(platelets) on {100} planes called GP-I Zones, as discussed in Sec-tion 5.3. In essence, the precipitated GP zones have a lower en-ergy state compared to the metastable solid solution. In other
6.3 • Practical Consequences
Diffusion Through Polymers
6.3.1 Age
Hardening
words, the diffusion of copper atoms to {100} planes and the for-mation of GP zones are driven by a gradient in the free energy.
The growth of grains is likewise driven by the tendency of ma-terials to assume the lowest possible energy state. Specifically, a large number of small grains and, thus, a large amount of grain boundary area represent a comparatively high energy state be-cause the atoms in or near grain boundaries are not efficiently packed, leaving a substantial amount of open space. In contrast, a few large grains (or a single crystal) are in a lower energy state.
In order to reduce the free energy, crystal structures tend to in-crease their grain size. The mechanism by which some grains grow at the expense of others involves the slight shift of atoms situated near grain boundaries from one grain to the next, thus adding atom by atom to the planes of neighboring grains.
As pointed out in Section 5.5, the strength of materials de-creases when only a few large grains are present. Thus, a large-grained microstructure is generally undesirable. (There are some exceptions where large grains or even single crystals are wanted, such as for turbine blades and at high temperatures to avoid creep or in microelectronic devices.) To prevent grain growth, impurity particles (which are selected so that they are essentially insoluble in the matrix) are occasionally added to metals or al-loys. They reduce the grain boundary area and therefore the to-tal grain boundary energy, thus reducing grain growth and, con-sequently, preventing a decrease in strength. This procedure is called grain boundary pinning. As with diffusion-controlled processes, an increase in temperature accelerates the grain growth. This could have unwanted consequences when materi-als are put in service at high temperatures.
Sintering is driven by a thermally activated process. This tech-nique involves the joining together of small (0.1- to 50-m) par-ticles consisting, for example, of high melting point metals, or of ceramics, or of composites. The powdered constituents are pressed into forms and then heated at high temperatures for ex-tended times, causing the surface atoms to diffuse into the empty spaces between the particles. Concomitantly, vacancies diffuse into the grain boundaries and are annihilated there. This way the pores eventually close up and the work piece shrinks, that is, it becomes dense. The powders are obtained either by grinding brit-tle materials (pulverization), by chemical conversion, or by di-recting a pressured gas stream toward a thin stream of liquid metal (“atomization”).
6.3.2 Grain Growth
6.3.3
Sintering
Annealing of metals and alloys is an important procedure that is applied, for example, to cold-worked metals and alloys to restore the ductility which the material had before plastic deformation.
Thus, it makes materials susceptible for renewed deformation and shaping. Annealing of cold-worked materials at moderate temperatures, called recovery or stress-relief annealing, causes the tangled dislocations to move. They eventually rearrange and form subgrains. The deformation-induced stress is reduced without substantially changing the number of dislocations. Thus, the strength of stress-relieved materials is almost maintained. The result is referred to as a polygonized structure. (Even though recovery is a thermally activated process, it is not classified as diffusion-controlled.)
It should be briefly added at this point that cold-working re-duces the electrical conductivity of metals (see Part II). The de-crease in conductivity is, however, restored by recovery anneal-ings. This is of great importance to industries which produce wires for electrical power transmission, because wire drawing causes high strength and moderate annealing reinstates high con-ductivity.
If the cold-worked material is annealed at approximately 0.4 times the absolute melting temperature (Tm), new grains nucleate and grow. This process is appropriately called recrystallization. It restores the original high ductility, low strength, and relatively low dislocation density. The reduction in strength thus obtained could have detrimental consequences when a material is put in service at high temperatures. Recrystallization is driven by the tendency to completely eliminate the deformation-induced strain energy.
The just-mentioned recrystallization temperature depends on the amount of cold-work. Specifically, a large amount of defor-mation reduces the recrystallization temperature because of the larger amount of strain energy which was introduced by the work hardening process. On the other hand, small amounts of cold-work (several percent) do not lead to appreciable recrystalliza-tion upon heating within a reasonable amount of time.
Metals and alloys that are heat-treated at temperatures above 0.4 Tm eventually tend to undergo further grain growth. We have al-ready discussed previously the implications of large-grained mate-rials on the mechanical properties and explained there why large-grained materials have a lower strength than fine-large-grained materials.
We briefly mentioned in Chapter 2 that materials, when held at high temperatures, generally undergo progressive plastic defor-mation while under a stress level that is well below the room temperature yield strength. This mechanism may be a
diffusion-6.3.4
Annealing
6.3.5 Creep
FIGURE6.10.Climbing of a dislocation at high temperatures caused by diffusion of atoms away from the bottom of the extra half-plane of an edge dislocation. The mov-ing atoms could either fill vacancies or jump into interstitial posi-tions. (The dislocation moves in the opposite direction when atoms are attached to it.)
controlled process that involves, among others, the climbing of edge dislocations. It is called dislocation creep. In Chapter 3, we talked extensively about dislocations and explained there that the slip of dislocations is the principle mechanism for plastic defor-mation under stress. We also elucidated that eventually the move-ment of dislocations may be blocked by precipitates or other ob-stacles. Now, if the temperature is above 0.3 times the absolute melting temperature and a metal is under stress, the pinned dis-locations may be unlocked. Specifically, the stress provides a dri-ving force that allows the atoms at the bottom of the extra half-plane of an edge dislocation to diffuse away and thus cause the dislocation to climb as depicted in Figure 6.10. (Alternatively, atoms may diffuse to the bottom of an edge dislocation, causing the “climbing” to be in the opposite direction.) Eventually the pinned dislocation has climbed away from the sphere of influ-ence of the pinning site. The dislocation may then undergo fur-ther slip until the next obstacle is encountered. This repeated climbing and gliding leads to continuous plastic deformation, that is, to creep.
The creep rate at a constant applied stress can best be visual-ized by plotting the creep strain, , as a function of creep time, t, as shown in Figure 6.11. Three regions may be distinguished.
Initially, the creep progresses quite rapidly but eventually slows down as the deformation of the material becomes more difficult due to work hardening, as discussed in Section 3.4. This region is called primary or transient creep. In a second range steady-state creep occurs when, as an average, the same amount of dislo-cations climb away from obstacles as dislodislo-cations are blocked on obstacles. In this case the creep rate is constant, as seen in
Fig-ure 6.11. The steady-state creep rate,.s (d/dt)s, obeys as usual an Arrhenius-type relation, which reads in the present case:
.s Anexp
冢
kQBT冣
, (6.14)where A is the creep constant, is the stress [Eq. (2.1)], n is an-other constant called the creep exponent, which varies between 3 and 8, and Q is the activation energy for creep (having about the value of that for self-diffusion). This type of creep is called power law creep.
After even longer times, the creep rate accelerates again (ter-tiary creep region), which leads to void formation at grain bound-aries and possibly necking of the work piece [Figure 2.5(a)]. Even-tually the voids join, causing fracture due to separation at grain boundaries. Likewise, internal cracks or cavities may join. At this point, the rupture lifetime, tr, has been reached.
At low stress levels and very high temperatures, an alternative mechanism may cause creep. It involves the force-induced elon-gation of grains in one direction (and shrinkage in the other) due to the migration of atoms or vacancies between grain facets; see Figure 6.12. Again, diffusion plays a decisive role which allows the motion of atoms within a grain. It is called diffusion creep (or Nabarro–Herring creep.) The creep rate is in this case pro-portional to the stress, , and inversely proportional to the square of the grain size, d. The activation energy, Q, is about that for self-diffusion; see Table 6.1. One finds:
. dd
FIGURE6.11.Schematic representa-tion of a creep curve as typically encountered for single-phase mate-rials in which the creep strain, is depicted as a function of creep time, t during which a constant stress is applied to the solid. The slope in the secondary range is termed the steady-state creep rate,