Micromechanics methods

Karkkainen RL, Sankar BV. A direct micromechanics method for analysis of failure initiation of plain weave textile composites. Compos Sci Technol 2006 66 137-50. 

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. 

In Odegard s study [48], a method has been presented for finking atomistic simulations of nano-structured materials to continuum models of tfie corresponding bulk material. For a polymer composite system reinforced with SWCNTs, the method provides the steps whereby the nanotube, the local polymer near the nanotube, and the nanotube/ polymer interface can be modeled as an effective continuum fiber by using an equivalent-continuum model. The effective fiber retains the local molecular stractuie and bonding information, as defined by MD, and serves as a means for finking tfie eqniv-alent-continuum and micromechanics models. The micromechanics method is then available for the prediction of bulk mechanical properties of SWCNT/polymer com-... 

A simple and direct micromechanical method to evaluate the IFSS is based on a tensile test in which a partially embedded single fiber is puUed out from a block of matrix material. This simulates the stress constraints acting on a fiber/matrix... 

Still another micromechanical method for single fiber simulation of a polymer composite interfacial adhesion is the microbond test. This method was developed by Miller et al. [52] and initially applied for S3mthetic fibers. As mentioned by Craven et al. [53], the microbond test is suitable for any fiber that can carry only low loads. This is the particular case of silk, a strong natural fiber but with limited load bearing capacity due to diameters that can be finer than 50 pm. This could be the case of some lignocellulosic fibers such as the ramie with diameters of the order of 10 pm. 

They Compare their results with Odegard, et al., [48] the micromechanic method was BEM Halpin-Tsai Eq. [68] with aligned fiber by perfect bonding. 

There have been a number of attempts to produce more appropriate predictions of the Young s modulus of particulate reinforced composites, without having such widely-separated bounds on the predictions. They have also been reviewed recently by Young et a/. A number of years ago, Halpin and Tsai developed an approach based upon the self-consistent micromechanics method of Hill that enabled prediction the elastic behaviour of a composite for a variety of both fibre and particulate geome-... 

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. 

Fig. 2.1 Top-down synthesis methods, (a) Micromechanical cleavage (b) ion intercalation (c) graphite oxide (d) liquid-phase exfoliation.

Microcomposite tests including fiber pull-out tests are aimed at generating useful information regarding the interface quality in absolute terms, or at least in comparative terms between different composite systems. In this regard, theoretical models should provide a systematic means for data reduction to determine the relevant properties with reasonable accuracy from the experimental results. The data reduction scheme must not rely on the trial and error method. Although there are several methods of micromechanical analysis available, little attempt in the past has been put into providing such a means in a unified format. A systematic procedure is presented here to generate the fiber pull-out parameters and ultimately the relevant fiber-matrix interface properties. 

Since the thickness and properties of the interphase strongly influence the characteristics of composites and the strength of the interaction determines the dominating micromechanical deformation process, many attempts have been made to characterize them quantitatively. Many various techniques are used for this purpose, and it is impossible to give a detailed account here. As a consequence a general overview of the most often used techniques is given with a more detailed account of some specific methods which have increased importance. A more detailed description of the surface characterization techniques can be found in a recent monograph by Rothon [15],... 

Bobrov also used this model of a syntactic foam to calculate hydrostatic strengths164). At the same time, he showed that this parameter cannot be obtained theoretically for a syntactic foam using traditional micromechanical, macromechanical, or statistical approaches, as they are unsuitable for these foams. The first approach requires a three-dimensional solution of the viscoelasticity boundary value problem of a multiphase medium, and this is very laborious. The second and third methods assume the material is homogeneous overall, and so produce poor estimates for syntactic materials. 

Veenstra, T. T., Lammerink, T. S. J., van den Berg, A., Elwenspoek, M. C., Characterization method for a new diffusion mixer applicable in micro flow injection analysis systems, in Proceedings of the Micromechanics Europe (MNE)... 

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. 

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