新型金属间化合物多孔材料有效弹性常数的理论预测

摘要

基于新型Ti-Al金属间化合物多孔材料的微结构特征分析,建立了该材料的Plateau多孔结构细观力学模型,通过能量法推导出该多孔材料有效弹性常数(含有效弹性模量、有效剪切弹性模量、有效泊松比)的理论预测公式.计算结果表明:有效弹性模量和有效剪切弹性模量均随着相对密度的增加而增加,但有效泊松比随着相对密度的增加而减小.与现有的六边形蜂窝模型及复合材料力学模型相比,非均匀Plateau多孔结构细观力学模型更适合于表征中密度多孔材料,更能准确地预测中密度多孔材料的有效弹性常数.现有的非均匀Plateau多孔结构模型仅给出有效弹性常数与微观结构参数之间的关系,而本文模型建立了有效弹性常数与宏观相对密度的显式表达式,更方便工程的实际应用.%Based on microstructure analysis of the new Ti-Al intermetallic compound porous material,a micromechanics model of heterogeneous Plateau porous structure was established and calculation formulas of elastic constants (including effective elastic modulus,effective shear elastic modulus and effective Poisson ratio) were derived by the energy method for this porous material.Calculation results show that both the effective elastic modulus and effective shear elastic modulus increase with the increase of the relative density while the effective Poisson ratio decreases.Compared with the currently-existing hexagonal honeycomb model and micromechanics model of composite materials,the micromechanics model of heterogeneous Plateau porous structure in this study is more suitable for characterizing the medium-density porous material and more accurate for predicting the effective elastic constants of the medium-density porous material.Moreover,the obtained explicit expressions of the effective elastic constants in term of the relative density rather than the microstructural parameters for the uniform and regular Plateau porous structure are more convenient to engineering application.