THE MULTI-STEP POSITIVE APPROACH FOR SHEET METAL FORMING SIMULATION BASED ON THE QUASI-DEFORMATION THEORY

The idea of incremental theory is introduced to propose a multi-step positive approach based on deformation theory. The basic principle is that on the basis of one step positive approach, several intermediate states are added properly, and the strain increments in each state are calculated in sequence. The iterative solutions are carried out using the Newton-Raphson method in the total form which is generated by accumulating the strain increments in the form of component. The calculation result is accumulated into the calculation in the next intermediate state in the form of strain component to calculate the corresponding elastoplastic constitutive matrix. Thus the influence of load history can be taken into account during the calculation, and the precision of the final simulation result can be improved. The multi-step experimental scheme of square box is designed. The circular elements are marked on the flat blank using electric corrosion method. Five square box samples of different steps including 10mm, 20mm, 30mm, 40mm, 50mm are achieved. The deformation of element is measured by optical measurement, and then the strain can be calculated. The thickness of blank in different steps is measured using ultrasonic thickness gauge. Through comparison of the calculation precision and calculation efficiency among several different algorithms, the multi-step forming positive algorithm is proved valid.