Stress Young’s modulus

Matuda, N., Baba, S. and Kinbara, A. (1981), Internal stress, Young s modulus... 

Modulus - A material constant defined as the ratio between the applied stress and any resulting elastic deformation (reversible on removing the stress). There are several commonly used variants - depending on the loading method and the direction in which the deformation is measured relative to the direction of the applied stress. Young s modulus is that where both are co-axial. 

Here, the subscripts F and S denote polyimide film and substrate, respective. The mbols polyimide film, respectively. For SiilOO) wafers, biaxial modulus, j/(l — Vj), is 1.805 X 10 MPa (8). Eq (1) has been driven under the assumption that the stress is isotropic and uniform in the film plane. Ibe application of this equation is limited to bending displacements smaller than the thidmess of... 

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. 

In the derivation of equations 24—26 (60) it is assumed that the cylinder is made of a material which is isotropic and initially stress-free, the temperature does not vary along the length of the cylinder, and that the effect of temperature on the coefficient of thermal expansion and Young s modulus maybe neglected. Furthermore, it is assumed that the temperatures everywhere in the cylinder are low enough for there to be no relaxation of the stresses as a result of creep. 

Fig. 3. Stress—strain curve of typical polyesterether elastomer showing the three main regions (I, II, and III) (181), where A is the slope (Young s modulus)...

Eor reinforcement, room temperature tensile strength and Young s modulus (stress—strain ratio) are both important. Typical values for refractory fibers are shown in Table 2. 

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). 

Young s modulus can be deterrnined by measuring the stress—strain response (static modulus), by measuring the resonant frequency of the body... 

As we showed in Chapter 6 (on the modulus), the slope of the interatomic force-distance curve at the equilibrium separation is proportional to Young s modulus E. Interatomic forces typically drop off to negligible values at a distance of separaHon of the atom centres of 2rg. The maximum in the force-distance curve is typically reached at 1.25ro separation, and if the stress applied to the material is sufficient to exceed this maximum force per bond, fracture is bound to occur. We will denote the stress at which this bond rupture takes place by d, the ideal strength a material cannot be stronger than this. From Fig. 9.1... 

F(FG = normal (shear) component of force A = area u(w) = normal (shear) component of displacement o-(e ) = true tensile stress (nominal tensile strain) t(7) = true shear stress (true engineering shear strain) p(A) = external pressure (dilatation) v = Poisson s ratio = Young s modulus G = shear modulus K = bulk modulus. 

So ceramics, at room temperature, generally have a very large lattice resistance. The stress required to make dislocations move is a large fraction of Young s modulus typically, around E/30, compared with E/10 or less for the soft metals like copper or... 

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