Мodelling of a fracture process in welded joints

A computer modelling of crack propagation in welded joints is carried out. The strength of welded joints having a crack-like defect is analyzed. The welded joint is modelled as a two-layer structured composite which contains a straight sharp internal crack in I mode. The fracture process of such a composite is described using the modified model of Leonov-Panasyuk-Dugdale. The model employs an additional parameter, equal to the diameter of the plastic zone (width of the pre-fracture zone) of the weakest material. The solid is modelled using the elastic-perfectly-plastic material model with a limited relative lengthening. The class of materials under consideration includes low-alloy steels, used in engineering structures working at temperatures below the cold brittleness temperature. The case where elastic properties of the materials coincide but the strength is different is analyzed in detail. Under conditions of a low-scale yield, where the stress field near the crack tip possesses a singular component, we suggest using a two-parametric discrete/integral strength criterion. The deformation-based fracture criterion is formulated at the tip of the real crack, whereas the force-based criterion for the normal stresses with averaging is formulated at the tip of the model crack. The length of the real and model cracks differ by the length of the pre-fracture zone. Since the welded material is weaker than the basic material, the plastic zone is localized in the weakest material. A numerical simulation of extension of plastic zones in square plates made of bi-metal is carried out for a quasistatic loading. The difference between the numerical and analytical models is that materials are analyzed which correspond to the deformation modes with both low-scale and full-scale yield of the weakest material (welded material). It is found that the results of the numerical experiments are coherent with the results obtained by the analytic model of fracture for structured materials in the crack I mode with a low-scale yield of the weakest material. The size of the plastic zone near the crack tip is estimated. Diagrams of a quasi-brittle fracture are obtained for the structured composite.