Scaled models for failure under impact loading

Small-scale experimentation is recognised to play an important role in the investigation of the behaviour of large-scale structures. Presently however, there exists no known procedure for analysing structures involving damage or failure by means of scaled experiments when high-rate impact loading is involved. The principal problem impeding the scaled approach is that similarity seldom exists for high-rate dissipative problems and consequently dimensional analysis provides an ineffective framework for experimental design and analysis. This paper is concerned with the application of the finite similitude theory which scales experiments by means of space distortion. Although finite similitude suffers many of the limitations of dimensional analysis it has one principal advantage, i.e. it is able to cater for inexact similitude where sources and effects of mismatch can be quantified. This feature is exploited in the work to answer the open question whether it is possible to determine the failure response of structures subjected to high rate loading by performing experimental tests on scaled structures manufactured with different materials. The efficacy of the proposed methodology for scaled experimentation is tested by means of numerical analysis on a number of well-known test cases, which are supported by experimental evidence. In particular the perforation of circular plates and the Taylor bar impacting on a rigid wall are analysed using the commercial finite element software package Abaqus. The Johnson-Cook thermo-viscoplastic constitutive equation together with the Johnson-Cook damage model are used to describe yielding, strain hardening, strain rate effects, thermal softening and material failure. It is revealed in the paper that although exact similitude is not achievable the results of the full-scale model can be predicted to good accuracy by means of scaled experimentation founded on finite similitude theory.