Study on Transient Thermal Response for Functionally Graded Materials Based on Peridynamic Theory

基于近场动力学理论的功能梯度材料瞬态热响应研究

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received: 9 October 2018

Abstract

The transient heat conduction formula of functionally graded materials (FGMs) is presented based on peridynamics (PD). The simplified micro-heat conductivity model for FGMs is proposed and the numerical discretization and the peridynamic numerical formation are also illustrated. A FORTRAN program is coded to implement calculations. The accuracy of the program is verified by comparing the FEM and analytical results with PD solution. The FGM rectangle plate composed by titanium alloy coating zirconium oxide is performed to calculate temperature fields. The effects of material gradient, porosity and temperature load on thermal response are studied. It is shown that the ceramic proportion of FGMs is increased with an increasing material shape parameter and the thermal shielding performance of FGMs is also improved. The effect of the porosity on thermal response is more and more significant with the increasing time step. The increasing temperature load only affects the temperature response of FGM ceramic area. The thickness of temperature distribution area is increased with the increasing of heat conduction time.

摘要

基于近场动力学 (peridynamics，简称PD) 理论推导了功能梯度材料 (functionally graded materials，简称FGMs) 的热传导控制方程，给出FGM简化微热导率模型与PD热传导方程离散过程及数值计算格式。编写了PD热传导数值计算FORTRAN程序，并与有限元解及解析解对比验证了程序正确性。计算了以钛合金表面涂覆氧化锆的FGM矩形板温度分布，研究了组分分布形状、孔隙率以及边界温度对FGM瞬态热响应的影响。结果表明：组分形状分布系数增大，使得陶瓷材料占比提高导致FGMs隔热性能增加；孔隙率对温度分布的影响随传热时间的增加而增加，导致FGMs隔热性能降低；温度荷载的升高只会影响FGM陶瓷区一定厚度内的温度响应，该温度分布厚度随传热时间的增加而增大。