Page 77 - Pipelines and Risers
P. 77
50 Chapter 3
Diameter/wall-thickness @/t) ratio 15-45
No ovality and no diameter expansion, cross sections remains circular throughout
deformations
Entire cross section in yield as a consequence of applied loads
The material model is elastic- perfectly plastic
The defect region is symmetic around the bending plan
Initial ovality is for simplicity ignored in the solution. The rationality of this is that an initial
ovality more or less will disappear when the pipe is subjected to high internal pressure under
operating conditions or pressure testing conditions.
When plastic deformation is involved, the interaction between axial tension and pressure can
be considered as the problem of material yielding under bi-axial loads. Neglecting all shear
stress components, Hill’s yield function can be expressed as a function of the longitudinal
stress ‘ol’, the hoop stress ‘oh’ and the yield stress in longitudinal direction ‘GOJ’, hoop
direction GO,^' and radial direction ‘oo,T), Hill, R. (1950), Kyriakides, S. et a1 (1988) and
Madhavan R. et a1 (1993):
(3.23)
Based on Fiq. (3.23) the material yield surface will vary with oo,h/oO,l and OO,,./OO,I as shown in
Figure 3.5.
Figure 3.5 Yield surface for CTO,&J = COJCOJ = 0.9,l.O & 1.1.
Solving the second-degree equation, Eq. (3.25) for the longitudinal stress CTL gives:
(3.24)
where:
