Material 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). 

Rather than bearing an infinite stress at the crack tip, yielding occurs resulting in a volume of inelastically deformed material along the crack front called the process zone, as shown in Fig. 2. The size of the inelastic zone, r j , under a monotonic tensile stress, o , can be approximated by substituting o = Oj into eq. 2 for the horizontal plane, 0 = 0... 

The continuum theory of deformation of elastic solids is old and well developed [65T01, 74T01], and, in its linear version, is widely applied. Nonlinear theory is of much more recent origin. Most application of nonlinear theory has been to the behavior of highly deformable materials such as rubber or to the explanation of subtle effects observed by precise ultrasonic... 

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

Intermetallics also represent an ideal system for study of shock-induced solid state chemical synthesis processes. The materials are technologically important such that a large body of literature on their properties is available. Aluminides are a well known class of intermetallics, and nickel aluminides are of particular interest. Reactants of nickel and aluminum give a mixture with powders of significantly different shock impedances, which should lead to large differential particle velocities at constant pressure. Such localized motion should act to mix the reactants. The mixture also involves a low shock viscosity, deformable material, aluminum, with a harder, high shock viscosity material, nickel, which will not flow as well as the aluminum. 

In addition to the alloy compositions being of importance with regard to susceptibility to stress-corrosion cracking, the resistance of the alloy can be altered by microstructural factors. Hanninen has reviewed the available literature quite thoroughly and has concluded that a fine grain size is likely to be beneficial. Strain imposed prior to use tends to be deleterious because deformed material usually acts anodic with respect to unstrained material and because the introduction of plastic deformation may also... 

In addition to plastic deformation, materials may fail by either brittle fracture or ductile fracture fracture being the separation of a body into two or more parts. 

The non-monotonous dependence of surface layer microhardness on deformation degree results from different mechanisms of nitrogen diffusion in deformed material. In our point of view, under the deformations of 3-8 and 20-30 % the greatest number of mobile dislocations, capable to provide the additional transfer of nitrogen interstitial atoms with Cottrell s atmospheres by the dislocation-dynamic mechanism [6-8], can be formed. 

The maximum rise of number of mobile dislocations in the deformed materials occurs in the range of 10-20 % [9, 10]. Such processes influence on kinetic of phase formation that results in the accelerated growth of s- and y-nitrides and in increase of microhardness of the surface diffusion layers. 

Elastic deformation is a reversible process, whereby, if the applied load is released before the elastic yield value is reached, the particles will return to their original state. Plastic deformation and brittle fragmentation are non-reversible processes that occur as the force on the particles is increased beyond the elastic yield value of the materials. Brittle fragmentation describes the process where, as the force is increased, particles fracture into smaller particles, exposing new, clean surfaces at which bonding can occur. For plastically deforming materials, when the force is removed, the material stays deformed and does not return to its original state. Plastic materials are also known as time-dependent materials because they are sensitive to the rate of compaction. We can also speak of viscoelastic-type materials which stay deformed when the force is removed, but will expand slowly over time. 

Gasket - A deformable material clamped between essentially stationary faces to prevent the escape of matter through an opening or joint. 

The windows are mostly sealed with thin films of PTFE, gold, indium and other corrosion-resistant easily deformable materials. 

Recrystallization occurs when a crystalline material is plastically deformed at a relatively low temperature and then heated [1]. The as-deformed material possesses excess bulk free energy resulting from a high density of dislocations and point-defect debris produced by the plastic... 

The problem above can also be solved analytically using tensor methods—the preferred technique when higher accuracy is required. In general, any homogeneous deformation can be represented by a second-rank tensor that operates on any vector in the initial material and transforms it into a corresponding vector in the deformed material. For example, in the lattice deformation, each vector, Ffcc, in the initial f.c.c. structure is transformed into a corresponding vector in the b.c.t. structure, Vbct, by... 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

Parker, K.H., Mehta, R.V. and Caro, C.G. (1987) Steady flow in porous, elastically deformable materials. J. Appl Meek, 54, 794-800. 

Transmission electron microscopy evidence shows little or no dislocations in super-plastically deformed material. 

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