关键词: 金属纤维, 烧结颈, 烧结结点, 分数阶微积分, 有限差分法

Abstract: Based on geometric model of metal fiber sintering nodes, with Caputo fractional differential equations, a time fractional surface diffusion model is established. Numerical solution by finite difference method is made. Numerical simulation of metal fiber sintering process is realized. Numerical simulation of sintering process and variation of neck length as fractional order varies from 0 to 1 are obtained. As the order is fixed at 0.9, sintering process at initial included angles of 0°, 30°, 60° and 90° are simulated. It shows that as the order is equal to 1 the result is consistent with integer order diffusion model. Neck radius with integer order and fractional order grows rapidly in initial stage of sintering. With progress of sintering, fractional simulation of sintering neck length appears local fluctuation, and finally grows at an increase rate greater than the integer order. As the order is fixed, the smaller the initial angle, the greater the rate of growth. The fractional order surface diffusion model describes well the complex change of sintering node during fiber sintering process than the integer order surface diffusion model.

Key words: metal fiber, sintering neck, sintering nodes, fractional calculus, finite difference method