Uniaxial Compression Modulus

Note 3 Young s modulus may he evaluated using tensile or compressive uniaxial deformation. If determined using tensile deformation it may be termed tensUe modulus. Note 4 For non-Hookean materials the Young s modulus is sometimes evaluated as ... 

By analogy we can define a uniaxial modulus of compression K(q>) and given that the volume fraction is inversely related to the total volume we get... 

Note 3 For elastomers, which are assumed incompressible, the modulus is often evaluated in uniaxial tensile or compressive deformation using X - as the strain function (where X is the uniaxial deformation ratio). In the limit of zero deformation the shear modulus is evaluated as... 

The effect of gas compression on the uniaxial compression stress-strain curve of closed-cell polymer foams was analysed. The elastic contribution of cell faces to the compressive stress-strain curve is predicted quantitatively, and the effect on the initial Young s modulus is said to be large. The polymer contribution was analysed using a tetrakaidecahedral cell model. It is demonstrated that the cell faces contribute linearly to the Young s modulus, but compressive yielding involves non-linear viscoelastic deformation. 3 refs. 

Deformational measurements were carried out in a uniaxial compression of cylindrical samples and the equilibrium shear modulus G was determined from [11]... 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

The agreement between fee bulk modulus deduced from Brillouin scattering measurements and fee ADX results is very good. The determination of fee elastic moduli by ultrasonics was made by fee measurement of surface acoustic wave velocities on thin films [22], The second ultrasonics experiment was made on sintered powder, by measuring fee longitudinal and transverse sound velocity at ambient and under uniaxial compression. From feat, fee bulk modulus and its pressure derivative were deduced, but this result seems to be quite imprecise. The ultrasonics experiment on thin films gives rise to a very small difference in fee bulk modulus (5%), but fee ADX or Brillouin determination should be utilised for preference. 

On the basis of what has been discussed, we are in the position to provide a unified understanding and approach to the composite elastic modulus, yield stress, and stress-strain curve of polymers dispersed with particles in uniaxial compression. The interaction between filler particles is treated by a mean field analysis, and the system as a whole is macroscopically homogeneous. Effective Young s modulus (JE0) of the composite is given by [44]... 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

Curves of uniaxial compressive stress against strain for hep are non-linear and vary somewhat with the strain rate. Caution is therefore needed in comparing values of Young s modulus obtained in different investigations, results obtained at very low stresses by the dynamic method in which a resonance frequency of vibration is determined being higher than ones given... 

Stiffness is the resistance of an object to deformation and is represented by a modulus (see section 10.2.1). The modulus is defined as stress per unit strain (which is dimensionless) and hence has stress units. Although even in the uniaxial compression of a homogeneous cylindrical or rectangular specimen the stresses distribution is far from being uniform, one can still use the average stress, the measured force divided by the specimen s cross-sectional area, for the modulus calculation. 

The jump from uniaxial elongation to uniform compression is a simple one in terms of defining all the stresses and strains. The final modulus we wish to define, the shear modulus., r, is a little different and you have to pay... 

Quasi-static Young s modulus measured by Hertzian indentation (b) Data taken from ref [5] (c) Measured by Dynamic Mechanical Thermal Analysis (D.M.T.A) at 1 Hz (T is taken as the temperature of the maximum in tan 5) (d) (7y and Oy are the yield stress under uniaxial and plane strain compression, respectively, for an equivalent strain rate of 5x10" s" (see ref... 

Fig. 9. Eqiulibrium stress-strain behavior of entangled networks in uniaxial extensicm and compression. The solid lines (p = 0.5, 0.75,1.00) were calculated for the primitive segment model (. 62 and II-5). The short-dash line is the Doi-Edwards model (Eq. 40 and 11-11). The long-dash line is the affine Gaussian network model (Eq. 41 and n-12) adjusted to have the same initial modulus...

Even with the gaps in the theory, the fundamental concepts developed for continuum systems are substantially the same for systems of pharmaceutical powders. Powders confined and subjected to a compressive stress will rearrange until there is insufficient free volume to allow translation of particles. As the stress increases, particles make contacts which increase in area with stress, they will deform elastically (i.e.. reversibly) with Young s modulus (E) as the linear proportionality constant. The normal strain (eO in the loading direction for a material undergoing elastic deformation under uniaxial tension (cr) may be expressed as (2) ... 

The modulus is the most important small-strain mechanical property. It is the key indicator of the "stiffness" or "rigidity" of specimens made from a material. It quantifies the resistance of specimens to mechanical deformation, in the limit of infinitesimally small deformation. There are three major types of moduli. The bulk modulus B is the resistance of a specimen to isotropic compression (pressure). The Young s modulus E is its resistance to uniaxial tension (being stretched). The shear modulus G is its resistance to simple shear deformation (being twisted). 

The equilibrium small-strain elastic behavior of an "incompressible" rubbery network polymer can be specified by a single number—either the shear modulus or the Young s modulus (which for an incompressible elastomer is equal to 3. This modulus being known, the stress-strain behavior in uniaxial tension, biaxial tension, shear, or compression can be calculated in a simple manner. (If compressibility is taken into account, two moduli are required and the bulk modulus. ) The relation between elastic properties and molecular architecture becomes a simple relation between two numbers the shear modulus and the cross-link density (or the... 

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