Failure of weld joints under single and cyclic pulsating loading conditions is under consideration. A weld joint is modeled by three-layer composite. Stepwise propagation of the internal I mode crack under cyclic loading is investigated. Delamination of bimaterial composed of two structured materials is considered when a crack is located at the interface between two media. Loads under pulsating loading conditions are studied for elastic-plastic material. For analysis of this process, diagrams of quasi-brittle fracture of solids under cyclic loading conditions are proposed to be used. 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.