Microscopic deformation

A1 Minimum or no adhesion between the polymer and filler is present. Only the polymer matrix plays an active role during the deformation. Microscopic parameters which are averages (draw ratio, mean direction of orientation, orientation distribution function) are taken over the volume occupied by the polymer matrix. 

A constitutive equation is a relation between the extra stress (t) and the rate of deformation that a fluid experiences as it flows. Therefore, theoretically, the constitutive equation of a fluid characterises its macroscopic deformation behaviour under different flow conditions. It is reasonable to assume that the macroscopic behaviour of a fluid mainly depends on its microscopic structure. However, it is extremely difficult, if not impossible, to establish exact quantitative... 

Foams that ate relatively stable on experimentally accessible time scales can be considered a form of matter but defy classification as either soHd, Hquid, or vapor. They are sol id-1 ike in being able to support shear elastically they are Hquid-like in being able to flow and deform into arbitrary shapes and they are vapor-like in being highly compressible. The theology of foams is thus both complex and unique, and makes possible a variety of important appHcations. Many features of foam theology can be understood in terms of its microscopic stmcture and its response to macroscopically imposed forces. 

Hardness. The Knoop indentation hardness of vitreous sihca is in the range of 473—593 kg/mm and the diamond pyramidal (Vickers) hardness is in the range of 600—750 kg/mm (1 4). The Vickers hardness for fused quartz decreases with increasing temperature but suddenly decreases at approximately 70°C. In addition, a small positive discontinuity occurs at 570°C, which may result from a memory of quartz stmcture (165). A maximum at 570°C is attributed to the presence of small amounts of quartz microcrystals (166). Scanning electron microscopic (sem) examination of the indentation area indicates that deformation is mainly from material compaction. There is htfle evidence of shear flow (167). 

Resistance to axial compressive deformation is another interesting property of the silk fibers. Based on microscopic evaluations of knotted single fibers, no evidence of kink-band failure on the compressive side of a knot curve has been observed (33,35). Synthetic high performance fibers fail by this mode even at relatively low strain levels. This is a principal limitation of synthetic fibers in some stmctural appHcations. 

Another chapter deals with the physical mechanisms of deformation on a microscopic scale and the development of micromechanical theories to describe the continuum response of shocked materials. These methods have been an important part of the theoretical tools of shock compression for the past 25 years. Although it is extremely difficult to correlate atomistic behaviors to continuum response, considerable progress has been made in this area. The chapter on micromechanical deformation lays out the basic approaches of micromechanical theories and provides examples for several important problems. 

Micromechanical theories of deformation must be based on physical evidence of shock-induced deformation mechanisms. One of the chapters in this book deals with the difficult problem of recovering specimens from shocked materials to perform material properties studies. At present, shock-recovery methods provide the only proven teclfniques for post-shock examination of deformation mechanisms. The recovery techniques are yielding important information about microscopic deformations that occur on the short time scales (typically 10 -10 s) of the compression process. 

Step 3. The set of fracture properties G(t) are related to the interfaee structure H(t) through suitable deformation mechanisms deduced from the micromechanics of fracture. This is the most difficult part of the problem but the analysis of the fracture process in situ can lead to valuable information on the microscopic deformation mechanisms. SEM, optical and XPS analysis of the fractured interface usually determine the mode of fracture (cohesive, adhesive or mixed) and details of the fracture micromechanics. However, considerable modeling may be required with entanglement and chain fracture mechanisms to realize useful solutions since most of the important events occur within the deformation zone before new fracture surfaces are created. We then obtain a solution to the problem. 

A substantial portion ( 15%) of the magnetite was found to be converted to hematite. As prior work showed small conversion (1%) of hematite to magnetite, the data indicate that the conversion can proceed in either direction depending upon the local microscopic deformation history of the powder particles. 

On a microscopic scale, the deformations are shown in Figure 3-15. Note that the matrix deforms more than the fiber in shear because the matrix has a lower shear modulus. The total shearing deformation is... 

As an indication of the changes in deformation modes that can be produced in ionomers by increase of ion content, consider poly(styrene-co-sodium methacrylate). In ionomers of low ion content, the only observed deformation mode in strained thin films cast from tetra hydrofuran (THF), a nonpolar solvent, is localized crazing. But for ion contents near to or above the critical value of about 6 mol%, both crazing and shear deformation bands have been observed. This is demonstrated in the transmission electron microscope (TEM) scan of Fig. 3 for an ionomer of 8.2 mol% ion content. Somewhat similar deformation patterns have also been observed in a Na-SPS ionomer having an ion content of 7.5 mol%. Clearly, in both of these ionomers, the presence of a... 

The failure of systems with dispersed fillers (exemplified by polystyrene plus glass spheres with different treatment) was studied by subjecting specimens to deformation in the microscope field [255,256]. Where adhesion was good the cracks were observed to be formed near the glass sphere pole, in regions corresponding to the maximum deformation, where adhesion was poor, anywhere between the pole and the equator. It was discovered that microcracks began to... 

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... 

Usually, the molecular strands are coiled in the glassy polymer. They become stretched when a crack arrives and starts to build up the deformation zone. Presumably, strain softened polymer molecules from the bulk material are drawn into the deformation zone. This microscopic surface drawing mechanism may be considered to be analogous to that observed in lateral craze growth or in necking of thermoplastics. Chan, Donald and Kramer [87] observed by transmission electron microscopy how polymer chains were drawn into the fibrils at the craze-matrix-interface in PS films [92]. One explanation, the hypothesis of devitrification by Gent and Thomas [89] was set forth as early as 1972. 

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