8
FRACTURE CONTROL OF PIPELINES BY DIRECT CALCULATIONS BASED ON LINESPRING TECHNOLOGY
by
Christian Thaulowa, Erling Østbyb, Bård Nyhusb, Bjørn Skalleruda and Matteo Chiesab
Abstract
The Failure Assessment Diagrams (FAD) used in BS 7910:1999 (Guide on methods for assessing the acceptability of flaws in fusion welded structures) represent high structural constraint applications. In addition, today's practice for calculating the crack driving force is usually taken from analytical equations for plates. Equations for the specific pipe geometries are very limited. There is evidently a need to include constraint corrections in failure assessments and to establish procedures for calculating the crack driving force for pipes. The paper presents constraint correction parameters and demonstrates how the JQM Approach can be applied for defect assessments with reference to high strength steel. With the increased use of FE calculations in the industry, a method for direct calculations is presented. A company, LINKftr as, has been established with the aim to develop software for direct calculations. The LINKftr concept is to link detailed crack tip calculations with the structural response, with the linespring as transfer-elemets.
presented at
Application & Evaluation of High-Grade Liniepipes in Hostile Enviroments
7-8 November 2002, Yokohama, Japan
a The Norwegian University of Science and Technology
b SINTEF Materials technology
Cracks
All materials will contain cracks or defects. The question is: When will cracks be of practical interest? Under which conditions will cracks influence upon the behaviour of structures and components? When can we ignore the existence of cracks?
Structural engineers normally judges the capacity or ultimate strength of a structure on the basis of a load-deflection diagram, where the maximum load or plastic collapse load is considered as the limit. The next step then is to impose a partial safety factor on this limit load combined with minimum tensile elongation requirements.
If we now introduce cracks in the structure, this can influence the load bearing capacity, Figure 1, either by brittle fracture, ductile tearing, plastic collapse or combinations of these failure modes.
Traditional structural design compares the design stress with the flow properties of the material, which is normally taken to some fraction of the yield stress. A material is assumed to be adequate if its strength is greater than the expected applied stress. In fracture mechanics there are two structural variables, design stress and flaw size, and fracture toughness replaces strength as the material resistance property. Fracture mechanics quantifies the critical combination of these three variables.
In fabrication with steel, the welded joints represents the most critical region. This is where cracks normally appear and regions of the weld metal or the heat affected zone can have low toughness. The weld metal, heat affected zone and the base material will have different material properties, and this mismatch in strength will influence the failure conditions. The effect of material mismatch on fracture depends upon the crack size, the location of the crack, the strength mismatch and the fracture toughness.
In this paper we first shortly introduce the principle of constraint and transferability. We then present the JQM Approach and show how the approach can be applied for a 690-steel. We then introduce the principle of direct calculations with the use of linespring-elements and how this can be utilized for pipelines.
Constraint
The starting point in fracture mechanics analysis is to consider a crack of a certain size located in a component or specimen. An external load is applied and the component is loaded until it fails. During loading a plastic zone develops from the crack tip, and at a certain load net section yielding occurs as the plastic zone reaches the through thickness surface.
As long as the plastic zone at the crack tip is limited compared with the geometry of the component or specimen, so-called small scale yielding, a single parameter fracture mechanics approach can be applied. K, J or CTOD characterizes the crack tip conditions and can be used as geometry independent fracture criterion.
The geometry dependence under linear elastic conditions for five standard fracture mechanics geometries are plotted in Figure 2. The pure tensile specimens, DENT and CCT, have the lowest constraint, while specimens dominated by bending have the highest constraint. Standard fracture mechanics testing procedures are based on the specimens with high constraint in order to reproduce the worst case conditions.
However, the single parameter fracture mechanics breaks down in the presence of excessive plasticity, and fracture toughness will now depend on the size, geometry and mode of loading.
McClintock (1) was one of the first to examine the near crack tip stress field under fully plastic conditions for various specimen geometries and non-hardening materials, Figure 3. For small scale yielding, the maximum stress is approximately three times the yield stress, while a centre cracked panel under tension is incapable of maintaining significant triaxiality. These effects are, however, less severe when strain hardening is taken into account. We notice that the DENT specimen, with low constraint under linear elastic conditions, Figure 2, now reach high stresses because of the interference between the two fields of deformation.
The history of constraint is how to deal with crack tip stresses under fully plastic conditions. The aim is to find a parameter that characterize the stress-strain fields, so that results from one test geometry can be transferred to another geometry.
One approach has been to restrict the application of fracture mechanics to high constraint since single-parameter fracture mechanics may be approximately valid in the presence of significantly plasticity, provided the specimens maintains a relatively high level of triaxiality. Most laboratory fracture mechanics specimens, as three-point bending and compact tension, represent this high triaxiality condition.
A more basic approach has been to define the crack tip triaxialtity as the ratio between the hydrostatic stress, or first invariant of the stress tensor, which does not cause any plastic deformation, and the Mises effective stress, which is the square root of the second invariant of the deviatoric stress being responsible for plastic flow. This parameter has been extensively applied to describe ductile crack initiation and growth. There are a number of mathematical models for void growth and coalescence, where the two most widely referenced models were published by Rice and Tracy (2) and Gurson (3). They found an exponential dependence of the void growth rate on the stress triaxiality, . Here is the hydrostatic stress, and is the yield stress. The yield stress has later, Needleman and Tvergaard (4), been substituted with , the Mises effective stress.
Another constraint parameter is the T-stress, Larsson and Carlsson (6), Du and Hancock (7). This is a non-singular linear elastic stress component parallel to the crack. The T-stress characterises the local crack tip stress field for linear elastic material, and the global in-plane constraint of a specimen with respect to predominantly local small scale yielding conditions. It has however been argued that the T-stress also can be applied under plastic conditions, Betegon and Hancock (8).
T increases or lowers the hydrostatic stress by
The T-stress is often presented dimensionless as a biaxiality factor
where KI is the Mode I stress intensity factor.
The idea of adding a second term has been taken over in elastic-plastic fracture mechanics by defining the so-called Q parameter, O`Dowd and Shih (9, 10)
The solution for is obtained by FE calculations.
The Q parameter, like the T stress, is supposed to characterize the geometry dependent constraint. Both quantities affect the hydrostatic stress in the same way, i.e. negative values lower, positive values raise the hydrostatic stress.
The J-Q theory has been further developed to take material mismatch into account, the so-called JQM Approach, Zhang et al (11), Thaulow et al (12).
The Failure Assessment Diagrams (FAD) used in BS 7910:1999 (Guide on methods for assessing the acceptability of flaws in fusion welded structures) represent high structural constraint applications. The standard gives literature references for constraint correction methods, based on T and Q, but none of these are included in the standard.
The constraint correction methodology will now be presented with reference to a 690-steel investigated, Thaulow et al (13).
JQM constraint correction for 690 steel
The material data for the 690-steel are presented in Figure 4. Notched tensile testing was applied to derive the stress-strain input data, Olden et al (14).
Three specimen geometries were selected, Figure 5. The idea was to cover a large variation in constraint with as simple test specimens as possible. The shallow notched SENT specimen has been extensively used the last year, and the testing methodology is now well established, Nyhus et al (15).
We have to distinguish between the crack driving force (expressed as J) induced at the crack tip because of loading and mismatch (applied J), and the material resistance (expressed as fracture toughness J).
The evolution of constraint for the three test specimens as function of applied J, is presented in Figure 6. When we add the mismatch effect, for cracks located at the fusion line, the constraint increases with weld metal overmatch, Figure 7. At a certain load ductile crack growth can be experienced. The effect of limited ductile crack growth has been examined, Østby et al (16), and an increase in constraint is observed, Figure 8. The constraint effect on ductile crack growth, J-R curves, has been further evaluated, Zhang et al (17) and Nyhus et al (18).
In order to establish material resistance curves, a large testing program has been performed, Nyhus et al (19). The lower bound toughness results from the heat affected zone shows that the toughness increases significantly as the constraint is reduced, Figure 9. The M parameter is not included in this calculation because it is close to evenmatch conditions.
By comparing the applied- and resistance curves, Figure 10, we can now determine the critical conditions for brittle fracture.
We can now select a structural component of interest, introduce a crack, and calculate the constraint and check if brittle fracture or plastic collapse will take place.
All we need are 3D calculations! Or new methodologies where high accuracy can be obtained without introducing complex or costly calculations. The LINKftr concept introduced in the next section is an answer to these challenges.
Direct calculations
At present stage 3D FE calculations are needed in order to calculate the constraint. But two approaches have been suggested to make the calculations simpler, more effective and less time consuming.
The first is an engineering or simplified approach where the need for calculations is reduced to a minimum. Polynoms for a range of typical stress-strain curves are calculated in beforehand and presented for practical use.
The other approach is the so-called direct calculations. The 3D crack geometry is represented by a so-called linespring FE element, Chiesa et al (20). This element is introduced in a shell FE analysis of a structure at critical locations, Figure 11
The part through surface crack is a 3D problem, Figure 12a. Here a(x1) is the crack depth at position x1. Now, this 3D problem can be formulated within 2D plate- or shell theory with the part through surface crack represented with linesprings.
Two straight lines can schematically represent the linespring element, 1-4 and 2-3 in Figure 13, and the lines are connected to each other by a series of springs. At zero deformation the lines lie upon each other. When deformation takes place the two lines displaces in opposite directions, and this displacement is constrained by the springs. The stiffness of the linesprings , with extensional and rotational degrees of freedom (), is derived from a plane strain edge-cracked strip loaded in tension and in bending (N, M), see Figure 12b.
The yield surfaces governing the plastic behaviour of the ligament under the crack can be plotted in the force space (Q1, Q2) for different crack depth to thickness ratios, Figure 14.
Having determined the plastic deformation increment, the next step is to calculate the crack tip opening displacement, CTOD, according to Lee and Parks (21). In addition, Wang and Parks (22) have proposed a method for calculating the T-stress for the linespring based on the analytical work of Sham, where the T-stress can be seen as the summation of the contributions by the membrane force, N(s) and the moment M(s). Thus, the T-stress can be calculated at any point along the crack front.
3D and direct calculations of cracks in pipelines
Non-linear small deformation FE analysis of a four meter long pipe, Figure 15, with a 450 mm long surface crack with crack depth a/W=0.75 loaded in tension has been carried out with abaqus software, Chiesa et al (23). The pipewall is 25.7 mm and the outer diameter 921 mm. Figure 16 illustrates the mesh for the pipe segment, by means of solid 3D mesh (7760 elements) and shell-elements (565 elements) combined with linespring-elements.
Figure 17 shows the stress vs. J-integral at the centre of the crack, with a good agreement between the 3D- and the shell-element models. In Figure 18 the T-stress is plotted from the crack tip along the crack flank for the deepest point of the crack. The T-stress from the shell model is somewhat higher than for the 3D model, but it seems that the relationship from Wang and Parks (22) can be utilized for the pipe geometry, even if further investigations are necessary to validate the method for different crack geometries.
The computed J-integral and T-stress will now be input to the failure analysis, and a loop of calculations is established to repeat the calculations for each load step, and to take eventual ductile crack growth into consideration.
Constraint corrected specimens for pipelines
SINTEF have in the last three years used SENT specimens to characterize the fracture properties in pipes, Nyhus et al (14). In several pipelaying projects the SENT specimens have been used to qualify the fracture properties and the ECA have been based on the results from the SENT specimens. These specimens have similar constraint as for cracks in pipes. When the constraint is the same also the crack tip fields are the same. The deformation field for a pipe with a circumferential surface crack is compared to the deformation field for a SENT and SENB specimen in Figure 19. It can be seen that the deformation for the SENT specimen and the pipe is quite similar, but for the SENB specimen the deformation is completely different.