Modeling and simulation of the dynamic process in high energy ball milling of metal powders

Mechanical alloying/mechanical grounding by using high-energy ball milling has been considered as a promising materials processing technique to synthesize materials. In this study, modeling simulation has been carried out to investigate the impacts, which are basic events in milling, as well as the milling dynamics in order to control and optimize this process. A 3-dimensional model has been developed to simulate the head-on impact process between two balls or between a ball and the vial wall with powder in between by considering the elastic deformation of impact objects, and the visco-plastic flow and elastic deformation of the powder compact. The comparison between the experimental results published in literature and the simulation outcome demonstrates that this model is the best to simulate the head-on impact process, which involves powder. Application of the model in high-energy ball milling shows that the ball-ball and ball-wall impacts do have some difference. It was also observed that the ball size, impact velocity and powder thickness all affect the impact pressure, and that the deformation of balls is substantial comparing to the powder thickness involved in an impact. 3-dimensional models have also been developed to simulate the movement of balls considering the effects of powder, ball spinning and oblique impact of balls. The multi-ball impacts, which have been proved to occupy a substantial fraction among impacts, were also considered. Having realised the importance of knowing the volume of the powder involved in each impact, a model was also developed to estimate this volume. The prediction of the weight of powder involved in each impact made based on this model was in good agreement with the observation reported. A 3-dimensional global model has been developed for the SPEX-8000 Mixer/Mill based on the mechanics of the machine. By using this model, the motion of the vial was numerically determined. Then the global model was coupled with the models for the impacts in order to predict the dynamics of milling process. The simulation results revealed that the movement of balls after milling starts can be separated into two stages. The first stage is the unstable stage, which lasts for less than 0.3 second and involves mostly rolling and slipping of balls on the vial wall. The second stage is the stable stage, when the impact frequency, the mean impact velocity and mean spinning velocity of balls do not change significantly over time. Numerical experiments indicate that the frequency of impacts between balls and the vial wall is linearly proportional to the number of balls and the frequency of impacts between balls is nearly proportional to the square of the number of balls and the square of radius of balls. It is also shown that the majority of the impacts occur at low velocities of less than 4 m/s and with impact angles in the range of 15∼75°. The prediction of the impact frequency and impact angle distribution made from the simulation agrees well with the probability analysis. An effective model has been developed for the first time to calculate the time needed for mechanical milling based on probability analysis. This model can be used once the effective impact frequency and the fraction of powder effectively mechanically milled powder are known. The latter can be achieved through modeling. The milling efficiency corresponding to various ball numbers and sizes have been evaluated. The results show that there is an optimum number for the best milling efficiency for a given size of balls. Global models for the milling process in a planetary mill and an attritor mill have also been developed. Preliminary simulation experiments have been conducted