均匀化方法对单向碳/铝复合材料弹性性能预测

Elastic Properties Prediction for Unidirectional Carbon /aluminum Composites by Homogenization Method

基于均匀化方法,预测单向碳/铝复合材料的等效弹性模量,得到单向碳/铝复合材料等效弹性常数的预测公式。首先,采用均匀化方法对单向玻纤/环氧复合材料等效弹性模量进行预测,得到玻纤/环氧复合材料的等效弹性常数,并与NASA经验公式的计算结果进行比较。结果表明,均匀化方法计算得到的等效弹性常数与NASA经验公式的计算结果相吻合,验证了周期性边界条件以及均匀化方法预测单向复合材料弹性性能的正确性。然后,采用均匀化方法对不同纤维含量的单向碳/铝复合材料等效弹性模量进行预测,并与NASA经验公式和混合法则的计算结果进行比较。结果表明,NASA经验公式和混合法则的计算公式可以预测单向碳/铝复合材料的纵向拉伸模量和纵向泊松比,但无法预测其横向拉伸模量和剪切模量。最后,采用最小二乘法拟合均匀化方法的计算结果对NASA经验公式进行修正,得到了单向碳纤维增强铝基复合材料横向拉伸模量和剪切模量的预测公式。

The equivalent elastic modulus of unidirectional carbon/aluminum composites are predicted based on homogenization method, and the prediction formula of equivalent elastic constants are gained. Firstly, the equivalent elastic modulus of unidirectional glass/epoxy composite are predicted, and compared with calculation results by NASA empirical formula. The result show that the calculation results by homogenization method is equal to those by NASA empirical formula, and the correctness of periodical boundary conditions and the homogenization method pre- dicting the equivalent elastic modulus of unidirectional composites was verified. Secondly, the equivalent elastic modulus of different volume fraction for unidirectional carbon/aluminum composites are predicted by homogeniza- tion method, and compared with those by NASA empirical formula and the mixing rule. The result show that NASA empirical formula and the calculation formula of the mixture rule earl predict longitudinal tensile modulus and lon- gitudinal Poisson＇s ratio,but can＇t predict transverse tensile modulus and the shear modulus of unidirectional car- bon/aluminum composites. Finally, the calculation results using homogenization method are fitted by least square method, and NASA Empirical formula is revised. Prediction formula of transverse tensile modulus and the shear modulus for unidirectional carbon/Aluminum composites are gained.