences in values can arise owing to density variations. The elastic modulus decreases with increasing density and Poisson s ratio increases (26). 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

Elastic behavior is commonly quantified by the Young s modulus E, the proportionality constant between the appHed tensile stress O, and the tensile strain (A length/original length). 

P = pressure of liquid Vl = volume of hquid Ey = Young s modulus of elasticity V = Poisson s ratio... 

M = Modulus of elasticity (Young s Modulus) in psi, or modulus of plasticity. 

The JKR model predicts that the contact radius varies with the reciprocal of the cube root of the Young s modulus. As previously discussed, the 2/3 and — 1/3 power-law dependencies of the zero-load contact radius on particle radius and Young s modulus are characteristics of adhesion theories that assume elastic behavior. 

The stiffness of a plastic is expressed in terms of a modulus of elasticity. Most values of elastic modulus quoted in technical literature represent the slope of a tangent to the stress-strain curve at the origin (see Fig. 1.6). This is often referred to as Youngs modulus, E, but it should be remembered that for a plastic this will not be a constant and, as mentioned earlier, is only useful for quality... 

Obviously, the assumptions involved in the foregoing derivation are not entirely consistent. A transverse strain mismatch exists at the boundary between the fiber and the matrix by virtue of Equation (3.8). Moreover, the transverse stresses in the fiber and in the matrix are not likely to be the same because v, is not equal to Instead, a complete match of displacements across the boundary between the fiber and the matrix would constitute a rigorous solution for the apparent transverse Young s modulus. Such a solution can be found only by use of the theory of elasticity. The seriousness of such inconsistencies can be determined only by comparison with experimental results. 

The elastic constants of bulk amorphous Pd-Ni-P and Pd-Cu-P alloys were determined using a resonant i rasound spectroscopy technique. The Pd-Ni-P glasses are slightly stiffer than the Pd-Cu-P glasses. Within each alloy system, the Young s modulus and the bulk modulus show little change with alloy composition. 

In the region where the relationship between stress and strain is linear, the material is said to be elastic, and the constant of proportionality is E, Young s modulus, or the elastic modulus. 

The constant is called the modulus of elasticity (E) or Young s modulus (defined by Thomas Young in 1807 although the concept was used by others that included the Roman Empire and Chinese-BC), the elastic modulus, or just the modulus. This modulus is the straight line slope of the initial portion of the stress-strain curve, normally expressed in terms such as MPa or GPa (106 psi or Msi). A... 

Small deformations of the polymers will not cause undue stretching of the randomly coiled chains between crosslinks. Therefore, the established theory of rubber elasticity [8, 23, 24, 25] is applicable if the strands are freely fluctuating. At temperatures well above their glass transition, the molecular strands are usually quite mobile. Under these premises the Young s modulus of the rubberlike polymer in thermal equilibrium is given by ... 

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