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Assessment of Cleavage Fracture in Specimens with a Curved Crack Front for High-Strength Steels in Offshore Applications
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21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Assessment of Cleavage Fracture in Specimens with a Curved Crack Front for High-Strength Steels in Offshore Applications Crack Front for High-Strength Steels in Offshore Applications Thermo-mechanical modeling of aChen, highAziz pressure Xudong Qian*, Shuang Ahmedturbine blade of an Xudong Qian*, Shuang Chen, Aziz Ahmed airplane gas turbine engine Department of Civil and Environmental Engineering, Centre for Offshore Research and Engineering, National University of Singapore,
XVAssessment Portuguese Conference on Fracture, PCF 2016,in 10-12 February 2016, Paço Arcos, Portugal of Cleavage Fracture Specimens with a de Curved
Singapore 117576 Department of Civil and Environmental Engineering, Centre for Offshore Research and Engineering, National University of Singapore, a b c Singapore 117576
P. Brandão , V. Infante , A.M. Deus *
a
Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal Abstract c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, The significant petroleum reserve in the Arctic drives the need for offshore facilities in the Arctic made of ferritic structural steels. Portugal b
Such steel materials oftenreserve exhibitinathe brittle fracture without noticeable priorinplastic deformations. This paper presents The significant petroleum Arctic drivesmode the need for offshore facilities the Arctic made of ferritic structural steels.a combined andexhibit numerical investigation assesswithout the cleavage fracture failure fordeformations. high-strength steels used in offshorea Such steelexperimental materials often a brittle fracturetomode noticeable prior plastic This paper presents applications. The experimental programinvestigation includes a set non-conventional, specialfailure single-edge notched bend, SSE(B) combined experimental and numerical to of assess the cleavage fracture for high-strength steels used specimens, in offshore Abstract to the conventional through-thickness specimens, which tested under aThe lower ambient temperature of -90 oaC. applications. experimental program includes setInofcontrast non-conventional, special single-edge notchedfracture bend, SSE(B) specimens, experience ana lower approximately uniform crack force alongtothe cracktofront, the specimens with a operating curved crack front During their operation, modern aircraft engine are subjected increasingly demanding conditions, In contrast theentire conventional through-thickness fracture specimens, which tested under ambient temperature of driving -90 oC. components especially high pressure turbine blades. forces Such cause along these parts tothe undergo different of time-dependent indicates strong variations in both the (HPT) crack driving and constraints the crack front. This study utilizes an experience anthe approximately uniform force conditions along the entire crack front, specimens withtypes atherefore curved crack front degradation, of which creep. Acrack model usingforces thetofinite method (FEM) was developed, in order to This be able to predict average toughness value calculated from the η-approach describe the scatter observed in the fracture study also indicates strongone variations in isboth the driving andelement constraints along the crack front. This toughness. study therefore utilizes an the creep behaviour of HPT blades. Flight records (FDR) atospecific aircraft, providedof by a commercial aviation presents a numerical investigation using localdata Weibull stress approach estimate the probability cleavage fracture the average toughness value calculated from the η-approach to describe thefor scatter observed in the fracture toughness. This studyin also company, were used to obtain and mechanical data for different flight cycles. In order to stress create the 3Din model fracture tests. A combination of thethermal fracture initiation zone defined by three the J-integral values a local Weibull driving force presents a numerical investigation using the local Weibull stress approach to estimate thewith probability of cleavage fracture the needed for Athe FEM analysis, HPT blade scrap scanned, and its chemical and material were predicts reasonably well the probability of fracture ofzone thewas experimental specimens. fracture tests. combination of theafracture initiation defined by the J-integral valuescomposition with a local Weibull stressproperties driving force obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D © 2016 The Authors. Published by Elsevier B.V. of the experimental specimens. predicts reasonably well the probability of fracture Copyright © 2016 The Authors.inPublished by Elsevier B.V. This is anofopen under BY-NC-ND license rectangular block shape, order to better establish the model, andaccess then article with the realthe 3DCCmesh obtained from the blade scrap. The Peer-review under responsibility of the Scientific Committee ECF21. © 2016 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a Peer-reviewunder under responsibility of Scientific the Scientific Committee of ECF21. Peer-review responsibility of the Committee ECF21. model can be useful in the goal of predicting turbine of blade life, given a set of FDR data. Keywords: Cleavage fracture; global approach; local approach; Weibull stress; Probability of fracture. Keywords: Cleavage fracture; global approach; local approach; Weibull stress; Probability of fracture.
© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.
Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* Corresponding author. Tel.: +65-6516-6827; fax: +65-6779-1635. address:author. [email protected] * E-mail Corresponding Tel.: +65-6516-6827; fax: +65-6779-1635.
E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. * Corresponding author. Tel.: +351 Peer-review underThe responsibility of218419991. theby Scientific Committee of ECF21. 2452-3216 © 2016 Authors. Published Elsevier B.V. E-mail address: [email protected] Peer-review under responsibility of the Scientific Committee of ECF21.
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.257
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1. Introduction The petroleum industry foresees upcoming exploration and production activities in the Arctic region, due to the significant amount of petroleum reserve in this region revealed by the geological survey (Gautier et al. 2009). The production and drilling facilities, to be made from primarily ferritic steels, face critical challenges when operating at an ambient temperature as low as -70 oC. The brittle fracture of the fatigue cracks at critical components, induced by cyclic environmental actions, pose a detrimental threat to the safety of these facilities. The unstable brittle fracture often occurs: a) at a remote stress level significantly lower than the material yield strength; 2) without noticeable prior deformations (indicators); and 3) with a significant scatter in the critical crack driving forces at the crack front. Previous developments in the assessment of cleavage fracture of ferritic steels have focused on the statistical treatment of the cleavage fracture through both the global model (Wallin, 1985, 1993, 2002) and the local model (Gao et al. 1998, Petti and Dodds 2004, 2005, Qian and Chen 2014, Qian et al. 2011, Wasiluk et al. 2006, Sobotka and Dodds 2014). The global model, as prescribed in ASTM E-1921 (2015) estimates the cumulative probability of fracture at a given temperature through a three-parameter Weibull model,
K K 4 min 1 exp Jc Pf K 0 K min
(1)
where K Jc denotes the crack driving force, K min refers to the threshold fracture toughness, fixed at 20 MPa m for all temperatures (ASTM E-1921 2015), and K0 defines the Weibull scale parameter, which follows the temperature dependence prescribed by the master curve,
K0 31 77 exp 0.019 T T0
(2)
where T refers to the temperature over the ductile-to-brittle transition regime, and T0 represents the reference temperature at which the median fracture toughness equals 100 MPa m or K 0 108 MPa m . The global approach applies strictly to crack fronts under high-constraint, small-scale yielding conditions. The local approach estimates the probability of fracture at a given temperature through a local scalar Weibull stress, m / 4 m / 4 4 w min Pf w 1 exp wm / 4 m/ 4 u w min
(3)
where w-min refers to the threshold Weibull stress and u denotes the Weibull scale parameter. The Weibull stress, w , computes from, 1/ m
1 w 1m dV f V0 V f
(4)
where V0 denotes a reference volume, and V f represents the volume of the fracture process zone. The local approach aligns well with the global approach via (Petti and Dodds 2004),
wm CBK J4 g ( M )
(5)
where g M denotes the constraint-correction function, quantifying the loss of plasticity-induced constraints in the specimens, and B refers to the thickness of the specimen. Previous works (Wasiluk et al. 2006) have recommended a rigorous procedure to calibrate the Weibull exponent m, which characterizes the distribution of micro-cracks in
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materials ahead of the crack tip, and the threshold toughness, K min . The local approach, based on a local crack driving force, has successfully overcome the bottleneck of the global approach, which limits itself to high-constraint crackfront conditions. Both the local and global approaches have successfully estimated the probability of fracture in specimens with a straight crack front. A limited number of research efforts (Gao et al. 2002, Wallin 2004) have subsequently extended the local and global approach to assess fracture specimens with a curved crack front, which experiences spatial variations in both the crack driving force and the crack-front constraint. This study, therefore, aims to extend the local Weibull stress approach to predict the probability of cleavage fracture failure in non-conventional fracture specimens with a curved crack front, through a combined experimental and numerical investigation. 2. Experimental Program
2.1. Material and Specimens
The experimental program consists of 14 special single-edge notched specimens [SSE(B)] with a curved crack front, fabricated from the same parent plate made of S550 steels. Table 1 shows the chemical composition of the S550 steel and Fig. 1 illustrates the uni-axial true stress-true strain curve of the S550 steel measured at the room temperature (28 oC) and that at an ambient temperature of -90 oC (Chen 2016). Chen (2016) has calibrated the Weibull exponent for this material to be m 12 and the threshold fracture toughness value K min 10 MPa m , based on the experimental results from conventional through-thickness fracture specimens. Table 1. Chemical composition of S550 steel. Weight% S550
Fe
C
Si
Mn
P
S
Cu
Cr
Ni
Mo
96.2
0.106
0.327
1.41
0.010
0.00150
0.121
0.454
0.918
0.462
1600
(MPa)
1200 800 28 °C -90 °C
400 0
0
0.4
0.8
1.2
1.6
2.0
Fig. 1. Uni-axial true stress-true strain curve for the S550 steel measured at 28 oC and -90 oC.
Figure 2 shows the configuration of the non-conventional SSE(B) specimens, which has a thickness (B) of 25 mm (1 inch) and a depth (W) of 25 mm. The SSE(B) specimen has a similar geometry with the standard SE(B) specimen, except that the machined notch follows a semi-elliptical profile, as shown in Fig. 2. The specimen experiences a threepoint bend for both the fatigue pre-cracking performed at the room temperature and the fracture test performed at -90 o C in an environmental chamber. The fatigue pre-cracking has generated a crack extension around 0.5~1.5 mm along the curved crack front. For the fracture test, the specimen resides within an environmental chamber, which is infilled with the liquid nitrogen. Two sets of thermocouples measures the temperature in the environmental chamber, one at the crack tip and the other at another location in the chamber. Upon reaching the target temperature (-90 oC), the specimen remains
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inside the chamber for about 15 ~ 30 minutes for a steady state temperature distribution around the specimen. A crack opening displacement (COD) gauge measures the crack mouth opening displacement (CMOD) during the fracture test. A universal testing machine applies a displacement controlled loading to the specimen until fracture occurs in the specimen. 1.3
4
8.8
B=25
2.2
Unit: mm
2.5
Top View
Notch Detail
P
W=25
62.5
4
11
See Notch Detail
S=100
B=25
Front View
Side View
Fig. 2. Configuration of the SSE(B) specimens.
2.2. Experimental Results
Figure 3 show the typical load versus the CMOD evolution for the 1T SSE(B) specimen measured at -90 oC, with a number of unloading-reloading events to monitor the compliance change in the specimen during the test. Both the post-test sectioning and the compliance measurement confirm negligible crack extensions prior to the cleavage failure. 50
P (kN)
40 30
fracture
20 10 0 0
T = -90 oC 1
2
3
CMOD (mm)
4
5
Fig. 3. Evolution of the load versus the CMOD measured during the fracture test at -90 oC.
The evaluation of the fracture toughness, J c or K Jc , follows the η-approach, originally proposed by Rice et al. (1973) and extended to surface-cracked specimens by Qian and Li (2013). The average energy release rate along the curved crack front follows,
Xudong Qian et al. / Procedia Structural Integrity 2 (2016) 2046–2053 Author name / Structural Integrity Procedia 00 (2016) 000–000
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U
J avg
5
(6)
Anet
where Anet measures the net intact area of the cracked section and U refers to the strain energy stored in the specimen,
U 2 Md
(7)
0
In Eq. 7, M denotes the applied bending moment on the cracked section of the specimen and θ indicates the rotation of the crack plane, derived from the measured CMOD value,
CMOD
(8)
2 a d (W a)
where a represents the crack depth, W refers to the specimen height (see Fig. 2) and d equals 0.56 for the SSE(B) specimen, derived from the deformed shape of the crack plane in a large-deformation finite element analysis. The η value in Eq. 6 derives by equating Eq. 6 with the average J value computed from the domain integral solution, or, N
U Anet
B J i
i
i
(9)
Btotal
where J i denotes the domain integral value computed at individual crack front nodes, Bi refers to the length of the individual crack-front segment, and Btotal corresponds to the length of the entire crack front. The η value thus derived equals 2.97 for the SSE(B) specimen. Substituting Eq. 7 into Eq. 6 allows measurement of the average fracture toughness along the crack front for the SSE(B) specimens from the measured load versus CMOD relationship. 1.0
Pf
0.8 0.6 0.4 0.2 0
0
T = -90 oC 300
600
900
Javg (kJ/m2)
1200
1500
Fig. 4. Rank probability of the measured fracture toughness for SSE(B) specimens at -90 oC.
Figure 4 shows the rank probability of the measured fracture toughness for the SSE(B) specimens at -90 oC. The rank probability of the fracture failure follows,
Pi rank
i 0.3 N 0.4
(10)
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where i denotes the rank number and N refers to the total number of specimens in the test. The microscopic examination of the post-sectioned fracture surfaces reveal that the cleavage fracture initiates at a distance of 3 to 7 mm away from the mid-thickness. 3. Numerical Analysis This study aims to extend the local Weibull stress approach to estimate the probability of fracture observed in SSE(B) specimens with a curved crack front. The numerical procedure therefore computes the Weibull stresses from a large-deformation, elastic-plastic analysis with a very detailed crack-front model. Figure 5 shows the typical, quartersymmetric finite element model used in the current study.
Fig. 5. Typical quarter-symmetric finite element model for the SSE(B) specimen.
The finite element model shown in Fig. 5 utilizes 20-node brick elements with reduced integration. The material property follows the uni-axial true stress-true strain curve measured at -90 oC shown in Fig. 1. The loading and boundary conditions simulate the experimental set-up shown in Fig. 2. The numerical analysis employs the large deformation, elastic-plastic analysis, implemented in an open source research code WARP3D (Healy et al. 2014), to compute the energy release rate along the crack front via the domain integral approach and the Weibull stress through the near-tip stress field (see Eq. 4). Figure 6 compares the variation of the J-integral and the Weibull stress, normalized against the corresponding maximum value along the crack front, at different applied CMOD levels. The coordinate z in the horizontal axis in Fig. 6 denotes the position in the through thickness direction, with z 0 at the free surface. The variations in the normalized J and w value along the crack front demonstrate negligible dependence on the applied load level. This study follows a similar criterion to define the fracture initiation zone along the crack front, as recommended by Chen et al. (2016). This criterion defines the fracture initiation zone as the crack-front zone with a J value larger than 90% of the peak J value along the crack front, i.e., J 0.9 J max . The fracture initiation zone defined by this criterion corresponds approximately to the cleavage initiation locations revealed in the post-test sectioning. In contrast, the variation in the Weibull stress remains much smaller over a significant region near the mid-thickness, with a rapid decrease in the Weibull stress near the free surface. The definition of the critical crack front based on the Weibull stress alone (say, w 0.9 w,max ) may not provide a good correlation with the experimental observation on the fracture initiation locations. The relationship between K J and w implies that the fracture initiation criterion under the
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Weibull stress framework shall consider both the Weibull stress and the Weibull exponent m, which requires prior calibration against extensive experimental fracture toughness data. 1.2
J / J max
(a)
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
CMOD 1 mm
0.4
0.2
CMOD 2 mm CMOD 3 mm
0.2
0
0
0.2
0.4
2z / B
0.6
0.8
0
1.0
w / w-max
(b)
m 12 CMOD 1 mm CMOD 2 mm CMOD 3 mm
0
0.2
0.4
2z / B
0.6
0.8
1.0
Fig. 6. Variation of: (a) the J-integral value; and (b) the Weibull stress; along the crack front.
With the identified crack front, the numerical procedure then treats this crack-front segment as an equivalent through-thickness specimen. The probability of cleavage fracture of the curved crack then depends on the Weibull stress calculated in this critical crack-front segment. Figure 7 compares the probability of cleavage fracture estimated using the Weibull stress approach and the rank probability of the experimental fracture toughness data. The Weibull stress approach provides a reasonable estimation on the rank probability of the experimental data. 1.0
Pf
0.8
m 12 K min 10 MPa m
0.6 0.4 Pf Test
0.2 0.0 0
100
200
K avg MPa m
300
400
Fig. 7. Comparison of the estimated probability of cleavage fracture with the estimated failure probability from the Weibull stress approach.
4. Conclusions
This paper extends the Weibull stress framework, originally developed for fracture specimens with a straight crack front, to assess the probability of cleavage in non-conventional specimens with a curved crack front, through a combined experimental and numerical approach. The experimental program consists of 14 special single-notched edge specimen made of S550 steels. The measurement of the cleavage fracture toughness follows an η-approach previously proposed and validated for surface-cracked specimens. The fracture initiation zone defined based on the energy release rate, J 0.9 J max , covers approximately the fracture initiation locations in the fracture specimens. By treating the identified critical crack-front segment as an equivalent through-thickness fracture specimen, the Weibull stress approach provides a reasonable estimation for the rank probability of the cleavage fracture observed in the experimental study.
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Acknowledgements
The authors would like to acknowledge the financial support provided the Maritime and Port Authority (MPA) Singapore (R-302-501-027-490), American Bureau of Shipping (R-302-501-027-592) and the Sembcorp Marine Technology Pte Ltd (R-302-501-028-592). References American Society of Testing and Material (ASTM) International, 2015. Test method for the determination of reference temperature for ferritic steels in transition range. ASTM E-1921. West Conshohocken, PA(United States): ASTM International. Chen, S., 2016. Cumulative probability of cleavage fracture for high strength steels. PhD Dissertation, National University of Singapore. Chen, S., Qian, X., Ahmed, A., 2016. Cleavage fracture assessment for surface-cracked plates fabricated from high strength steels. Engineering Fracture Mechanics, under review. Gao, X., Ruggieri, C., Dodds, Jr. R. H., 1998. Calibration of Weibull stress parameters using fracture toughness data. International Journal of Fracture 92, 175-200. Gao, X., Dodds, Jr. R. H., Tregoning, R. L., Joyce, J. A., Link R. E., 1999. A Weibull stress model to predict cleavage fracture in plates containing surface cracks. Fatigue & Fracture of Engineering Materials & Structures 22, 481-493. Gautier, D. L., Bird, K. J., Charpentier, R. R., Grantz, A., Houseknecht, D. W., Klet, T. R., Moore, T. E., Pitman, J. K., Schenk, C. J., Schuenemeyer, J. H., Sørensen, K., Tennyson, M. E., Valin, Z. C., Wandrey, C. J., 2009. Assessment of undiscovered oil and gas in the Arctic. Science, 324, 1175-1179. Healy, B., Gullerud, A., Koppenhoefer, K., Roy, A., RoyChowdhury, S., Walters, M., Bichon, B., Cochran, K., Sobotka, J., Messner, M., Dodds, R. H. Jr., 2014. WARP3D-Release 17.3.1 3-D dynamic nonlinear fracture analyses of solids using parallel computers. Structural Research Series No.607. University of Illinois at Urbana Champaign. Petti, J. P., Dodds, R. H. Jr., 2004. Coupling of the Weibull stress model and macroscale models to predict cleavage fracture. Engineering Fracture Mechanics 71, 2079-103. Petti, J. P., Dodds, R. H. Jr., 2005. Calibration of the Weibull stress scale parameter, σu, using the Master Curve. Engineering Fracture Mechanics 72, 91-120. Qian, X., Chen, S., 2014. A K0-based calibration procedure for the Weibull stress cleavage model. Fatigue & Fracture of Engineering Materials & Structures 37, 391-405. Qian, X., Li, Y., 2013. A compliance-based approach to measure fracture resistance curve for surface cracked steel plates. International Journal of Fracture 182, 1-19. Qian, X., Zhang, S., Swaddiwudhipong, S., 2011. Calibration of Weibull parameters using the conventional mechanism-based strain gradient plasticity. Engineering Fracture Mechanics 78, 1928-1944. Rice, J. R., Paris, P. C., Merkle, J. G., 1973. Some further results of J-integral analysis and estimates. ASTM STP 536, American Society for Testing and Materials, Philidelphia, 23–245. Sobotka, J. C. and Dodds, R. H. Jr., 2014. Effects of steady ductile crack growth on cleavage fracture from three-dimensional, small-scale yielding simulations. Engineering Fracture Mechanics 127, 211-225. Wallin, K., 1985. The size effect in KIC results. Engineering Fracture Mechanics 22, 149-163. Wallin, K., 1993. Irradiation damage effects on the fracture toughness transition curve shape for reactor pressure vessel steels. International Journal of Pressure Vessels and Piping 55, 61-79. Wallin, K., 2002. Master Curve analysis of the “Euro” fracture toughness dataset. Engineering Fracture Mechanics 69, 451-481. Wallin, K., 2004. Critical review of the theoretical basis of the ORNL letter report ORNL/NRC/LTR-01/08. Research report No. BTUO72-041250. VTT Technical Research Centre of Finland. Wasiluk, B., Petti, J. P., Dodds, R. H. Jr., 2006. Temperature dependence of Weibull stress parameters: Studies using the Euro-material. Engineering Fracture Mechanics 73, 1046-1069.
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21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy
Assessment of Cleavage Fracture in Specimens with a Curved Crack Front for High-Strength Steels in Offshore Applications Crack Front for High-Strength Steels in Offshore Applications Thermo-mechanical modeling of aChen, highAziz pressure Xudong Qian*, Shuang Ahmedturbine blade of an Xudong Qian*, Shuang Chen, Aziz Ahmed airplane gas turbine engine Department of Civil and Environmental Engineering, Centre for Offshore Research and Engineering, National University of Singapore,
XVAssessment Portuguese Conference on Fracture, PCF 2016,in 10-12 February 2016, Paço Arcos, Portugal of Cleavage Fracture Specimens with a de Curved
Singapore 117576 Department of Civil and Environmental Engineering, Centre for Offshore Research and Engineering, National University of Singapore, a b c Singapore 117576
P. Brandão , V. Infante , A.M. Deus *
a
Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal Abstract c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, The significant petroleum reserve in the Arctic drives the need for offshore facilities in the Arctic made of ferritic structural steels. Portugal b
Such steel materials oftenreserve exhibitinathe brittle fracture without noticeable priorinplastic deformations. This paper presents The significant petroleum Arctic drivesmode the need for offshore facilities the Arctic made of ferritic structural steels.a combined andexhibit numerical investigation assesswithout the cleavage fracture failure fordeformations. high-strength steels used in offshorea Such steelexperimental materials often a brittle fracturetomode noticeable prior plastic This paper presents applications. The experimental programinvestigation includes a set non-conventional, specialfailure single-edge notched bend, SSE(B) combined experimental and numerical to of assess the cleavage fracture for high-strength steels used specimens, in offshore Abstract to the conventional through-thickness specimens, which tested under aThe lower ambient temperature of -90 oaC. applications. experimental program includes setInofcontrast non-conventional, special single-edge notchedfracture bend, SSE(B) specimens, experience ana lower approximately uniform crack force alongtothe cracktofront, the specimens with a operating curved crack front During their operation, modern aircraft engine are subjected increasingly demanding conditions, In contrast theentire conventional through-thickness fracture specimens, which tested under ambient temperature of driving -90 oC. components especially high pressure turbine blades. forces Such cause along these parts tothe undergo different of time-dependent indicates strong variations in both the (HPT) crack driving and constraints the crack front. This study utilizes an experience anthe approximately uniform force conditions along the entire crack front, specimens withtypes atherefore curved crack front degradation, of which creep. Acrack model usingforces thetofinite method (FEM) was developed, in order to This be able to predict average toughness value calculated from the η-approach describe the scatter observed in the fracture study also indicates strongone variations in isboth the driving andelement constraints along the crack front. This toughness. study therefore utilizes an the creep behaviour of HPT blades. Flight records (FDR) atospecific aircraft, providedof by a commercial aviation presents a numerical investigation using localdata Weibull stress approach estimate the probability cleavage fracture the average toughness value calculated from the η-approach to describe thefor scatter observed in the fracture toughness. This studyin also company, were used to obtain and mechanical data for different flight cycles. In order to stress create the 3Din model fracture tests. A combination of thethermal fracture initiation zone defined by three the J-integral values a local Weibull driving force presents a numerical investigation using the local Weibull stress approach to estimate thewith probability of cleavage fracture the needed for Athe FEM analysis, HPT blade scrap scanned, and its chemical and material were predicts reasonably well the probability of fracture ofzone thewas experimental specimens. fracture tests. combination of theafracture initiation defined by the J-integral valuescomposition with a local Weibull stressproperties driving force obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D © 2016 The Authors. Published by Elsevier B.V. of the experimental specimens. predicts reasonably well the probability of fracture Copyright © 2016 The Authors.inPublished by Elsevier B.V. This is anofopen under BY-NC-ND license rectangular block shape, order to better establish the model, andaccess then article with the realthe 3DCCmesh obtained from the blade scrap. The Peer-review under responsibility of the Scientific Committee ECF21. © 2016 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a Peer-reviewunder under responsibility of Scientific the Scientific Committee of ECF21. Peer-review responsibility of the Committee ECF21. model can be useful in the goal of predicting turbine of blade life, given a set of FDR data. Keywords: Cleavage fracture; global approach; local approach; Weibull stress; Probability of fracture. Keywords: Cleavage fracture; global approach; local approach; Weibull stress; Probability of fracture.
© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.
Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* Corresponding author. Tel.: +65-6516-6827; fax: +65-6779-1635. address:author. [email protected] * E-mail Corresponding Tel.: +65-6516-6827; fax: +65-6779-1635.
E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V. * Corresponding author. Tel.: +351 Peer-review underThe responsibility of218419991. theby Scientific Committee of ECF21. 2452-3216 © 2016 Authors. Published Elsevier B.V. E-mail address: [email protected] Peer-review under responsibility of the Scientific Committee of ECF21.
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016.
Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.257
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1. Introduction The petroleum industry foresees upcoming exploration and production activities in the Arctic region, due to the significant amount of petroleum reserve in this region revealed by the geological survey (Gautier et al. 2009). The production and drilling facilities, to be made from primarily ferritic steels, face critical challenges when operating at an ambient temperature as low as -70 oC. The brittle fracture of the fatigue cracks at critical components, induced by cyclic environmental actions, pose a detrimental threat to the safety of these facilities. The unstable brittle fracture often occurs: a) at a remote stress level significantly lower than the material yield strength; 2) without noticeable prior deformations (indicators); and 3) with a significant scatter in the critical crack driving forces at the crack front. Previous developments in the assessment of cleavage fracture of ferritic steels have focused on the statistical treatment of the cleavage fracture through both the global model (Wallin, 1985, 1993, 2002) and the local model (Gao et al. 1998, Petti and Dodds 2004, 2005, Qian and Chen 2014, Qian et al. 2011, Wasiluk et al. 2006, Sobotka and Dodds 2014). The global model, as prescribed in ASTM E-1921 (2015) estimates the cumulative probability of fracture at a given temperature through a three-parameter Weibull model,
K K 4 min 1 exp Jc Pf K 0 K min
(1)
where K Jc denotes the crack driving force, K min refers to the threshold fracture toughness, fixed at 20 MPa m for all temperatures (ASTM E-1921 2015), and K0 defines the Weibull scale parameter, which follows the temperature dependence prescribed by the master curve,
K0 31 77 exp 0.019 T T0
(2)
where T refers to the temperature over the ductile-to-brittle transition regime, and T0 represents the reference temperature at which the median fracture toughness equals 100 MPa m or K 0 108 MPa m . The global approach applies strictly to crack fronts under high-constraint, small-scale yielding conditions. The local approach estimates the probability of fracture at a given temperature through a local scalar Weibull stress, m / 4 m / 4 4 w min Pf w 1 exp wm / 4 m/ 4 u w min
(3)
where w-min refers to the threshold Weibull stress and u denotes the Weibull scale parameter. The Weibull stress, w , computes from, 1/ m
1 w 1m dV f V0 V f
(4)
where V0 denotes a reference volume, and V f represents the volume of the fracture process zone. The local approach aligns well with the global approach via (Petti and Dodds 2004),
wm CBK J4 g ( M )
(5)
where g M denotes the constraint-correction function, quantifying the loss of plasticity-induced constraints in the specimens, and B refers to the thickness of the specimen. Previous works (Wasiluk et al. 2006) have recommended a rigorous procedure to calibrate the Weibull exponent m, which characterizes the distribution of micro-cracks in
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materials ahead of the crack tip, and the threshold toughness, K min . The local approach, based on a local crack driving force, has successfully overcome the bottleneck of the global approach, which limits itself to high-constraint crackfront conditions. Both the local and global approaches have successfully estimated the probability of fracture in specimens with a straight crack front. A limited number of research efforts (Gao et al. 2002, Wallin 2004) have subsequently extended the local and global approach to assess fracture specimens with a curved crack front, which experiences spatial variations in both the crack driving force and the crack-front constraint. This study, therefore, aims to extend the local Weibull stress approach to predict the probability of cleavage fracture failure in non-conventional fracture specimens with a curved crack front, through a combined experimental and numerical investigation. 2. Experimental Program
2.1. Material and Specimens
The experimental program consists of 14 special single-edge notched specimens [SSE(B)] with a curved crack front, fabricated from the same parent plate made of S550 steels. Table 1 shows the chemical composition of the S550 steel and Fig. 1 illustrates the uni-axial true stress-true strain curve of the S550 steel measured at the room temperature (28 oC) and that at an ambient temperature of -90 oC (Chen 2016). Chen (2016) has calibrated the Weibull exponent for this material to be m 12 and the threshold fracture toughness value K min 10 MPa m , based on the experimental results from conventional through-thickness fracture specimens. Table 1. Chemical composition of S550 steel. Weight% S550
Fe
C
Si
Mn
P
S
Cu
Cr
Ni
Mo
96.2
0.106
0.327
1.41
0.010
0.00150
0.121
0.454
0.918
0.462
1600
(MPa)
1200 800 28 °C -90 °C
400 0
0
0.4
0.8
1.2
1.6
2.0
Fig. 1. Uni-axial true stress-true strain curve for the S550 steel measured at 28 oC and -90 oC.
Figure 2 shows the configuration of the non-conventional SSE(B) specimens, which has a thickness (B) of 25 mm (1 inch) and a depth (W) of 25 mm. The SSE(B) specimen has a similar geometry with the standard SE(B) specimen, except that the machined notch follows a semi-elliptical profile, as shown in Fig. 2. The specimen experiences a threepoint bend for both the fatigue pre-cracking performed at the room temperature and the fracture test performed at -90 o C in an environmental chamber. The fatigue pre-cracking has generated a crack extension around 0.5~1.5 mm along the curved crack front. For the fracture test, the specimen resides within an environmental chamber, which is infilled with the liquid nitrogen. Two sets of thermocouples measures the temperature in the environmental chamber, one at the crack tip and the other at another location in the chamber. Upon reaching the target temperature (-90 oC), the specimen remains
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inside the chamber for about 15 ~ 30 minutes for a steady state temperature distribution around the specimen. A crack opening displacement (COD) gauge measures the crack mouth opening displacement (CMOD) during the fracture test. A universal testing machine applies a displacement controlled loading to the specimen until fracture occurs in the specimen. 1.3
4
8.8
B=25
2.2
Unit: mm
2.5
Top View
Notch Detail
P
W=25
62.5
4
11
See Notch Detail
S=100
B=25
Front View
Side View
Fig. 2. Configuration of the SSE(B) specimens.
2.2. Experimental Results
Figure 3 show the typical load versus the CMOD evolution for the 1T SSE(B) specimen measured at -90 oC, with a number of unloading-reloading events to monitor the compliance change in the specimen during the test. Both the post-test sectioning and the compliance measurement confirm negligible crack extensions prior to the cleavage failure. 50
P (kN)
40 30
fracture
20 10 0 0
T = -90 oC 1
2
3
CMOD (mm)
4
5
Fig. 3. Evolution of the load versus the CMOD measured during the fracture test at -90 oC.
The evaluation of the fracture toughness, J c or K Jc , follows the η-approach, originally proposed by Rice et al. (1973) and extended to surface-cracked specimens by Qian and Li (2013). The average energy release rate along the curved crack front follows,
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U
J avg
5
(6)
Anet
where Anet measures the net intact area of the cracked section and U refers to the strain energy stored in the specimen,
U 2 Md
(7)
0
In Eq. 7, M denotes the applied bending moment on the cracked section of the specimen and θ indicates the rotation of the crack plane, derived from the measured CMOD value,
CMOD
(8)
2 a d (W a)
where a represents the crack depth, W refers to the specimen height (see Fig. 2) and d equals 0.56 for the SSE(B) specimen, derived from the deformed shape of the crack plane in a large-deformation finite element analysis. The η value in Eq. 6 derives by equating Eq. 6 with the average J value computed from the domain integral solution, or, N
U Anet
B J i
i
i
(9)
Btotal
where J i denotes the domain integral value computed at individual crack front nodes, Bi refers to the length of the individual crack-front segment, and Btotal corresponds to the length of the entire crack front. The η value thus derived equals 2.97 for the SSE(B) specimen. Substituting Eq. 7 into Eq. 6 allows measurement of the average fracture toughness along the crack front for the SSE(B) specimens from the measured load versus CMOD relationship. 1.0
Pf
0.8 0.6 0.4 0.2 0
0
T = -90 oC 300
600
900
Javg (kJ/m2)
1200
1500
Fig. 4. Rank probability of the measured fracture toughness for SSE(B) specimens at -90 oC.
Figure 4 shows the rank probability of the measured fracture toughness for the SSE(B) specimens at -90 oC. The rank probability of the fracture failure follows,
Pi rank
i 0.3 N 0.4
(10)
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where i denotes the rank number and N refers to the total number of specimens in the test. The microscopic examination of the post-sectioned fracture surfaces reveal that the cleavage fracture initiates at a distance of 3 to 7 mm away from the mid-thickness. 3. Numerical Analysis This study aims to extend the local Weibull stress approach to estimate the probability of fracture observed in SSE(B) specimens with a curved crack front. The numerical procedure therefore computes the Weibull stresses from a large-deformation, elastic-plastic analysis with a very detailed crack-front model. Figure 5 shows the typical, quartersymmetric finite element model used in the current study.
Fig. 5. Typical quarter-symmetric finite element model for the SSE(B) specimen.
The finite element model shown in Fig. 5 utilizes 20-node brick elements with reduced integration. The material property follows the uni-axial true stress-true strain curve measured at -90 oC shown in Fig. 1. The loading and boundary conditions simulate the experimental set-up shown in Fig. 2. The numerical analysis employs the large deformation, elastic-plastic analysis, implemented in an open source research code WARP3D (Healy et al. 2014), to compute the energy release rate along the crack front via the domain integral approach and the Weibull stress through the near-tip stress field (see Eq. 4). Figure 6 compares the variation of the J-integral and the Weibull stress, normalized against the corresponding maximum value along the crack front, at different applied CMOD levels. The coordinate z in the horizontal axis in Fig. 6 denotes the position in the through thickness direction, with z 0 at the free surface. The variations in the normalized J and w value along the crack front demonstrate negligible dependence on the applied load level. This study follows a similar criterion to define the fracture initiation zone along the crack front, as recommended by Chen et al. (2016). This criterion defines the fracture initiation zone as the crack-front zone with a J value larger than 90% of the peak J value along the crack front, i.e., J 0.9 J max . The fracture initiation zone defined by this criterion corresponds approximately to the cleavage initiation locations revealed in the post-test sectioning. In contrast, the variation in the Weibull stress remains much smaller over a significant region near the mid-thickness, with a rapid decrease in the Weibull stress near the free surface. The definition of the critical crack front based on the Weibull stress alone (say, w 0.9 w,max ) may not provide a good correlation with the experimental observation on the fracture initiation locations. The relationship between K J and w implies that the fracture initiation criterion under the
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Weibull stress framework shall consider both the Weibull stress and the Weibull exponent m, which requires prior calibration against extensive experimental fracture toughness data. 1.2
J / J max
(a)
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
CMOD 1 mm
0.4
0.2
CMOD 2 mm CMOD 3 mm
0.2
0
0
0.2
0.4
2z / B
0.6
0.8
0
1.0
w / w-max
(b)
m 12 CMOD 1 mm CMOD 2 mm CMOD 3 mm
0
0.2
0.4
2z / B
0.6
0.8
1.0
Fig. 6. Variation of: (a) the J-integral value; and (b) the Weibull stress; along the crack front.
With the identified crack front, the numerical procedure then treats this crack-front segment as an equivalent through-thickness specimen. The probability of cleavage fracture of the curved crack then depends on the Weibull stress calculated in this critical crack-front segment. Figure 7 compares the probability of cleavage fracture estimated using the Weibull stress approach and the rank probability of the experimental fracture toughness data. The Weibull stress approach provides a reasonable estimation on the rank probability of the experimental data. 1.0
Pf
0.8
m 12 K min 10 MPa m
0.6 0.4 Pf Test
0.2 0.0 0
100
200
K avg MPa m
300
400
Fig. 7. Comparison of the estimated probability of cleavage fracture with the estimated failure probability from the Weibull stress approach.
4. Conclusions
This paper extends the Weibull stress framework, originally developed for fracture specimens with a straight crack front, to assess the probability of cleavage in non-conventional specimens with a curved crack front, through a combined experimental and numerical approach. The experimental program consists of 14 special single-notched edge specimen made of S550 steels. The measurement of the cleavage fracture toughness follows an η-approach previously proposed and validated for surface-cracked specimens. The fracture initiation zone defined based on the energy release rate, J 0.9 J max , covers approximately the fracture initiation locations in the fracture specimens. By treating the identified critical crack-front segment as an equivalent through-thickness fracture specimen, the Weibull stress approach provides a reasonable estimation for the rank probability of the cleavage fracture observed in the experimental study.
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Acknowledgements
The authors would like to acknowledge the financial support provided the Maritime and Port Authority (MPA) Singapore (R-302-501-027-490), American Bureau of Shipping (R-302-501-027-592) and the Sembcorp Marine Technology Pte Ltd (R-302-501-028-592). References American Society of Testing and Material (ASTM) International, 2015. Test method for the determination of reference temperature for ferritic steels in transition range. ASTM E-1921. West Conshohocken, PA(United States): ASTM International. Chen, S., 2016. Cumulative probability of cleavage fracture for high strength steels. PhD Dissertation, National University of Singapore. Chen, S., Qian, X., Ahmed, A., 2016. Cleavage fracture assessment for surface-cracked plates fabricated from high strength steels. Engineering Fracture Mechanics, under review. Gao, X., Ruggieri, C., Dodds, Jr. R. H., 1998. Calibration of Weibull stress parameters using fracture toughness data. International Journal of Fracture 92, 175-200. Gao, X., Dodds, Jr. R. H., Tregoning, R. L., Joyce, J. A., Link R. E., 1999. A Weibull stress model to predict cleavage fracture in plates containing surface cracks. Fatigue & Fracture of Engineering Materials & Structures 22, 481-493. Gautier, D. L., Bird, K. J., Charpentier, R. R., Grantz, A., Houseknecht, D. W., Klet, T. R., Moore, T. E., Pitman, J. K., Schenk, C. J., Schuenemeyer, J. H., Sørensen, K., Tennyson, M. E., Valin, Z. C., Wandrey, C. J., 2009. Assessment of undiscovered oil and gas in the Arctic. Science, 324, 1175-1179. Healy, B., Gullerud, A., Koppenhoefer, K., Roy, A., RoyChowdhury, S., Walters, M., Bichon, B., Cochran, K., Sobotka, J., Messner, M., Dodds, R. H. Jr., 2014. WARP3D-Release 17.3.1 3-D dynamic nonlinear fracture analyses of solids using parallel computers. Structural Research Series No.607. University of Illinois at Urbana Champaign. Petti, J. P., Dodds, R. H. Jr., 2004. Coupling of the Weibull stress model and macroscale models to predict cleavage fracture. Engineering Fracture Mechanics 71, 2079-103. Petti, J. P., Dodds, R. H. Jr., 2005. Calibration of the Weibull stress scale parameter, σu, using the Master Curve. Engineering Fracture Mechanics 72, 91-120. Qian, X., Chen, S., 2014. A K0-based calibration procedure for the Weibull stress cleavage model. Fatigue & Fracture of Engineering Materials & Structures 37, 391-405. Qian, X., Li, Y., 2013. A compliance-based approach to measure fracture resistance curve for surface cracked steel plates. International Journal of Fracture 182, 1-19. Qian, X., Zhang, S., Swaddiwudhipong, S., 2011. Calibration of Weibull parameters using the conventional mechanism-based strain gradient plasticity. Engineering Fracture Mechanics 78, 1928-1944. Rice, J. R., Paris, P. C., Merkle, J. G., 1973. Some further results of J-integral analysis and estimates. ASTM STP 536, American Society for Testing and Materials, Philidelphia, 23–245. Sobotka, J. C. and Dodds, R. H. Jr., 2014. Effects of steady ductile crack growth on cleavage fracture from three-dimensional, small-scale yielding simulations. Engineering Fracture Mechanics 127, 211-225. Wallin, K., 1985. The size effect in KIC results. Engineering Fracture Mechanics 22, 149-163. Wallin, K., 1993. Irradiation damage effects on the fracture toughness transition curve shape for reactor pressure vessel steels. International Journal of Pressure Vessels and Piping 55, 61-79. Wallin, K., 2002. Master Curve analysis of the “Euro” fracture toughness dataset. Engineering Fracture Mechanics 69, 451-481. Wallin, K., 2004. Critical review of the theoretical basis of the ORNL letter report ORNL/NRC/LTR-01/08. Research report No. BTUO72-041250. VTT Technical Research Centre of Finland. Wasiluk, B., Petti, J. P., Dodds, R. H. Jr., 2006. Temperature dependence of Weibull stress parameters: Studies using the Euro-material. Engineering Fracture Mechanics 73, 1046-1069.