Elasticity modulus, typical values

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

Concret does not have well defined elastic and plastic regions due to its brittle nature. A maximum compressive stress value is reached at relatively low strains and is maintained for small deformations until crushing occurs. The stress-strain relationship for concrete is a nonlinear curve. Thus, the elastic modulus varies continuously with strain. The secant modulus at service load is normally used to define a single value for the modulus of elasticity. This procedure is given in most concrete texts. Masonry lias a stress-strain diagram similar to concrete but is typically of lower compressive strength and modulus of elasticity. 

Elastic and viscous stress-strain curves can be experimentally determined from incremental stress-strain curves measured on samples of different tendons. Typical elastic and viscous stress-strain curves for rat tail and turkey tendons are shown in Figures 7.4 and 7.5. For both types of tendons the curves at high strains are approximately linear. As we discuss in Chapter 8, the elastic modulus can be calculated for collagen, because most of the tendon is composed of collagen and water, by dividing the elastic slope by the collagen content of tendon. When this is done the value of the elastic modulus of collagen in tendon is somewhere between 7 and 9 GPA. 

For small-molecule thermotropic smectic-A phases, typical values of two elastic constants are K 10 dyn and B 10 dyn/cm (Ostwald and Allain 1985). For lyotropic smectics, such as those made from surfactants in oil or water solvents, the layer compression modulus B can be much lower (see Chapter 12). From B and K, a length scale A. = ( 1 /B) 1 nm is defined it is called the permeation depth and its magnitude... 

Of course the modulus of a block copolymer with ordered spherical microdomains is much lower than that of a crystalline solid. Near the disordering transition, the potential energy holding each domain or atom in place is of order ksT, and the modulus is roughly vksT, where v is the number of domains or atoms. This gives an elastic modulus 10 -10 dyn/cm for typical block copolymers with spherical domains, as opposed to 10 -10 dyn/cm for atomic crystals. Ordered spherical diblock copolymers are therefore soft solids. They deflect under an imposed shear stress, but do not flow continuously unless that stress exceeds a critical value, the yield stress (Watanabe and Kotaka 1984). 

Linear elasticity is the most basic of all material models. Only two material parameters need to be experimentally determined the Young s modulus and the Poisson s ratio. The Young s modulus can be directly obtained from uniaxial tension or compression experiments, and typical values for a few select fluoropolymers at room temperature are presented in Table 11.2. 

The elastic behavior upon applied shear stress is primarily typical in the case of solids. The nature of elasticity is in the reversibility of small deformations of interatomic (or intermolecular) bonds. In the limit of small deformations the potential energy curve is approximated by a quadratic parabola, which corresponds to a linear t(y) dependence. Elasticity modulus of solids depends on the type of interactions. For molecular crystals it is 109 N m 2, while for metals and covalent crystals it is 1011 N m"2 or higher. The value of elasticity modulus is only weakly dependent (or nearly independent) on temperature. 

In continuous systems consisting of solid phases, the parameter G is the modulus of elasticity of rigid body. Its values may fall in the range between 109 and 10" N m 2. The elasticity modulus of common liquids under the conditions of uniform (hydrostatic) compression is also of the same order of magnitude. However, due to low viscosity, the shear elasticity of liquids may only be observed by rapid tests in which the time of stress action is close to the relaxation period. For this reason at typical times of mechanical action liquids with low r values behave as viscous media. 

Region IE (c to d) in Fig. 2.21 is described as-the rubbery plateau region. The modulus after a sharp drop, as described above, again becomes nearly constant in this region with typical values of 2x10 dyne/cm (2x10 Pa) and polymers exhibit significant rubber-like elasticity. 

This indicates that for an incompressible elastic solid, i.e., one having a Poisson ratio of 0.5, Young s modulus is three times larger than the shear modulus. These moduli have dimensions of pressure, and typical values for several polymeric and nonpolymeric materials can be compared at ambient temperatures in Table 13.1 (GN = 105 N). 

---