Micro-mechanical

Figure 5.22 Problem domain in the micro-mechanical analysis of the particulate polymer composite...

Nassehi, V., Dhillon,. 1. and Mascia, L., 1993a. Finite element simulation of the micro-mechanics of interlayered polymer/fibre conrposites a study of the interactions between the reinforcing phases. Compos. Sci. Tech. 47, 349-358. 

Fig. 2. Results of interfacial shear strength measurements of the same fiber/matrix systems using four different micro-mechanical tests during a round-robin program involving 12 different laboratories, (a) Results for untreated, unsized carbon fibers, (b) Results for carbon fibers with the standard level of surface treatment. Redrawn from ref. [13].

The aim of this chapter is to describe the micro-mechanical processes that occur close to an interface during adhesive or cohesive failure of polymers. Emphasis will be placed on both the nature of the processes that occur and the micromechanical models that have been proposed to describe these processes. The main concern will be processes that occur at size scales ranging from nanometres (molecular dimensions) to a few micrometres. Failure is most commonly controlled by mechanical process that occur within this size range as it is these small scale processes that apply stress on the chain and cause the chain scission or pull-out that is often the basic process of fracture. The situation for elastomeric adhesives on substrates such as skin, glassy polymers or steel is different and will not be considered here but is described in a chapter on tack . Multiphase materials, such as rubber-toughened or semi-crystalline polymers, will not be considered much here as they show a whole range of different micro-mechanical processes initiated by the modulus mismatch between the phases. 

It is necessary to consider the micro-mechanical processes of polymer glasses and elastomers separately as their mechanical properties are so different. In addition, cross-linking profoundly affects the deformation processes in glasses but very little is known about the micro-mechanical processe.s that occur in single phase cross-linked glasses so the latter materials will not be discussed further. 

The micro-mechanical processes will be presented next, followed by the models used to describe them. The predictions of the models will then be compared with results obtained using well-defined coupling chains. Application of the models to the joining of dissimilar polymers will then be described. Finally welding of glassy polymers will be considered. 

When the stress that can be bom at the interface between two glassy polymers increases to the point that a craze can form then the toughness increases considerably as energy is now dissipated in forming and extending the craze structure. The most used model that describes the micro-mechanics of crazing failure was proposed by Brown [8] in a fairly simple and approximate form. This model has since been improved and extended by a number of authors. As the original form of the model is simple and physically intuitive it will be described first and then the improvements will be discussed. 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

Micro-mechanical processes that control the adhesion and fracture of elastomeric polymers occur at two different size scales. On the size scale of the chain the failure is by breakage of Van der Waals attraction, chain pull-out or by chain scission. The viscoelastic deformation in which most of the energy is dissipated occurs at a larger size scale but is controlled by the processes that occur on the scale of a chain. The situation is, in principle, very similar to that of glassy polymers except that crack growth rate and temperature dependence of the micromechanical processes are very important. 

Hounslow, M.J., Mumtaz, H.S., Collier, A.P., Barrick, J.P. and Bramley, A.S., 2001. A micro-mechanical model for the rate of aggregation during precipitation from solution. Chemical Engineering Science, 56, 2543-2552. 

Pratola, F., Simons, S.J.R. and Jones, A.G., 2000. Micro-Mechanics of Agglomerative Crystallization Processes. Proceeding of Advances in particle formation, American Institute of Chemical Engineers National Meeting, November 2000, Paper 22 g. 

Kreuz-stein, m. cross-stone (chiastolite, harmo-tome, staurolite). -attick,n. crosspiece fourway cross(piece). -tisch, m. (Micros.) mechanical stage. 

In order to supplement micro-mechanical investigations and advance knowledge of the fracture process, micro-mechanical measurements in the deformation zone are required to determine local stresses and strains. In TPs, craze zones can develop that are important microscopic features around a crack tip governing strength behavior. For certain plastics fracture is preceded by the formation of a craze zone that is a wedge shaped region spanned by oriented micro-fibrils. Methods of craze zone measurements include optical emission spectroscopy, diffraction... 

St. Lawrence, S., Shinozaki, D.M., Puskas, J.E., Gerchcovich, M., and Myler, U. Micro-mechanical testing of polyisobutylene-polystyrene block-type thermoplastic elastomers. Rubber Chem. TechnoL, 74, 601-613, 2001. 

Volume 6 Micro Mechanical Systems (edited by T. Fukuda and W. Menz)... 

This machine is suitable for moulding latches and rotors for the watch industry, bearing caps for medical application, and locking wheels for micro-mechanics weighing 0.003 g to 0.02 g. 

Beaumont P.W.R. and Anstice P.D. (1980). A failure analysis of the micro-mechanisms of fracture of carbon fiber and glass fiber composites in monotonic loading. J. Mater. Sci. 15, 2691-2635. 

The analysis conducted in this Chapter dealing with different theoretical approaches to the kinetics of accumulation of the Frenkel defects in irradiated solids (the bimolecular A + B —> 0 reaction with a permanent particle source) with account taken of many-particle effects has shown that all the theories confirm the effect of low-temperature radiation-stimulated aggregation of similar neutral defects and its substantial influence on the spatial distribution of defects and their concentration at saturation in the region of large radiation doses. The aggregation effect must be taken into account in a quantitative analysis of the experimental curves of the low-temperature kinetics of accumulation of the Frenkel defects in crystals of the most varied nature - from metals to wide-gap insulators it is universal, and does not depend on the micro-mechanism of recombination of dissimilar defects - whether by annihilation of atom-vacancy pairs (in metals) or tunnelling recombination (charge transfer) in insulators. 

For these reasons, PMMA and its maleimide and glutarimide copolymers represent very suitable materials for investigating the effect of the chemical structure and of the solid state molecular motions on the plastic deformation, the occurrence of the various micro-mechanisms of deformation (chain scission crazes, shear deformation zones, chain disentanglement crazes), as well as the fracture behaviour. 

The plastic deformation, the micro-mechanisms of deformation, and the stable fracture are successively analysed. In each case the relation to the p transition motions is emphasised. 

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