科研之友
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摘要
Weight functions are a critical component of a damage tolerance fracture control plan in that they allow the stress intensity factor to be computed quickly from the stress along the uncracked crack line. The traditional method to compute weight functions is to use several (2-4) reference stress solutions or auxiliary conditions to develop the coefficients in a series solution. While this method has been shown to provide good results in many scenarios, the truncated series provides a source of error that is difficult to quantify and the method requires multiple high-quality reference solutions or other auxiliary information. In contrast, the WCTSE method presented here, provides a method to accurately and efficiently develop the weight function for an arbitrary geometry and loading scenario from a single complex variable finite element solution without other reference solutions or auxiliary information. The complex Taylor series expansion method is used within the finite element formulation to obtain the derivatives of the crack opening displacements with respect to crack length directly from the finite element analysis. These derivatives allow the direct evaluation of the weight function. The method requires a small perturbation of the crack length along the imaginary axis; the real coordinate mesh is unaltered. Since the real coordinate mesh is unaltered, standard finite element meshes and meshing algorithms can be used. Given that the error in the weight function is controlled by the accuracy of the mesh, typical convergence tests can be used to obtain high confidence in the weight functions. Several numerical examples are computed and compared to other well known published weight function solutions or finite element (J integral) or boundary element solutions.
- 出版日期2012-5
