Composite inclusion

The composite inclusion is modeled as in generalized 3D laminate theory, such that the deformation and stress within each phase are uniform but not necessarily identical and satisfy the constraints of interface compatibility and equilibrium. Let and be the inclusion-averaged strain rate and spin, respectively, that can be expressed as 

We assume that there is no relative slippage at the crystalline/amorphous interface. Then the interface compatibility condition demands velocity continuity across the crystalline/amorphous interface. These compatibility conditions in conjunction with incompressibility in both phases require definite continuity conditions on strain-rate and spin components in the inclusion between the crystalline and amorphous components. Moreover, the crystalline/amorphous interface also enforces shear-traction equilibrium across the interface. More complete statements of the compatibility, continuity, and incompressibility constraints necessary for the full implementation of the model can be found elsewhere (Lee et al. 1993a). 

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FIGURE41.1 Morphology of basic composite inclusions, (a) Particle, (b) fiber, and (c) platelet. 

It is important to emphasize the benefits of understanding the symmetry properties (and structural properties) of the composite inclusion compound in a superspace group, rather than restricting the structural description of such materials at the level of the separate basic structures. Knowledge of the structural properties of the separate basic structures contains no information on the modulations that each subsystem experiences in the real inclusion... 

The semi-crystalline HDPE being modeled is initially of a sphernlitic morphology described in Chapter 2. It is made up of a 3D packing of crystalline lamellae and their attached amorphous layers as idealized in Fig. 9.25(a). The basic elements of the spherulite are two-phase composite inclusions that consist of integrally coupled crystalline lamellae and their associated amorphous layers between lamellae. Owing to their large aspect ratio, the composite inclusions are modeled as infinitely extended sandwiches with a planar crystalline/amorphous interface as shown in Fig. 9.25(b). Each composite inclusion I is characterized by its interface normal rt and the relative fractional thicknesses and / = 1 / of... 

Fig. 9.25 Schematic representation of (a) a spherulite of HDPE (b) a composite inclusion of attached crystalline and amorphous domains (from Lee etal. (1993a) courtesy of Elsevier).

A local/global interaction relation must be imposed to relate the average mechanical behavior of each composite inclusion to the macroscopically imposed boundary conditions. The collective plastic deformation of aggregates, such as grains in a polycrystalline assembly, has been the subject of many studies on the crystal... 

Fig. 9.27 Pole figures from 244 randomly oriented composite inclusions that represent the initial isotropic texture of undeformed HDPE (a) the crystallographic texture of the (002) and (200) planes and (b) the distribution of the normals to the composite inclusions...

Glucans are useful as raw materials for starch processing industries, dietary compositions, compositions for food additives, adhesive compositions, inclusion compounds and absorbing compounds, medical and cosmetic compositions, film-type product compositions, and as an alternative for starches used in biodegradable plastics. Methods for the production of glucan have been described (4). The reaction starts from glucose and inorganic phosphate, such as... 

The lamellar composite inclusion in Fig. 17 can support forces with a strength which depends on its orientation with respect to those forces. In two of the three spatial directions, this strength represents a parallel additivity of components in the third direction, a series additivity is involved. Since these inclusions have various orientations in a test sample, we assume macroscopic isotropy and thus obtain the average modulus by a strictly probabilistic weighting of the series and parallel values ... 

Figure 3 shows that highly modified RP layers can be developed with eluents consisting of acetone and water up to a maximum water content of approximately 60% by volume. In contrast to these plates, partially modified RP layers can be used in this phase system with all eluent compositions inclusive of pure water. The times of development of the partially modified plates pass through a maximum at an eluent composition in the range of 40% acetone. 

J. Garboczi and J.G. Berryman 2001 Elastic moduli of a material containing composite inclusions Effective medium theory and finite element computations, Mech. Mater. 33,455-470. 

Lee et al. [218,219] defined a dedicated polymer micromechanical model in which the material is represented by an aggregate of layered two-phase composite inclusions (Figure 1.16). Large plastic deformation and texture evolution... 

Figure 1.16. Aggregate of layered two-phase composite inclusions [222]...

Most important is the case of two immiscible fluids (Fig. 3.2) two fluids A and B for instance (H2O + NaCl) and (CO2) occur in contemporaneous healed cracks or more typically in the same crack, but they homogenize at the same ten eratiire (temperature of exsolution. Fig. 3.2). Rare composite inclusions (mechanical mixture of A and B) homogenize at a slightly higher temperature which theoretically fits the crest of the miscibility gap between A and B. 

Different samples of pack ice exiting into the North Atlantic may have quite different histories, characterised by thickness, age, place of origin, crystal structure, chemical composition, inclusion of pollutants and associated sea ice biota. Changes in the ex-... 

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