Materials often exhibit significant damage or failure when the impact test conditions of scaled model are complex and the impact energy is high. Due to the influence of material distortion, it is usually hard to strictly satisfy the geometric similarity for model test. Meanwhile, the damage or failure behavior of materials further introduces more complex similarity requirements, and thus it is much more difficult to fully consider the thermal-visco-plastic constitutive properties as well as damage or failure characteristics of materials in model test and achieve comprehensive similarity. In order to overcome this problem and further expand the similarity law of the damage or failure behavior of materials, the present study proposes a set of material dimensionless numbers related to material failure strain and analyze its physical meaning. Subsequently, the specific expression of these dimensionless numbers corresponding to the failure criterion is deduced as an example, which reflects the essential properties of the dependency of material failure strain on stress triaxiality, strain rate and temperature, etc. The rationality and practicability of new dimensionless numbers are verified based on several numerical simulation results involving various impact conditions, including Taylor bar impact test with moderate velocity, flat-nosed rigid projectile impacts medium target, and ogive-nosed rigid projectile perforates thin target. Based on these results, the basic method of selecting the optimum similitude material in scaled model test considering both thermal-visco-plasticity and damage or failure behavior of materials will be proposed. It is demonstrated that after the satisfaction of thermal-visco-plastic similarity of materials, the scaled model can accurately replicate the deformation and damage or failure characteristics of prototype structure by further introducing the failure similarity criterion of materials, and selecting the optimum similitude materials with both thermal-visco-plastic similarity and failure similarity. Meanwhile, in the case that the damage or failure behavior of structure is more significant than its plastic deformation, the requirement from failure similarity is more important, and correspondingly the appropriate relaxation for thermal-visco-plastic similarity of materials is allowed. The proposed dimensionless numbers considering material damage or failure properties, as well as the corresponding selection method for optimum similitude materials, are of great significance for accurately predicting the dangerous points in prototype structure under impact and taking protective measures accordingly by the scaled model test.
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