Dynamic Stress-strain State Of Cellular Materials And Its Anti-blast Property

Cellular metal materials have been extensively used as core materials for anti-blast sacrificial claddings and impact energy absorbers in the field of vehicles, high-speed train and aerospace engineering for their lightweight and superior energy absorption capability. The quasi-static compressive deformation of cellular metal materials can be approximately subdivided into three stages, i.e. linear-elastic, long plateau and densification stages. Moreover, the quasi-static stress-strain curve can be treated as the constitutive relation under quasi-static loading for its behavior is independent of specimen’s size. Under high loading rates, cellular materials have typical features of deformation localization and stress enhancement. However, the dynamic response of cellular materials is still unclear. Recently, Zheng et al. obtained the dynamic stress-strain states of cellular materials with the aid of the mesoscopic finite element model and the local strain field calculation method, and proposed a dynamic rigid-plastic hardening (D-R-PH) idealization to characterize the dynamic stress-strain states. However, the D-R-PH shock models are only suitable for high velocity loading and this insufficiency may limit the application range. The issue of the stress-strain states of cellular materials under moderate velocity impact is still open. The deformation mode of cellular materials under moderate velocity is not a single mode, which could not be characterized by the shock wave model. In this paper, the dynamic stress-strain response of cellular materials is investigated by using the wave propagation technique, which does not rely on the pre-assumed constitutive relation of specimen or the shock wave assumption. We reveal the local stress-strain curves under different impact velocity, and obtain a unique dynamic stress-strain state curve of the cellular material. In addition, we investigate the dynamic response of cellular sacrificial cladding under blast loading, and obtain the empirical solution and the asymptotic solution of critical length of cellular sacrificial cladding.The wave propagation technique is to determine the dynamic constitutive relation of materials from the information of stress wave propagation combining with initial or boundary conditions, and its main advantage is that no pre-assumed constitutive relationship is required. Based on the mesoscopic finite element model of cellular materials, the dynamic response of cellular materials is investigated by the wave propagation method. Based on a virtual "Taylor bar" test, a series of local dynamic stress-strain curves under different loading rate are obtained by the "lsv+nv" Lagrangian analysis method, which is one of the wave propagation techniques. The local stress-strain curve exhibits elastic loading, plastic deformation and elastic unloading stages. A unique dynamic stress-strain state curve of the cellular material is summarized by extracting the critical stress-strain point just before the unloading stage on the local dynamic stress-strain history curves, and the result shows that the dynamic stress-strain states are independent of the initial loading velocity. It is evident that the stress-strain states of cellular materials are deformation-mode dependent (quasi-static, transitional and shock modes). An obvious difference is found between the dynamic stress-strain states and quasi-static ones under the transitional and shock modes. Under shock mode, the phenomenon that dynamic strain is larger than the quasi-static strain under the same stress level illustrates that the cellular material is collapsed more tightly under shock mode than that under quasi-static mode. Under moderate mode, the phenomenon that the dynamic stress is higher than the quasi-static stress under the same strain level reveals that the local initial effect under moderate mode cannot be neglected. Finally, the loading-rate and strain-rate effects of cellular materials are investigated. It is concluded that the dynamic initial crushing stress is mainly controlled by the strain-rate effect, but the dynamic densification behavior is velocity-dependent.Under high loading rate, the dynamic behavior of cellular materials can be well characterized by the shock model. However, several shock models are determined based on the quasi-static stress-strain curve of cellular materials, and do not consider the dynamic effects of cellular materials. The shock speed vs. impact velocity and the strain behind the shock wave vs. impact velocity Hugoniot relations were investigated to analyze the effectiveness and correctness of several shock models for the cellular materials. It is demonstrated that the dynamic rigid-plastic hardening (D-R-PH) idealization is more suitable for the cellular materials under high loading rate. Based on the conservation conditions across the shock wave, the thesis introduces the experimental determination of the D-R-PH idealization for the cellular material.In the application, cellular materials possess superior cushioning and anti-blast capability. The anti-blast behavior of cellular sacrificial cladding is investigated based on a continuum-based nonlinear plastic shock model (rate-independent, rigid-plastic hardening (R-PH) model). Under a triangle blast loading, a shock model is developed and an equation governed the shock wave propagation in the sacrificial cladding is obtained. Results reveal the shock wave propagation characteristics in the sacrificial cladding. The influence of the attached mass and the strength of blasting load on the anti-blast capability of cellular sacrificial cladding are studied by the parametric analysis. Comparison of sacrificial cladding structure designs based on the rigid-perfectly plastic-locking (R-PP-L) model and the R-PH model is carried out and the applicable conditions of the two shock models are given. The target parameter of cellular sacrificial cladding in engineering is its critical length, which is minimum length to fully absorb the energy induced by the blast loading. Dimensional analysis is employed to study the critical length of cellular sacrificial cladding and an empirical expression is determined by the controlling valuable method. An asymptotic solution is also obtained by applying the regular perturbation theory. The result reveals that the asymptotic solution of the critical length is unhandy for engineering design since its complex mathematical form. Thus, the empirical solution could be considered as a design guide for the blast alleviation of cellular sacrificial cladding. Finally, the design criteria of cellular sacrificial cladding based on the R-PH shock model is verified by a cell-based finite element model.