Mechanical behavior deformation

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

Deformation Under Loa.d. The mechanical behavior of coal is strongly affected by the presence of cracks, as shown by the lack of proportionahty between stress and strain in compression tests or between strength and rank. However, tests in triaxial compression indicate that as the confirming pressure is increased different coals tend to exhibit similar values of compressive strength perpendicular to the directions of these confining pressures. Except for anthracites, different coals exhibit small amounts of recoverable and irrecoverable strain underload. 

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 mechanical properties of polymers are of interest in all applications where they are used as structural materials. The analysis of the mechanical behavior involves the deformation of a material under the influence of applied forces, and the most important and characteristic mechanical property is the modulus. A modulus is the ratio between the applied stress and the corresponding deformation, the nature of the modulus depending on that of the deformation. Polymers are viscoelastic materials and the high frequencies of most adiabatic techniques do not allow equilibrium to be reached in viscoelastic materials. Therefore, values of moduli obtained by different techniques do not always agree in the literature. 

This model was applied by Mukherjee et al. [20] for various natural fibers. By considering diverse mechanisms of deformation they arrived at different calculation possibilities for the stiffness of the fiber. According to Eq. (1), the calculation of Young s modulus of the fibers is based on an isochoric deformation. This equation sufficiently describes the behavior for small angles of fibrils (<45°) [19]. 

The physics of this effects is quite understandable. Indeed, polymers by their nature are capable of great reversible deformation and therefore linearity of their mechanical behavior remains up to deformations of the order of 100%. But the structure formed by a filler undergoes brittle failure and hence, even for very small deformations the materia] changes and linearity of its behavior vanishes. 

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

This chapter summarizes several studies of PTFE utilizing a range of techniques and leading to an interpretation of mechanical behavior in terms of structure at all stages of deformation, up to and including fracture. 

Polyurethanes based on the HDI cyclic trimer show a rubberlike mechanical behavior. In fact, the Z1030/1072 and Z1031-H films show a low elastic modulus E, no yielding, and an ultimate, widely reversible, deformation beyond 100-150%, likely underestimated owing to the difficulty in assessing the ultimate properties of self-supported thin films. 

The specific material properties of most import to the compaction operation are elastic deformation behavior, plastic deformation behavior, and viscoelastic properties. These are also referred to as mechanisms of deformation. As mentioned earlier, they are equally important during compression and decompression i.e., the application of the compressional load to form the tablet, and the removal of the compressional load to allow tablet ejection. Elastic recovery during this decompression stage can result in tablet capping and lamination. 

At room temperature, well below Tg, a brittle failure is generally observed. The ductile behavior appears when yielding becomes a competitive mechanism of deformation. At high speeds the brittle stress is not too much affected but ductile-brittle transition to higher temperatures. 

A) As the material is cooled it undergoes a martensitic transformation. By transforming to equal amounts of two variants, the macroscopic shape is retained. (B) Deformation occurs by movement of variant boundaries so the more favorably oriented variant grows at the expense of the other. Reprinted with permission of Cambridge University Press from W. F. Hosford, Mechanical Behavior of Materials (New York Cambridge Univ. Press, 2005). 

Singamaneni S, Bertoldi K, Chang S, Jang JH, Young SL, Thomas EL, Boyce MC, Tsukruk VV (2009) Bifurcated mechanical behavior of deformed periodic porous solids. Adv Funct Mater 19 1426-1436... 

The macroscopic properties such as mechanical behavior of block copolymers or polymer blends depend directly on the relative concentrations of different constituents and their meso-structures. How to predict the exact macroscopic properties of polymer blends or block copolymers with meso-phase separation structures from pure component properties remains a big challenge. Some theoretical efforts have been explored. For example, Buxton et al. found that the deformations and fractures of polymer blends can be described by the... 

The temperature increase of a pellet by this rather simplified treatment can be calculated knowing p, cp, estimating dLp/dt, and thus A p, and evaluating experimentally (F/Ap)(Tp). This treatment is similar to that of Kim and Gogos in its ability to estimate pellet heating by PED in a simple fashion, needing only the experimental evaluation of the large deformation mechanical behavior of polymer solids. 

Although a key characteristic of the mechanical behavior of rubber-like materials is their ability to undergo large elastic deformations, we will present here some important results from the theory of linear elasticity [1], which is valid only for small deformations. These serve our present purposes better than the nonlinear theory, because of their simpler character and physical transparency. 

S. Guruswamy, K. T. Faber, and J. P. Hirth, Mechanical Behavior of Compound Semiconductors S. Mahajan, Deformation Behavior of Compound Semiconductors J. P. Hirth, Injection of Dislocations into Strained Multilayer Structures... 

This property of viscoelasticity is possessed by all plastics to some degree, and dictates that while plastics have solid-like characteristics, they also have liquid-like characteristics (Figure 1.2). This mechanical behavior is important to understand. It is basically the mechanical behavior in which the relationships between stress and strain are time dependent for plastic, as opposed to the classical elastic behavior of steel in which deformation and recovery both occur instantaneously on application and removal of stress.1... 

The discussion in the Introduction led to the convincing assumption that the strain-dependent behavior of filled rubbers is due to the break-down of filler networks within the rubber matrix. This conviction will be enhanced in the following sections. However, in contrast to this mechanism, sometimes alternative models have been proposed. Gui et al. theorized that the strain amplitude effect was due to deformation, flow and alignment of the rubber molecules attached to the filler particle [41 ]. Another concept has been developed by Smith [42]. He has indicated that a shell of hard rubber (bound rubber) of definite thickness surrounds the filler and the non-linearity in dynamic mechanical behavior is related to the desorption and reabsorption of the hard absorbed shell around the carbon black. In a similar way, recently Maier and Goritz suggested a Langmuir-type polymer chain adsorption on the filler surface to explain the Payne-effect [43]. 

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