STUDY OF THE KINETICS OF STATIC RECRYSTALLIZATION USING AVRAMI EQUATION AND STRESS RELAXATION METHOD

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1 , Brno, Czech Republic, EU STUDY OF THE KINETICS OF STATIC RECRYSTALLIZATION USING AVRAMI EQUATION AND STRESS RELAXATION METHOD Jaromír HORSINKA a), Jiří KLIBER a), Marcin KNAPINSKI b), Ilija MAMUZIC c) a) Department of Materials Forming, VŠB -TU Ostrava, Czech Republic, jaromir.horsinka@vsb.cz b) Czestochowa University of Technology, Czestochowa, Poland c) Faculty of Metallurgy University of Zagreb, Sisak, Croatia Abstract In order to design and use forming processes, one has to cover a body of knowledge including the recovery phenomena. Recovery can be described using the Avrami equation, which yields the proportion of recrystallized structure as a function of various deformation-related variables. However, some constants and exponents of the equation must be known. Their values can be obtained by measuring either by metallographic or mechanical methods the fraction of recrystallized structure in specimens deformed under prescribed conditions. A metallographic technique consists in quenching the material and mapping the locations of grains, their sizes and shapes in an optical microscope to find the ratio of recrystallized grains. It is possible to use a more up-to-date technique: electron microscopy combined with electron backscattered diffraction. However, these methods are in fact very complicated and often infeasible. Mechanical methods include intermittent tests in compression or torsion plastometers, which can be evaluated using various techniques. The difficulties of this approach lie in separating recovery from recrystallization, as well as in the vast number of test, which must be performed in order to describe the kinetics of static recrystallization in a single material. Another modern technique uses the stress relaxation phenomenon. By analysing the stress vs. time plot, one can obtain information on the specimen's flow stress during the hold after deformation. A Gleeble simulator was used for an experiment with four temperatures and five strain rates and the resulting strain magnitude of.2. After deformation, specimen was held in the grips at constant temperature and stress was recorded. The resulting stress vs. time plot was analysed. Points denoting the start and end of recovery were identified on the curve. Constants of the Avrami equation were determined using these points. The advantages of stress relaxation tests include their simplicity, the opportunity to obtain a full-range curve for the volume fraction of recrystallized structure in a single test run and the effectiveness of mapping softening phenomena. Keywords: Stress-relaxation, Avrami equation, static recrystalization kinetics, Gleeble. KINETICS OF STATIC RECRYSTALLIZATION Kinetics of static recrystallization, which is a process that follows upon hot deformation in steel, are often characterized in terms of the time required for recrystallization of 5% of the material, i.e.. The most general expression for this relationship is as follows [1]: ( ) (1) where denotes the grain size in μm,

2 , Brno, Czech Republic, EU is the static recrystallization activation energy in -, denotes strain, is the Zener Hollomon parameter given in s -1, is temperature in K, stands for the universal gas constant in Jmol -1 K -1, are material constants. The time dependence of the fraction of statically recrystallized material is commonly described through Avrami general equation: Where is the recrystallized fraction, accounts for the effects of thermal and mechanical conditions of forming, is Avrami exponent. However, it is even more often expressed in the form of the following equation: [ ( ) ] (3) (2) For the recrystallization kinetics to be described as ( ), constants A and Q rex and values of exponents in the equation must be known. These values can be obtained by measuring by metallographic or mechanical methods the recrystallized fraction in specimens deformed under pre-defined conditions. Once the material is quenched, the fraction of recrystallized grains can be established by mapping the locations of grains, their sizes and shapes using an optical microscope. It is possible to use a more modern technique as well: electron microscopy combined with electron backscattered diffraction. This allows the dislocation density to be assessed (by image analysis or artificial intelligence methods). It can also differentiate between unrecrystallized deformed grains with greater number of dislocations and low-angle boundaries and the recrystallized ones [1]. However, in real-world applications, recrystallized grains are very difficult to distinguish from unrecrystallized ones by using just light microscope. In case of some bainitic or martensitic microstructures, where dislocations and low-angle boundaries are present in all grains (packets, sheaves), even electron microscopy techniques fail. The above-mentioned mechanical methods include interrupted tests and stress relaxation tests. Results of interrupted tests carried out in compression or torsion plastometers can be evaluated using various techniques. In these tests, it is difficult to distinguish between the effects of recovery and recrystallization. Another complication is that these tests must be performed under specific deformation conditions with a single pause between deformation steps. Therefore, a large number of tests ( ) are required for the static recrystallization kinetics of a single material to be described. In this aspect, stress-relaxation testing is more convenient: a single test yields a full curve describing the recrystallized fraction vs. time relationship. This reduces the total number of tests required for characterizing a single material to about Fig 1 Typical test schedule for relaxation test 15 [2].

3 Stress [MPa] , Brno, Czech Republic, EU STRESS-RELAXATION METHOD The stress relaxation testing procedure is presented in the following diagram (Figure 1). Its steps include heating to a required temperature, cooling down to deformation temperature, deformation at a prescribed rate, and then holding the strain constant Stress vs. time while recording the force (load/stress) and time (from the start of the hold) [3]. Very 15 suitable for this type of testing are versatile Gleeble plastometers, which offer sufficient 1 measurement frequency and accuracy. Graphite and tantalum foils are applied to 5 reduce friction and to prevent sticking between the material and anvils. Figure 2 shows the stress relaxation curve,1,1, for a test in concentric arrangement. Gleeble Time [s] simulator was used for testing microalloyed steel at 11 C with the strain of.5 and a Fig 2 Stress - relaxation curve strain rate of 1 s -1. The stress vs. logarithmic time curve has three distinct parts. In the first one, the stress decrease is linear, at a constant rate. In the second part, the decrease is much more rapid, whereas in the third it is linear again but at lower stress values. The stress decrement in the first part of the curve is associated with the recovery of austenite after deformation. The steeper slope of the second part of the curve is due to the material s quicker softening caused by starting static recrystallization. Once the recrystallization is complete, decrease can be explained by the relaxation in recrystallized austenite [3]. CALCULATION OF DEGREE OF SOFTENING BY STRESS RELAXATION METHOD Using the figures, one can describe the behaviour of stress in regions 1 and 3 with a simple equation [4]: (4) Where denotes the natural stress in MPa, denotes relaxation time in seconds, and are constants. The stress value in the second part of the curve can be calculated as [4]: (5) Where indices 1 and 3 refer to the first and third part of the curve, respectively. Using this equation, one can also calculate the recrystallized fraction at given time instant [5]: {[ ] } { } (6) Where α is the slope of the curve, recovery stage, final stage, σ 1, σ 2 is the stress value associated with the time instant t = 1s. Corresponding values of constants in figure 2 are given in table 1: Table 1 Computed constants and parameters of the Avrami equation (MPa) (MPa) (MPa) (MPa) (s) ,3 2,3

4 X Log Ln (1/(1-X)) X , Brno, Czech Republic, EU It is now possible to plot the recrystallized fraction vs. time curve using equation 6. The softening curve is confined between (deformed) and 1 (fully recrystallized condition). The behaviour of the recrystallized fraction parameter is consistent with theory Softening curve and its shape is sigmoidal (Figure 3). It is due to inhibiting factors taking effect at the 1 beginning and end of static recrystallization.,5,1, Fig 3 Softening curve - recrystallized fraction computed from relaxation curve Double Log plot,6,3, ,3 -,6 Fig 4 Double Log plot giving the Avrami exponent Recrystallized Fraction 1,5 Avrami eq. Stress-relaxation,1, Fig 5 Softening curve - recrystallized fraction computed from relaxation curve and from Avrami equation On this curve, it is possible to find time t.5 required for 5% recrystallization. In this case, it was. The last variable in Avrami equation can be found using a double logarithm curve, the slope of which is given by Avrami exponent (Figure 4). Linear regression yielded the value of = 1.3. Upon substituting in Avrami equation, one obtains a neat sigmoidal curve matching the above recrystallized fraction curve from the stress relaxation test. CONCLUSION This study dealt with describing static recrystallization in stress relaxation test using Avrami equation. This technique proved to be very effective, saving experimental costs, as well as time required for finding the degree of softening. For instance, data from compression test conducted in Gleeble plastometer can be used to calculate constants in Avrami equation. It is, however, important to carefully determine the time of the start of relaxation stage (after deformation figure 1), as it may have profound effect on the results. Slopes of the first and third parts of the stress relaxation curve must be determined with great care as well. When these guidelines are followed, the recrystallized fraction vs. time curve of the expected sigmoidal shape (Figure 5) can be obtained. In our follow-up experiments, we will use apply this novel method, which has not been tried at our department yet, to a broader range of data obtained from experiments with deformation at various temperatures and strain rates. We will also attempt to compare this method with conventional techniques that are based on calculating the degree of softening from interrupted test data.

5 , Brno, Czech Republic, EU ACKNOWLEDGEMENTS The described methodology and results were obtained in the framework of the solution of Research Plan SP212/33, SP212/196, CZ.1.5/2.1./1.4. LITERATURE [1] Somani, M., C.; Suikkanen, P., P.; Lang, V., T., E; Porter, D., A.; Karjalainen, LP.: The stress relaxation technique to determine the recrystallization kinetics in processing of advanced steels by thermomechanical processing. (Artikkeli tieteellisessä konferenssijulkaisussa). - MEFORM 211, Werkstoffkennwerte für die Simulation von Umformprozessen, 3. März bis 1. April 211 in Freiberg, Deutschland. -. Freiberg, Technische Universität Bergakademie Freiberg, Institut für Metallformung [2] Horsinka, J. Komplexní teoretická, počítačová a metalografická studie plastometrických zkoušek materiálu, Teze dizertační práce, 212, 32 str. [3] C. García-Mateo, B. López, J.M. Rodriguez-Ibabe: Static recrystallization kinetics in warm worked vanadium microalloyed steels. Materials Science and Engineering A33 (21), Volume: 33, Issue: 1-2, Pages: , ISSN: [4] Gallot, Edith. Effect of heat treatment and hot working on the microstructural characteristics of TWIP steels, Universitat Politècnica de Catalunya. Departament de Ciència dels Materials i Enginyeria Metal lúrgica, Master thesis, 74 p. [5] YANG Iing-hong!" LIU Qing-you2 SUN Dong-bail, LI Xiang-yang!. Recrystallization Behavior of Deformed Austenite in High Strength Microalloyed Pipeline Steel. Journal of Iron and Steel Research, International, Volume 16, Issue 1, January 29, Pages 75 8, ISSN: 16-76X