HISTORY OF MATHEMATICS AND APPLICATIONS

Numerical evaluation of crack resistance of welded compositions made of titanium sheets manufactured in the superplasticity mode

A. K. Galimov, R. Ya. Lutfullin

Institute of Problems of Metal Superplasticity of the Russian Academy of Sciences (Ufa)

Abstract: A numerical assessment of the crack resistance of titanium alloy sheet blanks with various microstructures connected by pressure welding in the superplasticity mode is considered. The structural and mechanical model of the object under consideration is represented as a graph. Based on functional averaging, an iterative method for finding stress and strain parameters for its vertices is implemented as a generalization of Newton's method. The presented results of a mathematical analysis of the mechanics of the origin and development of cracks in a two-layer welded billet made of VT6 titanium alloy with a fundamentally different microstructure indicate the prospects of using such layered titanium compositions in critical products in order to increase their structural strength.

Keywords: graph, Newton's method, structural and mechanical model, titanium alloy, structurally inhomogeneous billet, crack resistance.

UDC: 539.5


Accepted: 17.10.2025

DOI: 10.22405/2226-8383-2025-26-4-486-495