Local material yielding
As soon as the equivalent stress level at a point of the pipeline reaches the yield stress. Local yielding will occur in case the material-non-linearity module has been activated (Material model: Non-linear).
Influence of non-linear ovalisation
The MAT iteration process starts as soon as the preceding OVAL iteration process has reached the ‘near stability’ status. The MAT iteration is based on the disequilibrium resulting from the stress correction (reduction) as shown in the diagram below. The reduced stresses result in reduced internal forces. These corrected internal forces together with the calculated strains in fact can be simulated through a reduced stiffness of the cross section, resulting in larger strains in a next iteration. The iteration process ends if the disequilibrium norm vector is sufficiently small. The stability of the calculated equilibrium state is checked as well.
At the point shown in the figure below, a larger strain will not result in a higher stress, but through neighbouring points, where the stress level had not yet reached the yield stress level, a new equilibrium may be found, unless these points have reached as well the ultimate stress level. In that case the pipe section will collapse. This method is used in Design Function 5.
The correctness of the method can be concluded from the comparison with TNO measurements on the bend used as an example here and shown in the above figure.
In design function 6 the stresses and strains in the cross section are determined numerically by applying the κ and ε and ovalisation of the cross section found in Design Function 5 on a slice of the pipe Rdφ.
The sides of the slice are kept flat.
The ovalisation deformation from additional lateral loadings form the overburden weight and top loads are added in Design Function 6.
LocalMaterialYielding, last changed: 1/31/2020