Bézier base extended isogeometric numerical method for thermo elastic-plastic analysis of crack propagation in cracked plate under welding residual stress and thermal load

A new procedure in the field of Bézier base extended isogeometric method (XIGA) has been introduced to analyze the effect of welding residual stress and thermal load on crack propagation rate and fatigue life. This new procedure is based on the constitutive thermoelastic plastic equation. The main parts of this procedure are using the B´ezier base XIGA method to calculate the redistribution of welding residual stress due to crack growth and to compute the value of stress intensity factor (SIF) in the welding residual stress field. For this purpose, the grid points of Bézier elements (with C0-continuity) around the crack line and the crack tip are identified by the level set representation. Then, discontinuous enrichment functions are added to the isogeometric analysis approximation. Thus, this method does not require the re-meshing process. The results show that there is a good agreement between the results of proposed numerical method and the Hole-Drilling Strain-Gage method. The interaction integral method has been used to extract SIF. The effects of welding residual stress and thermal load on the SIF are considered using the superposition method. Also, the Walker equation has been modified to calculate the fatigue life caused by thermal loading and welding residual stress. The results display a good agreement between the proposed method and the finite element method. Due to the advantages of the Bézier based XIGA method, which eliminates parametric space and allows the precise addition of enrichment functions to the basis functions of cracked elements (crack line or crack tip), the obtained results are highly accurate that shows this method is effective for analyzing discontinuous problems