Materials Science Forum Vols. 558-559

Abstract: The development of a digital material framework is presented, allowing to build virtual microstructures in agreement with experimental data. The construction of the virtual material consists in building a multi-level Voronoï tessellation. A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way. A corresponding finite element mesh can be generated automatically in 3D, and used for the simulation of mechanical testing under large strain. In the examples shown in this work, the initial mesh was non uniform and anisotropic, taking into account the presence of interfaces between grains and sub-grains. Automatic remeshing was performed due to the large strains, and maintained the non uniform and anisotropic character of the mesh. A level set approach was used to follow the grain boundaries during the deformation. The grain constitutive law was either a viscoplastic power law, or a crystallographic formulation based on crystal plasticity. Stored energies and precise grain boundary network geometries were obtained directly from the deformed digital sample. This information was used for subsequent modelling of grain growth with the level set approach, on the same mesh.

Abstract: The classical JMAK equation was modified by combination with distribution density of the rate parameter k, which was deduced from a normal distribution of local strain. The modified equation is able to calculate the JMAK plots and the average Avrami exponent to characterize the entire heterogeneous recrystallization process. This new extension can successfully describe the relevant experimental observations, such as a smaller exponent than the basic JMAK theory predicts, and a decreasing slope of JMAK plots with the proceeding recrystallization. Moreover, it reveals that the Avrami exponent observed experimentally should significantly decrease with the increasing standard deviation of local strain distribution. In addition, it has a great potential to explain why most of experimentally observed values of Avrami exponents are less than 2 and why the Avrami exponent is insensitive to temperature and deformation conditions when the real standard deviation of local strain distribution in deformed metals is known.

Abstract: The competitive behaviors between recrystallization and transformation during annealing in dual phase high-strength steels are studied both by experiments and by computer simulations. The Monte Carlo code was applied to simulate such competing behavior, explained the experimental results, as follows. (1) The progress of the transformation is affected by the starting point of the transformation in the course of recrystallization. Namely, if the transformation starts at the later stage of recrystallization, the n-value in JMAK equation is relatively high. (2) If the stored energy (driving force) of the transformation is above 5 times larger than that of the recrystallization, the effect of the stored energy is quite small. (3) If the number of nuclei were increased, the transformation proceeds a little faster, and then the transformed microstructures are significantly refined. When the transformation initiates at the early stage of the recrystallization, the number of nuclei can be increased by nucleation from the deformed matrix compared with the one from fully recrystallized matrix.

Abstract: The generalized deterministic vertex model was successfully used to study the recrystallization process and the corresponding results were published elsewhere [1]. In its classical form the vertex model has analytical formulation, basing on the total energy (i.e. boundary energy and stored energy) minimization. A change of grain boundary configuration in classical vertex model is found by the calculation of vertex velocities. Consequently, a global and complex system of equations has to be solved in each step. In order to simplify calculations and to handle the problem in a more flexible way, the statistical model was proposed. Typical elements of Monte Carlo algorithm were incorporated into the vertex model: a random (and small) modification of microstructure is accepted with the probability proportional to Boltzmann factor. This approach is closer to the stochastic nature of recrystallization process. The model was used to study the recrystallization of 70% and 90% cold rolled polycrystalline copper. It predicts correctly recrystallization textures for high and low strains.

Abstract: Classical vertex model till now described only the grain growth stage and not the primary recrystallization. In the present work the vertex model is first extended in order to take into account the both stages of recrystallization process. The influence of the stored energy is taken into account and some phenomenological laws describing the evolution of grain boundary energy and mobility with misorientation angle are used. Nucleation is considered to be site-saturated. The experimentally determined stored energy values, crystallographic orientations and boundary misorientation distributions are used in order to characterize the initial microstructure. The model is tested to study the recrystallization of 70% and 90% cold rolled polycrystalline copper during an annealing treatment. In order to explain the texture evolution in both cases, it is necessary to introduce an energy threshold for grain boundary movement, i.e. a minimal value of the stored energy difference between a nucleus and the deformed material necessary to provoke grain boundary motion. The developed model is shown to predict texture evolutions in good agreement with experimental data.

Abstract: A 2D cellular automaton model developed for the simulation of grain growth in hexagonal metals is presented here. It allows the direct use of experimental measurement as input data. Texture evolution of a titanium alloy and a zirconium alloy are simulated on the basis of simple hypothesis and compared with experimental evolution as well as the results from a 3D Monte Carlo model. Results from both models are discussed with regards to their characteristics.

Abstract: A refined view of particle stimulated nucleation of recrystallization is presented, which utilizes a combination of advanced modeling tools. FEM simulations were carried out in order to model the evolution of the deformation zone around particles for various particle sizes and shapes. The results of these simulations were complemented by EBSD measurements to determine the number and orientation of nuclei. Finally, this information on particle stimulated nucleation was incorporated into a 3D cellular automaton recrystallization model CORe to model microstructure evolution. From these simulations the dependence of grain size and texture on particles size and shape was derived.

Abstract: The kinetics and topology of ideal grain growth were simulated using the phase-field model. Large scale phase-field simulations were carried out where ten thousands grains evolved into a few hundreds without allowing coalescence of grains. The implementation was first validated in two-dimensions by checking the conformance with square-root evolution of the average grain size and the von Neumann-Mullins law. Afterwards three-dimensional simulations were performed which also showed fair agreement with the law describing the evolution of the mean grain size against time and with the results of S. Hilgenfeld et al. in 'An Accurate von Neumann's Law for Three-Dimensional Foams', Phys. Rev. Letters, 86(12)/2685, March 2001. Finally the steady state grain size distribution was investigated and compared to the Hillert theory.

Abstract: Based on topological considerations and results of Monte Carlo Potts model simulations of three-dimensional normal grain growth it is shown that, contrary to Hillert’s assumption, the average self-similar volume change rate is a non-linear function of the relative grain size, which in the range of observed grain sizes can be approximated by a quadratic polynomial. In particular, based on an adequate modification of the effective growth law, a new analytical grain size distribution function is derived, which yields an excellent representation of the simulated grain size distribution.

Abstract: The effects of second-phase particles on the recrystallization kinetics in two-dimensional polycrystalline structures were investigated. Numerical simulations of recrystallization were performed by coupling the unified subgrain growth theory with a phase-field methodology. Simple assumptions based on experimental observations were utilized for preparing initial microstructures. The following results were obtained: (1) The presence of second-phase particles retarded recrystallization speeds. (2) If the mean subgrain size was small enough recrystallized region covered whole system for various values of the particle fraction, f. (3) On the other hand, if the mean subgrain size was not small enough the progress of recrystallization was frozen at some point.