Plastic deformation dislocation creep

As in time-independent plastic deformation, dislocations play an important role in the time-dependent plastic deformation of metals. At the onset of creep deformation, the number of dislocations in the material usually increases, causing hardening that can be experimentally observed by the reduction in the creep rate at constant stress. However, the dislocation density cannot increase arbitrarily since recovery occurs simultaneously (see section 6.2.8), with dislocations annihilating by climb. This process becomes the easier, the closer the dislocations are. Accordingly, after some transition time, an equilibrium between the generation of additional dislocation segments by plasticity and the annihilation of dislocations by recovery will be found. This equilibrium causes the creep rate to become constant in the secondary stage. 

As we saw in Chapter 10, the stress required to make a crystalline material deform plastically is that needed to make the dislocations in it move. Their movement is resisted by (a) the intrinsic lattice resistance and (b) the obstructing effect of obstacles (e.g. dissolved solute atoms, precipitates formed with undissolved solute atoms, or other dislocations). Diffusion of atoms can unlock dislocations from obstacles in their path, and the movement of these unlocked dislocations under the applied stress is what leads to dislocation creep. 

PLASTIC DEFORMATION. When a metal or other solid is plastically deformed it suffers a permanent change of shape. The theory of plastic deformation in crystalline solids such as metals is complicated but well advanced. Metals are unique among solids in their ability to undergo severe plastic deformation. The observed yield stresses of single crystals are often 10 4 times smaller than the theoretical strengths of perfect crystals. The fact that actual metal crystals are so easily deformed has been attributed to the presence of lattice defects inside the crystals. The most important type of defect is the dislocation. See also Creep (Metals) Crystal and Hot Working. 

It is well established that the plastic deformation of crystalline solids occurs by the movement of lattice dislocations and/or diffusional creep. The rate of diffusion is expressed as... 

The history of the development of the theory of low-temperature plasticity of solids resembles very much the development of tunneling notions in cryochemistry. This resemblance is not casual it is related to the similarity of the elementary act pictures this was noted by Eyring, who successfully applied the theory of absolute rates to a description of fracture kinetics [202]. Plastic deformation at constant stress (creep) is stipulated by dislocation slip... 

The deformation and damage mechanisms in creep of ceramics and hard materials are similar to those in metals [150,151]. Under normal loading conditions (in the absence of severe elastic constraint) ceramics fracture at room temperature before any significant plastic flow. Dislocation glide in ionically bonded ceramics is complicated by the presence of both anions and cations, which create electrostatic (Coulombic) barriers to shear. As in metals, three creep regimes have been identified. The initial high strain-rate, observed on applying the load, decreases rapidly... 

The so called nanoindentation , which is frequently used to measure < 1 pm thin films, is subject to a number of possible errors [27,28]. For example, when measuring soft materials, such as aluminum or pure iron with a small load and indentation depth, the dislocations are pinned in the surface contaminant layer (oxides, carbides) and, consequently, unrealistically high values of hardness are found. The plastic deformation may also need a certain time to reach equilibrium under the given load because of a finite velocity of dislocation movement. This can be seen as creep (increase of the indentation depth) when a constant load is applied for 10-30 s. 

Before entering into a detailed discussion of the above list and based on what has been said thus far on the subject, briefly summarized (a) creep in materials (including ceramics), namely time-dependent plastic deformation, may occur during mechanical stresses well below the yield stress and (b) in general, two major creep mechanisms characterize the time-dependent plastic-deformation process-dislocation creep and diffusion creep. Now, a detailed discussion of paragraphs (a)-(d) follows. 

Besides dislocation movement, there are other mechanisms of plastic deformation. These are the martensitic transformation we already discussed, diffusion creep at high temperatures (to be covered in chapter 11), and finally the so-called twinning. Mechanical twinning usually contributes only slightly to plastic deformation and is in general more difficult to activate than dislocation movement. Therefore, it will be discussed only briefly. 

Similar to time-independent plastic deformation, creep deformation in metals is dominated by dislocation movement, especially at higher stresses. Mechanisms that impede dislocation movement are thus also important in producing creep>-resistant materials. However, these mechanisms have to be temperature resistant. 

Unified Plasticity Model The time-independent plastic deformation and fee time-dependent creep deformation arise from fee same fundamental mechanism of dislocation motion. Hence, a constitutive model which captures both of these deformation mechanisms is desirable. Such a constitutive model is referred to as a unified plasticity model. A commonly-used unified plasticity model is the Anand s model. This is a rate-dependent phenomenological model (Ref 17 and 18). There are two basic characteristics of fee Anand s model. First, no explicit yield criterion is specified, and second, a single internal state variable (ISV) s, the deformation resistance, represents the isotropic resistance to inelastic strain hardening. Anand s model can represent fee strain rate and temperature sensitivity, strain rate history effects, strain hardening, and fee restoration process of dynamic recovery. Equation 9 shows the functional form of fee flow equation that accommodates fee strain rate dependence on the stress ... 

Three principal types of deformation take place upon the application of loads to turbine materials. Elastic deformation is instantaneous reversible deformation that results from the distortion of the crystal lattice. Plastic deformation is the irreversible deformation that takes place instantaneously through the movement of dislocations through the crystal matrix. Creep deformation takes place by a variety of diffusion-controlled processes over time, resulting in continuing strain tmder the applied load. 

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