Elastic stress field, interaction with

SFM s can be also classified according to static and dynamic operating modes. Under quasi-static conditions, the microscope measures the instantaneous response of the cantilever when it interacts with the sample. Dynamic SFM enables separation of the elastic and inelastic component in the cantilever deflection when the sample surface is exposed to a periodically varying stress field. The dynamic modes are useful for investigation of viscoelastic materials such as polymers and results in additional improvements in the signal-to-noise ratio. 

Once plastic deformation has started in a specimen an increase in stress is needed to produce further deformation. In microscopic terms this means that as deformation proceeds, the movement of dislocations on their slip planes becomes progressively more difficult. This hardening of the material may arise from elastic interactions between dislocations, through their strain fields, it may arise from dislocation reactions that produce segments that cannot sUp and it may also arise from interactions with other defects such as vacancies, impurities and grain boundaries. 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

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]... 

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