Large-strain material behavior

Before dealing with reinforcement of elastomers we have to introduce the basic molecular features of mbber elasticity. Then, we introduce—step-by-step—additional components into the model which consider the influence of reinforcing disordered solid fillers like carbon black or silica within a rabbery matrix. At this point, we will pay special attention to the incorporation of several additional kinds of complex interactions which then come into play polymer-filler and filler-filler interactions. We demonstrate how a model of reinforced elastomers in its present state allows a thorough description of the large-strain materials behavior of reinforced mbbers in several fields of technical applications. In this way we present a thoroughgoing line from molecular mechanisms to industrial applications of reinforced elastomers. 

In a recent study, Saintier et al. ° investigated the multiaxial effects on fatigue crack nucleation and growth in natural mbber. They found that the same mechanisms of decohesion and cavitation of inclusions that cause crack nucleation and crack growth in uniaxial experiments were responsible for the crack behavior in multiaxial experiments. They studied crack orientations for nonproportional multiaxial fatigue loadings and found them to be related to the direction of the maximum first principal stress of a cycle when material plane rotations are taken into account. This method accounts for material rotations in the analysis due to the displacement of planes associated with large strain conditions. 

The success of the developed model in predicting uniaxial and equi-biaxi-al stress strain curves correctly emphasizes the role of filler networking in deriving a constitutive material law of reinforced rubbers that covers the deformation behavior up to large strains. Since different deformation modes can be described with a single set of material parameters, the model appears well suited for being implemented into a finite element (FE) code for simulations of three-dimensional, complex deformations of elastomer materials in the quasi-static Emit. 

Dynamic mechanical measurements are performed at very small strains in order to ensure that linear viscoelasticity relations can be applied to the data. Stress-strain data involve large strain behavior and are accumulated in the nonlinear region. In other words, the tensile test itself alters the structure of the test specimen, which usually cannot be cycled back to its initial state. (Similarly, dynamic deformations at large strains test the fatigue resistance of the material.)... 

Hyperelastic finite element analysis Accommodates complex geometries. Can handle nonlinearity in material behavior and large strains. Rapid analysis possible. Standard material models available. Does not include rate-dependent behavior. Cannot predict permanent deformation. Does not handle hysteresis. Some material testing may be required. Can produce errors in multiaxial stress states. 

An important distinction between polymeric liquids and suspensions arises from their different microstructures and is evidenced by the elastic recoil phenomena that polymers exhibit but suspensions do not. The polymeric or macromolecular system when deformed under stress will recover from very large strains because like an elastic material the restoring force increases with the deformation. With a suspension, however, the forces between the particles decrease with increasing separation so that there is limited mechanism for recovery. There are, however, a variety of rheological properties common to polymeric liquids that suspensions will exhibit including shear rate dependent viscosity and time-dependent behavior. We shall discuss these differences in more detail in the following section. 

Rubber becomes harder to deform at large strains, probably because the long flexible molecular strands that comprise the material cannot be stretched indefinitely. The strain energy functions considered up to now do not possess this feature and therefore fail to describe behavior at large strains. Strain-hardening can be introduced by a simple modification to the first term in Eq. (1.18), incorporating a maximum possible value for the strain measure J, denoted Jm (Gent, 1996) ... 

Inelastic deformation can occur in crystalline materials by plastic flow . This behavior can lead to large permanent strains, in some cases, at rapid strain rates. In spite of the large strains, the materials retain crystallinity during the deformation process. Surface observations on single crystals often show the presence of lines and steps, such that it appears one portion of the crystal has slipped over another, as shown schematically in Fig. 6.1(a). The slip occurs on specific crystallographic planes in well-defined directions. Clearly, it is important to understand the mechanisms involved in such deformations and identify structural means to control this process. Permanent deformation can also be accomplished by twinning (Fig. 6.1(b)) but the emphasis in this book will be on plastic deformation by glide (slip). 

For CNTs not well bonded to polymers, Jiang et al. [137] established a cohesive law for CNT/polymer interfaces. The cohesive law and its properties (e g. cohesive strength and cohesive energy) are obtained directly fiom the Lennard-Jones potential from the vdW interactions. Such a cohesive law is incorporated in the micromechanics model to study the mechanical behavior of CNT-reinforced composite materials. CNTs indeed improves the mechanical behavior of composite at the small strain. However, such improvement disappears at relatively large strain because the completely debonded nanotubes behave like voids in the matrix and may even weaken the composite. The increase of interface adhesion between CNTs and polymer matrix may significantly improve the composite behavior at the large strain [138]. 

A superplastic phenomenon occurs in solid crystalline materials, including ceramics, and is a state in which the material may be deformed before fracture and may reach large strains, well above 100 %, often even in the range of 200-500 %. Figure 2.44 shows superplastic behavior in Si3N4 with a 470 % elongation. 

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