| In this paper, fracture problems of surface cracks are researched which are on the welding structure used widely in engineering practice, by the method of combining the line-spring model and weight function. The main achievements are summarized as follows:1,Based on the theory of line-spring model, the transform for the residual stress from nonlinear gradients to linear ones is realized with the weight function. Consequently, the problem of applying the line-spring model to nonlinear stress is solved, which formed theoretical foundation for the whole work in this paper.2,The line-spring model for single surface crack in a residually stressed plate is established. Based on the Reissner's plate theory along with continuously distributed dislocation thought, the governing equations and the expression of stress intensity factor are formulated with integral transfer method. The numerical results, which are resolved by Gauss-Chebyshev method, are compared with that of finite element method. It is shown that the results are in good agreement and that the model for surface cracks in residual field is reasonable and reliable.3,The line-spring model for multitudinous coplanar surface cracks in a residually stressed plate is established. Based on the continuously distributed dislocation solution of multitudinous coplanar through cracks in infinite Reissner's plate, the governing equations of the problem about multitudinous coplanar surface cracks is derived. After the model is testified, the intensity factors of some examples are given and compared with the intensity factors that do not include residual stress.4,Take some pressure vessel for engineering example. The above theoretical achievements are applied to the fracture assessing of the vessel in the paper. The fracture problems of axial surface cracks, annulus surface cracks and multitudinous coplanar axial surface cracks that may be led by welding faults are fully researched. At last, a couple of useful conclusions are gained.
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