泡沫金属的动态压溃模型和率敏感性分析
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摘要
与传统的金属材料相比,泡沫金属材料由于含有多种多样的细观结构,从而具有超轻、高能量吸收等优良的力学性能和减震、散热、隔热和电磁屏蔽等多功能复合特性。细观结构的随机性和缺陷可能对泡沫金属的宏观力学性能有较大的影响。实验的方法很难讨论细观结构的随机性等特性对泡沫金属宏观力学行为的影响,通过数值模拟的手段可以很方便地揭示这一问题,可以为泡沫金属材料和泡沫金属复合结构在工程中的应用提供理论指导。动态冲击情况下泡沫金属的惯性效应和泡沫金属材料的率效应通常耦合在一起。然而泡沫金属在动态冲击过程中产生的变形局部化导致采用传统的SHPB实验的方法来解耦其惯性效应和作为材料的率效应是非常困难的。本文采用冲击波理论对泡沫金属的动态冲击行为进行了理论分析,然后通过泡沫金属材料应变场的计算方法,给出了泡沫金属材料在冲击过程中的应力-应变状态等力学特性。
基于三维随机Voronoi技术,我们构建了三维开孔泡沫金属模型和三维闭孔泡沫金属模型。统计了泡沫金属的不规则度与其细观胞元体积分布的相互关系。为保证泡沫金属细观有限元模型计算的正确性,对有限元网格的特征长度进行收敛性分析。研究表明开孔泡沫金属和闭孔泡沫金属在胞元数量很少的时候它们的平台应力均随着胞元数量的增加而增加,最终趋于一个稳定的值。当胞元个数达到一定数量时,模型的尺度效应是可以忽略的。另外,通过数值模拟的方式讨论了细观结构的随机性对于开孔和闭孔泡沫金属模型宏观动静态力学行为的影响。研究表明,细观结构的不规则度对开孔和闭孔泡沫金属模型的宏观动静态力学性能的影响均是不显著的,这种影响也是可以忽略的。
本文研究了闭孔和开孔两种泡沫金属模型的动态塑性泊松比问题和微惯性效应问题。计算结果表明,无论对于开孔泡沫金属模型还是闭孔泡沫金属模型,泡沫金属的塑性泊松比随着名义应变的增加而下降,塑性泊松比的峰值随着冲击速度的增加而下降,相对密度增加时,泡沫金属塑性泊松比增加。微惯性对平台应力的影响不大。实验中侧向约束情况下,闭孔泡沫金属的压溃应力随着加载速率的提高而下降,这个现象可以由泡沫金属塑性泊松比峰值随着冲击速度的增加而下降和微惯性效应来给出较好的解释。
本文还研究了准静态压缩条件下闭孔泡沫金属内部气体压强对其宏观力学性能的影响。计算结果表明,在相对密度比较低的泡沫金属模型中,泡沫金属的应力增量是比较显著的,泡沫金属气体压强引起的应力增量也随着名义应变的增大而增大。同时发现,当内部孔穴初始气体压强较大时,气体压强会对泡沫金属的名义泊松比产生一定的影响。最后,通过数值模拟的结果,给出了泡沫金属在内部气体压强影响下的应力增量的估算公式。
针对泡沫金属模型撞击刚性壁的情形建立了两类动态压溃模型,一维冲击波模型和三维细观有限元模型。以连续介质框架下的应力波理论为基础,并假定了刚性-非线性塑性硬化的加载和刚性卸载的本构关系,建立了一维冲击波模型,给出了冲击波波后应变与冲击时间的隐式表达式。使用有限元软件模拟了闭孔泡沫金属模型的动态压溃过程,并基于最小二乘法计算局部变形梯度和局部应变得到了三维泡沫结构的应变场。通过理论解和数值解的比较,发现该理论模型能够较好的预测泡沫金属杆撞击刚性壁的力学行为。
我们还对泡沫金属材料在动态冲击情况下的率敏感性进行了探讨。动态冲击过程中泡沫金属产生的局部变形使得实验中解耦其惯性效应和作为材料的率效应是非常困难的。为了研究泡沫金属率效应的影响,泡沫金属细观有限元模型以一定的初始冲击速度直接撞击固定的刚性壁,借助于细观模型的应变场的计算方法,可以获得泡沫金属模型动态冲击下的应变分布。计算结果表明,泡沫金属模型的动态压实应变随着冲击速度的增加而增大,且细观有限元模型的动态压实应变要大于采用准静态本构关系定义的动态压实应变和采用R-P-P-L模型定义的压实应变。根据冲击波理论,反推出冲击波波阵面前方的应力值,发现冲击波波阵面前方的应力值大于准静态情况下的初始压溃应力值。最后得出了泡沫金属模型的动态下的应力-应变状态,并发现动态应力-应变状态和准静态情况下的名义应力-应变关系有显著差异的。通过分析细观模型的变形模式给出了这种差异性的解释,当前的结果表明变形模式的差异是导致泡沫金属材料加载速率敏感性的主要原因。
Compared with traditional metal materials, metallic foams have super light, excellent energy absorption capacity, electromagnetic shielding and novel thermal properties because of the variability of their meso-structures. The irregularity and defects of the metallic foam meso-structures maybe have large influence on the mechanical properties of metallic foams. It is difficult to determine the influence of the irregularity and defects on the mechanical properties of metallic foams in experiment. However, the numerical simulation method can depict the problem conveniently. The relation between the irregularity/defects and the mechanical properties of metallic foams can give theoretical guidance for the application of metallic foams and their composite structures. Under dynamic impact condition, local inertia effects and the definition of the relevant parameters associated with the dynamic response are usually coupled together, and it is hard to decouple them using SHPB experimental equipment because of the deformation localization of the metallic foams. In this paper, using the shock wave theory, we analyse the dynamic impact behaviour of metallic foams. Then, based on the local strain calculation method, the dynamic stress strain states of metallic foams under dynamic impact can be obtained.
Based on the3D Voronoi technique, we construct a3D open-cell metallic foam model and a3D closed-cell metallic foam. The relations between the irregularity of metallic foams and the cell volume distribution are also obtained. In order to guarantee the validity of the finite element models, we analyse the convergence of the characteristic length of the finite elements. The simulation results show that the plateau stress of open-cell/closed-cell metallic foams increases with the increase of the metallic foam cell number, when the number of metallic foam cells is small; then the plateau stress trends to a fixed value. This means that the size effect of the metallic foams is negligible, when the number of cells reaches a certain level. We also use the simulation method to explore the relation between the irregularity of open-cell/closed-cell metallic foams and the mechanical properties of metallic foams. The results show that influence of the irregularity of metallic foams on the mechanical properties of metallic foams is unapparent.
In this thesis, we investigate the micro-inertia effect and dynamic plastic Poisson's ratio of closed-cell/open-cell metallic foams. The simulation results indicate that the plastic Poisson's ratio varies with the nominal strain, its peak value decreases as the impact velocity increases and the Poisson's ratio increases with the relative density increasing. The micro-inertia effect plays little role in enhancing the plateau stress of metallic foams. A significantly decreasing influence of lateral constraint on the crushing stress with increasing loading rates has been found for a closed-cell metallic foam. This interesting phenomenon can be interpreted by the micro-inertia effect and the decrease of Poisson's ratio in dynamic compression.
In this thesis, we also explore the relation between the inner gas pressure of closed-cell metallic foams and theirs mechanical properties in quasi-static crushing condition. The simulation results show that the stress increment affected by the inner gas pressure is obviously in low-density closed-cell metallic foams. The stress increment also increases with the increase of the nominal strain. When the inner gas pressure reaches a high level, the gas pressure can affect the Poisson's ratio of the metallic foams. Finally, we give the estimated formula between the inner gas pressure and the stress increment from the simulation results.
Two models are developed for describing the dynamic crushing of metallic foams striking a rigid wall:a one-dimensional shock model and a3D cell-based finite element model. The shock model is proposed by using the continuum-based stress wave theory and assuming the rigid-nonlinear hardening plastic constitutive relation of foam, and then an implicit expression for determining the relation between local strain behind the shock front and the impact time is obtained. The dynamic crushing process of cell-based finite element model is simulated by using the ABAQUS/Explicit software. The local strain field is obtained by using the least squares method to calculate the deformation gradient and local strain. By comparing with the simulation results, the shock model presents good predictions of the stress and the strain behind the shock front.
We also explore rate sensitivity of metallic foams under dynamic impact. Current experimental techniques make it difficult to obtain the dynamic constitutive relations of cellular metals since local inertia effects are not easily decoupled from the definition of the relevant parameters associated with the dynamic response. In order to study this effect, a cell-based metallic foam is considered in which the foam specimen impinges normally with an initial velocity, Vo, on a stationary rigid wall. Using the local engineering strain calculation method, we can obtain the local strain distribution of the metallic foam under dynamic impact. The simulation results show that the dynamic densification strain increases with the increase of impact velocity and is larger than the quasi-static densification strain used in the R-P-P-L shock model. According to the shock wave theory, the stress ahead of the shock front can be obtained, which is found to be larger than the initial crush stress in the quasi-static compression. Finally, it is found that the dynamic stress-strain states are obviously below the quasi-static stress-strain relation. This difference is explained by analysing the deformation modes at the cell level. The present results reveal that the difference of deformation modes is the main reason of the loading-rate sensitivity of metallic foams.
基于三维随机Voronoi技术,我们构建了三维开孔泡沫金属模型和三维闭孔泡沫金属模型。统计了泡沫金属的不规则度与其细观胞元体积分布的相互关系。为保证泡沫金属细观有限元模型计算的正确性,对有限元网格的特征长度进行收敛性分析。研究表明开孔泡沫金属和闭孔泡沫金属在胞元数量很少的时候它们的平台应力均随着胞元数量的增加而增加,最终趋于一个稳定的值。当胞元个数达到一定数量时,模型的尺度效应是可以忽略的。另外,通过数值模拟的方式讨论了细观结构的随机性对于开孔和闭孔泡沫金属模型宏观动静态力学行为的影响。研究表明,细观结构的不规则度对开孔和闭孔泡沫金属模型的宏观动静态力学性能的影响均是不显著的,这种影响也是可以忽略的。
本文研究了闭孔和开孔两种泡沫金属模型的动态塑性泊松比问题和微惯性效应问题。计算结果表明,无论对于开孔泡沫金属模型还是闭孔泡沫金属模型,泡沫金属的塑性泊松比随着名义应变的增加而下降,塑性泊松比的峰值随着冲击速度的增加而下降,相对密度增加时,泡沫金属塑性泊松比增加。微惯性对平台应力的影响不大。实验中侧向约束情况下,闭孔泡沫金属的压溃应力随着加载速率的提高而下降,这个现象可以由泡沫金属塑性泊松比峰值随着冲击速度的增加而下降和微惯性效应来给出较好的解释。
本文还研究了准静态压缩条件下闭孔泡沫金属内部气体压强对其宏观力学性能的影响。计算结果表明,在相对密度比较低的泡沫金属模型中,泡沫金属的应力增量是比较显著的,泡沫金属气体压强引起的应力增量也随着名义应变的增大而增大。同时发现,当内部孔穴初始气体压强较大时,气体压强会对泡沫金属的名义泊松比产生一定的影响。最后,通过数值模拟的结果,给出了泡沫金属在内部气体压强影响下的应力增量的估算公式。
针对泡沫金属模型撞击刚性壁的情形建立了两类动态压溃模型,一维冲击波模型和三维细观有限元模型。以连续介质框架下的应力波理论为基础,并假定了刚性-非线性塑性硬化的加载和刚性卸载的本构关系,建立了一维冲击波模型,给出了冲击波波后应变与冲击时间的隐式表达式。使用有限元软件模拟了闭孔泡沫金属模型的动态压溃过程,并基于最小二乘法计算局部变形梯度和局部应变得到了三维泡沫结构的应变场。通过理论解和数值解的比较,发现该理论模型能够较好的预测泡沫金属杆撞击刚性壁的力学行为。
我们还对泡沫金属材料在动态冲击情况下的率敏感性进行了探讨。动态冲击过程中泡沫金属产生的局部变形使得实验中解耦其惯性效应和作为材料的率效应是非常困难的。为了研究泡沫金属率效应的影响,泡沫金属细观有限元模型以一定的初始冲击速度直接撞击固定的刚性壁,借助于细观模型的应变场的计算方法,可以获得泡沫金属模型动态冲击下的应变分布。计算结果表明,泡沫金属模型的动态压实应变随着冲击速度的增加而增大,且细观有限元模型的动态压实应变要大于采用准静态本构关系定义的动态压实应变和采用R-P-P-L模型定义的压实应变。根据冲击波理论,反推出冲击波波阵面前方的应力值,发现冲击波波阵面前方的应力值大于准静态情况下的初始压溃应力值。最后得出了泡沫金属模型的动态下的应力-应变状态,并发现动态应力-应变状态和准静态情况下的名义应力-应变关系有显著差异的。通过分析细观模型的变形模式给出了这种差异性的解释,当前的结果表明变形模式的差异是导致泡沫金属材料加载速率敏感性的主要原因。
Compared with traditional metal materials, metallic foams have super light, excellent energy absorption capacity, electromagnetic shielding and novel thermal properties because of the variability of their meso-structures. The irregularity and defects of the metallic foam meso-structures maybe have large influence on the mechanical properties of metallic foams. It is difficult to determine the influence of the irregularity and defects on the mechanical properties of metallic foams in experiment. However, the numerical simulation method can depict the problem conveniently. The relation between the irregularity/defects and the mechanical properties of metallic foams can give theoretical guidance for the application of metallic foams and their composite structures. Under dynamic impact condition, local inertia effects and the definition of the relevant parameters associated with the dynamic response are usually coupled together, and it is hard to decouple them using SHPB experimental equipment because of the deformation localization of the metallic foams. In this paper, using the shock wave theory, we analyse the dynamic impact behaviour of metallic foams. Then, based on the local strain calculation method, the dynamic stress strain states of metallic foams under dynamic impact can be obtained.
Based on the3D Voronoi technique, we construct a3D open-cell metallic foam model and a3D closed-cell metallic foam. The relations between the irregularity of metallic foams and the cell volume distribution are also obtained. In order to guarantee the validity of the finite element models, we analyse the convergence of the characteristic length of the finite elements. The simulation results show that the plateau stress of open-cell/closed-cell metallic foams increases with the increase of the metallic foam cell number, when the number of metallic foam cells is small; then the plateau stress trends to a fixed value. This means that the size effect of the metallic foams is negligible, when the number of cells reaches a certain level. We also use the simulation method to explore the relation between the irregularity of open-cell/closed-cell metallic foams and the mechanical properties of metallic foams. The results show that influence of the irregularity of metallic foams on the mechanical properties of metallic foams is unapparent.
In this thesis, we investigate the micro-inertia effect and dynamic plastic Poisson's ratio of closed-cell/open-cell metallic foams. The simulation results indicate that the plastic Poisson's ratio varies with the nominal strain, its peak value decreases as the impact velocity increases and the Poisson's ratio increases with the relative density increasing. The micro-inertia effect plays little role in enhancing the plateau stress of metallic foams. A significantly decreasing influence of lateral constraint on the crushing stress with increasing loading rates has been found for a closed-cell metallic foam. This interesting phenomenon can be interpreted by the micro-inertia effect and the decrease of Poisson's ratio in dynamic compression.
In this thesis, we also explore the relation between the inner gas pressure of closed-cell metallic foams and theirs mechanical properties in quasi-static crushing condition. The simulation results show that the stress increment affected by the inner gas pressure is obviously in low-density closed-cell metallic foams. The stress increment also increases with the increase of the nominal strain. When the inner gas pressure reaches a high level, the gas pressure can affect the Poisson's ratio of the metallic foams. Finally, we give the estimated formula between the inner gas pressure and the stress increment from the simulation results.
Two models are developed for describing the dynamic crushing of metallic foams striking a rigid wall:a one-dimensional shock model and a3D cell-based finite element model. The shock model is proposed by using the continuum-based stress wave theory and assuming the rigid-nonlinear hardening plastic constitutive relation of foam, and then an implicit expression for determining the relation between local strain behind the shock front and the impact time is obtained. The dynamic crushing process of cell-based finite element model is simulated by using the ABAQUS/Explicit software. The local strain field is obtained by using the least squares method to calculate the deformation gradient and local strain. By comparing with the simulation results, the shock model presents good predictions of the stress and the strain behind the shock front.
We also explore rate sensitivity of metallic foams under dynamic impact. Current experimental techniques make it difficult to obtain the dynamic constitutive relations of cellular metals since local inertia effects are not easily decoupled from the definition of the relevant parameters associated with the dynamic response. In order to study this effect, a cell-based metallic foam is considered in which the foam specimen impinges normally with an initial velocity, Vo, on a stationary rigid wall. Using the local engineering strain calculation method, we can obtain the local strain distribution of the metallic foam under dynamic impact. The simulation results show that the dynamic densification strain increases with the increase of impact velocity and is larger than the quasi-static densification strain used in the R-P-P-L shock model. According to the shock wave theory, the stress ahead of the shock front can be obtained, which is found to be larger than the initial crush stress in the quasi-static compression. Finally, it is found that the dynamic stress-strain states are obviously below the quasi-static stress-strain relation. This difference is explained by analysing the deformation modes at the cell level. The present results reveal that the difference of deformation modes is the main reason of the loading-rate sensitivity of metallic foams.
引文
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