A new method of identification of constitutive equations according to the results of technological experiments

Abstract

A method is proposed which allows one to search for a solution to inverse problems of identifying constitutive relations from the results of technological experiments. The method uses simplified mathematical models of technological plastic metal forming processes based on the membrane theory of shells, which allows for calculations of material constants K and m entering Backofen’s constitutive relation for superplasticity from the results of experiments carried out directly on a technological equipment. The method differs from others by the fact that for its implementation results of only two test formings of hemispherical domes at a constant gas pressure are sufficient. The set of experimental data include gas pressure, forming time and thickness in the pole of the dome. The method consists of three steps: calculation of initial material constants K and m; fitting of coefficient m* until the coincidence of computed value of the thicnkness at the dome pole with experimentally determined value; correction of the value of constant K*. Finite-elements simulations of superplastic forming (SPF) are done by means of ANSYS software. Computational model of material is considered in the framework of creep theory. Time dependencies of relative dome height and relative thickness of semispheres at the dome pole using approximate formulas and simulations using ANSYS are plotted. The method is verified on an example of superplastic forming of semispheres with 35 mm radius from sheet blanks of titanium alloy VT6 (analogue of Ti-6Al-4V) with thickness of 1 mm to a cylindric matrix with diameter 70 mm and height 35 mm with entry radius of 1 mm at two constant values of gas pressure 0.5 and 0.7 MPa. The forming temperature was equal to 900°C. As a result of validation, agreement of experimental and computational data acceptable for engineering calculations has been obtained.