Equilibrium tensile force,

If the equilibrium tensile force is F and the displacement dl then the work done by... 

Thus, the equilibrium tensile force F is determined by the change in internal energy with deformation and the change in entropy with deformation. An ideal rubber is defined as a material for which the change in internal energy with deformation equals zero. Thus, the only contribution to the force F is from the entropy term ... 

The integration of Eq. (8.17) between specified limits leads to a relation between the equilibrium tensile force, /eq, and the melting temperature. This is analogous to integrating the Clapeyron equation for vapor-liquid equilibrium. In this case, if the equation of state relating the pressure and volume of the Uquid is known, the dependence of the pressure on temperature is obtained. For the present problem the equation of state relating the apphed force to the length of the network is required. This information can be obtained from the theory of rubber elasticity.(6-9)... 

Li is the length of the isotropic amorphous network, i.e. the length under zero force. La is the length in the amorphous state under the equilibrium tensile force /and (a) is a parameter which measures the geometric mean of the hnear dilation of the actual network relative to that in the isotropic state." The relation between / and L is completely general and applies equally to networks formed from polymer molecules in random configuration and to those formed from highly oriented chains. 

Yielding is a manifestation of the possibility that some of the atoms (or molecules) in the stressed material may slip to new equilibrium positions due to the distortion produced by the applied tensile force. The displaced atoms can form new bonds in their newly acquired equilibrium positions. This permits an elongation over and above that produced by a simple elastic separation of atoms. The material does not get weakened due to the displacement of the atoms since they form new bonds. However, these atoms do not have any tendency to return to their original positions. The elongation, therefore, is inelastic, or irrecoverable or irreversible. This type of deformation is known as plastic deformation and materials that can undergo significant plastic deformation are termed ductile. 

Values of stress and strain obtained from Figure 1 and from similar plots of data obtained on the other elastomers yield the plots of Xo vs. (X — 1) in Figure 2, where Xo is the true stress, i.e., the force per unit cross-sectional area of the deformed specimen. The data at strains up to 1.0 (100% elongation) give straight lines whose slopes equal the equilibrium tensile moduli, E values of 1 /3 are given in Table I. 

A convenient way to visualize the elastic bond between two atoms is to place an imaginary spring between the atoms, as illustrated in Figure 5.1. For small atomic deformations, either away from each other with what is called a tensile force (shown in Figure 5.1) or toward each other with what is called a compressive force (not shown), the force stored in the spring causes the atoms to return to the undeformed, equilibrium separation distance, ro, where the forces are zero (cf. Figure 1.3). Attractive forces between the atoms counteract the tensile force, and repnlsive forces between the atoms connteract the compressive forces. 

PRESSURE. If a body of fluid is at rest, the forces are in equilibrium or the fluid is in static equilibrium. The types of force that may aci on a body are shear or tangential force, tensile force, and compressive force. Fluids move continuously under the action of shear or tangential forces. Thus, a fluid at rest is free in each part from shear forces one fluid layer does not slide relative to an adjacent layer. Fluids can be subjected to a compressive stress, which is commonly called pressure. The term may be defined as force per unit area. The pressure units may be dynes per square centimeter, pounds per square foot, torr. mega-Pascals, etc. Atmospheric pressure is the force acting upon a unit area due to the weight of the atmosphere. Gage pressure is the difference between the pressure of the fluid measured (at some point) and atmospheric pressure. Absolute pressure, which can be measured by a mercury barometer, is the sum of gage pressure plus atmospheric pressure. 

Force = tensile force exerted on fiber — at mechanical equilibrium fiber exerts an equal and opposite inward force... 

When a solid body is stressed, which requires the addition of energy from the outside, the tensions that are produced within stretch all bonds between the molecules. Theoretically, if the solid features an ideal structure with no imperfections and only tensile forces are applied, the bonds separate in a structural plane in which the load exceeds the bond strength and the solid splits cleanly into two parts. Then all other areas return to their equilibrium structure, and the unused energy is freed and converted into other forms kinetic and thermal energy and/or sound. 

When particles make elastic contact with a surface, equilibrium is not attained immediately. Time is required for the contact spot to enlarge, and more time is needed for the contact to separate when a tensile force is imposed. This is adhesive drag. Indeed, equilibrium may never be attained. On making the contact, the spot size has a certain diameter at a given load. When breaking the contact at an identical load, the contact spot is bigger. This is known as adhesive hysteresis, which was observed by Drutowski in 1969. These effects may be studied systematically with smooth elastomer spheres at zero load as shown in Fig. 9.23." ... 

The analogy between cold drawing and a phase transition emerges clearly from Ericksen s often cited discussion [6] of instabilities that can occur in a one-dimensional theory of the equilibrium of bars under tension in that discussion it is assumed that the total tensile force T at a cross-section is given by a function T of the local stretch ratio 1. and that the material function t has the non-monotone, single-loop, form shown here in Figure 1. 

The prepreg fibre bed is typically assumed to be an elastic porous medium with incompressible and inextensible fibres and fully saturated with the resin. The resin is assumed to flow in the pores between the fibres, and the fibre mass in the laminate remains constant during cure. The governing equations of the system must describe the behaviour of the composite constituents the fibre bed and the resin. Firstly, the equilibrium of forces on the representative element is considered. Secondly, the mass conservation for the representative element must be satisfied. For a porous medium saturated with a single phase fluid, the total stress tensor a,) is separated into two parts as (tensile stresses are considered positive) ... 

In the equilibrium conformation the centerline of the tube represents a random walk with a step length that corresponds to the tube diameter. If the tube is treated as a system of slip links through which the chain can pass, the mean field of the surrounding chains results in an equivalent tensile force F q that acts on the chain ends (63,121) ... 

In order to maintain equilibrium of the FED, the change in FRP laminate tensile force (AF) between any two adjacent ERSG positions (e g. SG4 and SGs) due to a difference in their corresponding strain readings ( 4 - 5)... 

The strain measures for dry (unswollen) vulcanizates of a large number of natural rubbers, butadiene-styrene and butadiene-acrylonitrile copolymers, polydimethylsiloxanes, polymethylmethacrylates, polyethylacrylates and polybutadienes with different degrees of crosslinking and measured at various temperatures re confined within the shaded area in Fig. 1. These measures were determined from the stress as a function of extension at (or near) equilibrium, i.e. by applying Eq. (7). Therefore they only reproduce the equilibrium stress-strain relation for the crossllnked rubbers. In all cases the strain dependence of the tensile force (and hence of the tensile stress) was expressed in terms of the well-known Mooney-Rivlin equation, equating the equilibrium tensile stress to ... 

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