Similarity error of scaled model under impact

When different materials are used to substitute prototype material in scaled model, the error derived from complex thermal-visco-plastic effects of materials, including strain hardening, strain rate, temperature softening, etc., would lead to distortion of traditional similarity law. Though some scaled methods to treat the distortion caused by different materials have been developed in recent two decades, it is still hard to quantitatively estimate and control the corresponding similarity error of scaled model. To essentially overcome this basic problem, the definition of similarity error scope (SES) for input parameter and output response of scaled model is introduced in the present paper for the first time, and the mathematical relation between SES for input parameter of scaled model and material dimensionless numbers (i.e., dimensionless phase diagrams of material similarity) is derived for complex thermal-visco-plastic effects of materials, and then the general transfer function of SES from input parameter to output response is further derived. The rationality and practicability of proposed relation are verified based on related analytical models and numerical simulations, involving three impact conditions, i.e., a clamped beam subjected to transverse pulse velocity impact, a thin spherical shell subjected to radial pulse velocity impact and a Taylor bar impact test. Related result shows that the relation between SES for input parameter and average phase diagram difference is almost linear, while the relation between SES for output response and that for input parameter usually displays an obvious nonlinear feature. In practical engineering application, by selecting the optimum similitude material within proposed error tolerance, SES for structural response can be obtained directly, and thus quantitative estimation and accurate control of similarity error of scaled model can be achieved.