Fatigue life prediction of casing welded pipes by using the extended finite element method

The extended finite element (XFEM) method has been used to simulate fatigue crack growth in casing pipe, made of API J55 steel by high-frequency welding, in order estimate its structural integrity and life. Based on the critical value of stress intensity factor KIc, measured in different regions of welded joint, the crack was located in the base metal as the region with the lowest resistance to crack initiation and propagation. The XFEM was first applied to the 3 point bending specimens to verify numerical results with the experimental ones. After successful verification, the XFEM was used to simulate fatigue crack growth, position axially in the pipe, and estimate its remaining life.


INTRODUCTION
n order to keep pipeline safe and reliable in operation, its fatigue life estimation is of utmost importance, [1].Toward this aim, extensive experimental and numerical investigation is needed.In this paper the extended finite element method (XFEM) has been used for modeling and analysis of crack propagation in a seam casing pipe made of API J55 steel by high-frequency (HF) contact welding, but only after its verification, based on the comparison of the xFEM results with experimental results obtained on the standard three-point bending specimen.

RESISTANCE TO CRACK GROWTH OF API J55
odified CT specimens with thickness d = 6.98 mm (equal to the pipe wall thickness) have been used to evaluate critical values of fracture mechanics parameters (J Ic , K Ic ), and the critical crack length, a c , as shown in more details in [2] for new and exploited pipes.Here only results obtained for exploited pipe are shown in Tab. 1. Table 1: The values of J Ic K Ic and a c -pipe taken from service.
Based on the obtained values of KIc for the base metal (BM), heat-affected-zone (HAZ) and weld metal (WM), one can conclude that the BM has the lowest resistance to crack initiation and propagation.

VERIFICATION OF THE METHOD USING EXPERIMENTAL RESULTS OBTAINED ON STANDARD SPECIMEN
he XFEM is relatively new method of numerical simulation and it has to be verified by experimental results, [3].
For this purpose the results from experimental testing and from numerical simulation using XFEM, both carried out on the standard Charpy specimen, were compared.The specimen is made of API J55 steel, the same steel as the pipe is made of.The three-point-bending test was conducted on standard Charpy specimen made from BM, since it has the lowest resistance to crack initiation and propagation.The test was conducted on high-frequency pulsator RUMUL-CRACKTRONIC at the room temperature providing relation between the crack length, a, and the number of cycles N. A finite element model of the Charpy specimen was created using the Abaqus software.Mesh was refined around the initial crack, as shown in Fig. 1.The crack growth to its critical size was simulated by using Paris equation: where da/dN [m/cycles] is the fatigue crack growth, ΔK [MPam] the stress intensity factor range, Cp and mp material parameters, which have the following value in this paper: C p =2.1110 -15 , exponent m p =6.166, [2].

T
The initial crack length used in the analysis was 2 mm.The growing crack was incremented at steps of 0.16 mm (chosen by the software) and 28 steps were performed.The first step in 3D analysis using XFEM was crack "opening" (Fig. 2).In this step stresses in the specimen are obtained, as well as stress intensity factors (SIFs) at the crack tip.Based on that, Morfeo/Crack for Abaqus, computes the SIFs for mode I, II and III, for every step of the crack propagation, and the corresponding crack growth.Fig. 2 shows crack at beginning (1 st step-crack opening), Fig. 3, after 8 th step, while Fig. 4 shows the crack after the 27 th step.The SIF values at the crack tip determine the appropriate crack growth increment.This procedure was performed in 28 steps in order to simulate incremental crack growth.Values obtained in Abaqus for the 16 th crack growth step are shown in Tab. 1, indicating SIF values Keq, KI, KII, and KIII) in the last four columns.As expected, crack growth was characterized by K I , since values of K II and K III are negligible.Therefore, data for all crack growth steps is given only for KI, Tab. 2, including its average, minimum and maximum values along the crack front.Tab. 2 also shows number of point in each crack growth step, being between 66 and 68.

Curvilinear abscissa along the crack front [mm]
x front coordinate [mm] Chart in Fig. 5 shows very similar behavior of experimentally tested specimen and its 3D numerical simulation.Beyond 10 6 cycles very small number of cycles to collapse is left, and in this area two curves are exactly the same.Generally speaking, one can say that experimental and numerical results agree well, with some differences which require further investigation.The geometry used in simulations is pipe with axial surface crack in the base metal (BM), Fig. 6.The pipe is made of API J55.On the outer surface of the pipe there is an initial axial surface crack with dimensions: a=3.5 mm and 2c=200 mm.The wall thickness is 6.98 mm.A finite element model of the pipe was created using the software.The initial crack length used in the analysis was 200 mm, and it was 3.5 mm deep (the wall thickness is 6.98 mm).Mesh was refined around the initial crack, and a uniform template of elements was used.The growing crack was incremented at steps of 0.2 mm.The first step was crack opening, and after that, the crack was growing through the inner side of wall, in radial and axial direction, while, in 7th step, it becomes through-wall crack.Fig. 7 shows the crack growth at beginning (1 st step -crack opening), whereas Fig. 8 shows crack growth after 7 th step when the crack "breaks" through the wall.Afterwards, crack grows in axial direction only T through inner side of the wall, and "outer" initial crack remains the same as it was in the beginning of simulation, until 64 th step, when "inner" and "outer" crack become equal, 200 mm long, and it has become complete through-wall crack, Fig. 9.Further crack growth is in axial direction until the final step of 3D simulation, when the crack is 209.42 mm long.Fig. 10 shows 3D chart of "inner" and "outer" crack growing.The prediction of crack growth rate and residual strength of pipe demands accurate calculation of stress intensity factors (SIFs), which determine the appropriate crack growth increment for the crack.This calculation was performed 100 times in order to simulate incremental crack growth.The obtained relationship between equivalent stress intensity factor K eq and crack length a, Fig. 11, shows tendency of increasing Keq with increased crack length a, while the crack was reached up to 210 mm.The fastest increase of Keq, as expected, was before the seventh step, when crack penetrated the pipe wall.The chart in Fig. 12 shows the obtained relationship between steps and number of cycles.After the 7th step, when the crack penetrates the pipe wall, the number of cycles becomes significantly lower and remains at about the same values until the final step.The chart in the Fig. 13 shows the obtained relationship between the crack length a [mm] and the total number of cycles N.For crack growth from initial crack length until final length of 209.42 mm, 10548 cycles are necessary.Obviously, the most of them occur until the seventh step, in which the crack becomes through-wall crack (8606 cycles), while the further cracks growth requires a very small number of cycles.

CONCLUSION
ased on the presented results, one can conclude that experimental and numerical results agree well, with some differences which require further investigation.Therefore, the obtained stress intensity factor histories can be used to predict fatigue crack growth rates.B

Figure 1 :
Figure 1: Standard Charpy specimen: dimensions of the specimen and 3D model obtained using Abaqus software.

Figure 2 :
Figure 2: Step one -crack opening and Von Mises stresses at crack tip.

Figure 7 :
Figure 7: Step 1 -crack opening and Von Mises stresses at crack tips.

Figure 8 :
Figure 8: The 7 th step -crack became through-wall and stresses around the crack.

Figure 9 :
Figure 9: Step 64 when "inner" and "outer" crack going to be equal (crack length is 200 mm) and stresses around the crack.

2 ]Figure 11 :
Figure 11: Relationship between equivalent stress intensity factor K eq and propagation step.

Figure 12 :
Figure 12: Obtained relationship between steps and number of cycles.

Figure 13 :
Figure 13: Relationship between crack length a and number of cycles N using 3D simulation.

Table 2 :
Values for K eq , K I , K II , and K III in the 16 th crack growth step.

Table 3 :
Values for KI for all steps (28) growth.