基于Cowper-Symonds方程的相似理论修正方法

针对应变率敏感材料冲击实验的指导需求，给出了一种传统相似理论的修正方法。该方法在已有的动态相似理论基础上，考虑了因实验时模型与全尺寸原型制造材料不同，而导致外载条件相似系数对应变率效应对结果造成的影响:通过引入Cowper-Symonds方程，重新推导了外载条件相似系数的计算公式，并对两种不同材料（是否应变率敏感）的缩放模型冲击实验结果进行讨论，表明该方法相较于传统理论能够准确给出外载条件相似系数、提高模型预测精度。

Modified method for scaling law based on Cowper-Symonds equation

In this paper we proposed a method for modifying classical similarity theories to meet the guidance need in the impact experiment of strain rate sensitive materials.This method,based on recent dynamic similarity theories,took into account the effect of the initial load's similarity coefficients on the strain-rate effect during the impact experiment due to the differences in materials between the prototype and the model.We rebuilt the calculation formulas of the initial load's similarity coefficients using the Cowper-Symonds equation,and discussed the results obtained in the impact experiment on two scaled models,made from two different materials,as to whether they were strain-rate sensitive or not,showing that,compared with the classical similarity theories,our newly proposed method could provide the initial load's accurate similarity coefficients and thus improve the model prediction precision.