Lecture 18 Strain Hardening And Recrystallization

Transcription

1 -138- Lecture 18 Strain Hardening And Recrystallization Strain Hardening We have previously seen that the flow stress (the stress necessary to produce a certain plastic strain rate) increases with increasing plastic strain as σ t = κ' ε t m 18.1 Now we realize that the plastic strain is produced by the motion of dislocations, we should eamine the microscopic basis for this strain hardening behavior. A logical first step is to eamine the dislocations in a highly strain hardened metal. We can do that (at least in thin foils of metal) using the transmission electron microscope (TEM). Please see: ructurevg.html Figure 18.1 (Courtesy C. Cho) A typical TEM micrograph of a heavily deformed metal (in this case Al) is shown in Figure One can see very dense regions of dark lines (the dislocations) surrounding other regions which have very few dislocations. This structure is called a cell structure and the dense dislocation regions are called cell walls. These are tangles of immobile dislocations (if they were able to move the dislocations would glide out of the thin foil). If we want to produce more plastic strain we must produce fresh dislocation from dislocation sources and push these through the tangled immobile dislocations of the cell structure. This process requires more applied stress (more force on the dislocation) than to push a fresh dislocation through a region free of dislocation tangles. The (immobile) dislocation density in the cell structure increases with plastic strains. In fact below a certain strain dense tangles are not formed. An eample of this increase in dislocation density with strain is shown in Figure See ationcellstemvg.html

2 -139- Figure 18.2 From: A.S. Keh in Direct Observations of Imperfections in Crystals ed J.B. Neukirk and J.H. Wernick (1962, Metallurgical Society AIME, Interscience Pub.) p.216. The increasing density of immobile dislocations in the cell walls as the plastic strain increases makes these walls or tangles more effective obstacles to fresh dislocation motion. Hence the flow stress increases resulting in the observed strain hardening. Although many details of the nature of the interactions between the fresh dislocations and the tangles are obscure (for some eamples, see Barrett, Ni and Tetelman p.270 & 271) the increase in flow stress is predicted to be proportional to the square root of overall dislocation density ρ (since fresh dislocations are present at much lower density than the immobile dislocations, ρ ρ immobile ). In fact all theories predict σt = σ o + α Gb ρ 18.2 where G is the shear modulus, b is the magnitude of the dislocation Burger vector and α is a constant which varies from theory to theory but which is approimately equal to 0.2. Eperimentally this relation is obeyed quite well as can be seen from Figure 18.3 which shows typical data for copper τ G b ρ 10-3 Figure 18.3 Effect of dislocation density on the flow stress of polycrystalline copper.

3 -140- All that is necessary to finally describe strain hardening then is to know how ρ (the density of immobile dislocations in the cell structure) builds up with plastic strain ε p. Unfortunately this is difficult to predict since the dislocation tangles form statistically (especially in single crystals). In polycrystals however (where multiple slip occurs even at low strains) one finds that 2 m ρ = ρ o + κ ε p 18.3 If one substitutes ρ from Eq into Eq and makes the approimation that ρ o and σ y are small compared to ρ and σ t one arrives at the empirical equation for strain hardening, Eq A particularly interesting application of these ideas is the prediction of the strain hardening behavior of metals with hard uncuttable particles. We learned in Lecture 13 that dislocations circumvent such particles by etruding between them, leaving a loop of dislocation around the particle. If we push many dislocations through the array of particles, as we need to do to achieve large plastic strains, we will rapidly produce a very large immobile dislocation density where the dislocations are loops around the particles. One would predict that the metal with hard particles would have a much larger strain hardening rate (higher) than the metal without particles. The eperiments (Fig. 18.4) show eactly the predicted behavior. 300 Shear Stress (MN/m ) % Shear Strain γ Figure 18.4 Strain hardening then is the hardening of the metal by immobile dislocation debris left as a result of plastic strain. In many pure metals it is the most important way to harden the material. On the other hand there are many instances where

4 -141- strain hardening is a nuisance or worse. For eample, in attempting to roll a bar of metal into a thin sheet the metal may become so hardened that cracks develop in the outside edges of the sheet. In such situations one would like to periodically soften the metal as the sheet is rolled thinner and thinner, i.e., one wants to remove the strain hardening. To do that it is necessary to remove the immobile dislocation debris. The primary way of removing the dislocation debris is by recrystallization. Recrystallization Not only can one remove the dislocation tangles built up in the course of strain hardening by the process of recrystallization but one also can use it to manipulate and control the grain size of the metal. The grain size is defined as the average diameter of the crystallites or "grains" in the polycrystal. One usually desires a small grain size. Small grained samples have higher yield stress σ y than large grained samples. In steels the ductile-to-brittle transition moves to lower temperatures (the steel becomes more ductile at room temperature) as the grain size is decreased. A large grain size leads to a large scale rumpling of the surface ("orange peel" effect) if the material is to undergo further plastic deformation during fabrication. Only for certain high temperature creep applications does one want a large grain size (in fact in these one would like a single crystal). Recrystallization takes place on annealing at elevated temperatures by the nucleation of new nearly dislocation-free grains in the dense dislocation tangles of the cell walls. The nuclei of these new grains are very small (often <100Å diameter) and the microscopic processes by which they form are not well understood. What is known is that they form in the densest parts of the dislocation tangles and that the driving force for their formation (nucleation) is the very high (local) strain energy in the dislocation tangle. [Remember the strain energy of a dislocation per unit length is ~Gb 2 (its line tension); if there is a high local ρ, there is a high local strain energy.] That strain energy is wiped out if a new dislocationfree grain is formed. It is known that the nuclei do not form by a melting and refreezing as implied by the word "recrystallization", but rather they form entirely in the solid state, for eample, by a shuffling of atoms across an eisting grain boundary. The number of nuclei formed per unit volume is directly proportional to the number of high strain energy (very dense) dislocation tangles per unit volume. In

5 -142- fact recrystallization will not take place at all until such dense tangles are formed. Thus a metal given no, or only a small plastic strain, will not recrystallize. It would not be possible to recrystallize the metal in Fig. 18.2a whereas in Fig. 18.2d where dense tangles are present recrystallization is possible. The fact that the number of new grain nuclei is proportional to the number of dense dislocation tangles is what allows us to control the final grain size of the metal after recrystallization is complete. After nucleation the new grains grow in size by migration outwards of the grain boundary surrounding the new grain. As the boundary moves outwards (actually by the shuffling of atoms across the grain boundary it destroys the high strain energy dislocation debris structure and replaces it with a low strain energy nearly dislocation-free material resulting from the grain boundary migration). After a certain time however, new grains growing from different nuclei eliminate all the old high dislocation density metal between them and impinge, forming a grain boundary between two strain free grains. When this impingement has occurred everywhere in the sample recrystallization is over. There is no more dislocation debris to cause either nucleation of new grains or migration of grain boundaries. (But see the process of grain growth, net lecture). Since each new grain nucleus ends up as a larger, strain free grain in the final recrystallized grain structure, the more nuclei we have to begin with, the smaller the size of the final grains will be. Thus if we want a large grain size we plastically deform to a strain where only a few very dense dislocation tangles have formed so that only a few new grains nucleate. The final recrystallized grain size will thus be very large. [It is even possible, but tedious, to grow a single crystal this way by knowing there is only one dislocation tangle in the entire sample capable of nucleating a new grain]. Conversely if one wants a very small grain size, one deforms to very high plastic strains where the number of dense dislocation tangles per unit volume is very high. The number of nuclei of new grains is very large and when they finally impinge, the grain size will be very small. Fig shows the recrystallized grain diameter vs. prior plastic strain for a brass. Notice that at low prestrains there is no recrystallization and one has the original grain structure of the metal. It is possible to produce grain sizes larger than or smaller than the original grain size by suitable plastic prestrain.

6 -143- Recrystallization grain si ze, mm Initial grain size, 0.5 mm Initial grain size, 0.05 mm % deformation, rolling Figure 18.5 After S. Channon and H. Walker, Trans. Am. Soc. Metals, 45, 200 (1953). Kinetics of Recrystallization From optical microscopy one can determine the percentage of the material that is recrystallized (that eists as new, rather than old, high dislocation density, grains.) Fig shows micrographs as various percentages of recrystallization. Figure 18.6 From: Nes and Ryum, Acta. Met (1975) The fraction recrystallized increases as a function of time at a given T as shown in Fig The process may take as much as 2 decades of time from start (nucleation) to finish (impingement) and the result is a characteristic sigmoidal (S shaped) curve. If one wanted to characterize the kinetics of the recrystallization by

7 -144- a single number one can use the time to 50% recrystallization, t 50%. Recrystallization (%) Incubation period { Time for 50% recrystallization Time of Annealing Figure 18.7 If we anneal at different temperatures we will find that the sigmoidal curve shifts to shorter times at higher temperatures as shown in Fig If we plot log t 50% from Fig vs. 1/T where T is the absolute temperature we find that the data are described by a straight line (Fig. 18.9). One can use that straight line relationship to etrapolate to conditions where eperiments are impractical. For eample one can use Figure 18.8 to predict that very pure copper will be 50% recrystallized at 24 F ( 3 C) in 25 years. Processes or mechanisms which give kinetic laws where log rate or log time varies as 1/T are said to be thermally activated. (Diffusion is another such process.) 275 F 235 F 191 F 109 F Recrystallization, % Time of Heating, min. Figure 18.8

8 F Temperature, F ,000 1,000,000 Time for 50% Recrystallization, mi n. 25 years Figure 18.9 Isothermal recrystallization of % pure copper. (After Decker and Harker.) One should mention that if one looks in handbooks (such as the Metals Handbook) one will find for various metals something called the "recrystallization temperature". Clearly from the eample above there is no such thing since if we wait long enough we can get recrystallization at almost any annealing temperature. However the Metals Handbook is designed for practical engineers and practical engineers do not like to anneal anything for much more than one hour. The recrystallization temperature T R is defined as the temperature at which T 50%, the time for 50% recrystallization, is one hour. For the eample of Cu used above, T R is about 240 F (116 C). A number of other material variables affect the recrystallization kinetics and thus the recrystallization temperature. Small amounts of trace impurities can drastically increase the T R since they slow down outward growth of the grain boundary surrounding the new dislocation-free grain. For eample T R for % Al (less than 1 part per million impurities) is 50 C whereas commercially pure Al (99% pure) has a T R of 250 C! The amount of prior plastic strain also affects the T R (can you think why?) giving rise to a decrease in T R with prior plastic strain as shown in Figure

9 T R ( F) % Al % Plastic Strain Figure Effects of the Amount of Cold Work on Kinetics - the greater the amount of cold work, the lower the T R on the lower t 50% at a given T. Just as strain hardening can produce large increases in the flow stress, recrystallization annuls these increases. Starting with a highly strain hardened metal (well-developed dislocation cell structure) the decreases in flow stress (or hardness) as a function of annealing temperature are shown schematically in Figure (Specimens are given a one hour anneal at each temperature before testing). There is a small decrease in flow stress below temperatures where recrystallization begins. This decrease is due to processes of dislocation rearrangement and a small amount of dislocation annihilation in the cell walls, processes which are called recovery processes. The major decrease in flow stress, to approimately its value before plastic deformation, occurs as a result of recrystallization. True Flow Stress σ t original flow stress before strain hardening recovery recrystallization begins T R microstructure is fully recrystallized Annealing Temperature Figure 18.11