Plastic deformation materials

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). 

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. 

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. 

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. 

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

As a force is applied to the item through the die, the metal first becomes elastically strained and would return to its initial shape if the force were removed at this point. As the force increases, the metal s elastic limit is exceeded and plastic flow occurs via the motion of dislocations. Many of these dislocations become entangled and trapped within the plastically deformed material thus, plastic deformation produces crystals which are less perfect and contain internal stresses. These crystals are designated as cold-worked and have physical properties which differ from those of the undeformed metal. 

Figure 2. Schematic of the cross section through a number stamped into metal. Removal of metal down to level (a) results in incomplete obliteration although the number may no longer be readily visible because metal has been smeared into the groove forming the number recovery is easiest in this case. Removal of metal to level (b) leaves behind plastically deformed material this is the situation for which recovery techniques, e.g., etching, can bring out the obliterated numbers. Removal of metal down to level (c) removes all metal plastically deformed during the stamping of the number in this case, recovery is impossible.

The equation of Heckel has been discussed again and again. One main issue of critique is that pharmaceutical powders are not purely plastically deforming materials and thus particle size and deformation mechanisms influence the derived parameters [129, 130]. Already very small errors in displacement determination or the measurement of true density can induce huge errors in the derived parameters [75-77, 129, 131, 132], Spnnergaard [126] referred the equation of Walker and Bal shin for his characterization of materials. He criticized further that the yield strength derived from the Heckel equation is directly dependent on the true density of the powders [127]. 

The earliest reported pharmaceutical applications of roller compaction were published in 1966 (12). A typical formulation for roller compaction wilt contain a fragmenting material (e.g., lactose), a plastically deforming material such as MCC or com starch, binder (e.g., hydroxyIpropylmethylce Iulose. HPMC). actives, and lubricants (magnesium stearate). 

Figure 13-14. Generation of a primary wear particle by plastic shear, (a) A bulge forms ahead of the slider. (b) A crack propagates from the surface into the plastically deformed material. (c) The "chip" is ejected ahead of the slider. After Bates, Ludema and Brainard [51].

The high elastic strains in polymers affect the pattern of plastic flow in hardness tests. The analysis for metals often assumes an infinite Young s modulus, so the plastically deformed material must flow to free surfaces at the sides of the indenter. For polymers, the yielding process largely occurs directly below the indenter, with elastic expansion of the surrounding region. Figure 8.1 showed the shear band patterns when a strip indenter... 

Another mode of the penetration has been proposed as diffusion of a lubricant to the chip-tool interface through the plastically deforming material within the primary shear zone, but the existence of such bulk diffusion through the chip is still under controversy. 

Compactibility, as expressed by the compact tensile strength of lactose (brittle deforming material) was lower than the one of sorbitol (plastic deforming material). Therefore, lactose was virtually not affected by blending time since new lubricant-free surfaces are constantly formed counteracting the effect of lubricants. On the contrary, sorbitol had an effective particle coating and thus, the formation of bonding points between particles required for the... 

The postyield ductile fracture of polymers was extensively investigated (170-183), resulting in a conclusion that the crack is initiated from cavities growing from defects in the drawn material. These cavities have a rhombic shape with the long and short diagonals perpendicular and parallel to the draw direction. These cavities were observed in PVC, PE, polyethylene terephthalate (PET) at room temperature and in PC, PMMA, polyether sulfone (PES), and PS at elevated temperatures. At slow strain rates, the growth of these cavities in a plastically deformed material loaded in tension is stable until the critical size is reached resulting in an unstable catastrophic failure. 

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