Elastic modulus polymer composites

The low elastic modulus of composites has been used to lower the stress level around implants. Such polymer-hydroxylapatite coatings have been successfully manufactured by thermal spraying (Sun et al. 2002). Finite element analysis has illustrated that a coating at the neck of a dental implant lowers the stress gradient at the coating-bone interface and the stress level in the surrounding bone (Abu-Hammad et al. 2000). 

In the case of micro-composites, specific filler smface area of common fillers is usually less than the value 10 m /g. In these systems, a very small portion of polymei- molecules is in direct interaction with the filler surface. Moreover, dimensions of polymer chains and volumes chai acteristic of microscopic relaxar tion modes are orders of magnitude smaller compared to the dimensions of filler particles (see Table 6.1). Thus, continuum mechanics approaches, such as micromechauical models can be successfully used for description of their mechanical behavior. The continuum mechanics model, well usable for prediction of the mechanical contribution (i) to the modulus of elasticity of polymer composites, is the simple Kerner-Nielsen (K-N) model [66] ... 

The importance of polymer composites arises largely from the fact that such low density materials can have unusually high elastic modulus and tensile strength. Polymers have extensive applications in various fields of industry and agriculture. They are used as constructional materials or protective coatings. Exploitation of polymers is of special importance for products that may be exposed to the radiation or temperature, since the use of polymers make it possible to decrease the consumption of expensive (and, sometimes, deficient) metals and alloys, and to extent the lifetime of the whole product. 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

Fig. 6. Variation of elasticity modulus (E) under tension and yield strain (es) of the polymer matrix (I, I ) and polyethylene-based composites polymerization filled with kaolin (2,20 in function of polymer MM [320], Kaolin content 30% by mass. The specimens were pressed 0.3-0.4mm thick blates stretching rate e = 0.67 min-1...

From the experimental results, the ER effect in polymer gels is explained as follows (Fig. 8). When an electric field is applied, the particles electrically bind together and cannot slip past each other. Larger shear forces are needed in the presence of an electric field. Thus, the electric field apparently enhances the elastic modulus of the composite gel. The difference in ER effects between an oil and a gel is that the polarized particles necessarily cannot move between the electrodes to produce the ER effect in a gel. In order for the ER effect to occur, it is important to form migration paths before application of an electric field. 

Asloun, El. M., Nardin, M. and Schultz, J. (1989). Stress transfer in single-fiber composites Effect of adhesion, elastic modulus of fiber and matrix and polymer chain mobility. J. Mater. Sei. 24, 1835-1844. 

This is a theoretical study on the structure and modulus of a composite polymeric network formed by two intermeshing co-continuous networks of different chemistry, which interact on a molecular level. The rigidity of this elastomer is assumed to increase with the number density of chemical crosslinks and trapped entanglements in the system. The latter quantity is estimated from the relative concentration of the individual components and their ability to entangle in the unmixed state. The equilibrium elasticity modulus is then calculated for both the cases of a simultaneous and sequential interpenetrating polymer network. 

This is a theoretical study on the entanglement architecture and mechanical properties of an ideal two-component interpenetrating polymer network (IPN) composed of flexible chains (Fig. la). In this system molecular interaction between different polymer species is accomplished by the simultaneous or sequential polymerization of the polymeric precursors [1 ]. Chains which are thermodynamically incompatible are permanently interlocked in a composite network due to the presence of chemical crosslinks. The network structure is thus reinforced by chain entanglements trapped between permanent junctions [2,3]. It is evident that, entanglements between identical chains lie further apart in an IPN than in a one-component network (Fig. lb) and entanglements associating heterogeneous polymers are formed in between homopolymer junctions. In the present study the density of the various interchain associations in the composite network is evaluated as a function of the properties of the pure network components. This information is used to estimate the equilibrium rubber elasticity modulus of the IPN. 

Since the stiffness of the bonds transfers to the stiffness of the whole filler network, the small strain elastic modulus of highly filled composites is expected to reflect the specific properties of the filler-filler bonds. In particular, the small strain modulus increases with decreasing gap size during heat treatment as observed in Fig. 32a. Furthermore, it exhibits the same temperature dependence as that of the bonds, i.e., the characteristic Arrhenius behavior typical for glassy polymers. Note however that the stiffness of the filler network is also strongly affected by its global structure on mesoscopic length scales. This will be considered in more detail in the next section. 

On the basis of what has been discussed, we are in the position to provide a unified understanding and approach to the composite elastic modulus, yield stress, and stress-strain curve of polymers dispersed with particles in uniaxial compression. The interaction between filler particles is treated by a mean field analysis, and the system as a whole is macroscopically homogeneous. Effective Young s modulus (JE0) of the composite is given by [44]... 

By analyzing the compositional dependent relaxation time, the stress-strain relationships of polymer composites are determined as a function of the filler concentration and strain rate. As the volume fraction of filler increases, both the effective elastic modulus and yield stress increases. However, the system becomes more brittle at the same time. 

---