A Numerical Model for Predicting the Zener-Hollomon Parameter in the Friction Stir Processing of AZ31B

Abstract

Grain size determines to a large degree the mechanical properties of the friction stir processed (FSP) material. Developed in this work is a numerical (FEM) based-model for predicting values of the Zener-Hollomon parameter (Z-parameter) as function of input process parameters during friction stir processing of AZ31B. Prediction of Z values is desirable given that direct relations exist between the Z-parameter and the average grain size in the dynamically recrystallized zone (DRX). For this purpose, utilized in this work is a robust finite element model with a suitable constitutive equation and boundary conditions the results of which have been previously validated against published experimental data. A virtual test matrix constituting of 16 cases (4 spindle speed, N, x 4 feed, f) was run. Based on resulting state variables of strain rates and temperatures at a representative point within the stir zone, a statistically-validated power equation model was developed that relates Z-parameter values to input parameters of speed and feed. The results of the numerically developed power equation were validated against experimental results. This model can be readily used in future control frameworks to FSP produce AZ31B sheets of a predefined target grain size.