Scaling of bi-material sandwich panels subjected to impact loadings

Abstract

Scaling is a widely used concept in impact and explosion engineering which is mainly utilized to predict the response behaviour of large-scale mechanical structures by conducting experiments on scaled trial models. However, the practical application of currently available conventional scaling methodologies for impact and explosive processes are significantly restricted by their inability to properly capture the scale effects of strain rate and strain hardening. Also, they are suffering from an insufficient number of independent degrees of freedom. Furthermore, the zeroth-order finite similitude theory, which can annihilate the non-scalability of rate and hardening effects, doesn’t provide us with efficient scaling methods when the investigated structure is made out of different materials. More precisely, the zeroth-order finite similitude theory and the classical dimensional analysis, which are suffering from a limited number of independent degrees of freedom, cannot scale the elastic-plastic behaviour represented by different parts of a structure made out of different materials. In other words, classical scaling methodologies including dimensional analysis and even the zeroth-order finite similitude theory cannot fix two different features having the same unit using different degrees of freedom, which make them useless for structures made of more than one material such as bi-material sandwich panels. In the presented paper, a new scaling methodology is developed based on the recently proposed first-order finite similitude theory which for the first time enables us to capture the rate dependent plastic behaviour of an impacted structure made out of two different materials. A sandwich panel made of two different materials which is subjected to an impact loading is considered as the case study in order to investigate the efficiency of the proposed first-order based scaling technique. The numerical results are determined using Abaqus finite element software in which the Johnson-Cook constitutive equation is utilized to take into account the rate and hardening effects on the initial yield stress. The results reveal that the behaviour of impacted full-scale bi-material sandwich panels can be predicted with a high accuracy when the extra degree of freedom provided us with the first-order finite similitude (i.e. R₁) is set to vary between −1 and 1 (i.e. $-1\le R_1\le 1$ ). Furthermore, it is found that the pure mechanical and thermo-mechanical behaviour of the impacted core honeycomb are highly accurately predicted using scaled-down trial models which are made from dissimilar materials and designed based on the zeroth-order finite similitude theory.