Analysis of methods for constructing true deformation diagrams of elastoplastic materials under large deformations

To study the deformation and strength properties of materials, it is important to use an experimental and computational approach that allows taking into account the ununiaxiality and heterogeneity of the stress-strain state without accepting simplifying hypotheses. True deformation diagrams are constructed using an iterative procedure of updating the strain intensity-stress intensity relation proportionally to the relative difference in the values of axial forces as obtained numerically and experimentally for an inhomogeneous stress-strain state, accounting for necking, up to rupture. The procedure requires multiple solutions of the problem, which is a time-consuming computational task. Two scenarios of analyzing the boundary-value problem are considered. The first scenario involves analyzing the entire direct problem over the whole loading interval; in the second one, the entire loading process is subdivided into several intervals defined by discrete values of an experimentally found generalized displacement-generalized force relation. At each small interval, a deformation diagram is constructed, using a nonlinear extrapolation procedure. At the end of each interval, the difference between the calculated and experimentally determined generalized forces is checked, and the stress intensity value is iteratively updated. The presented numerical studies show that constructing a deformation diagram with accuracy less than 1% according to the first scenario required 5-10 repeated analyses of the direct problem, whereas in the second scenario not more than two direct analyses suffice. Monotonous convergence and computational efficiency of the proposed iterative algorithms are shown for a number of tasks: stretching solid cylindrical rods and bolts M8 with smooth and threaded working parts. Based on the experimental and computational approach, the true deformation diagrams for steels 12H18N10T, 10HSND and St35 up to destruction are determined.