Micromechanical concepts

In most spherulitic polymers, touching spherulites occupy whole of the space. Their microstructure is too complex to be completely modelled, especially if there is twisting of lamellar stacks about spherulite radii. Consequently, models simplify the structure, and use composite micromechanics concepts. A stack of parallel lamellar crystals with interleaved amorphous layers (Fig. 3.20) has a similar geometry to a laminated rubber/metal spring (Fig. 4.1). The crystals have different Young s moduli E, Eb and E (Section 3.4.3), and different shear moduli when the... 

An important aspect of micromechanical evolution under conditions of shock-wave compression is the influence of shock-wave amplitude and pulse duration on residual strength. These effects are usually determined by shock-recovery experiments, a subject treated elsewhere in this book. Nevertheless, there are aspects of this subject that fit naturally into concepts associated with micromechanical constitutive behavior as discussed in this chapter. A brief discussion of shock-amplitude and pulse-duration hardening is presented here. 

The evolution of T, is just an exercise in mesoscale thermodynamics [13]. These expressions, in combination with (7.54), incorporate concepts of heterogeneous deformation into a eonsistent mierostruetural model. Aspects of local material response under extremely rapid heating and cooling rates are still open to question. An important contribution to the micromechanical basis for heterogeneous deformation would certainly be to establish appropriate laws of flow-stress evolution due to rapid thermal cycling that would provide a physical basis for (7.54). 

The mechanics of materials approach to the micromechanics of material stiffnesses is discussed in Section 3.2. There, simple approximations to the engineering constants E., E2, arid orthotropic material are introduced. In Section 3.3, the elasticity approach to the micromechanics of material stiffnesses is addressed. Bounding techniques, exact solutions, the concept of contiguity, and the Halpin-Tsai approximate equations are all examined. Next, the various approaches to prediction of stiffness are compared in Section 3.4 with experimental data for both particulate composite materials and fiber-reinforced composite materials. Parallel to the study of the micromechanics of material stiffnesses is the micromechanics of material strengths which is introduced in Section 3.5. There, mechanics of materials predictions of tensile and compressive strengths are described. 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

Our reason for stressing the concept of representative volume element is that it seems to provide a valuable dividing boundary between continuum theories and molecular or microscopic theories. For scales larger than the RVE we can use continuum mechanics (classical and large strain elasticity, linear and non-linear viscoelasticity) and derive from experiment useful and reproducible properties of the material as a whole and of the RVE in particular. Below the scale of the RVE we must consider the micromechanics if we can - which may still be analysable by continuum theories but which eventually must be studied by the consideration of the forces and displacements of polymer chains and their interactions. 

Estimates for the macroscopic drained stiffness tensor Chom(f) as a function of the morphological parameter can be derived from various micromechanical techniques. The micromechanical approach classically refers to the concept of strain concentration tensor, denoted here by A. By definition, in an evolution... 

As already mentioned, the concepts of integration and miniaturization are not new in separation science, but the tools at our disposal for the realization of such systems have changed dramatically with the advent of micromechanical fabrication methods. The advantages of this technology are best appreciated by a closer look at earlier attempts to construct integrated small volume analysis systems using conventional techniques. 

Important current concepts of the micromechanisms involved in crazing and environmental aspects of this subject have been developed by Kramer and coworkers they are described in Chapter 1 of this volume. 

Introductory approaches have been described to formally evaluate design concepts for select structural components made from composites including intraply hybrid composites and strip hybrids. These approaches consist of structural analysis methods coupled with composite micromechanics, finite element analysis in conjimction with composite mechanics, and sensitivity analyses using structural optimization. Specific cases described include ... 

Since the assumption of uniformity in continuum mechanics may not hold at the microscale level, micromechanics methods are used to express the continuum quantities associated with an infinitesimal material element in terms of structure and properties of the micro constituents. Thus, a central theme of micromechanics models is the development of a representative volume element (RVE) to statistically represent the local continuum properties. The RVE is constracted to ensure that the length scale is consistent with the smallest constituent that has a first-order effect on the macroscopic behavior. The RVE is then used in a repeating or periodic nature in the full-scale model. The micromechanics method can account for interfaces between constituents, discontinuities, and coupled mechanical and non-mechanical properties. Their purpose is to review the micromechanics methods used for polymer nanocomposites. Thus, we only discuss here some important concepts of micromechanics as well as the Halpin-Tsai model and Mori-Tanaka model. 

The third concept is the average properties of composites which are actually the main goal of a micromechanics model. The average stiffness of the composite is the tensor C that maps the uniform strain to the average stress ... 

The properties for the basic layers of CSM and WR constituting the different parts of the panel were computed using micromechanics as detailed in the EUROCOMP Design Code. More specifically, elastic constants of a monolayer of CSM were derived using the theory of composites with randomly orientated continuous fibres, and those of WR were computed using the concept of ply efficiency equal to 0.5 for a bi-directional balanced cloth ply. Table 1 shows the respective proportions and properties of the glass fibres and resin used in the fabrication of the panels and the subsequent elastic constants for a monolayer of CSM and WR. 

A new concept in the field of sutures is the development of barbed material, which is a monofilament product that has micromechanically machined barbs on the surface. The presence of barbs, which are either mono- or bidirectionally oriented, allows sutures to be held in tissues without a... 

New concepts combining micromechanical models with the macromechanics of composite bodies were able to explain experimental data and predict limits of mechanical properties. Proposed models were used as the link between micro-and macromechanics of the composite body. In the calculations, in addition to properties of the matrix and the filler, properties and spatial arrangement of the interphase have been included (5). This model allows for a prediction of the structure-property relationships in PP filled wifh randomly distributed core-shell inclusions with EIL shell. This is of a pivotal importance in an attempt to develop and manufacture materials tailored to a particular end-use application. 

The Modular Fluid System (MFS) concept as base system for the realization of Micro-TAS, as well as a number of different micromechanical components for use in Micro-TAS are presented. The correspondence of MFS to electronic breadboards is discussed, and an example of a possible "mixed" fluidic/electronic board is given. The consequences of downscaling for the operation of sensors in Micro-TAS are discussed, and a number of components, sensors, sieves, mixers, valves and pumps are presented. Finally, the importance of the development of design tools and rules, especially bondgraph modelling, for MFS is emphasized. 

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