Afshin K Motarjemi
Paper presented at ASME Pressure Vessels and Piping Conference 25-29 July 2004, San Diego, CA., USA: Computational weld mechanics, constraint, and weld Fracture.
Fracture assessment procedures such as BS 7910 and API 579 are formulated based on the Fracture Mechanics concept for assessing integrity of structures such as pipelines, pressure vessels, etc. In the current study those procedures are applied to through-wall and surface cracked pipe geometry under four-point bending. The predicted maximum tolerable applied loads are then compared with pipe full-scale fracture testing results published by Miura et al (2002). Other assessment schemes namely, GE/EPRI, Net-section plastic collapse, LBB.NRC and finally LBB.ENG2, as reported in the same publication are also included in the current paper for sake of comparison. The comparative study showed that BS 7910 and API 579 predict similar maximum tolerable load for through-wall pipes but different value for surface-cracked pipes. Difference in predictions for the latter geometry is owing to the use of different stress intensity factor/reference stress solution by BS 7910 than API 579. However, both procedures provided conservative results compared with the experimental data as well as other engineering routes mentioned in Miura et al (2002).
Fitness-for-service (FFS) assessment is a multi-disciplinary engineering analysis of equipment to determine if it is fit for continued service until the end of a desired of operation, such as until next turnaround or planned shutdown. The main products of FFS are (API 579, 2000) a decision to run, alter, repair, monitor, or replace the equipment and (API 579, 2002) guidance on inspection interval for the equipment. FFS applies analytical methods to evaluate flaws, damage, and material ageing. API 579 (2002) recommendation practice and BS 7910 (1999) standard are among the recognised assessment procedures, which provide information for assessing fitness-for-service. Other methods such as Net-section collapse criterion and several other estimation schemes, namely, GE/EPRI (1988), LBB.NRC (1986) and LBB.ENG (1987) methods also exist.
BS 7910 and API 579 procedures use fracture mechanics to assess crack-like flaws. A failure assessment diagram (FAD) is applied to crack-like flaws. Linear elastic stress analysis is used to compute the toughness ratio (K r ) and the load ratio (L r ) for a component with a crack-like flaw. K r is the ratio of the linear elastic stress intensity factor (K I ) to the material fracture toughness (K mat ), while L r is the ratio of the reference stress ( σ Ref ) to the material yield stress ( σ ys ). For a given flaw and load, the value of K r as a function of L r is plotted on a FAD. No failure is predicted for points below the failure assessment envelope, whereas failure is likely to occur for points at or above the failure assessment envelope. Calculations are repeated for other condition to see where they fall with respect to the envelope or to determine the critical conditions (a point on the failure envelope) at which failure is predicted to be more likely to occur.
In both procedures, there are three choices for the FAD curve: the standard FAD curve can be used (API 579 Level 2, which is equivalent to the BS 7910 Level 2A FAD), or a material-specific FAD (BS7910 level 2B) that requires a stress-strain curve can be selected. Alternatively, a user-defined FAD curve can be input. In the current paper material-specific FAD approach is used. This level generally gives more accurate results compared with the case where FAD is constructed based on the single values of tensile properties (Generalised or standard FAD). Stress-strain data are required at the appropriate temperature for parent material and/or weld metal. The lower yield or 0.2 % proof strength, tensile strength, and modulus of elasticity should be determined together with sufficient co-ordinate stress/strain points to define the FAD curve.
There are subtle differences in the way in which the two methodologies compute the assessment point. Stress intensity factor and reference stress solutions within the API579 are used independent of the analysis type selected.
The FAD analysis can be performed either with a single toughness value or with a resistance curve.
Other assessment methods aforementioned are based on the limit analysis or elastic-plastic J-calculations.
Current study is aimed to use assessment approaches mentioned earlier for prediction of the maximum load applied to two pipes with through-wall and surface semi-elliptical flaws, under four-point bending. The predicted maximum loads are compared with the experimentally determined values reported elsewhere (Miura et al, 2002).
Input data for assessment
All the required input data for the assessment of the pipes are collected from Miura et al (2002). Those include the information listed below.
Tensile Properties of the Pipe Materials
The material used for the pipes was STP410 carbon steel specified in Japanese industrial standard with tensile properties as reported in Table 1. As the pipes were used in the high temperature conditions, tensile values for 300°C are also reported separately. The Table also included Ramberg-Osgood fitting parameters for room temperature as well as 300°C.
Table 1 Tensile properties of STP410 carbon steel (Miura et al, 2002)
|Temp. °C||σ 0.2,|
|σ U ,|
|Young's modulus, E|
|σ 0 ,|
Fracture Toughness of the Pipe Materials
Maximum load value of J, J m , was calculated based on the information given in the Miura et al (2002) and used in the current study. It should be noted that value of J was estimated in that paper only for a through-wall cracked pipe at room temperature and 300°C (there was no reported data for surface cracked pipe to be used in the current study). Values of maximum-load fracture toughness are estimated 1744N/mm for room temperature and 1396.1N/mm for 300°C.
Table 2 shows crack geometry and dimensions of the pipes tested. As it can be seen all the pipes have similar outside diameter and wall thickness but different crack length/geometry. For better tractability, pipes are numbered 01 to 03 ( Table 2).
Table 2 Crack geometry and dimensions of pipes (Miura et al, 2002)
|Crack type||Crack length, 2c|
|Crack height, a|
Table 3 shows results of the pipe fracture tests at room temperature and 300°C. As it can be seen, pipe with surface crack (pipe 03) tolerate higher level of applied load compared with the through-wall cracked ones owing to larger ligament size ( Miura et al, 2002).
Table 3 Results of pipe fracture tests (Miura et al, 2002)
|Maximum applied load,|
Prediction of maximum load
The equations used to construct the assessment line in the current study are the following:
is the true strain obtained from the uniaxial tensile stress-strain curve at a true stress, L r
( σ Y
is the yield strength of the flawed-material) and the other parameters explained earlier.
Single-point fracture toughness values ( J mat ) for Room and 300°C, is converted to
and is used as input for fracture toughness. Relevant K I and reference stress values for each pipe were also implemented in the calculations to determine assessment points co-ordinates,
Critical parameter analysis was carried out for applied load and maximum values obtain for each case is given in Table 4. This maximum load is associated with the assessment points, which locate on the Failure Assessment Lines ( Fig.1). As it clearly shown in Table 4, both BS 7910 and API 579 procedures predicted similar maximum load for the through-wall-cracked pipes. However, the prediction for surface-cracked pipes is inconsistent between the two procedures: API 579 predicts higher maximum load (with less conservatism in comparison with experimental results) compared with BS 7910.
Table 4 Comparison of experimental and predicted maximum load for pipes tested in Miura et al (2002)
|Experimental maximum load,|
|Maximum load predicted, kN|
|Material flow stress||Design flow stress|
Fig.1. FAD curves with assessment points for all the pipe geometries studied. Failure mode for all the pipes is plastic collpase
Predictions made by other engineering methods such as net-section collapse criterion ( Kanninen etal, 1976), GE/EPRI (1988), LBB.ENG (1986) and LBB.NRC (1987) are also summarised in Table 4. For the net-section collapse criterion, two inputs for flow stress namely, materials flow stress and design flow stress was used in Miura et al (2002) for the calculations. It can be seen that net-section collapse method in general over-estimates the maximum load values for through-wall cracked pipes at room and higher temperatures. However the prediction for surface cracked pipes provides good margin of conservatism especially for the case of using material flow stress in the calculation. Predictions by other engineering ways are also showing acceptable conservatism compared with the experiments.
Assessment of the pipes 01-03 under four-point bending showed that plastic collapse is dominant failure mode for all of them. This can be seen from Figs.1a to c, with failure assessment points close to the plastic collapse region. This justifies sensitivity of assessment results on reference stress value as well as tensile properties of the pipe material.
Predictions by BS7910 and API579 for through-wall cracked pipes are conservative (on the safe side) relative to the experimental results ( Fig.2).
Fig.2. BS 7910 and API 579 maximum load predictions for the through-wall and surface cracked pipes at RT and 300°C
For the pipe 03 with surface crack, API 579 compared with BS 7910 predicts higher maximum applied load. Two reasons can be mentioned:
One is that BS 7910 implements Kastner equation ( Kastner et al, 1981) for estimation of reference stress of circumferential surface cracked pipes, whereas API 579 recommends using of different solution ( Eiber etal, 1971). A separate study conducted at TWI ( Cheaitani et al, 2002) revealed that Kastner equation is more conservative than the API 579 solution ( Eiber et al, 1971). This conclusion are drawn when both solutions were compared with the result of a verified finite element study ( Cheaitani et al, 2002). Since plastic collapse is dominant failure mode for the pipe 03, hence less conservative reference stress value will result in less conservative predicted maximum load as shown in Table 3 and Fig.2.
Another reason for the difference between BS 7910 and API 579 predictions could be the result of using flat plate solution by BS 7910 (Raju et al, 1979) for the current surface cracked pipe (Pipe 03). This is done owing to geometrical restrictions. On the contrary API 579 implements using of different solutions ( Klecker et al, 1986) for the same pipe geometry. Although the pipe dominant failure mode is plastic collapse but nevertheless the effect of input stress intensity factor should not be neglected thoroughly.
Fig.3. Comparison of the maximum load prediction for the through-wall pipe at room temperature
Fig.4. Comparison of maximum load predictions for the through-wall cracked pipe at 300°C
Figures 5-7 also show comparative study between all the aforementioned engineering methods, including BS7910 and API579. Apart from the net-section collapse method, rest of the Engineering routes predicts maximum load for through-wall cracked tested pipes conservatively. The level of conservatism is less for LBB. NRC (1986) compared with other methods used.
Fig.5. Comparison of maximum load predictions for the surface cracked pipe at 300°C
Assessment of two through-wall-cracked pipes and a surface cracked pipe were conducted based on the BS 7910 and API 579. Following conclusions can be drawn from the results obtained:
- Similar maximum load carrying capacity for the through-wall cracked pipes was predicted by BS 7910 and API 579. The predictions showed reasonable amount of conservatism compared with the experiments.
- For the surface cracked pipes BS 7910 and API 579 predicted the maximum load differently with more conservatism which is due to different source of stress intensity factor as well as reference stress solution and use of lower bound fracture toughness values in the assessment.
- Predictions made with other engineering calculation routes also predict the pipes maximum load with good margin.
API 579, 2000, 'Recommended practice for fitness-for-service-API 579', 1 st edition.
BS 7910:1999 (incorporating Amendment No. 1), 'Guide on methods for assessing the acceptability of flaws in metallic structures' BSI.
Brust, F., 1987, 'Approximation methods for fracture analysis of through-wall cracked pipes', NURGE/CR-4853.
Cheaitani, M. J. and Wignall, C. M., 2002, 'Acceptance criteria for pipe girth welds inspected using Automated Ultrasonic Testing (AUT), Sub-task 3.1, Development of Girth weld-specific ECA procedures', TWI REPORT NO.: 13545/17/02.
Eiber, R. J., Maxey, W. A., Duffy, A. R., and Atterbury, T. J., 1971, 'Investigation of the initiation and extent of ductile pipe rupture, 'Battelle Report to the pipeline committee of the American Gas Association.
Kanninen, M. F., Broek, D., Marschall C. W., Rybicki, E. F., Sampath, S.G., Simonen, F. A., and Wilkowski, G. M., 1976, 'Mechanical Fracture Predictions for Sensitised stainless steel Piping with circumferential cracks', EPRI/NP-192.
Kastner, W., Rohrich, E., Schmitt, W. and Steinbuch, R., 1981, 'Critical crack sizes in ductile piping, International Journal of pressure vessels and piping'. 9(3) 197-219.
Klecker, R., Brust, F., and Wilkowski, G., 1986, 'NRC Leak-Before-Break (LBB.NRC) analysis method for circumferential through-wall cracked pipes under axial plus bending loads', NURGE/CR-4572.
Kumar, V., and German, M.D., 1988, 'Elastic-plastic fracture analysis of through-wall and surface flaws in cylinders', EPRI/NP-5596.
Miura, N., Kashima, K., Miyazaki, K., Hisatsune, M. and Hasegawa, K., 2002, 'Ductile fracture behaviour of carbon steel cracked pipes with moderate-toughness' ASME PVP 2002 conference proceeding, PVP-Vol. 437, service experience and failure assessment applications, pp. 55-60.