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Procedía Engineering 130 (2015) 784 - 802
Procedía Engineering
www.elsevier.com/locate/procedia
14th International Conference on Pressure Vessel Technology
Advances in Fracture Toughness Test Methods for Ductile Materials
in Low-Constraint Conditions
X.-K. Zhu!
Edison Welding Institute
a1250 Arthur E Adam Drive, Columbus, OH 43221, USA
Abstract
Fracture toughness is an important material property in the fracture mechanics methods, and often described with the fracture parameters of ./-integral and crack-tip opening displacement (CTOD) for ductile cracks. ASTM, BSI and ISO have developed their own standard test methods for measuring initial toughness and resistance curves in terms of / and CTOD using deeply cracked bending specimens. Such specimens are of high crack-tip constraints and give conservative toughness or resistance curves.
Actual cracks in pressure vessels and welds are often shallow and dominated by tensile forces, resulting in low crack-tip constraint conditions and rising resistance curves. Thus the standard resistance curves could be overly conservative for a shallow crack in real structures. To obtain more reasonable fracture toughness for ductile cracks in low-constraint conditions, many experimental and analytical methods have been developed in the recent decades. This paper presents a critical technical review of fracture toughness test methods for standard and non-standard specimens, including (1) ASTM, BSI and ISO standard test methods for high-constraint specimens, (2) constraint correction methods for determining a family of constraint-dependent resistance curves, and (3) direct test methods for a low-constraint specimen: single edge-notched tension (SENT) specimen. This includes the basic concepts, basic methods, estimation equations, test procedures, limitations, historical effects, and recent progresses.
©2015 The Authors.Published byElsevierLtd. 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 organizing committee of ICPVT-14
Keywords: fracture toughness; /-R curve; CTOD-R curve; constraint correction; ASTM E1820; BS 8571; ISO 12135
* Corresponding author. Tel.: +1-614-688-5135; fax: +1-614-688-5001. E-mail address: xzhu@ewi.org
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. 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 organizing committee of ICPVT-14
doi:10.1016/j.proeng.2015.12.195
Nomenclature
a, ao Crack length, original crack length
A Area under a load-displacement curve
A2 Constraint parameter in the J-A2 theory
ASTM American Society for Testing and Materials
b Uncracked ligament (b = W-a)
B Specimen thickness
BSI British Standards Institution
CanMet Canada Center for Material and Energy Technology
CCP Central cracked plate
CT Compact tension
CTOA Crack tip opening angle
CTOD Crack tip opening displacement
CTOD-R CTOD resistance
CMOD Crack mouth opening displacement
DNV Det Norske Veritas in Norway
E Young's modulus
FEA Finite element analysis
G Energy release rate
h Stress triaxiality ratio
ISO International Organization for Standardization
J J-integral
Jic Plane strain fracture toughness for ductile material
J-R J-integral resistance
K Stress intensity factor
Kic Plane strain fracture toughness for brittle material
LLD Load-line displacement
m Factor used to relate J and CTOD
P Applied force on fracture specimens
rp Plastic rotation factor
R-curve Resistance curve
Q Constraint parameter in the J-Q theory
SENB Single edge notched bend
SENT Single edge notched tension
T T-stress
V V=CMOD
Vi, V2 Clip gage displacements
W Specimen width
z, zi, Z2, hi, h2 Clip gage knife heights
A A = LLD
Aa Crack extension (Aa=a-ao)
8 8 =CTOD
8ic Critical value of CTOD in plane strain conditions
"q, y Dimensionless plastic geometry factors
Gys Yield stress of material
Guts Ultimate tensile stress of material
cty Effective yield stress (cty = (ctys +CTuts)/2)
v Poisson's ratio
1. Introduction
Fracture toughness is an important material property used to describe material resistance against fracture in a structure containing a crack. For an elastic crack, the stress intensity factor K proposed by Irwin [1] is used as a fracture parameter. For a ductile crack, the J-integral proposed by Rice [2] and the crack-tip opening displacement (CTOD, or S) proposed by Wells [3] are used as fracture parameters. These fracture parameters are able to describe both a crack driving force and the material toughness in a fracture mechanics analysis. Thus, they were adopted in different fitness for service codes, such as API 579 [4], and have extensively been used in the engineering critical analysis or structural integrity assessment [5-6] for various engineering structures, including pressure vessels, pressure equipment and oil and gas pipelines.
Fracture toughness measurement is essential to the fracture mechanics methods, and extensive efforts have been made to develop reliable fracture toughness test methods over the past half century since the early 1960s. Recently, Zhu and Joyce [7] and Zhu [8] presented a comprehensive technical review of fracture toughness test methods and standardization at the American Society for Testing and Materials (ASTM) in USA. Among the standard fracture test methods, ASTM E399 [9] and ASTM E1820 [10] are two representatives. ASTM E399 was the first fracture test standard developed for measuring the elastic plane strain fracture toughness KIc for brittle materials. ASTM E1820 is a combined fracture test standard developed for determining the elastic-plastic plane strain fracture toughness Jic or Sic, and J-R curves or 8-R curves for ductile materials. Recently ASTM published a newer fracture test standard E2472 [11] for measuring crack-tip opening angle (CTOA) in low-constraint conditions. Because CTOA is often used to describe large stable crack growth, but not for small crack extension, and thus it will not be discussed hereafter. Numerous fracture toughness test standards have been developed worldwide. For example, the British Standard Institution (BSI) developed a set of standard fracture toughness test methods with a designation of BS 7448 [12-14]. International Organization for Standardization (ISO) developed a combined fracture toughness test standard ISO 12135 [15] that corresponds to ASTM E1820.
In order to obtain conservative fracture resistance, most fracture test standards adopted deeply cracked bending specimens with high crack-tip constraint conditions. Among them, compact tension (CT) specimen and single edge notched bend (SENB) specimen are two most often used ones in a fracture toughness test. However, many experiments [16-19] showed that the crack-tip constraint levels due to crack size, specimen geometry, and loading type have a strong effect on fracture resistance in terms of J-R or 8-R curves. In general, a high-constraint specimen gives a lower R-curve, while a low-constraint specimen produces a higher R-curve.
Most real cracks found in pressure vessels and other engineering structures are not deep, but shallow ones with low-constraint conditions. In this case, standard fracture resistance results may give overly conservative toughness for real shallow cracks that could result in an unnecessary repair or replacement of components. To reduce the over-conservatism and to determine more realistic fracture toughness, standard toughness results must be transferred to actual cracks in low-constraint conditions. To solve this transferability issue, Zhu and his co-workers [20-22] proposed a constraint correction method for developing a family of constraint-dependent J-R curves based on a series of selected standard and non-standard specimen tests, a fracture constraint theory and the finite element analysis (FEA) of tested specimens. For a real crack, one FEA calculation is needed to determine the crack-tip constraint level, and then the fracture resistance curve for this real crack can be predicted from the proposed constraint-corrected resistance curve. This constraint correction method has been successfully applied to pipeline integrity assessments [21-22].
For oil and gas pipelines, Nyhus et al. [23] showed that the crack-tip constraint level for a single edge notched tension (SENT) specimen is much closer to that for a crack in a line pipe than the standard SENB specimen, and suggested use the SENT specimen to measure more realistic fracture toughness for that pipe. Cravero and Ruggieri [24] showed that pin-loaded SENT specimens in plane strain conditions generate crack-tip constraint levels similar to axial surface cracks in a pipe with identical crack lengths, particularly for moderate to shallow crack sizes. Later, Cravero et al. [25] showed that clamped SENT specimens in three-dimensional conditions have crack-tip constraint levels similar to those for identical circumferential surface cracks in pipe under combined loading. As a result, SENT specimens in pin-loaded or end-clamped conditions can be used to directly measure a fracture resistance curve for an axial or circumferential crack in a line pipe.
Due to the nature of low-constraint conditions in SENT specimens, the oil and gas industry prefers to develop direct test methods to measure less conservative fracture toughness using low-constraint SENT specimens, and several direct test methods have been developed by different companies [26]. Of which, three typical ones are the multiple specimen method developed by DNV [27], the single specimen method with use of a single clip gage developed by CanMet [28-29], and a single-specimen method with use of a double clip gage arrangement developed by ExxonMobil [30-31]. To date, however, a detailed review of the constraint correction methods and direct SENT test methods is not available in public literature. Such a review will facilitate to develop better low-constraint fracture toughness test methods and to benefit the fracture mechanics community and eventually the industries.
So motivated, this paper presents a critical technical review of the existing fracture toughness test methods for ductile cracks in low constraint conditions. This includes (1) ASTM, BSI and ISO standard test methods for high constraint specimens, (2) constraint correction methods for determining a family of constraint-dependent fracture resistance curves, and (3) direct test methods for low-constraint SENT specimens. The basic concepts, basic methods, estimation equations, test procedures, limitations, historical effects and recent progresses are discussed in this review.
2. Standard fracture toughness test methods
2.1. ASTM E1820 standard fracture test methods
2.1.1. Basic test method for /Ic testing
(1). LLD-based method. The early /-integral test methods were developed based on the load vs load-line displacement (LLD), as standardized by the ASTM, see Zhu and Joyce [7]. The first /-R curve test standard ASTM E1152-87 (the earliest version of E1820 [10]) separated the total /-integral into elastic and plastic components to be determined separately:
/ = /i + /Pi (1) where the elastic component /el is calculated directly from the stress intensity factor K for a plane strain crack:
/., - ^^ (2)
where E is the Young's modulus and v is the Poisson's ratio. For a stationary crack, the plastic component /pi is determined from the following ^-factor equation:
/pl ~ BNb (3)
where ^ is a plastic geometry factor, b=W-a is the specimen ligament, BN is the net thickness of side grooved specimen, and Apl is the plastic area under the load-LLD curve obtained in a fracture test. Note that the original crack size a0 is used in the elastic and plastic / -integral calculations. Equations (1) - (3) were adopted first in ASTM E1152, and now in ASTM El820 [10] as the basic procedure to evaluate the plane strain initiation toughness /¡c, when a crack growth resistance is not needed.
(2). CMOD-based method. Experiments showed that crack-mouth opening displacement (CMOD) is easier to measure in a higher accuracy than LLD for SENB specimens, particularly for a shallow crack. Using the CMOD-based plastic "q factor, Kirk and Dodds [32] proposed a CMOD-based / estimation equation that is similar to Eq. (3):
/ _ VcMODACMOD /a\
/pl = BNb (4)
where the subscript CMOD denotes the CMOD-based values. Equation (4) was adopted by ASTM E1820 as an alternative basic procedure to determine JIc. Note that the basic test procedure was originally developed only for multiple specimen tests, but now is applicable to the single specimen method with an appropriate crack growth correction.
2.1.2. Resistance curve test method for J-R curve testing
(1). LLD-based method. While the basic test method determines fracture initiation toughness in a point value, the resistance curve test method determines fracture toughness in a format of resistance curve from a single specimen test. The J-integral estimation Eq. (3) or (4) is valid only for a stationary crack to determine the critical JIc at ductile tearing initiation. For a growing crack, the J-estimation equation needs to correct the crack growth effect because the J-integral was defined in terms of deformation theory of plasticity [33]. To this end, Ernst et al. [34] proposed an incremental J-integral equation to consider the crack growth correction in a J-R curve evaluation. ASTM E1820 still calculates the elastic Jei directly from the stress intensity factor using Eq. (2), but uses the Ernst incremental J-integral equation to calculate the plastic J-integral component - Jpr.
J | fy-l Ai~l-i PKi-V n L pi
BNbi-l
1 _IbtL{ai -aM)| (5)
where "q and y are two plastic geometry factors, and Aj'1 denotes the incremental plastic area under the measured load-LLD curve and calculated by:
A? = ^ (pi + P-1 )(ap (i) ~An (i-D) (6)
where Api is the plastic component of LLD. The unloading compliance technique is recommended by ASTM E1820 for determining the instantaneous crack length through measuring CMOD-based elastic unloading compliance in a single specimen test. As such, the load, LLD, and CMOD records are required in the J calculation, and in a J-R curve evaluation from a single specimen test. Recently, Zhu [35] developed a more accurate incremental J-integral equation than Eq. (5) for a J-R curve evaluation.
(2). CMOD-based method. The above-noted LLD-based resistance curve test method has been adopted by ASTM El820 for more than 30 years. In order to meet the long-time desire at ASTM for eliminating LLD measurement and for increasing the accuracy of J-R curve evaluation, Zhu et al. [36] in 2007 developed a CMOD-based incremental J-integral equation:
J pi (i) ={JPl (i-D a-a«)) W
to calculate the plastic component of J, where tjcmod and yCMOD are two CMOD-based plastic geometry factors, and A,^'' denotes the incremental plastic area under the measured load-CMOD curve:
4? = \ (pi+ pi-i X^ici, " Vpi(i-i)) (8)
Note that Eq. (7) only requires load and CMOD data to develop a J-R curve, and thus ASTM E1820 in its 2008 and later versions adopted Eq. (5) as an alternative resistance curve test method for a J-R curve evaluation. This new J-R curve evaluation method is good not only for SENB or CT specimens, but also for SENT specimens. However, to date, ASTM E1820 has not considered the SENT specimen in its standard test methods.
2.1.3. /-integral conversion method for CTOD testing
ASTM E1290 [37] was developed for CTOD testing to determine the critical 8ic to quantify ductile crack initiation or cleavage instability. The earliest version of E1920 utilized the plastic hinge model as used by BS 74481 [12] to calculate the 8ic. Because the rotation radius depends on the crack size and strain hardening, E1290 in 2002 discarded the plastic hinge model and changed to use the /-integral conversion method to calculate the 8ic. Correspondingly, ASTM E1820 [10] in 2005 adopted the /-integral conversion method to determine 8ic in its basic method and 8-R curves in its resistance curve method:
CTOD (9)
where cty = (ctys + CTuts)/2, ays is the yield stress, CTuts is the ultimate tensile stress, and m isa factor to be a function of a/W and CTys/CTuts. Note that m was determined by FEA with the CTOD defined at the 90° interception of a line from the blunted crack tip with the deformed crack surfaces. Due to the duplication of E1820, E1290 [37] was withdrawn in 2013.
2.1.4. Fracture toughness test method for shallow cracks
The ASTM E1820 test methods and equations overviewed above were suitable for standard SENB, CT and disk-shaped CT specimens with deep cracks of 0.45<a0/W<0.70 and larger specimen width of 1<W/B <4. Since 2011, ASTM E1820 in its appendix X2 has provided guidelines for measuring the fracture toughness of materials with shallow cracks of 0.05<a0/W<0.45. This is a non-mandatory appendix, and serves as an option for users. The nonstandard specimen adopted is SENB with a shallow crack in three-point bending conditions. Only the CMOD-based /-integral equation is used, and the crack growth correction is not considered for a /-R curve testing. This may cause confusions and disputes because it is inconsistent with Eq. (5) for the deep cracks.
2.2. BS 7448 standard fracture test methods
2.2.1. /-integral test methods
(1). Jic testing. BS 7448-1 [12] provides the standard test method for determination of point-value toughness /¡c for metallic materials. The /¡c evaluation procedure in BS 7448-1 is the same as the basic method in ASTM E1820 with use ofEqs (1) to (3), but only LLD measurements are allowed.
(2). J-R curve testing. BS 7448-4 [14] provides the standard test method for determination of fracture resistance curves and initiation values for stable crack extension in metallic materials. Again, the procedure of resistance curve evaluation in BS 7448-4 is similar to that in ASTM E1820, but a different/-integral equation is used:
where /0 is the total value calculated from Eqs (1) - (3) with use of LLD based on the basic procedure. Although the /-integral Eq. (10) is completely different from the /-integral incremental Eq. (7), but experimental results have shown that the resistance curve test procedures in BS 7448-4 and ASTM E1820 determine nearly identical /-R curves for the same test.
2.2.2. CTOD test methods
(1). Plastic hinge model. Both BS 7448-1 and BS 7448-4 adopt a plastic hinge model to calculate CTOD that is defined at the original crack tip. This model assumes that two arms of the specimen rigidly rotate around a plastic hinge point on the ligament of specimen in a test. The total CTOD was separated into an elastic part calculated from the stress intensity factor K, and a plastic part calculated by the plastic hinge model.
(2). Sic testing. BS 7448-1 recommends use the following equation to calculate the 8ic value using CMOD data:
5 = g2(l-v2) | [rp(W-q0)]vpl
2aysE [rp(W-a0)+a0+z] '
where rp is a plastic rotation factor that depends on crack size and specimen type (rp = 0.4 for SENB, and rp = 0.46 for CT), Vpl is the plastic component of CMOD, z is the height of the knife edge measurement point from the front face on specimen.
(3). 8-R curve testing. BS 7448-4 adopts the crack growth corrected plastic hinge model to calculate CTOD in a S-R test:
S = K2(l-v2) | [rp(W-a)+&q]vpl
2aysE [rp(W-a)+a+z] '
Equation (12) reduces to Eq. (11) if a=a0 and Aa=0. It was found that the rotation-based CTOD strongly depends on crack length if a/W<0.45 if material strain hardening is present. This is the reason that ASTM E1290 in 2002 and E1820 in 2005 discarded the plastic hinge model, and changed to use the /-conversion method for the CTOD testing.
2.3. ISO 12135 standard fracture test methods
2.3.1. /-integral test methods
Basically, the standard fracture test methods in ISO 12135 [15] are the extension of BS 7448-1 for /Ic testing and BS 7448-4 for /-R curve testing. The /-integral calculation uses LLD data, rather than CMOD data.
2.3.2. CTOD test methods
For 8ic testing, ISO 12135 [15] uses the plastic hinge model in BS 7448-1 with use of Eq. (11) to calculate the Sic for a stationary crack. For 8-R curve testing, however, ISO 12135 adopts the /-integral conversion method in ASTM E1820 to calculate CTOD from Eq. (9) for a growing crack.
The ASTM, BSI and ISO standard test methods were briefly reviewed above, and the focus was put on the basic concepts and methods with primary estimation equations. Many other important details including test data validation requirements, definition of initiation toughness and valid test data ranges are not discussed here due to space limitation, but can be found from the test standards.
3. Constraint correction methods for formulating constraint-dependent J-R curves
3.1. Experimental observations - constraint effect on /-R curves
For a variety of ductile metals, including nuclear pressure vessel steels, structural steels, and pipeline steels, extensive experiments [16-19, 38-41] have shown that the crack-tip constraint levels have a significant effect on ductile fracture resistance in terms of /-R curves or 8-R curves due to crack size, specimen geometry and loading type. In general, a high-constraint fracture specimen (i.e., deep crack in bending dominant conditions) gives a lower R-curve, whereas a low-constraint fracture specimen (i.e., shallow crack in tensile dominant loading conditions) produces a higher R-curve for ductile cracks.
Joyce and Link [19, 38] showed that SENB specimens subjected to three-point bending can be tested over a wide range of a/W ratios from shallow to deep cracks, and the measured /-R curves demonstrated a wide spectrum of effective toughness. Since this specimen is a relatively easy geometry to test, the SENB specimens with different a/W ratios have been often used to investigate the constraint effect on /-R curves for ductile materials. Figure 1 shows the constraint-dependent /-R curves of HY80 steel that were obtained by Zhu and Joyce [41] using the normalization method for a set of SENB specimens. As evident in this figure, significant differences exist between the /-R curves for deep and shallow cracks due to the constraint effect.
In order to reduce or eliminate the constraint effect on conventional deformation /-R curves, Ernst [42] proposed a so-called modified /M-integral. Recently, Zhu and Lam [33] showed that a /M-R curve is actually the deformation
J-R curve without crack growth correction, and thus Jm-R curves should not be used in practice of fracture testing and engineering applications.
Crack extension (mm)
Fig. 1. Experimental J-R curves ofHY80 steel obtained by Zhu and Joyce [41] using SENB specimens and normalization method.
3.1.1. Constraint correction method - concept and procedure
In order to quantify the constraint effect on J-R curves and to transfer the standard J-R curves to a low constraint crack, the present author and his coworkers [20-22] developed a general constraint correction method. This method integrated three basic analyses of theoretical, experimental, and numerical studies into one result. This includes using the fracture constraint theory, experimental tests, and FEA simulations. In ASTM E1820 [10], a J-R curve is assumed to be a power-law function within its valid range. Similarly, a constraint-corrected J-R curve is assumed to be a power-law function of crack extension and constraint parameter in a form of:
( a \c2(q>
J (Aa, q) = QCq)!-^] (13)
^ 1mm )
where Aa is crack extension, q is a general dummy constraint parameter, C1 and C2 are two coefficients to be functions of the q. In the fracture constraint theories, three typical asymptotic solutions are adequate to use for quantifying the crack-tip constraint level and the stress and strain field for a ductile crack. They are the J-T theory [43], J-Q theory [44] and J-A2 theory [45]. Therefore, the dummy constraint parameter q in Eq. (13) can be T, Q, and A2. For most ductile steels, the large-scale yielding occurs as a crack grows, and so Q andA2 are the appropriate constraint parameter to use.
To calibrate the constraint parameter q and two coefficient functions C1(q) and C2(q) in Eq. (13), a four-step procedure has been developed to use: (1) test at least three fracture specimens with standard and nonstandard cracks to cover low to high constraint conditions, (2) perform elastic-plastic FEA calculations for each tested specimen for loading up to the fracture initiation toughness, (3) select a fracture constraint theory, like J-Q or J-A2 solution, and calculate the constraint parameter q for each tested crack using the FEA result and selected asymptotic solution, (4) calibrate the two coefficients C1(q) and C2(q) based on the experimental J-R curves and the FEA calculated constraint parameter values using a regression approach. Once the calibration procedure is completed, each experimental J-R curve is uniquely correlated to a specific value of the constraint parameter, and a family of constraint-dependent J-R curves is eventually formulated for the tested material. Provided that the constraint parameter is obtained for a real crack ofinterest, its J-R curve can conveniently be predicted from Eq. (13).
In terms of the modified constraint parameter Q, Zhu and Jang [46] and Zhu and Leis [22, 47] determined constraint-corrected J-R curves for different ductile metals. In reference to the constraint parameter A2, Chao and
Zhu [20], Lam et al. [39] and Zhu and Leis [21] obtained constraint-corrected J-R curves also for ductile materials. For example, Fig. 2 shows the experimental and predicted constraint-dependent J-R curves for X80 pipeline steel obtained by Zhu and Leis [47] using SENB specimens and the modified constraint parameter Q. In this figure, the constraint-corrected J-R curve is expressed as:
f \ (-0.066Q+0.637)
J{6a, Q) = (- 1225Q + 6451 -^1 (14)
^ 1mm j
where 6a is in mm, and the J-integral has units of kj/m2. This equation demonstrates that the experimental results of constraint-dependent J-R curves for a given material can simply be approximated in a closed-form function of a single constraint parameter only. Figure 2 shows that the predicted J-R curves from Eq. (14) match well with the experimental results for both deep and shallow cracks. If a real crack in the X80 pipe needs to be assessed for its integrity, an elastic-plastic FEA calculation is required for determining the constraint parameter Q, and then the J-R curve for that real crack is predicted from Eq. (14).
1800 1500 1200 I 900 600
0.0 0.5 1.0 1.5 2.0 2.5
Aa (mm)
-r-.- X80 SENB / / x°
/ □ test data, a/W=0.24
-Prediction, Q=-0.48 0 Test data, a/W=0.42
/fry - Prediction,Q=-0.26 a test data, a/W=0.64
- Prediction, Q=-0.09
¡TSs / 0.2mm offset line S}» 0 ' W f.......................
Fig. 2. Experimental J-R curves ofX80 pipeline steel and their predictions obtained by Zhu and Leis [47] using the modified constraint parameter Q.
3.2. Constraint correction method - recent progresses
Since the constraint correction method was developed, many investigations and applications have been made on this topic. For example, Wang et al. [48] in 2009 applied the constraint correction method with the constraint parameter A2 to 18G2A structural steel, and developed a constraint-corrected J-R curve for this steel. Yin et al. [49] in 2012 applied the constraint correction method to a large European project of structural integrity for lifetime management, and transferred constraint-dependent J-R curves measured from standard specimens to a large-scale mock-up experiment configuration. Zhou et al. [50-51] in 2009 and 2011 extended the constraint correction method to cracks described by the T-stress, and improved the regression procedure in determination of C1(q) and C2(q). Then these authors obtained three families of constraint-corrected J-R curves using the constraint parameter Q, A2 andTforHYlOO steel.
More recently, Huang et al. [52] in 2014 reinvestigated the constraint correction method for a set of constraint parameters, including Q and its variations, A2, TZ and the stress triaxiality ratio h. In their analysis, all constraint parameters were determined from the three-dimensional FEA calculations. For each constraint parameter, they obtained the constraint-corrected J-R curve of X80 pipeline steel, as investigated by Zhu and Leis [22, 47]. As such,
those authors were able to identify the most effective constraint parameter to be used in determination of a more accurate constraint-corrected J-R curve using the constraint correction method.
In addition, Wang et al. [53-54] in 2013-2014 and Chen et al. [55] in 2015 also investigated the constraint correction method using a modified T-stress as the constraint parameter, where the J-R curves for calibration were either measured experimentally, or obtained numerically using a micromechanics damage (i.e., Gurson-Tvergard-Needleman: GTN) model. Because the damage model was introduced, the ductile crack growth can be simulated and the associated J-R curve can be determined for a specific fracture specimen, including SENB, CT, SENT and central cracked plate (CCP). In this way, those authors successfully determined the family of constraint-dependent J-R curves from a set of SENB tests for a nuclear pressure vessel steel A508 and its dissimilar welds. They also validated their results using the CT, SENT and CCP specimens, and applied their results to determine constraint-dependent LBB curves for pipes with circumferential through-wall cracks.
In a summary, the constraint correction method is an integrated technique, and thus can be used reliably to develop a family of constraint-dependent J-R curves and to predict a J-R curve for a specific crack provided that the constraint parameter is numerically obtained a priori for that crack. As a result, the constraint correction method provides an effective compliment means to the experimental measurements of ASTM E1820, and can serve as a vital tool to transfer laboratory measured fracture toughness to those for actual engineering applications in an indirect test manner.
4. Direct test methods for measuring low-constraint fracture toughness using SENT specimens
The constraint correction method described above is a general approach used to transfer Lab measured standard fracture toughness to actual components, and to predict a resistance curve for a real crack of interest. However, it is an indirect semi-test method, and involved in a multiple-step procedure in determination of a low-constraint resistance curve for a shallow crack. Thus, different direct methods were developed to measure low-constraint fracture toughness using SENT specimens, as discussed next.
4.1. Early SENT test methods for J-R curve evaluation
(1). Historical SENT testing. The SENT specimen is not an ASTM standard specimen so far, but has a long history to be used for fracture toughness testing [56]. SENT specimen was first introduced by Irwin, Krafft, and Sullivan for measuring the elastic plane strain fracture toughness (Kic or Gic) in an unpublished memorandum to the ASTM Special Committee on Fracture Testing in August, 1962. Later in 1964, Sullivan [57] presented a design of SENT specimen in a pin-loaded condition, as shown in Fig. 3(a), and Srawley et al. [58] measured the elastic energy release rate G using the pin-loaded SENT specimens. In 1965, Srawley and Brown [59] obtained a closed-form expression of K for the SENT specimens. In 1973, Tada et al. [60] obtained more accurate functions of K and elastic compliance for the pin-loaded SENT specimens. However, the primary interest was to measure lower-bound plane strain toughness to ensure conservative results, the high-constraint bending dominant CT and SENB specimens became the focus for developing standard fracture toughness test methods. Based on the bending dominated specimens, the first fracture toughness test standard ASTM E399 [6] for the KIc testing was developed and published in 1972.
(2). SENT testing for J-R curves. As a low-constraint specimen, SENT has been used for studying the crack-tip constraint effect on J-R curves. Joyce et al. [18] in 1993 extended the resistance curve test procedure in ASTM E1152 to SENT specimens, and measured the J-R curve using pin-loaded SENT specimens. Their experiments showed that the SENT-measured J-R curves have (1) rising values in comparison to those for the standard SENB specimens, (2) less sensitivity to the crack length, and (3) initial crack backup at the beginning of crack extension. Then they proposed a rotation correction factor to correct the unloading compliance and to remove the initial crack backup occurred in their J-R curves.
W <* *
Fig. 3. Schematic diagram of SENT specimen in (a) pin-loaded condition, and (b) clamped condition.
4.2. DNV multiple specimen method for J-integral testing
For offshore pipelines installed by the reeling approach, large plastic strains are introduced, and girth welds fracture may occur. To assess a shallow crack, DNV favored to develop a direct method to measure low-constraint fracture toughness using clamped SENT specimens, as shown in Fig. 3(b). In 2006, DNV published their own SENT test method: DNV recommended practice DNV-RP-F108 [27]. This practice adopts the multiple specimen method for developing a J-R curve with SENT specimens in a pin-loaded or clamped condition. The specimen thickness B=2W, the distance between the two grips is H=10W, and the pre-cracked length is in the range of 0.2 <a/W< 0.5. Side grooves are not required. The maximum crack extension is set as 3 mm.
To develop a J-R curve, DNV requires a minimum of six SENT specimens (6 valid results) be tested in a procedure similar to the basic method of ASTM El820. The total J-integral was separated into the elastic and plastic parts, as shown in Eq. (1), and calculated separately. The elastic J was calculated from the stress intensity factor K from Eq. (2), and the plastic J-integral is calculated by the CMOD-based Eq. (4). The CMOD can be measured directly on the crack mouth of the specimen or estimated from double clip gage measurements.
As well known, the multiple specimen method is costly in terms of test time and materials. As a result, a single specimen method has been sought for the SENT testing.
4.3. CanMet single specimen method for J-integral testing
4.3.1. CanMet method for J-R curve testing
An effective direct test method, i.e., single specimen method was developed by CanMet [28-29] for clamped SENT specimens. The specimen width W=B, the clamping distance H=10 W, and the pre-fatigued crack size is in the range of 0.1<a/W<0.7, and a total side groove of 15% of thickness is recommended. The CanMet procedure is similar to the resistance curve method in ASTM E1820 in determination of a J-R curve or CTOD-R curve. The unloading compliance technique is recommended for measuring crack length. A single clip gage is mounted on the crack mouth of the specimen so as to measure the CMOD in a SENT test. Apparatus required for measuring load and CMOD are similar to those for SENB specimens described in E1820. Due to significant rotation occurred during the SENT test, a rotation correction factor was proposed from FEA simulations [61].
As a result, most test details are similar to those for standard SENB specimens as specified in E1820. The CMOD-based incremental J-integral Eq. (7) is adopted in the SENT J-R curve evaluation. Using the CanMet
method, Shen et al. [62] and Park et al. [63] determined fracture toughness for X100 pipeline steel and its welds. They found that J-R curves are less sensitive to crack length, which is consistent to the observation by Joyce et al. [18] for pin-loaded SENT specimens.
To assess the viability of CanMet draft procedure for SENT toughness testing and to examine its application to pipeline steels, a round-robin program was completed and the results were reported by Tyson and Gianetto [64]. Nine Labs participated in this round-robin program. All J-R curves measured by these Labs using clamped SENT specimens are shown in Fig. 4, where the material is X100 pipeline steel and the crack size is a/W=0A. The standard deviation between the J-R curves is ~ 20%, and this difference is not small. Thus the accuracy of CanMet expressions needs to restudy [56].
4.3.2. CanMet method for S-R curve testing
CanMet adopts the ASTM E1820 J-integral conversion method and Eq. (9) for their SENT CTOD testing. Shen and Tyson [65] performed detailed elastic-plastic FEA calculations and obtained a curve-fitted function of the m factor in Eq. (9) for clamped SENT specimens. A single clip gage is used to measure the CMOD, then the J-integral is calculated from the load-CMOD data, and the CTOD is converted from the calculated J from Eq. (9). Once a J-R curve is developed for a clamped SENT, the associated S-R curve is easily determined.
Crack growth, mm
Fig. 4. J-R curves developed by nine labs using clamped SENT specimens ofa/W=0.4 for X100 pipeline steel [64].
4.4. Other J-R curve test methods
In addition, Cravero and Ruggieri [66-67] also developed a single specimen method to measure J-R curves for SENT specimens. Their test procedure is similar to ASTM E1820 and CanMet procedures with use of the unloading compliance technique. These author numerically obtained the K solution, compliance equation, and geometry factors required in a J-R evaluation for a SENT test in pin-loaded and clamped conditions. Their results showed that the CMOD-based incremental J-integral Eq. (7) determines more accurate J-R curves for SENT specimens.
4.5. ExxonMobil single-specimen method for CTOD testing
4.5.1. ExxonMobil CTOD test method
In contrast to the CanMet CTOD test method, ExxonMobil Company [30-31] developed another single specimen method for SENT 8-R curve testing with use of a double clip gage arrangement. Based on the rigid rotation assumption, both CMOD and CTOD are directly inferred from the double clip gage measured displacements by:
CMOD = V1-^ (V2-V1) (15)
CTOD = V1-^(V2-V1) (16)
where V1 and V2 are the crack opening displacements measured at two heights hi and h2 above the specimen front edge. Note that CTOD in Eq. (16) is defined at the original crack tip.
In the ExxonMobil method, the clamped SENT specimens have W=B and H= 10 W, the initial crack length is in 0.25<ao/W<0.35, and the total side groove of 10% of thickness is recommended. The double clip gage procedure is simple and convenient to use for measuring a S-R curve with SENT specimens, and thus it is of great practical importance. However, the allowed crack size is too small, the CTOD definition is different from ASTM E1820 [10].
4.5.2. Comparison of two S-R curve test methods
The two S-R curve test methods discussed above are completely different. While the CanMet method uses the single clip gage measurement and the J-conversion method to calculate CTOD at the current crack tip, and the ExxonMobil method uses the double clip gage measurement and the rotation model to infer CTOD at the original crack tip. To see if these two procedures determine a similar 8-R curve for a specific SENT specimen, different investigators have made comparisons based on their experimental results.
Recently, Weeks et al. [68-69] experimentally determined 8-R curves for X100 pipeline steel on clamped SENT specimens using the two CTOD test methods, and showed big differences of the two 8-R curves. As shown in Fig. 5, the 8-R curves obtained using the double clip gage method are higher than those obtained by the J-conversion method for larger crack growth, although similar results have been observed in the initial area of crack extension.
Likewise, Park et al. [70] performed a similar comparison of the two 8-R curve test methods for X70 pipeline steel welds. They showed that the CMOD inferred from the double clip gage measurements is nearly identical to the CMOD measured directly using a single clip gage, but the 8-R curves obtained using the double clip gage method are higher than those obtained using the J-conversion method, as shown in Fig. 6. Which CTOD test method is more adequate to use in practice leaves for further investigation.
« tt* o ♦
« ' *♦* ^ **
* CTOD-R Method
» 105 HT-11 (CTOD-R - Corrected)
• J-R Method
o 105 HT-11 (J-R)
Crack Extension (mm)
Fig. 5. Comparison ofCTOD-R curves ofXIOO steel determined using the double clip gage method and the J-conversion method [68].
4.6. Other CTOD test methods
In addition, Denys and his co-workers [71-72] developed their own procedure to determine 8-R curves for SENT specimens. They defined the CTOD based on the 90° intercept method starting from the original crack tip, and derived an equation similar to Eq. (16) for the double clip gage method. This CTOD definition is different from that defined by the CanMet or ExxonMobil method. Other test details are similar to the ExxonMobil test procedure, and the double clip gage arrangement is employed to determine the total CTOD for SENT specimens in the clamped conditions.
5. Recent progresses in fracture toughness test methods using SENT specimens
5.1. British standard SENT test method - BS 8571:2014
To improve DNV-RP-F108 [27], Pisarski [73] at TWI reviewed the basis of SENT testing as described in the DNV standard, and addressed its limitations with respect to specimen preparation, testing, and analysis procedures. In order to develop a SENT test standard in U.K., Pisarski et al. [74] reported their broad efforts and investigations to extend the DNV practice. In December 2014, BSI published their new standard test method for determination of fracture toughness in metallic materials using SENT specimens with a designation ofBS 8571: 2014.
SE(T), 17.8 mm thick HAZ- double clip gauges
O Peak load -Regression HAZ - single clip gauge
WM-double clip gauges
WM - single clip gauge
'mK: —i—i—i— 1 I 1 1
0 0.5 1 1.5 2 2.5
Aa (mm)
Fig. 6. Comparison of CTOD-R curves of X70 steel welds determined using the double clip gage method and the J-conversion method [70].
In the BS 8571, the J-R curve test procedure allows both the multiple specimen method and the single specimen method, but the J estimation equations are the same as Eqs (1) - (3) without crack growth correction. The double clip gage arrangement is utilized to measure displacements, the CMOD used to calculate J is not directly measured on crack mouth of the specimen, but inferred from the double clip gage measured displacements using Eq. (15). In a 8-R cure evaluation, the CTOD is calculated by:
where the first term determines the elastic CTOD, and the second term determines the plastic CTOD with Vpl1 and Vpi2 being plastic parts of the double clip gage measured displacements at the heights zi and Z2. Note that Eq. (17) is
different from Eq. (16). The difference is that ExxonMobil uses the total CTOD without separation of elastic and plastic components.
5.2. Corrected K solutions for SENT specimens
Because an extremely complicated solution of K factor was used for clamped SENB specimens in BS 8571, Zhu and McGaughy [76] restudied this complicated, but analytical K solution in order to simplify the K solution. These authors showed that the stress intensity factor Kused in BS 8571 for the clamped SENT is incorrect for deep cracks of a/W>0.6. Thus, they corrected the analytical solution of K factor for the clamped SENT specimens over the full range of a/W, and also gave a curve-fitted closed-form solution of the corrected analytical K solution in a simple six-order polynomial function:
K-T^BWr fW (18a)
where the geometric function f(a/W) was expressed as:
1.985+ 0.7lfaVll.glfaY _48.0l/aY ^/of .121.5/aY + 51.67faT
^ W J { W J X W J { W J { W J { W J
This new K solution is very accurate for clamped SENT specimens over a wide range of 0<o/W<0.98, and its error is less than 1% of the corrected analytical K solution. Due to its simplicity and accuracy, this K solution is a good alternative for BS 8571 or other SENT test standard to use.
5.3. Improved r/-factor and unloading compliance equations
In addition to the stress intensity factor solution, the limit load, the CMOD compliance equation, plastic geometry factors used and compliance rotation correction used in BS 8571 or CanMet procedure may also need recalibration and revalidation to ensure their correctness and accuracy. Recently, Paredes [77] discussed the plastic limit load and its application to determine the plastic geometry factor -q for clamped SENT specimens. Huang and Zhou [78] determined the "q factor for clamped SENT specimens using three-dimensional FEA calculations. Wang and Omiya [79] and Huang and Zhou [80] updated the CMOD compliance equations that are used for determining crack length in an unloading compliance test for clamped SENT specimens. Nevertheless, these updated results are subject to experimental validation. Once they get validated broadly, the standard SENT test methods in BS 8571 are able to measure more accurate R-curves.
5.4. Strain based direct measurement method
Most recently, Weeks and Read [69] developed a strain based direct method to measure a J-R curve for a clamped SENT specimen. The experimental technique measured the J-integral using strain gages, and calculates the J-integral from a far-field contour. The contour encompasses the front surface, through thickness and back surface of the specimen symmetric about the notch plane spaced at 4W. Two different strain gage configurations were used with each loop of 27 gages to capture the strain gradient on the front and back surfaces, and two extensometers were mounted at designed posts to measure the tensile displacements. With these measured strains, displacements at each loading, the J-integral is calculated. The results showed that the J-R curves of X100 pipeline steel measured from the strain-based direct measurement method are very close to those determined from the CanMet method within a small crack extension of ~1 mm, and then deviate to be lower curves. In spite of this, the strain-based direct
measurement method provides us an approach to verify the J-R curves obtained by the CanMet method or BS 8571 method.
In addition to use SENT specimens to directly measure low-constraint fracture toughness, SENB specimens with shallow cracks can also be used to do the same thing. It is likely better to use the SENB specimen than the SENT specimen for the diriment measurement of fracture toughness, because ASTM E1820 is a matured test standard, and has guidelines for shallow crack toughness testing and evaluation. Recently, Mathias et al. [81] showed that a SENB specimen with a shallow crack can determine a similar J-R curve to that by a clamped SENT with the same shallow crack.
6. Conclusions and Remarks
The present paper delivered a technical review of fracture toughness test methods for ductile metals in low-constraint conditions. The reviewed fracture test methods include the standard fracture toughness test methods developed by ASTM, BSI and ISO, the constraint correction methods, and the direct test methods using the low-constraint SENT specimens.
ASTM, BSI and ISO have the similar methods to determine Jic and J-R curves, but different methods for CTOD testing. While ASTM uses the J-integral conversion method to obtain Sic and S-R curves, BSI uses the plastic hinge model to determine 8ic and 8-R curves. ISO uses the plastic hinge model to calculate Sic, but the J-conversion method to evaluate 8-R curves. Further study needs to unify a CTOD test method for these fracture test standards.
The constraint correction method is an effective tool to develop a family of constraint-dependent J-R curves for ductile materials. This method is technically sound due to its integration of theoretical, numerical and experimental results into one constraint-corrected J-R curve, and is unique to be able to solve the transferability issue. The constraint-corrected J-R curve can transfer laboratory measured fracture resistance curves to real shallow cracks in a structural integrity assessment. It has gained many applications in determination of low-constraint resistance curves for a variety of ductile steels, including nuclear pressure vessel steels.
The direct test methods using SENT specimens have obtained the extensive attentions and investigations worldwide. Different direct test methods were developed, including the multiple specimen method by DNV, single specimen method with a single clip gage measurement by CanMet, and single specimen method with a double clip gage measurement by ExxonMobil. More recently, BSI published the new standard BS 8571 for SENT testing. However, recalibration of its estimation equations is needed to improve its accuracy for developing a more accurate result of low-constraint fracture toughness from a SENT test.
In addition to SENT specimens, SENB specimens with shallow cracks in three-point bending can also be used directly to measure fracture toughness in low-constraint conditions. Because ASTM E1820 provides the guidelines for testing shallow cracks of SENB specimens, and the SENB test is worth further study to measure low-constraint fracture toughness to meet engineering needs.
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