The following two figures show the displacement vector sum (USUM) and the Von Mises Stresses, respectively:

Figure 16.13: USUM Results (Rectangular Block)

Figure 16.14: Von Mises Stress Plot (Rectangular Block)

The plot shows the maximum Von Mises stress occurring at the crack tip.

To verify the SIF accuracy obtained via the interaction integral method, the results are compared to analytical results of Newman and Raju and finite-element result of Kamaya. The results agree closely with those obtained in the references.

Because the crack exists at the center of the rectangular block, the results for half of the crack are therefore plotted in this figure, where normalized SIF = :

Figure 16.15: Normalized KI Results

The T-stress results for the semicircular surface flaw are plotted in this figure, where normalized T-stress = T-stress / σ_o :

Figure 16.16: Normalized T-Stress Results: Semicircular Surface Flaw

The following figures show the displacement vector sum (USUM) and Von Mises Stresses plot of the x-joint pipe with the warped flaw at the welded joint:

Figure 16.17: USUM Results (X-joint Pipe)

Figure 16.18: Von Mises Stress Plot (X-joint Pipe)

The SIFs of the mixed-mode 3D problem with the warped crack surface were compared with those of Rhee.[4] The comparison shows that the normalized KI, KII and KIII results agree well with the reference results near the end points, as shown:

Figure 16.19: Normalized SIFs Results: Comparison with Rhee[4]

where T is the thickness of the pipe, and the normalized distance is the distance from center of the crack along the crack front divided by half of the crack tip length.

A fine mesh (using meshing bias (LESIZE,,,,,SPACE)) at the end-point regions improves the results.

The T-stress results for the X-joint pipe with warped flaw are plotted in this figure, where normalized T-stress = T-stress / σ_o :

Figure 16.20: Normalized T-Stress Results: X-Joint Pipe with Warped Flaw