Deformation hardening

As screw dislocations move, since they are nearly cylindrically symmetric in simple metals, they move readily from one glide plane to another, and back 

For one screw dislocation to move past another parallel one, where the distance between them is h, requires a shear stress, x  

Recall that an indentation hardness number does not measure an initial stress for deformation in metals. It measures the stress needed for further deformation after about 40 percent deformation has already occurred. 

The author believes that dipoles cause deformation hardening because this is consistent with direct observations of the behavior of dislocations in LiF crystals (Gilman and Johnston, 1960). However, most authors associate deformation hardening with checkerboard arrays of dislocations originally proposed by G. I. Taylor (1934), and which leads the flow stress being proportional to the square root of the dislocation density instead of the linear proportionality expected for the dipole theory and observed for LiF crystals. The experimental discrepancy may well derive from the relative instability of a deformed metal crystal compared with LiF. For example, the structure in Cu is not stable at room temperature. Since the measurements of dislocation densities for copper are not in situ measurements, they may not be representative of the state of a metal during deformation (Livingston, 1962). 

Whatever mechanisms operate to cause deformation-hardening, it is phenomenologically the most general determinant of hardness for metals. 

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Thus, in simple metals, interactions between dislocations rather than interactions between atoms, are most important. The hardnesses of metals depend on deformation hardening (dislocation interactions) rather than individual mobilities. The elastic resistance to shear plays a dominant role because it is directly involved with dislocation mobility. 

If slip-line fields do not control plastic indentation, what does The answer is not the beginning of the plastic deformation, but the end of it. The end means after deformation hardening has occurred. That is, it is not the initial yield stress, Y0, that controls indentation, but the limiting yield stress, Y. This is... 

Figure 2.6 Schematic stress-deformation curve with linear deformation-hardening.

The flow stress in Figure 2.6 is given approximately by Y = Y0 + h8 where h is the deformation-hardening coefficient. It is assumed that the elastic strain is fully recovered in a hardness measurement, so it need not be considered further in this approximate treatment. Then H = 2.2h8, and since 8 = 2x/L = tan 0 = 0.414 then H = 0.89 h. Hence H — h. That is, the indentation hardness number approximately equals the deformation-hardening coefficient. 

This analysis is consistent with the conclusion of Gerk (1977) that the behavior that determines hardness is deformation-hardening not the yield stress. He was one of the first authors to point this out. For other types of materials, it is the maximum stress that the material can bear after deformation (plastic, or that associated with phase transitions in eluding twinning). Hardness is not directly related to the elastic limit, although there is an indirect connection with the offset plastic deformation of metals as demonstrated by Tabor (1951). 

Deformation-hardening in the 5-50% deformation range is known to be proportional to either the Young s modulus, Y, or the shear modulus, G, in metals. The Young s modulus depends strongly on the shear modulus since Y = 2(1+v) G where v = Poisson s ratio. For both fee and bcc pure metals data... 

Irregularities of a specimen s surface will result in local deformation with accompanying deformation hardening. This may lead to erroneous hardness numbers, although such errors may be small. 

Although this sometimes occurs through the operation of Frank-Read sources it is not generally observed. What does generally occur is similar, but more complex. The process is called multiple-cross-glide, and was proposed by Koehler (1952). Its importance was hrst demonstrated experimentally by Johnston and Gilman (1959). In addition to its existence, they showed that the process produces copious dislocation dipoles which are responsible for deformation-hardening. 

In metals, the incremental stress of deformation-hardening is often reported to be proportional to the square root of the dislocation density. However, In view of the mechanism of dislocation multiplication, and the subsequent deformation hardening, this is highly unlikely, so this author believes that either the data are faulty, or they are being misinterpreted. 

The Chin-Gilman parameters (H/G) are given in the figure captions. Note that the value for the bcc metals (0.02) is about five times greater than the value for the fee metals (0.0044). Thus the bcc metals deformation harden much more rapidly than the fee metals. 

Some measured values of hardness are given in Table 8.1 which shows how the hardness varies with stoichiometry (Qian and Chou, 1989). The values in the table are averages of 30 measurements for each composition. The stoichiometric value is 16X the yield stress (albeit from different authors). Since hardness numbers for metals are determined by deformation-hardening rates, the latter is very large for Ni3Al causing the hardness numbers to be 16X the compressive yield stress instead of the 3X of pure metals. 

Another possibility is that the vibrational frequency difference increases the cross-gliding rate, and therefore the deformation-hardening rate. In this case, when the temperature becomes high enough, dislocation climb causes rapid enough recovery to cancel the deformation-hardening rate. 

The crystal structure of NiAl is the CsCl, or (B2) structure. This is bcc cubic with Ni, or A1 in the center of the unit cell and Al, or Ni at the eight comers. The lattice parameter is 2.88 A, and this is also the Burgers displacement. The unit cell volume is 23.9 A3 and the heat of formation is AHf = -71.6kJ/mole. When a kink on a dislocation line moves forward one-half burgers displacement, = b/2 = 1.44 A, the compound must dissociate locally, so AHf might be the barrier to motion. To overcome this barrier, the applied stress must do an amount of work equal to the barrier energy. If x is the applied stress, the work it does is approximately xb3 so x = 8.2 GPa. Then, if the conventional ratio of hardness to yield stress is used (i.e., 2x3 = 6) the hardness should be about 50 GPa. But according to Weaver, Stevenson and Bradt (2003) it is 2.2 GPa. Therefore, it is concluded that the hardness of NiAl is not intrinsic. Rather it is determined by an extrinsic factor namely, deformation hardening. 

In contrast to the rubbery state, the properties of glassy networks (mechanical, thermal) at temperatures markedly below T p do not practically depend on chemical composition and cure conversion at the latest stages of the cure process. The sensitivity of the properties to the chemical structure of the network is very weak. The shortness of intercrosslinked chains is displayed only in small values of eb, e and in the absence of deformation hardening for the glassy state of the considered polymers. 

Taking this circumstance into account some above topics will be analyzed lower in more details. Namely, these are limiting hardening created as a result of obtaining ultra-fine grains, some topics of deformation hardening additionally, considered will be some aspects of development of new generation of titanium-based materials (systems Ti-B-X and Ti-Si-X, where X is Al, Zr, etc.). 

This procedure may be used unless the rate-dependence, load history-dependence, or deformation-hardening characteristics of the isolation system necessitate explicit consideration of their nonlinear and/or velocity-dependent force-deflection properties. 

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