轮胎破片冲击机身的非等比例相似模型研究

为降低机身结构抗冲击性能的实验成本，利用相似理论建立机身的非等比例缩放模型，开展模型实验是行之有效的方法。基于量纲分析的方法，建立Johnson-Cook线性应变率函数的修正关系；鉴于生产制造技术的限制，考虑扭曲厚度的非等比例机身模型对相似性行为的影响，采用指数函数法建立了非等比例模型的相似修正关系。通过对比实验中破片冲击过程的变形形态、靶板的应变时间历程曲线和最终变形轮廓，验证了数值模型的有效性。此外，分析了破片偏航姿态、机身材料、厚度和质量等因素对机身结构抗冲击性能的影响。结果表明：(1) 150 m/s的冲击速度下，破片冲击角度90º和着靶角度180º是最严苛的冲击条件。综合多种因素，分析认为3.5 mm厚的钛合金为机身结构的最佳选择，并以此作为全尺寸原型验证相似模型；另外，提出了一种可以快速获取缩比模型的设计方法。(2)应变率效应对轮胎破片冲击机身结构的影响并不显著，等比例缩放模型与原型结果吻合较好。(3)厚度扭曲的非等比例模型能够有效地预测原型结构的变形行为；虽然，在时间尺度上，模型与原型存在一定的偏差；但是，在空间尺度上，非等比例相似模型能够有效地修正扭曲厚度造成中心最大挠度的预测误差，修正后的最大误差不超过5.1%，这表明该方法能够有效地指导机身结构的相似模型设计。

A study of incomplete similar models for tyre fragment impact on fuselage structures

In order to reduce the cost for the impact test of the full-size airframe structures, an incomplete similar model was established by the similarity theory. Based on dimensional analysis, the correction relation for the Johnson-Cook linear strain-rate function was formulated. Due to the limitation of manufacturing technology, the effect of the incomplete similar model with distorted thickness on similarity behaviors should be taken into account, so an exponential function was adopted to establish the correction formula for the distorted thickness model. The validity of the simulation model was then verified by comparisons relevant to the deformation on the fuselage, the strain-time curves of target plates and the final deformation profile. In addition, the influences of fragment angle, material property, distortion thickness and light weight on the deformation behavior of the fuselage structure were analyzed. The following main results were obtained. (1) Under the impact velocity of 150 m/s, the most severe impact conditions appear at the impact angle of 90° and the fragment attitude of 180o; by considering various factors, the 3.5-mm-thickness titanium alloy plate is regarded as the best choice for fuselage structures, and it is used as a full-size prototype to verify the similar method. Besides, it’s worth noting that an unconventional phenomenon takes place at the impact angle of 30o, while a reasonable explanation is given. (2) The effect of strain rate on the impact of tire fragments on the fuselage structure is not notable, so the incomplete similar model is in good agreement with the prototype results. (3) The incomplete scaled-down model corrected by this method can effectively predict the deformation behavior of prototype fuselage subjected to the impact of tyre fragments. Although there is a certain deviation between the model and the prototype on the time scale, on the spatial dimensions, the incomplete scaled-down model can effectively correct the prediction error for the maximum center deformation caused by the distortion thickness, and the corrected maximum error is less than 5.1%, indicating that the method can effectively guide the design for airframe structures.