A method for converting an experimental torsion diagram for a cylindrical specimen to the stress-strain diagram of the material

The main problem with diagnostics and testing is that the overwhelming number of physical quantities cannot be measured directly. Only a limited number of physical quantities can be measured directly, the values of these physical quantities being indirectly influenced by the other (unmeasurable) parameters. Hence the problem arises to determine physical quantities by the results of their manifestations. The same problem concerns the determination of material properties in all the stages of deformation, including the softening stage. This problem is rather laborious. The complexity of the problem is that the material is physically instable at the stage of strain softening. Thus, special devises are needed to obtain material characteristics. Often, they cannot be obtained even by means of non-trivial technical tools. One of the real ways to solve the problem is the testing of special structural components followed by the conversion of obtained data into material properties. The article deals with a well-known methodology of solving inverse ill-posed problems, which was developed by A.N. Tikhonov and V.K. Ivanov. The method is based on the trial-and-error method and the concept of quasi-solution. The problem of determining the stress-strain diagram with a negative slope in the “principal shear stress - shear strain” coordinates by the diagram of torsion of a cylindrical specimen is discussed as an example. It is shown that the problem requires the solution of the first-kind Volterra integral equation. Therefore, the problem is ill-posed. The problem is reduced to a system of linear algebraic equations with an inaccurate right-hand side. After solving the system by the trapezium method, we obtain a particular sawtooth solution. The solution is regularized by a special interpretation of the trial-and-error method. Experimental data obtained from torsion of cylindrical specimens made of steel St3sp is shown in the article. The stated method is used to convert the diagram of torsion of a cylindrical specimen to the material stress-strain diagram with a negative slope.