13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- given in Ref.[10], two minutes is enough to complete a residual strength analysis by using the present method. Furthermore, once the crack growth analysis program for a given crack configuration is available, there is no modeling time. These advantages are very useful for parametric analysis. (a) Schematic geometrical dimensions for five collinear cracks 80 90 100 110 120 130 140 150 160 170 180 190 0 10 20 30 40 50 60 70 80 90 Crack tip position, mm Load, KN : Test : Prediction 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 Crack tip location, mm Load, KN : Test : Prediction (b) a1=90mm, l1=6mm, l2=15mm; (c) a1=60mm, l1=15mm, l2=60mm; Fig.11 Experimental and predicted Δa-P curves for sheet with five collinear cracks 4 Conclusions An analytical approach, the weight function method for dealing with the MSD problems is presented in this paper. The study leads to the following conclusions: 1．For special collinear crack configurations which can be treated as a single crack problem, such as three collinear cracks with strip yield plastic zones critical coalescence in a finite sheet, the strip yield model solutions can be easily solved by the weight functions for a single crack. The results are in perfect agreement with FEM results. 2．Weight function formulas for more general collinear cracks have been derived, which are markedly different from those for the single crack cases. With the derived weight functions, the key fracture mechanics parameters, stress intensity factors and crack opening displacements for the three collinear cracks under arbitrary load conditions are easily computed by a simple quadrature. 3. A unified method based on the weight function for a single crack is proposed to solve the strip yield models for collinear cracks in infinite and finite sheet. The method is used to solve the strip yield models for two and three symmetrical collinear cracks in infinite and finite sheets to obtain plastic zones, crack opening displacements and stress distributions along the elastic ligaments between cracks. These results are widely compared with exact solutions and FEM results, perfect agreements are observed. This method is simple, efficient, reliable, and versatile. 4. Combined with CTOD criterion, the WFM is used to predict the stable crack growth behaviors and residual strengths of MSD configurations in finite-width sheets subjected to monotonic loading. The solution efficiency is significantly better than the FEM. In summary, the present WFM for MSD provides a powerful analytical approach for fracture mechanics analyses and residual strength assessment for MSD-contained aircraft structures.
RkJQdWJsaXNoZXIy MjM0NDE=