Analytical modeling of strain rate distribution during friction stir processing

Friction Stir Processing (FSP) is becoming an acceptable technique for modifying the grain structure of sheet metals. One of the most important issues that hinder the widespread use of FSP is the lack of accurate models that can predict the resulting microstructure in terms of process parameters. Most of the work that has been done in the FSP field is experimental, and limited modeling activities have been conducted. In this work, an analytical model is presented that can predict the strain rate distribution and the deformation zone in the friction stir processed zone as a function of process parameters. In the model, the velocity fields within the processed zone are determined by incorporating the effects of both the shoulder and the pin of the tool on the material flow. This is achieved by introducing state variables and weight functions. The model also accounts for different interfacial conditions between the tool and the material. The effects of different process parameters and conditions on the velocity fields and strain rate distributions are discussed. The results clearly show that the model can successfully predict the shape of the deformation zone and that the predicted strain rate values are in good agreement with results reported in the literature.