M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... 475–483 PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL USING CELLULAR AUTOMATA AND A NOVEL EVALUATION METHOD FOR GRAIN SIZE INHOMOGENEITY NAPOVED RAZVOJA MIKROSTRUKTURE AUSTENITNEGA NERJAVNEGA JEKLA VRSTE 316LN Z UPORABO CELI^NIH AVTOMATOV IN NOVA METODA ZA OVREDNOTENJE NEHOMOGENE VELIKOSTI KRISTALNIH ZRN Min Qin * , Jiansheng Liu School of Materials Science and Engineering, Taiyuan University of Science and Technology, 030024 Taiyuan, China Prejem rokopisa – received: 2023-22-15; sprejem za objavo – accepted for publication: 2023-07-28 doi:10.17222/mit.2023.796 Inhomogeneous grain size is a significant structural defect in large forgings. This study employed cellular automata to simulate the dynamic recrystallization (DRX) of 316LN steel and analyzed the grain distribution during DRX. The accuracy of the CA method was verified by comparing its results with the results of a thermal simulation test on Gleeble 1500D. Subsequently, a novel method for evaluating grain size inhomogeneity was proposed. The grain size inhomogeneity coefficient Gu was intro- duced to determine the evolution of grain size inhomogeneity during DRX. This coefficient accurately and objectively reflects grain inhomogeneity. The impact of the initial and recrystallized grain size on the inhomogeneity during DRX was also ana- lyzed. Keywords: grain size inhomogeneity, 316LN, cellular automata, evaluate Nehomogena velikost kristalnih zrn je pomembna strukturna pomanjkljivost oziroma napaka v velikih odkovkih. V tej {tudiji avtorja opisujeta uporabo metode celi~nih avtomatov (CA) za simulacijo procesa dinami~ne rekristalizacije (DRX) v nerjavnem jeklu vrste 316LN in analizo porazdelitve velikosti kristalnih zrn med DRX.Natan~nost CA metode sta verificirala s primerjavo z eksperimentalnimi rezultati dobljenimi s testi termi~ne simulacije na napravi Gleeble1500D. Nato sta avtorja raziskave predlagala novo metodo za ovrednotenje nehomogene velikosti kristalnih zrn. Uvedla sta parameter (koeficient) nehomogenosti za dolo~itev razvoja neenakomerne velikosti kristalnih zrn med DRX. Ta koeficient se objektivno odra`a v nehomogenosti kristalnih zrnin jo natan~no opisuje. Avtorja sta prav tako analizirala vpliv za~etne in rekristalizirane velikosti kristalnih zrna na nehomogenost med DRX. Klju~ne besede: nehomogena velikost kristalnih zrn; nerjavno jeklo vrste 316LN; celi~ni avtomati; ovrednotenje 1 INTRODUCTION During a forging process, the distribution of grain size can become uneven due to incomplete recryst- allization, the pinning effect of second-phase particles and the influence of trace elements, resulting in one of the most critical structural defects of large forgings. 1 This can cause a reduction in the yield strength, impact toughness, and overall quality and service performance. Ryabykin et al. identified grain size macro inhomo- geneity as the most negative feature of the structure of a ring fabricated from high-alloy alloys, resulting from non-uniform deformation. 2 Feng et al. investigated the effect of grain size inhomogeneity on the dynamic soft- ening behavior and processing map of Al-8Zn-2Mg-2Cu alloy, and found that the suitable hot-deformation pro- cess for rolling large ingots should be carried out in a temperature range of 440–450 °C and at a strain rate of 0.1–0.3s –1 , taking into account the ingot grain size inhomogeneity. 3 Sun et al. studied the microstructure inhomogeneity of prefabricated Co-28Cr-6Mo-0.23C- 0.17N alloy cylindrical bars and found that the growth of the existing -hcp grains increased the volume fraction of the -hcp phase more easily than the nucleation and growth of the new -hcp grains, leading to differences in the grain size. 4 Betsofen et al. used the X-ray rocking curve method (RCM) to characterize the microstructure texture of Al and its alloys and found that grains with orientations of {111} and {100} grew much faster than those with orientations of{113} and{110}, contributing to grain size inhomogeneity. 5 Landgraf et al. linked the grain size inhomogeneity of semi processed electrical steel to work hardening inhomogeneity in cold rolling of hot bands that were annealed to obtain large grain size. 6 In the 1980s, Wolfram et al. developed the mesoscale cellular automata (CA) method, which has been widely used in material science research to simulate the micro- structure evolution of various metal materials during hot Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 475 UDK 669.14.018.8 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 57(5)475(2023) *Corresponding author's e-mail: wsqm2008@163.com (Min Qin) forming. 7 For example, Alavi et al. studied the static recrystallization and microstructure evolution using austenitic stainless steel 304L. 8 A microstructural-ther- mal model based on CA was constructed to evaluate the rate of static recrystallization within rolled steel. The static recrystallization process was analyzed by Shi et al. based on the CA method. 9 The static recrystallization be- havior of LZ50 steel was accurately predicted. Su et al. established a three-dimensional CA model to analyze the austenitization of GCr15 steel at different temperatures and under different processing times, and the degree of austenitization was predicted. 10 Iwamoto simulated the deformation behavior of the martensitic phase under plane strain condition using the CA method coupled with a formulated constitutive equation and fi- nite element method (FEM). 11 Qian et al. investigated the microstructure evolution and plastic flow characteristics of an HY-100 steel using a simulative model that coupled the CA method with the basic metallurgical principle of dynamic recrystallization (DRX). 12 Moreover, Alavi et al. coupled an artificial neural network technique with the thermal-CA model to predict the martensite rever- sion, temperature history, and recrystallization progress during subsequent non-isothermal heat treatments. 13 However, few studies have investigated specific eval- uation methods for grain size inhomogeneity and may rely on metallographic photos for observation. Given that the CA method is an intuitive and accurate way to study the microstructure evolution during hot forming, this pa- per uses it to analyze the grain size inhomogeneity dur- ing the DRX of 316LN steel. The proposed method pro- vides a rational approach to evaluating grain size inhomogeneity. 2 CA MODEL OF DRX AND SIMULATION The paper focuses on studying the grain size inhomogeneity of 316LN steel during deformation, which is mainly influenced by microstructure inheritance and incomplete recrystallization. To understand this inhomogeneity, we focused on the recrystallization of 316LN steel and the associated changes in the grain size. To this end, we established a DRX model that includes nucleation, dislocation density evolution and gain growth. 15 2.1 Modeling of DRX nucleation Modeling of DRX nucleation can be described with Equation (1), as follows: 16,17 neT C Q RT (, ) exp =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ m N (1) where C is the constant that can be obtained by experi- mentally measuring the fraction of dynamic recryst- allization under specific deformation conditions, m is set to 1.0 in the present simulation, Q N is the activation energy, is the strain rate, R is the universal gas con- stant, and T is the absolute temperature. 2.2 Modeling of dislocation density The flow stress is proportional to the square root of dislocation density as given by Equation (2), as fol - lows: 18,19 =ab (2) where is the dislocation interaction term, = 0.5,bis the Burgers vector, is the mean dislocation density, and μ is the shear modulus. =−× − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 10 9 1 300 . T T m (3) Here, μ 0 is the shear modulus corresponding to a tem- perature of 300 K, and T m represents the melting point temperature. In the CA simulation can be expressed as: N ij ij iAjB , , , == ∑ (4) where N 0 is the total number of cells in the CA model and i,j is the dislocation density of the site (i,j). During hot deformation, work hardening caused by deformation led to the proliferation of dislocation den- sity, and softening caused by dynamic recovery and dy- namic recrystallization resulted in the annihilation of dis- location density. The KM model 18 holds that dislocation density and strain are related and this relationship is expressed as: d d ij ij ij kk , ,, =− 12 (5) where k 1 is the effect of work hardening on dislocation density and k 2 is the effect of dynamic softening on dis- location density. The critical dislocation density, cr, can determine whether DRX nucleation occurs in CA simulations; cr can be calculated as: cr = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 20 i blM (6) where i is the large angle grain boundary energy, b is the Burgers vector, l is the mean free path of dislocation, is the energy of dislocation line per unit length, M is the grain boundary mobility. 2.3 Modeling of the grain growth The grain boundary movement speed of the i th recrystallized grain is expressed as follows 20 : vM f ii = (7) where is the blocking migration parameter. 316LN steel is a single-phase steel, so is primarily related to the strain rate; f i is the driving pressure acting on the M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... 476 Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 grain boundary, and M is the grain boundary mobility, which can be expressed as: M Db KT Q RT =− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ob b exp (8) where is the grain boundary thickness of the material, D ob is the self-diffusion coefficient of the grain bound- ary at absolute zero, Q b is the activation energy of grain boundary diffusion, and K is the Boltzmann constant. Assuming that the new DRX grain is spherical, f i can be expressed as: f r ii i i =−− () m 2 (9) where i and r i are the dislocation density and radius of the ith recrystallized grain, respectively, m is the dislo- cation density of the matrix material, and i is the inter- facial energy, which is determined by the orientation difference between two adjacent grains. i i = ≥ m 15 11 5 ° − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ <° ⎧ ⎨ ⎪ ⎩ ⎪ m mm ii i ln Here, i is the orientation difference between the recrystallized grains and the adjacent grains, m and m are the orientation difference and grain boundary energy of the large angle grain boundary, respectively. The value of m can be calculated using the following equation: m m = b v π 1 where is the Poisson’s ratio. 2.4 Procedures of the simulation The simulation in this study utilized the cellular au- tomaton method, which involved discretizing a two-di- mensional computational domain into square cells. The von Neumann neighbor type was utilized to simulate the equiaxed growth of recrystallized grains, focusing on the impact of the four closest neighboring cells on the cen- tral cell state. Each cell was assigned four state variables for calculation, including dislocation density, orientation, grain boundary, and recrystallization fraction, as well as three structural variables for statistical purposes, such as grain number, color and recrystallization time. The dislo- cation density variable represented the deformation stor- age energy of grains, while the grain boundary variable was used to record whether the cells were located at grain boundaries or within grains. In this simulation, the two layers of cells at the grain boundary were taken as grain boundaries, and the recrystallization fraction vari- able represented the proportion of recrystallization oc- curring in each cell. This can be calculated using the fol- lowing equation: f vt l i i t 0 t d = ∫ 0 (10) where f i t is the recrystallization fraction of a cell (i, j)a t time t, and l 0 is the unit length of a cell. In this simula- tion, l 0 = 2 μm. If a cell became a recrystallized nucleus, the recrystallization fraction variable of that cell was 1. Each dynamically recrystallized grain had a unique grain number which was used to calculate the recrystallized grain size. In the CA simulation of DRX, several conditions had to be satisfied for the cell state change (DRX): 1) The driving force for the grain growth was greater than 0, or f i >0 . 2) A cell was located at the grain boundary, and cells were present within its von Neumann neighborhood that had a greater recrystallization number than its own. 3) The recrystallization fraction variable of the cell was 1. 4) After satisfying the above three conditions, the cell could undergo recrystallization transition using the probability of P = m/4. Here, m was the number of cells with the same orientation as their neighbors. Constant 4 represents the number of cells in the von Neumann neighborhood. A flowchart of the CA simulation of the DRX pro- cess can be seen in Figure 1. The material and process parameters required to simulate the DRX process were input first, and all cells were assigned the initial values. In our work, the judgment of ≥ total depended on the total number of cycles. The total number of cycles was established based on material parameters and hot work- ing parameters. The minimum time required to grow a cell was chosen as the time step, t, of the model, which is the ratio of the cell size l 0 to the maximum grain boundary movement rate 21 . Δt l v kl Mk == 02 2 0 1 2 max (11) With Equation (11), = μb 2 /2 and the strain incre- ment Δ CA =⋅ t could be calculated. The total number of cycles was calculated based on the total strain total : n CA_ dynamic total CA = (12) The change in the dislocation density within each cell was calculated based on the strain increment. When the increase in the dislocation density reached the critical dislocation density for dynamic recrystallization, recrystallization nuclei formed at the grain boundaries. Cells that met the four conditions for the recrystallization state transition underwent a state transition, resulting in the growth of recrystallized grains. After the deformation was complete, the recrystallization percentage, original grain size, recrystallized grain size, and total average M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 477 grain size were calculated. The grain area for each de- gree of grain was counted to determine the grain size inhomogeneity coefficient. Table 1 lists the key parame- ters used in this modeling. Table 1: Key parameters used in the simulations μ 0 (GPa) v Q N (kJ mol –1 ) D ob (m 2 s –1 ) Q b (kJ mol –1 ) m (J m –2 ) 77 0.28 467 5.6×10 –10 147 0.63 In this paper, CA simulations were used to study the grain distribution. If the research area is too small, it may not be representative of the actual grain distribution. In order to facilitate comparison with the later metallo- graphic test data, an area of 2000 μm × 2000 μm was se- lected for the simulation. It was found through simula- tion experiments that excessively large cell sizes would reduce simulation accuracy and result in rough grain edges, which would not reflect the local characteristics of the material well. Conversely, using smaller cells would improve simulation accuracy, but increase the computing time and resources. To ensure accuracy and efficiency, the simulation area was divided into 1000 × 1000 cells, where each cell was equivalent to 2 μm × 2 μm. Simulations of the dynamic recrystallization pro- cess in metals were conducted using the MATLAB soft- ware. During the simulation process, custom MATLAB scripts were developed to define the simulation parame- ters and algorithms necessary for capturing the key as- pects of dynamic recrystallization. On average, a single simulation took approximately 3 h. Throughout the sim- ulations, the progress was monitored and relevant data were recorded for further analysis. M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... 478 Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 Figure 1: Flowchart of the CA model for the DRX process Figure 2: Experimental metallographic images and CA simulation results under different reduction rates (a forging temperature of 1200 °C; a de- formation rate of 0.1s –1 ), Metallography: a) 20 %, b) 30 %, c) 40 %, CA simulation: a1) 20 %, b1) 30 %, c1) 40 % 3 EXPERIMENTAL WORK A thermal simulation test was conducted on 316LN austenitic stainless steel using a Gleeble-1500D simula- tion tester. The material was processed into standard samples with a size of 8 × 12 mm prior to compres - sion. 14 The experimental procedure involved heating a sample to 1250 °C at a rate of 10 °C/s, holding it for 3 min, cooling it to 1200 °C at 5 °C/s, and holding it for 60 s to eliminate any internal temperature gradient. Sub- sequently, hot compression was performed at a strain rate of 0.1 s –1 , with total compressive deformations of 20 %, 30 % and 40 %. After the completion of hot compres- sion, the sample was immediately subjected to water cooling treatment. Metallographic images and CA simulation results of the DRX process under the same process parameters are presented in Figure 2. It was observed that the CA simu- lation results were in good agreement with the experi- mental results, indicating the accuracy of the CA simula- tion. As the deformation increased, the recrystallization zones also increased. At a reduction rate of 20 %, few dynamically recrystallized nuclei were observed at the grain boundaries. When the reduction rate was increased to 30 %, the DRX zone expanded and the recrystallized M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 479 Figure 3: CA simulation results and grain distribution at different DRX percentages (a forging temperature of 1200 °C; a deformation rate of 0.1 s –1 ): (a)(a1) 0 %; (b)(b1) 10.12 %; (c)(c1) 27.1 %; (d)(d1) 47.33 %; (e)(e1) 54.25 %; (f)(f1) 70.95 % grains concentrated at the grain boundaries began to grow. At a reduction rate of 40 %, the DRX area in- creased to 70 %. Recrystallization occurred again in the recrystallization zone, resulting in continuous refinement of the grains and an increase in the average grain size. The CA simulation results provided a clear and de- tailed visualization of the changes in the grain size at dif- ferent stages of DRX. The simulation also enabled the calculation of important parameters such as the DRX area, recrystallization percentage and grain size distribu- tion. Throughout the DRX process, the grain size distri- bution underwent several stages of inhomogeneity, in- cluding the ALA stage, wide differential stage, bimodal stage, cross-sectional stage and necklace stage. The CA simulation results for the DRX of 316LN steel are shown in Figure 3, for a forging temperature of 1200 °C and a deformation rate of 0.1s –1 , along with the grain distribution at different DRX percentages. Without recrystallization, the initial grain size was concentrated in grade 2–5, and the area distribution showed a typical unimodal pattern. At 10.12 % DRX, dynamically recrystallized grains appeared, the grain size grade in- creased (the minimum was grade 12) and the area ac- counted for 6.67 %. The overall distribution of grain area had a bimodal pattern. The dominant grain size grade of big grains (the grains with the largest area) was 3, while the grade of small grains (dynamically recrystallized grains) was 7, yielding a grade difference of 4. At 27.1 % DRX, the dominant grade of big grains was still 3, but the area percentage decreased. The dominant grade of small grains was 6, and the occupied area increased. The distribution of grain area was bimodal. At 47.55 % DRX, the area of big grains continued to decrease and the area of small grains continued to increase. The area of grades 3–6 was almost the same, forming a wide differential pattern. At 54.25 % DRX, the initial grain area decreased and the total area of dynamically recrystallized grains in- creased alongside the progress of recrystallization. The distribution of grain area changed to a unimodal pattern. At 70.95 % DRX, the initial grain size decreased, the dy- namically recrystallized grains continued to grow and the two grain sizes tended to be the same. At this point, the dominant grain size grade was 5, and the distribution of grain area showed the typical unimodal pattern. As DRX progressed, the initial grains continued to decrease, the grains recrystallized, the dominant grain size decreased and the average grain size decreased. Figure 4 depicts the changes in the grain cross-sec- tional area and grain size grade in the CA simulation re- sults for the DRX of 316LN steel. The trend of the change in the grain cross-sectional area was opposite to that of the grain size grade. As shown in Figure 4b, the average grain size grade of the original grains and the to- tal average grain increased during the process of grain refinement. However, the average grain size grade of recrystallized grains decreased, reflecting the process of the nucleation and growth of dynamically recrystallized grains. In the early stages of DRX, the total average grain size grade was between the average grain size grade of the original grains and the average grain size grade of the recrystallized grains. Later in the process, the total average grain size grade was mainly determined by the average grain size grade of recrystallized grains. When the DRX percentage reached 70 %, the total aver- age grain size grade was consistent with the average grain size grade of recrystallized grains. 4 NEW EVALUATION METHOD AND ITS APPLICATION An evaluation method for the degree of grain size inhomogeneity usingDD max / m had been proposed previ- ously where D max represents the mean chord length of the largest grain and D m represents the mean chord length of all the grains in a sample. 22 However, this method may M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... 480 Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 Figure 4: Change in the grains during DRX throughout the CA simulation: a) changes in the average cross-sectional area of grains, b) changes in the average grain size grade not accurately reflect the inhomogeneity as D m contains D max , resulting in a higher proportion of the largest grain in the ratio. As a result, larger values ofDD max / m may lead to larger ratios and a more severe degree of inhomogeneity, which is not reasonable. An alternative method proposed by Chang et al. usesDD max / 0 to evalu- ate the degree of grain size inhomogeneity where D 0 rep- resents the average diameter of the grain grade with the highest frequency in the field of view. 23 However, this method intentionally ignores small-diameter grains and may not accurately reflect bimodal stages such as neck- lace stage, section stage and ALA stage. In this paper, a new evaluation method of the grain size inhomogeneity was proposed. This method is suit- able for unimodal and bimodal patterns, and can be de- scribed by the following equation: GGGA um 0 =−+ (/ ) 0 2 (8) where G u is the grain size inhomogeneity coefficient, G m is the mean grain size grade, G 0 is the preponderant grain size grade, which is the largest area occupied by the grain size grade in the field of view, and A 0 is the area fraction of G 0 . G u can simply and clearly allows an assessment of the grain size inhomogeneity in the field of view. The evaluation method is applicable to various states of the grain distribution. A higher G u value indicates a greater degree of inhomogeneity, and this method is applicable to both unimodal and bimodal grain distributions. The average grain size can be easily obtained by calculating or measuring the preponderant grain size grate and its area fraction, while measurement errors have a minimal impact on the final result. Therefore, the G u method is an accurate, easy-to-understand and practical way to evalu- ate the grain size inhomogeneity. Different evaluation methods were used to evaluate the grain size inhomogeneity for different DRX percent- ages under the forging temperature of 1200 °C and de- formation rate of 0.1 s –1 , as shown in Figure 5. Larger values obtained with these evaluation methods indicate a more severe inhomogeneity. Figure 5a shows that the G u value increased rapidly when the DRX percentage was less than 47.3 %, which was consistent with the change in the grain distribution from unimodal to bimodal dur- ing DRX. When the DRX percentage was greater than 47.3 %, G u increased and decreased repeatedly in a small range after a rapid decrease, reflecting the process of re- fining and homogenizing grains during DRX. As DRX is a dynamic process of continuous nucleation and growth, G u increased and then decreased repeatedly. Overall, G u increased and then decreased with the increase in the DRX percentage, and ultimately decreased, which aligns with the fact that DRX can refine and homogenize grains. Therefore, the G u evaluation method accurately characterizes the state of the grain size inhomogeneity during DRX. In Figure 5b, it can be observed thatDD max / m shows an increasing-decreasing trend with the increase in the DRX percentage. This method does not accurately re- flect the effect of DRX on the grain refinement and ho- mogenization. Similarly, Figure 5c shows thatDD max / 0 exhibits an overall increasing trend with the increase in the DRX percentage, which is contrary to observations. Therefore, these methods cannot accurately characterize the grain size inhomogeneity of the material. In contrast, the new method for evaluating inhomogeneity proposed in this paper, G u , accurately characterizes the state of the inhomogeneity of materials. A comparison between Figure 3 and Figure 5a re- veals that the G u value of the initial grains was 0.67 be- fore DRX commenced. As DRX progressed, new dy- namically recrystallized grains were continuously generated, causing the mean grain size grade to rapidly increase. The grain size grade/area percentage curve ex- hibited a bimodal distribution (Figure 3)a n dG u in- creased rapidly. When recrystallization reached 47.33 %, the grain size grade/area percentage curve exhibited a wide differential state, and G u reached its maximum. At the 54.2 % recrystallization, DRX continued to nucleate, leading to grain refinement and an increase in the pre- ponderant grain size grade, causing G u to drop rapidly to 1.66. The grain size grade/area percentage curve returned to the unimodal state. As DRX progressed, the grains M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 481 Figure 5: Different evaluation methods used to evaluate the grain size inhomogeneity during DRX: a) the new evaluation method, b)DD max / m , c)DD max / 0 continued to nucleate and grow, causing G u to increase and decrease repeatedly within a small range until recrystallization was complete. Generally, the evolution of the grain size inhomogeneity during DRX can be di- vided into two stages. In the early stage of DRX, the grain size polarization is significant, and G u shows an upward trend. The later stage of DRX is mainly the pro- cess of grain refinement, and G u shows a downward trend. Since DRX involves repeated nucleation and growth when the degree of DRX is high, G u becomes re- petitive within a small range. The new method for evaluating grain size inhomo- geneity is useful for analyzing the evolution of grains during metal deformation and for studying the impact of different factors on inhomogeneity. Figure 6a displays the change in G u during DRX with different initial grain sizes. The average cross-sectional areas of the initial grains were 18,000 μm 2 , 9,100 μm 2 and 5,586.2 μm 2 . The trend of G u during recrystallization was the same for all the initial grain sizes, with an overall increase followed by a decrease, as seen in Figure 6a. When the DRX per- centage was below 50 %, large initial grain sizes resulted in faster increases in G u due to the greater size difference between the initial and recrystallized grains, and the more significant grain size inhomogeneity. However, when the percentage of DRX exceeded 50 %, the initial grains were fully refined, reducing the effect of the ini- tial grain size on inhomogeneity. The values of G u were similar and irregularities were present. Figure 6b illustrates the changes in the coefficient G u value during the DRX process with different recryst- allized grain sizes. The average cross-sectional areas of the recrystallized grains were 198 μm 2 , 291 μm 2 and 478 μm 2 . When the DRX percentage was below 15 %, coefficient G u increased rapidly. Since the recrystallized grains began to nucleate and did not grow in size, there was little difference in G u even if there were different recrystallized grain sizes. When the DRX percentage was above 15 %, the recrystallized grains began to grow, and the growth rate of G u slowed down. Coefficient G u of the smaller recrystallized grains was larger. The main reasons for this were the facts that the size of the recrystallized grains was small, and the difference be- tween the initial grain size and the recrystallized grain size was large, resulting in a larger G u value. When the recrystallization percentage reached about 50 %, the ini- tial grain area decreased, and the dominant grain grade increased as the recrystallized grains grew, leading to a sudden decrease in coefficient G u . When the recryst- allized area exceeded 50 %, coefficient G u of the larger recrystallized grains was larger. 5 CONCLUSION In this study, the cellular automation method was used to simulate the DRX of 316LN, and the resulting grain distribution was analyzed. A new method for eval- uating the grain size inhomogeneity was proposed, intro- ducing coefficient G u to accurately and objectively mea- sure the grain inhomogeneity. Coefficient G u was found to accurately reflect the changes in the grain size inhomogeneity during DRX. Regardless of the initial grain size, G u showed an overall trend from an increase to a decrease during recrystallization. When the percentage of DRX exceeded 50 %, the effect of the initial grain size on inhomo- geneity was reduced. Conversely, when the recrystallized area exceeded 50 %, the G u coefficient of smaller recrystallized grains was smaller, indicating a more uni- form grain distribution. In conclusion, the new evalua- tion method proposed in this study can accurately char- acterize the state of grain size inhomogeneity and is M. QIN, J. LIU: PREDICTION OF MICROSTRUCTURE EVOLUTION OF 316LN AUSTENITIC STAINLESS STEEL ... 482 Materiali in tehnologije / Materials and technology 57 (2023) 5, 475–483 Figure 6: Changes in G u during DRX with different initial grain sizes and recrystallization grain sizes: a) different initial grain sizes, b) different recrystallization grain sizes applicable to various states of grain distribution. The G u coefficient is easy to use and can be applied to analyze the grain evolution during a metal deformation and in- vestigate the influence of different factors on inhomo- geneity. 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