基于细观有限元模型的多胞材料中的局部应力计算方法及应用

发布时间：2018-05-30 19:17

本文选题：多胞材料 + 均匀蜂窝　；参考：《中国科学技术大学》2017年博士论文

【摘要】：多胞材料是一种内部含有大量空隙并由一定的胞结构组成的具有明显多尺度特征的材料,具有高比刚度和高比强度,作为轻质结构被广泛应用于冲击防护和吸能领域。多胞材料在动态冲击情形下呈现出应力增强和变形局部化的典型特征,基于连续体定义的宏观名义应力-应变曲线失去物理意义,不能描述多胞材料在动态冲击情形下的本构行为。由于冲击端的应力增强,传统的基于端面的名义应力不能反映材料中所处的真实应力状态。在高速的情形下,变形集中于撞击端并像冲击波一样传播。为了描述这一特征,已有文献中已经提出了一系列的冲击波模型,例如经典的R-PP-L(率无关、刚性-理想塑性-锁定)模型和R-PH(率无关、刚性-塑性硬化)模型。但这些模型都是在准静态的应力-应变曲线上近似得到的,因此很有必要对动态冲击下的多胞材料的应力-应变的关系进行研究。为了获得多胞材料在动态压溃下的局部的应力信息,本文发展了一种拉格朗日截面上工程应力的计算方法。利用该方法研究了多胞材料中的应力分布信息,结合局部应变场计算方法研究了多胞材料的动态应力-应变行为。本文基于细观有限元模型提出了截面工程应力的计算方法,得到了多胞材料中的局部应力信息。截面工程应力定义在拉格朗日截面位置上,由两部分应力组成,即节点传递应力和接触引发应力。由节点传递的应力是通过基体材料单元所传递的节点力所引起的,而由接触引发的应力是由胞壁间的接触所引起的。在冲击初始阶段,接触引发应力几乎为零,节点传递应力与截面工程应力相等。在发生接触之后,节点传递应力变化不大,接触引发应力急剧增加几乎等于截面应力。接触引发应力对应力增强起决定作用。通过截面应力计算方法研究了均匀蜂窝在恒速压缩下的应力历史和应力分布。结合应力变化历史和局部应变历史得到了不同冲击速度下的应力-应变历史曲线。在低速压缩下,应力-应变关系与准静态应力-应变曲线几乎重合。但是在中速和高速压缩下,应力和应变从波前初始压溃状态经历塑性压溃阶段变化到波后动态压实状态。应力-应变的历史曲线包含Rayleigh线的发展过程,随着冲击速度的提高,Rayleigh线的斜率变大,即冲击波速度变大。冲击波波后的应力-应变状态点全部位于准静态应力应变曲线的右侧,即同等应力下,动态压实应变大于准静态压实应变。由应力分布证实了塑性冲击波在试件中的传播,得到了冲击波速度与冲击速度的关系并与冲击波模型做了比较。基于冲击波速度与冲击速度的关系以及一维冲击波理论,提出了一种分段模型,基于分段模型推导得到了均匀蜂窝在动态情形下的率无关本构模型。梯度的引入使得多胞材料呈现不同的力学性能,研究了梯度蜂窝在恒速压缩情形下的应力分布情形。直接通过应力分布观察到梯度蜂窝中存在单波和双波传播模式。基于R-PP-L和R-PH假设推导了梯度蜂窝冲击波传播的单波和双波理论模型并由截面应力方法进行验证。R-PP-L模型不适合表征多胞材料在动态压溃下的力学行为。R-PH模型得到的应力分布和冲击波速度与有限元结果相近。关于多胞材料在动态加载下的初始压溃应力在已有的文献中存在看似矛盾的认识。通过局部应力和应变信息对多胞材料在动态加载下的初始压溃行为进行了全面的分析。采用了截面应力计算方法和局部应变场计算方法来决定基于细观有限元模型的均匀蜂窝在不同加载情形下的初始压溃应力和初始压溃状态的应变率。在恒速压缩下,初始压溃应力与准静态初始压溃应力相等但是小于直接撞击情形下的初始压溃应力。也就是说,初始压溃应力在不同的冲击情形下是不同的,即使基体材料是没有应变率效应的。当局部应变率大于一个临界应变率时,发展了初始压溃应力与应变率之间的幂次关系来描述蜂窝中初始压溃应力的应变率效应。小于临界应变率的时候,初始压溃应力没有应变率效应。研究了均匀蜂窝在不同的加载情形下的初始压溃行为的变形机理,发现塑性压缩波前方的初始压溃区域的变形模式在不同的冲击情形下是不同的。
[Abstract]:Multi cell material is a kind of material with a large number of gaps and a certain number of cellular structures, with high specific stiffness and high specific strength. As a lightweight structure, it is widely used in the field of impact protection and energy absorption. Multi cell materials exhibit stress enhancement and deformation localization under dynamic impact. Characteristics, the macroscopic nominal stress strain curve based on the continuum definition loses physical meaning and can not describe the constitutive behavior of multi cell materials under dynamic impact. Due to the increase of the stress at the impact end, the traditional nominal stress based on the end face can not reflect the real stress state in the material. In high speed case, the deformation is concentrated in the case. In order to describe this feature, a series of shock wave models have been proposed in the literature, such as the classical R-PP-L (rate independent, rigid ideal plastic locking) model and R-PH (rate independent, rigid plastic hardening) model, but these models are all approximated on a quasi-static stress-strain curve. Therefore, it is necessary to study the stress-strain relationship of multi cell materials under dynamic impact. In order to obtain the local stress information under dynamic crushing of multi cell materials, a method of calculating the stress on the Lagrange section is developed. The dynamic stress strain behavior of multi cell materials is studied by the local strain field calculation method. Based on the mesoscopic finite element model, the calculation method of the stress of the section engineering is proposed and the local stress information in the multi cell material is obtained. The section engineering stress is defined on the Lagrange section position, which is composed of two parts of stress, that is, node transfer. Stress and contact cause stress. The stress transmitted by the node is caused by the nodal force transmitted by the matrix material unit, and the stress caused by contact is caused by contact between the cell walls. In the initial stage of the impact, the contact stress is almost zero, the transfer stress of the node is equal to the cross section stress. After the contact, the stress is equal to the cross section stress. The stress change of the node is little, and the sharp increase of contact stress is almost equal to the cross section stress. The contact initiation stress corresponds to the force enhancement. The stress history and stress distribution of the uniform honeycomb under constant velocity compression are studied by the cross section stress calculation method. Stress strain history curves under the velocity of shock. Under low velocity compression, the stress-strain relationship is almost coincided with the quasi-static stress-strain curve. However, under the medium speed and high velocity compression, the stress and strain change from the initial stage of the pre wave crushing to the dynamic compaction state. The historical curve of stress strain includes Rayleigh. With the increase of the impact speed, the slope of the Rayleigh line becomes larger, that is, the velocity of the shock wave becomes larger. The stress strain state after the shock wave is all located on the right of the quasi-static stress-strain curve, that is, under the same stress, the dynamic compaction strain is larger than the quasi static compressive strain. The stress distribution confirms the plastic shock wave in the test. The relation between shock wave velocity and impact velocity is obtained and compared with shock wave model. Based on the relationship between shock wave velocity and impact velocity and one dimensional shock wave theory, a piecewise model is proposed. Based on the piecewise model, the rate independent constitutive model of uniform honeycomb is derived. The stress distribution in the gradient honeycomb under constant velocity compression is studied. The single wave and double wave propagation mode in the gradient honeycomb are observed directly through the stress distribution. Based on the hypothesis of R-PP-L and R-PH, the theoretical model of the single wave and double wave propagation of the gradient honeycomb wave is derived. The surface stress method is proved that the.R-PP-L model is not suitable for the characterization of the mechanical behavior of multi cell materials under dynamic crushing. The stress distribution and the shock wave velocity are similar to the finite element results. The initial pressure stress in the dynamic loading of multi cell materials appears to be contradictory in the existing literature. The local stress is through the local stress. The initial crushing behavior of multi cell materials under dynamic loading is comprehensively analyzed and the strain information is used to determine the strain rate of the initial crushing stress and the initial crushing state of the homogeneous honeycomb based on the meso finite element model. The initial crushing stress is equal to the quasi static initial crushing stress but less than the initial crushing stress in the case of direct impact. In other words, the initial crushing stress is different under different impact conditions, even if the matrix material has no strain rate effect. When the local strain rate is larger than a critical strain rate, the initial pressure is developed. The power relation between the crushing stress and the strain rate is used to describe the strain rate effect of the initial crushing stress in the honeycomb. When the critical strain rate is less than the critical strain rate, the initial crushing stress has no strain rate effect. The deformation mechanism of the initial crushing behavior of the uniform honeycomb under different loading conditions is studied, and the initial crushing pressure in front of the plastic compression wave is found. The deformation modes of the region are different under different impact situations.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB30

【参考文献】