基于逆向建模方法的闭孔泡沫铝多轴唯象本构参数研究

Closed-cell aluminum 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 the 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 closed-cell aluminum 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 alloy 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 foam specimen, various stress states including uniaxial, hydrostatic and proportional loading compression are realized. Based on numerical results, the phenomenological constitutive parameters of several crushable foam models are analyzed quantitatively. The results of this project provide technical and theoretical support for ultra-light porous sandwich protective structure engineering design. The methods of this project also have the significant reference value to mechanical behavior research on the other materials featuring irregular shape and random distribution.

闭孔泡沫铝在受压时具有低应力水平、高效吸能和低回弹的特点，是用作轻质防护结构的绝佳材料。但是，由于闭孔泡沫铝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，并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，再改变边界条件计算获得闭孔泡沫铝可信的多轴加载数据，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。本项目的研究成果能够为超轻多孔夹芯防护结构的工程设计提供技术参考和理论支持。本项目的研究方法对于其它具有不规则形状和无规律分布材料的力学行为研究有重要的借鉴价值。

本项目以填充闭孔泡沫铝的复杂超轻夹芯结构的吸能防护设计为导向，直面目前多孔金属多轴加载实验难以实施和唯象本构参数难以确定的现状，以单轴实验结果为基础，使用三维细观有限元模型定量研究闭孔泡沫铝在多轴压缩载荷作用下的大变形力学行为，通过逆向思路解决闭孔泡沫铝三维细观有限元模型建立过程中遇到的复杂几何构型和难以测量的孔壁材料本构参数两大难题。（1）基于闭孔泡沫铝的Micro CT断层扫描影像信息，使用逆向工程方法重构了闭孔泡沫铝三维细观实体几何模型并生成六面体剖分单元。根据单轴压缩实验结果拟合了孔壁材料的弹塑性本构参数。（2）改变三维细观有限元模型的边界条件，研究了闭孔泡沫铝在多轴压缩应力状态下的力学行为。通过侧面耦合单轴压缩、静水压缩和等比压缩三种边界条件，实现了闭孔泡沫铝试件11个加载路径的大变形压缩过程。各应力状态下闭孔泡沫铝试件的初始平台应力基本重合。随着轴向应变的增大，泊松比经历了增高-降低-再增高的“S”型变化过程。对于静水压缩，ABAQUS的各向同性强化可压缩泡沫本构模型屈服面会发生非常严重的偏离，Chen-Lu本构模型屈服面会略微低估静水压缩的屈服应力，而体积强化本构模型的屈服面有着很好的精度。（3）基于各向同性可压缩泡沫本构模型框架，定义特征应变为塑性体积应变，采用两参数对称椭圆型屈服面、体积强化和非关联塑性流动法则，参照图形返回应力更新算法，编写了ABAQUS的VUMAT接口子程序，并加入破坏准则。根据三维细观有限元模型计算结果确定了闭孔泡沫铝的本构参数，通过进行不同应力状态下试算，验证了VUMAT接口子程序的正确性和可靠性，可以为泡沫金属用于防护吸能工程设计提供技术支持。