Failure of welded joints under single and cyclic loading conditions is under consideration. A welded joint is modeled by three-layer composite. Stepwise propagation of the internal I mode crack under cyclic loading is considered. Delamination of bimaterial composed of two structured materials is considered when a crack is located at the interface between two media. Loading is studied for elastoplastic material. For analysis of this process, it is proposed to use diagrams of quasi-brittle fracture of solids under cyclic loading conditions. One of curves of the proposed diagram bears resemblance to the Kitagawa-Takahashi diagram. Estimates of average dimensionless velocity of stepwise crack propagation per loading cycle have been obtained in an explicit form for plain specimens of finite width. The relations derived for the average crack growth rate can be considered as structural expressions for plotting Paris’ curves.