Basic Micromechanical Mechanisms

In the past, numerous studies of toughening mechanisms in rubber-modified polymers have been performed, mostiy via eiectron microscopy. Three main mechanisms can be distinguished that are strongiy reiated to the morphoiogy (disperse or network structures) and to the micromechanicai deformation behavior of the matrix [1, 2, 6]  

A primary effect of the first two mechanisms is the stress concentration at softer rubber particles. Depending on the size of the shear modulus ratio between particie and matrix, the maximum stress concentration at spherical particles (and at voids) is 2.045 (i.e., the locally increased stress is 2.045 times larger than the applied stress). With increasing particle modulus (and decrease of the Poisson ratio), the stress concentration decreases. The stress concentration at particles/ voids decrease very rapidly with increasing distance r from the particle/matrix interface (with about 1/r see Fig. 5.6). If the distance r is larger than the particle diameter D, no stress concentration occurs [6]. 

In a polymer system with many closely neighboring particles, the individual stress concentration fields of the particles interact with each other, and a larger resultant stress concentration appears see Fig. 5.7. 

The resultant stress concentrations are sketched for a smaller particle volume content of 2.4% (left) and for a larger one of 21% (right). In rubber-modified polymers, the effect of the superposition of the stress fields initiates an increased 

The different processes have been summarized in a three-stage mechanism of 

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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. 

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. 

The micromechanics approaches presented in this book are an attempt to predict the mechanical properties of a composite material based on the mechanical properties of its constituent materials. In nearly all fiber-reinforced composite materials, there is considerable difference between expectation and reality. Thus, we must ask what is the usefulness of micromechanical analysis beyond gaining a feeling for why composite materials behave as they do Basically, there are two answers one related to designing a material and one related to designing a structure. 

Basic mechanical behaviours, such as plastic deformation, deformation micromechanisms, and fracture, are successively presented. The characteristics of the studied polymers are gathered in Table 7. 

A complete series of mechanical testing of these joints shall be made after the whole array of the data will be obtained. In order to disclose the general peculiarities of FG-joints, the calculations of their basic properties were made by a micromechanical model [2,4]. 

From a strictly theoretical point of view, the so-called constituent testing approach or micromechanics approach is the most valuable. Tests performed on composite constituents supply the required material constants of each phase of the composite material— namely for long-liber-reinforced composite— for the fiber and the matrix, to use in appropriate mixture rules. These rules obtained by physical and mechanical considerations are the basic relationships between the composite constituents, and they leads to a complete characterization of the final composite. 

The mechanical, thermal, and hygrothermal properties of FRP composites are a function of selected constituent materials, namely fiber and matrix, and the fiber, matrix, and void volume fractions that are a result of the manufacturing process. In this analysis, the influence of fiber volume fraction on the failure probability of FRP-rehabilitated piping components is also examined. Procedures for micromechanical and macromechanical analysis of lamina (i.e., determination of lamina elastic moduli and strength properties) from basic constituent properties are well established and readily available in standard texts (Kaw, 2006). Table 5.2 summarizes the constituent properties of carbon fiber, glass fiber, and epoxy matrix utihzed in the reliability analyses presented in this chapter. These standard properties were obtained from Kaw (2006). 

The mechanics of materials approach is taken in developing micromechanical relationships between constituent and composite material properties. The basic assumptions inherent in this approach are the following ... 

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