Diffusion in Aluminum Alloys and its Dynamic Recovery - Dissertation Example

?Chapter 2: Literature Review: Diffusion of Aluminum alloys 2 Diffusion Diffusion or the movement of solute particles from high concentration to low concentration in order to obtain an equilibrium and even spread forms the basic mechanism through which processes like homogenization, solution and aging occur. Diffusion also leads to the changes in the micro-structure s such as grain boundary movement and recrystallization (Askeland and Phule, 2003). Diffusion rates are calculated from the following equation: D = Co exp(-Q/RT) Where: D= rate of diffusion T = absolute temperature (273 K) Q = Activation energy required to make atom move R = Gas constant Co = Constant Thus the rate of diffusion is dependent on time and temperature, and the activation energy and diffusion constant (which are different for specific alloys). The activation energy and diffusion constants are calculated using a variety of factors like the solid solubility, alloying content and the state of the matrix microstructure in terms of grain boundary size, dislocation density and vacancy concentration [PAPM]. The mean distance travelled by the atom during diffusion in turn is dependent on the rate of diffusion D as follows: L = (Dt)? Where L = the mean distance travelled by the atom. t = time (s) All atoms above absolute zero (-273oC) vibrate and the frequency of vibrations acts as the driving force for the movement of the atoms or for their diffusion. The frequency of vibration and diffusion increases with the rise in temperature. However, for atoms to be able to move from one lattice point to the other, the atoms need to overcome the activation energy. This activation energy is low around the metal surface and at the grain boundaries, and this is the reason for the high concentration of the precipitating solute at the grain boundaries. The reason for this lower activation energy is that there is less packing friction and hence less resistance and restriction to the movement of atoms around the grain boundaries. The process of diffusion leads to the creation of vacancies and initiates a process of the exchange of the vacancies thus created (Scha?fer, Song and Gottstein, 2009; Swiler, Tikare and Holm, 1997). For example, a diffusing atom moves to a vacancy site and in turn creates a new vacancy site at its original location in effect setting up a counter current flow of vacancies. Also, temperature has a greater effect on the diffusion distance compared to time as increasing the temperature increases both the number of vacancies in a metal as well as the energy of the diffusing atoms (Wolverton, 2007). Thus, in an increased temperature, atoms are able to diffuse faster and farther. The rate of diffusion differs for atoms of different alloys and hence the reduction of micro-segregation with homogenization differs for different alloys due to the difference in their compositions. As seen from the diffusion equations presented above, the distance that atoms need to travel (which depends on the dendrite arm spacing, the relative abundance of atoms) impact on the time and temperature needed to attain the desired level of diffusion for reduction of micro-segregation. Figure1: Relative homogenization times for given dendrite cell sizes and temperatures in common aluminum alloys. (Source: Chakrabarti, 2001) According to Verlinden et al [1990] found that the dissolution of theta and S particles in an as-cast 2024 billet during a homogenization at 460oC was not possible even after 24 hours. The volume fraction was found to decrease with time but with an associated coarsening of the remaining S and theta particles resulting in coarser particles than when in the as-cast condition. A homogenization temperature of 500oC was found to completely eliminate both the S and theta particles. Due to the distances that diffusing solute atoms travel during practical homogenization treatments, these treatments are effective at removing microsegregation effects but may have little impact on macrosegregation. 2.2 Theory related to Hot Deformation Hot rolling is the process by which ingots gets broken down into the blooms and billets (bloom is the product after the first stage of breakdown and has a cross sectional area of > 230 cm square. Billet is the product after a further hot rolling is carried out and has a cross sectional area > 40x40mm square). Once the process of breakdown is completed, the processes of further hot rolling into required forms such as plates, rods, bars, pipes etc. is carried out (Mishin and Herzig, 1999). The purpose of hot rolling is to reduce the thickness of the slab. During this process, the length of the slab gets increased but the increase in width is not much. The process of hot rolling happens at roughing mills, typically which have 0.6-1.4m diameter. During Hot rolling, the slabs are first heated to a temperature ranging between 1100 and 1300 degree Celsius (Zhu et al, 2001). In the last finishing stand, there would be a variation in temperature of about 700-900 degree Celsius, but in order to ensure that the ferrite grains are uniformly equiaxed, it is necessary to ensure that the temperature remains above the upper critical temperature. In hot rolling, a flat plate, in the range of 10-50mm is passed repeatedly through rolls, thereby reducing the thickness (). Then, the hot strip is coiled in order to lessen the increase in length that comes along when it becomes thinner. During this process, it is also necessary to reduce the complication of the controlling strips of different speeds because thinner section would move faster and the thicker section would move slower (). 2.3 Recovery The process of recovery occurs when any crystal defects that would have happened in a micro structure at an increased temperature begin to rearrange in order to restore to the original `structure (Huang and Humphreys, 2000). This re-arrangement towards the original structure can happen through spatial rearrangement of dislocations. Recovery is the process by which the properties of the alloys are modified during the process of annealing of the deformed material. This modification occurs prior to the development of the new recrystallized grains of the metals that are strain free (Kwiecikski and Wyrzykowski, 1989). These modifications of the properties of the metals are the result of the changes in the lattice structure as well as in the density of the lattice defects (Humphreys, 2001). The dynamic recovery process acts opposite to the strain hardening process during deformation at the melting point temperature for aluminum alloys. Dynamic Recovery results in the softening of the alloy and for the alloys of aluminum which have lower levels of alloying additions, his softening is often evidenced during deformation at much lower temperatures (). The Dynamic Recovery process may even lead to complete absence of strain hardening, or even strain softening (Huang and Humphreys, 2000). Recent research has also highlighted the fact that grain boundaries (GBs) play a major role in poly-crystals’ recovery process (Kwiecikski and Wyrzykowski, 1989), and the annihilation of the defects in GB that leads to density changes in the defects during deformation is controlled by GB diffusions (Kwiecikski and Wyrzykowski, 1989). Trapped Lattice Dislocations (TLD) are developed when GB comes in contact with a lattice dislocation, and at temperatures higher than the melting point of metals, TLD converts into Extrinsic Grain Boundary Dislocation (EGBD) leading to the relaxation of the stress on the lattice dislocations. In the case of aluminum, this happens at the room temperature itself. During this process, the dislocation products are spread across the GB but lose the ability to pass on shear stress. This inability to transfer stress across the boundary leads to the annihilation of dislocations in GB. The spreading of dislocations entangled with the GB is therefore an essential mechanism of recovery and in the case of aluminum, the diffusion rate of GB is the controls the rate of recovery. Also, the recovery process is dependent on the GB properties of the metal, and hence it is expected to be different for each metal or alloy. It is also essential to understand the kinetics of recovery in order to understand the recovery process better, and experimental studies have found that for aluminum, the recovery mechanism can be depicted by the logarithmic law within the range of 0.31-0.43 T,,,. . See figure below: Figure 2: Recovery in GB for Poly-crystalline Aluminum in States G and S, at 293K. 2.4 Recrystallization Recrystallization is the phenomenon through which any deformed grains get taken over by un-deformed grains. The new un-deformed grains have the property that they nucleate and hence, they can expand until all the original deformed grains get replaced (Swiatnicki, W. Lojkowski and M. W. Grabski, 1986). There are two types of recrystallization - static and dynamic. In dynamic recrystallization, the process of nucleation (the first process that happens in the formation of crystals, where atoms, ions molecules get arranged in a specific pattern) and the formation and growth of new grains happens during the deformation (McQueen, 2004). However, in static recrystallization, nucleation and formation and growth of new grains happen at a later stage (Kwiencinski and Wyrzykowski, 1989). Typically, when plotted on a stress-strain curve, the starting of dynamic recrystallization shows as a peak but this is not true in all the cases because some metals do not show proper peaks in hot working conditions. One of the ways to detect the beginning of the process of recrystallization is through Inflection points (the point where curvature changes from negative to positive and vice versa) when the rate of strain hardening is plotted along with stress, and this is used to identify the process in cases where the shape of flow curve is not prominent or is ambiguous (McQueen, 2004). Discontinuous and Continuous Dynamic recrystallization In metals with low stacking fault energy or SFE, discontinuous dynamic recrystallization is observed as in such metals the dynamic recovery process is slow which leads to the retarding of the process of grain formation (Gao, Belyakov, Miura and Sakai, 1999). This in turn leads to the discontinuous recrystallization as shown in the following figure. Source: Sakai and Jonas, 2001 The above figure highlights the fact that as the temperature increases, the curve changes from a multiple-peak to single peak one. On the other hand, Aluminum that has a high stacking fault energy or SFE, the process of continuous dynamic recrystallization is observed (Sakai and Jonas, 2001). The process of deformation produces dislocations that flow steadily and get annihilated leading to the formation of sub grain structures. Thee sub grain structures do not change much due to the external strain, but the original grains do deform with the external changes and get flattened in shape (Gao, Belyakov, Miura and Sakai, 1999). This results in simple shape curves that show steady state flow at high strains and strain hardening at lower levels of strains (Sakai and Jonas, 2001). However, later studies have highlighted the fact that even for metals that have low SFE, continuous recrystallization process can be initiated at temperatures that are much below the temperatures applicable for discontinuous dynamic recrystallization and when the strains applied are substantially large (Humphreys and Hatherly, 1996; Doherty et al, 1997). Dynamic recrystallization can occur also in different forms. Geometric Dynamic Recrystallization, which commonly occurs in aluminum alloys, the grains get flattened in such a way that only a small distance remains on the boundaries between the grains (McQueen, 2004). Another form is the sub grain rotation recrystallization where the sub grain boundaries which were at a low angle are rotated in such a manner that the level of mismatch between lattices reaches a level that can be considered as grain boundaries (Doherty, 1997). 2.5 PSN during Deformation Nucleation of Recrystallization is a heterogeneous process as it appears only as a result of some heterogeneity around particles that are larger than a given size. Such larger particles have heterogeneous regions and these are high gradient and stored energy. The level of heterogeneity around the particles is therefore an indicator of the amount of nucleation that can take place. Particle Stimulated Nucleation (PSN) of new grains is therefore dependent on effectiveness of the particle sites on deformation heterogeneities. However, it is not only the nucleation of the new grain around the deformation site that is of essence, but also the growth of similar grains in sites outside of such deformed zones (Humphreys, 1977). The new grains are found to grow away from the deformation zone, but the mechanism through which this happens is complex and not similar to the growth of grains at the site or zone of deformity. For example, it is observed that new grains can be expected to grow around particles (outside of the deformed zone) that have a particular size, which is larger than a given critical size. The critical size is calculated as: = grain boundary energy = stored deformation energy in the matrix outside of the deformation zone. So, for particles that are greater in size than, nucleation can be expected as shown in the following figure: Figure 4: PSN of Recrystallization after rolling reduction It is also found that that the process of nucleation is largely dependent on the strength of the PSN sites thus generated, instead of only on the nucleation due to the deformation heterogeneities (). In the context of PSN, it is also observed that dispersion of very small particles affect the process differently from larger particles. See figure below: Figure 5: Different size and second phase dispersion level (Nes and Hutchinson 1989) For example, it is seen that small particles interact with the moving grain boundaries at high angles, and by doing so impact on the recrystallization process (). The following figure depicts the grain boundary interaction with the spherical particle and the pinning force ‘F’ which results in the Zenner Drag Pz Figure: 6: grain boundary interacting and spherical particle (source: Miodownik, 2001) or assuming that angle is 90 degrees because the particles exert maximum force (PZ = Force divided by volume of a sphere or 4/3 pie r square) This, known as the Zenner drag, is responsible for impacting the nucleation of new grains as well as their growth and movement (). In fact, the Zenner drag leads to the slow-down of the process of nucleation as it reduces the of the stored deformation energy in the matrix external to the heterogeneity site, by creating a restraining pressure. This restraining pressure or Pz, is created due to the existence/distribution of the small spherical particles. Where ‘f’ is the volume fraction and ‘r’ is the radius of the fine particles. So, as can be seen from the equation , with the reduction of , a larger size of the particle is needed to initiate nucleation (Doherty and Martin (1962). Not only these secondary sites are affected, but also the formulation of new grains at the sites of deformation heterogeneity is impacted by the small particles. This occurs due to the reduction in the effective driving pressure , which impacts on the migration rate of the reaction front. In addition to the slowdown of the nucleation, the subsequent growth of the grains is also inhibited by these small particles and this leads to the Stagnation Phenomenon, where the final particles after recrystallization are smaller in size. PSN is therefore used as a control measure for monitoring and standardizing grain size in aluminum alloys. References Askeland, D. R., and Phule, P.P. 2003. The Science and Engineering of Materials. (4th edition) USA: Cole Publishers Chakrabarti, D. ‘Metallurgy 201.’ Preheating, Alcoa Technical Centre, pp 13, Doherty, R. D., Hughes, D. A., Humphreys, F. J., Jonas, J. J., Jensen, D., Kassner, M. E., King, W. E., McNelley, T. R., McQueen, H. J., and Rollett, A. D. 1997. ‘Current issues in recrystallization: a review’. Material Science Engineering, A(238): 219-274 Du, Y., Chang, Y.A., Huang, B., Gong, W., Jin, Z., Xu, H., Yuan, Z., Liu, Y., He, Y., and Xie, F.-Y. 2003‘Diffusion coefficients of some solutes in fcc and liquid Al: critical evaluation and correlation.’ Materials Science and Engineering, A(363):140-151 Gao, W., Belyakov, A., Miura, H., Sakai, T. 1999. ‘Dynamic recrystallization of copper polycrystals with different purities.’ Material Science Engineering, A (269): 238-239 Huang, Y. and Humphreys, F. J. 2000. ‘Subgrain growth and low angle boundary mobility in aluminium crystals of orientation.’ Acta Mater. 48, 2017-2030 Humphreys, F. J. and Hatherly, M. 1996. Recrystallization and Related Annealing Phenomena. Pergamon, Oxford, UK. Humphreys, F. J. 2001. ‘Development of dynamic recrystallization theory.’ Encyclopedia of Materials: Science and Technology, pp. 8061-8064 Kwiencinski, J. and Wyrzykowski, J. W. 1989. Kinetics of Recovery on Grain Boundaries in Polycrystalline Aluminium. Acta metal, 37(5): 1503-1507 McQueen, H. J. 2004. ‘Materials Science and Engineering.’ Acta metal, A (387–389): 203–208 Miodownik, M. A. 2001. ‘Zener Pinning.’ Encyclopedia of Materials: Science and Technology, pp. 9855-9859 Mishin, Y. and Herzig, C. 1999. ‘Grain boundary diffusion: recent progress and future research.’ Materials Science and Engineering, A(260): 55–71 Nes. E.2001Primary Recrystallization in Two-phase Alloys.’ Encyclopedia of Materials: Science and Technology, pp.7850-7854 Nes, E., and Hutchinson, W. B. 1989. ‘Texture and grain size control during processing of metals. In: Bild-Surensen J B, Hansen N, Juul Jensen D, Leffers T, Lilholt H, Pedersen O B (eds.) Proc. 10th Risu Int. Symp. Metallurgy and Materials Science. Risu National Laboratory, Roskilde, Denmark, pp. 233±49 Sakai, T. and Jonas, J. J. 2001. ‘Plastic Deformation: Role of Recovery and Recrystallization’. Encyclopedia of Materials: Science and Technology: pp. 7079-7084 Scha?fer, C., Song, J., Gottstein, G. 2009. ‘Modeling of texture evolution in the deformation zone of second-phase particles.’ Acta Materialia, 57: 1026–1034 Swiatnicki, W. A., Lojkowski W., and M. W. Grabski, 1986. Acta metal, 34, 599. Swiler, T.P. , Tikare, V. and Holm, E.A. 1997. ‘Heterogeneous diffusion effects i n polycrystalline microstructures’ Materials Science and Engineering, A(238): 85-93 Verlinden, B., Wouters, P., McQueen, H. J., Aernoudt, E., Delaey, L., and Cauwenberg, S. 1990. ‘Effect of Different Homogenization Treatments on the Hot Workability of Aluminium Alloy’ Materials Science and Engineering, A(123):229-237 229 Wolverton, C. 2007. ‘Solute–vacancy binding in aluminum.’ Acta Materialia, 55: 5867–5872 Zhu, J., Chen L-Q, Shen, J. and Tikare, V. (2001). Microstructure dependence of di€usional transport. Computational Materials Science,20: pp. 37-47 Read More