不同细观力学方法预测高聚物粘结炸药有效模量的比较

高聚物粘结炸药（PBX）不同于普通颗粒增强复合材料，其颗粒含量超过85%，组分弹性模量相差3~4个数量级，导致其有效模量的细观力学理论预测出现很大偏差。结合有限元细观模拟，对Mori-Tanaka法、自洽法、微分法3种细观力学方法的预测结果进行了比较分析。结果表明：界限法上下界之间有量级上的差异；当颗粒含量小于10%，颗粒间相互作用较小，不同方法计算的有效模量差异不大；含量大于20%时，颗粒间相互作用增强，3种解析法预测的结果逐渐出现差异，而微分法与有限元结果比较接近；当颗粒含量为94.9%，微分法预测的PBX杨氏模量比实测值高3.7%，Mori-Tanaka法和自洽法结果都有量级上的偏差；对于颗粒含量高、组分性能反差大的复合材料，微分法较合理地计及了颗粒间的相互作用，能较准确地预测其有效模量。

Comparison of Effective Moduli of Polymer Bonded Explosive Predicted by Different Micromechanical Methods

Polymer bonded explosives (PBXs) are different from conventional particle reinforced composites.PBXs possess over 85％ of particle volume fraction,and the elastic modulus of particle can be three or four orders of magnitude higher than that of binder.Large deviations are observed on the effective moduli predicted by micromechanical methods.The predicted results of several micromechanical methods for the effective moduli of PBX are analyzed based on finite element method.Results indicate that both Voigt-Reuss bounds and Hashin-Shtrikman bounds give rather large estimated regions;when particle fraction is less than 10％,the differences among the effective moduli estimated by the different methods are not obvious since the particle interaction is negligible;when particle fraction exceeds 20％,the estimated results of three analytic methods are different from each other gradually due to the enhancement in particle interactions,and the estimated results of differential method agree with those of finite element method.For the particle fraction of 94.9％,Young's modulus calculated by differential method is only 3.7％ higher than the experimental value of PBX,while a huge error occurs using Mori-Tanaka method or selfconsistent method.For the composites that possess high particle fraction and strong contrast in their ingredient properties,the differential method provides better estimates of effective modulus owing to its relatively favorable evaluation on particle interactions.