Introduction
A J-R curve show applied Integral J versus crack extension. Different stages in crack extension can be studied with small scale yielding conditions (SSY). In SSY, resistance depends on crack extension only, therefore a J-R curve (J Resistance) is a material property. Nevertheless, when plasticity is excessive, crack extension resistance becomes a function of specimen size and geometry. However, J-R curves determination is still a main Elastoplastic Fracture Mechanics (EPFM) procedure for material characterization.
Different specimens geometry are available for testing. A particular J Integral value was defined as JIC, it corresponds to the onset of stable extension. Tests consist of load application to specimens, start of stable crack extension and then unloading when crack reaches a specified length.
Standard methods with single test specimen require simultaneous recording of load, load-line displacement and crack length. In this work, crack length was measured only once by elastic compliance technique for comparison with a graphical-analytical method.
The development of direct methods is interesting because no estimation of crack length is necessary during the test. Besides they are applicable in almost all conditions (for example, dynamic load and/or aggressive environment). Therefore, they are very useful when the standardized methods cannot be applied.
The principle of load separation is applied in direct methods, like normalization [1] and linear normalization [2]. However, semi-empirical direct methods are under consideration when methods like normalization are not applicable.
Iorio [3] has developed a graphical-analytical technique for determining the J-R curve. Figure 1 shows basic determinations in a P-δ curve. The procedure has the following steps:
1. Toughness test performed recording load (P) and load-line displacement (δ).
2. Determination of the onset of stable extension (P1, δ1) in curve P-δ through the intersection between elastic line extrapolation and maximum load (P2, δ2) tangent line. Final crack length is determined when test is stopped, and corresponds to the point (P3, δ3).
3. Crack lengths corresponding to each point of a P vs. δ curve are calculated using a specified growth law, for example, linear.
4. Evaluation of J Integral in each Pi and δi point.
This procedure was proved before, yielding comparable results with standard methods and other direct methods [4]. Our aim is its evaluation in materials where stable crack growth occurs with delamination and tunneling. In this case, materials hardly match validity conditions according to standard methods. In this paper, application of a graphical-analytical method is discussed.
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Figure 1. Diagram showing measured load (P) vs. load-line displacement (δ).
Experimental
The material analyzed is a low-medium resistance API 5L x 42 steel, used in natural gas transportation pipelines in Argentine. Specimens were extracted from a plate with 9 mm in thickness. Table 1 shows chemical composition, determined by spectrometric analysis. API specification is fulfilled, excepting a lightly excess in carbon content.
Metallographic specimens were prepared with a standard procedure. Final polish with diamond compound, grade 0,25mμ, was used. Nital 4 was the etchant used for revealing microstructure. Microstructure is ferrite-pearlite with a marked banding as shown in Figure 2.
Table 1. Chemical composition (weight %). *Maximum API values.
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API 5L*
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0.16
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1.20
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0.35
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0.025
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0.035
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Sample
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0.17
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0.62
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0.10
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0.015
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0.023
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Figure 2. Metalography showing dark pearlite and bright ferrite.
Mechanical Properties
Tensile tests were performed in an MTS 810 testing machine, according to ASTM E8M-04. Specimens dimensions were 6 x 9 mm of cross section and 25 mm of gauge length. Test results are reported in Table 2. Two specimens were cut parallel to the lamination direction (TGBL_1 and TGBL_2), the other two at 90° from the previous orientation (TGBT_1 and TGBT_2).
Table 2. Tensile test results. * Minimum API values.
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API 5L x 42*
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293
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426
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35
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TGBL_1
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408
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443
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42
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TGBL_2
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409
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440
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42
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TGBT_1
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392
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441
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38
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TGBT_2
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385
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425
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37
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Banding produces variation in mechanical properties with crack orientation. Besides, banding is mainly responsible for delamination mechanism in fracture process.
Impact tests were performed according to ASTM E23-06 standard at 20°C using a Shimadzu Impact Testing Machine (300 J in capacity). Charpy energy mean value was 184 J/cm2.
Toughness tests were made according to ASTM E1820-05a, in an MTS 810 testing machine. Bend specimens, SE(B), were used. The specimen dimensions are indicated in Figure 3. Specimens were cut from a plate with a T-L crack plane orientation. Notches were obtained by electrical discharge machining. All specimens were fatigue precracked according to ASTM procedure. Tests consisted in applying load until crack extension reaches a targeted length. Load line displacement is the controlling signal that fix the load. The load line displacement speed was 1mm/min. Crack extension was marked by heat tinting after test.
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Figure 3. All lengths are in mm, angles are in degrees.
Figure 4 shows a typical SEM fractography, obtained in a tested toughness specimen, where delamination is observed.
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Figure 4. SEM fractography, specimen FGB_1, showing fatigue crack (A)
and stable propagation with delamination (B).
Results and discussion
A graphical-analytical method was applied in three specimens (named FGB_1, FGB_2 and FGB_6) and therefore performed an analysis of load versus load-line displacement (P-δ) records according to above introduced procedure. Elastic compliance technique (standard method) was only used in specimen FGB_5 for crack length estimation during test.
Relevant parameters obtained through load versus load-line displacement (P-δ) curves and initial and final crack lengths are reported in Table 3. A typical load versus load-line displacement measurement is showed in Figure 5.
Table 3. P-δ curve parameters
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FGB_1
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9122
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8475
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2.18
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22.80
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26.47
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FGB_2
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9012
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8740
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1.99
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22.56
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25.02
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FGB_5
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8664
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8299
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1.37
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23.32
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25.35
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FGB_6
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7569
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6859
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1.68
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25.42
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27.22
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Figure 5. Typical tests record.
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Figure 6. J-R curves comparison.
A linear crack growth law was used in graphical-analytical method, so crack length and load (Pi ,ai) pairs can be obtained with both elastic compliance and graphical-analytical methods. Therefore, evaluation of J Integral is possible in each Δai. Figure 6 shows J-R curves given by both methods.
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Figure 7. Tunneling is observed.
Standard method validity conditions are not fulfilled because tunnelling is observed (Figure 7). Usually, tunnelling is controlled through side grooves, but in this case tunnelling is related with delamination that is coupled to thickness effect [5].
That coupled effect invalidates side grooves improvement. Besides, it affects P-δ curve, so we can suppose a similar effect in crack growth. In the graphical-analytical method, we propose to use a relation between total load-line displacement and crack length, therefore we can obtain an approximate resistance curve for engineering purposes. Moreover, we could evaluate materials which hardly match ASTM validity conditions.
Graphical-analytical method has very simple assumptions, without restrictive validity conditions. We selected a linear crack growth law, then we can obtain conservative results (Figure 6).
This approximation seems to be proper. For example, conventional initiation of tearing toughness values, designated J0.2 , are similar as listed Table 4.
Table 4. Results about initiation of tearing. *Standard method does not match validity conditions because tunneling is observed. **Mean value.
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Standard*
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39
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Graphical-analytical**
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34±6
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Conclusions
1. Crack growth resistance was evaluated through SE(B) specimens extracted from a plate with a T-L crack plane orientation.
2. Both methods, standard and graphical-analytical, show similar results for the material tested that shows tunneling and delamination.
3. Additional research on C(T) specimens is required to set up graphical-analytical method as an alternative one. Also other crack growth laws could be explored.
4. Graphical-analytical method is especially useful when standard methods are not available.
References
1. J.D. Landes, Z. Zhou, K. Lee and R. Herrera, Journal of Testing and Evaluation, 19(4) (1991), 305-311.
2. E.D. Reese and K.H. Schwalbe, Fatigue & Fracture of Engineering Materials & Structures, 16 (3) (1993), 271-280.
3. A.F. Iorio, COTEQ 96 (1996), 21-24
4. N. Alvarez Villar, V. Fierro, F. Agüera, Jornadas SAM/CONAMET-MEMAT 2005, Mar del Plata, Argentina (2005).
5. W.Guo , H.Dong, M.Lu, X.Zhao, International Journal of Pressure Vessels and Piping, 79 (2002), 403-412
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