泡沫金属材料唯象动态本构关系研究

Metallic foams have been considered as a candidate energy absorption material because of their large deformation at nearly constant plateau stress combined with low resilience. The compressive behaviour of metallic foams is dependent on the hydrostatic stress states, and a single uniaxial experimental test is not enough to completely characterize the material behaviour. However, the experimental results of metallic foams show noticeable scatter in data. And arbitrary stress states are hardly feasible in experiments. So it is difficult to obtain some important constitutive parameters such as plastic poisson's ratio, bulk modulus based on experimental results. In this study, a 3D discrete FE model for real closed-cell aluminium foam specimen fabricated via the powder metallurgy foaming technique is constructed by employing the microfocus X-ray CT system, the 3D reconstruction program and the commercially mesh generation program. The cell-wall material properties are precisely determined by comparing the computed uniaxial compressive stress versus strain curves with the measured ones in tests. By changing the boundary conditions of the closed-cell aluminium foam specimen, various stress states including uniaxial, hydrostatic and proportional/non-proportional compressive loading are realized. Based on the numerical results, the phenomenological constitutive parameters of crushable foam models are analyzed quantitatively. With theoretical and numerical analysis as well as experimental tests, the influence of the material microstructure, porosity and porosity radius on properties of the stress states is presented. At the same time, the relationship between the porous material dynamic properties and its porosity as well as the stress-strain-time constitutive law are established phenomenologically. It reveals that the damage mechanism is closely associated with macroscopic properties from the point of the microstructure of metallic foams. It is expected that this project can provide a theoretical and technical foundation for all kinds of civil and military applications of the metallic foams.

泡沫金属在受压时具有低应力水平、高效吸能的特点，是用作轻质防护结构的优良材料。但是，由于泡沫金属的多轴大变形压缩实验难以实施，目前对其多轴力学行为的研究很不充分，一些非常重要的本构参数如塑性泊松比、体积模量等都难以确定。本项目拟基于真实闭孔泡沫铝材料的显微CT扫描影像信息，通过逆向建模方法构建不同相对密度闭孔泡沫铝的三维细观有限元模型，采用数值模拟和单轴实验测试相结合的科学方法逆向反推孔壁材料的弹塑性本构参数，设置合适的边界条件模拟计算得到闭孔泡沫铝的多轴加载数据，进而研究确定闭孔泡沫铝本构参数与相对密度间的定量函数关系，描述不同加载速度下闭孔泡沫铝材料的动态力学性能对其相对密度的依赖关系，建立泡沫金属材料唯象动态本构模型，从泡沫金属材料细观结构上揭示其破坏规律和机理及与宏观力学行为间的关联。本项目的研究将为轻质多孔金属材料在民用和军用工程中的广泛应用提供理论基础和技术支撑。

本项目采用理论分析和数值模拟方法，对闭孔泡沫铝在多轴加载及动载荷作用下的力学行为及本构关系开展研究。在闭孔泡沫铝的唯象本构关系中，塑性泊松比是一个十分关键的参数，本项目建立了闭孔泡沫铝的3D-Voronoi随机细观模型，深入研究了泡沫铝弹塑性泊松比随轴向对数应变的变化规律及其特征点的物理意义，并对其在闭孔泡沫铝唯象本构关系中的作用进行了验证。基于各向同性可压缩泡沫本构模型框架，考虑不同加载速率下闭孔泡沫铝的动态屈服特性，修改和完善了泡沫金属唯象率相关的本构模型。设计并制备了泡沫铝芯层和金属空心小球芯层两种夹芯球壳试件，进行了爆炸冲击载荷作用下结构抗冲击性能的试验和数值计算，重点研究了泡沫铝夹芯球结构对爆炸冲击波的削弱作用及冲击波压力衰减的机理。研究结果发现，在结构框架尺寸与质量相同时，内面板薄外面板厚的夹芯结构具有更好的吸能特性；负梯度泡沫夹芯结构、并列型小球夹芯结构、小半径小球夹芯结构具有更好的抵抗爆炸载荷和吸收冲击能量的性能；金属空心小球夹芯结构的整体强度更高，而泡沫铝夹芯结构能更充分地发挥芯层的缓冲性能。开展了负泊松比金属蜂窝夹芯结构的泡沫铝子弹冲击试验，结合有限元数值模拟研究了负泊松比金属蜂窝材料在多种压缩速度下的失效模式和能量吸收机理。结果表明，负泊松比蜂窝压缩变形模式不同于正泊松比蜂窝材料，传统的名义应变计算方法无法准确描述负泊松比蜂窝压缩行为，需要考虑负泊松比收缩效应，并且负泊松比效应会增强材料动态压缩过程中的惯性效应。