Similitude theory helps engineers and scientists to accurately predict the behaviors of real systems through the application of scaling laws to the experimental results of a scale model related to the real system by similarity conditions. The theory was applied when studying the deep drawing process of a bathtub made from cold rolled low carbon aluminum-killed steel from the point of view of material limits. The bathtub model was created on the basis of geometric, physical, and mechanical similarity on a scale of 1:5. Thus, simulations and physical models were created. The simulation model was used to verify the combination yield locus/hardening law on the basis of comparing the thickness change. As a result, Hill 48/Krupkowski showed the minimal deviation by comparing data evaluated from numerical simulations and that measured on the physical model. Additionally, material anisotropy was modelled when virtual materials were defined from experimentally measured values of the plastic strain ratio. As an outcome, extra deep drawing quality steel with an average plastic strain ratio of rm ≥ 1.47 and an average strain hardening exponent of nm ≥ 0.23 must be used for the deep drawing of the bathtub.
The elastic counterpart of the plastic strain ratio is derived from ultrasonic data measured on twenty
commercial deep drawing steels. It is shown that the observed variations in plastic r are related to the
evolution of texture, and are not affected either by the elastic range of deformation or by the
propagation of Lüders bands. Further quantitative analysis suggests that the elastic strain ratio,
determined non-destructively, can be used to predict plastic r-values by means of an empirical
relationship.
Al-Mg alloys developed for auto body sheets with different Cu contents were fabricated in the laboratory scale. The effects of Cu content on the microstructures, formability and Portevin–Le Chatelier(PLC) effect of the alloys were investigated by polarizied optical microscopy and room temperature tensile testing. It has been found that with increasing Cu content, there was little change of the strain hardening exponent, but the plastic strain ratio and limiting drawing ratio increased firstly and then decreased. A quantitative statistical analysis of the characteristics of the PLC effect was made, including the stress drop and the reloading time, which follow a common linear relationship with plastic strain, and the increase rate of stress drop and reloading time was bigger with more Cu content. A detailed discussion of the corresponding mechanism of Cu and Cu-containing precipitates on the dynamic strain aging(DSA) was made.
Physical Modelling and Numerical Simulation of the Deep Drawing Process of a Box-Shaped Product Focused on Material Limits Determination