Crack growth characterization in single-edge notched tension testing by means of direct current potential drop measurement

International Journal of Pressure Vessels and Piping xxx (2017) 1e11

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Crack growth characterization in single-edge notched tension testing by means of direct current potential drop measurement *, Matthias A. Verstraete, Wim De Waele Koen Van Minnebruggen, Stijn Hertele Ghent University, Dept. EEMMeCS, Soete Laboratory, Technologiepark Zwijnaarde 903, 9052 Zwijnaarde, Belgium

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 March 2017 Received in revised form 19 June 2017 Accepted 26 June 2017 Available online xxx

Single-edge notched tension (SENT) testing has gained attention for the characterization of crack growth resistance in scenarios of low crack tip constraint conditions. One challenge of SENT testing is the experimental characterization of crack extension during the test. Two common methods exist: unloading compliance and direct current potential drop (DCPD). Whereas the former method is fairly extensively described in existing procedures, applying the latter mostly depends on user experience and in-house developed analysis algorithms. This paper describes Ghent University's approach for DCPD measurements of ductile crack extension in SENT testing. A reference voltage drop measurement is advised, aiming to account for current leak and changes in electrical conductivity. Then, attention goes to the sensitivity of the procedure with respect to changes in crack size and its robustness with respect to probe positioning errors. Finally, DCPD is shown to have similar capabilities to unloading compliance with respect to defect sizing accuracy. The results of this paper are aimed to contribute to a more prescriptive description of DCPD measurements in revised SENT test procedures or standards. © 2017 Elsevier Ltd. All rights reserved.

Keywords: SENT test Direct current potential drop Johnson Unloading compliance

1. Introduction During the last decade, the fracture mechanics research community has witnessed a strongly increased interest into fracture toughness testing in low crack tip constraint conditions. These conditions are highly relevant to thin walled structures (such as pressure vessels, oil and gas pipelines and offshore structures), for which the ligament of a shallow (weld) defect or crack is primarily loaded in tension rather than bending. These loading conditions are poorly represented by conventional toughness test configurations such as single-edge notched bending (SENB) or compact tension (CT), which underestimate the fracture toughness of the material in the structure. The resulting (over)conservatism leads to unnecessary repairs of safe defects, which can be alleviated by executing low constraint fracture toughness tests. The single-edge notched tension test has become a mainstream solution for fracture toughness testing under low crack tip constraint conditions [1]. The SENT specimen has a constraint level similar to (and slightly higher than) that of thin walled structures under tension, having similar wall thickness and defect depth (e.g.

* Corresponding author. ). E-mail address: [email protected] (S. Hertele

[2,3]). Albeit initially developed in the 1960s [4] for quantification of fracture toughness, the current application of SENT testing is aimed towards the characterization of tearing resistance curve. This curve can be obtained by multiple specimen methods or from a single specimen approach. The latter requires experimental procedures to derive crack driving force (J-integral or crack tip opening displacement CTOD) and crack extension on a regular basis as the test progresses. Measurement of crack driving force requires specific clip gauge mounting strategies (e.g. direct mounting on the crack mouth for J [5]; double clip gauge assembly for CTOD [6,7]) and a good definition of the quantity of interest. For instance, there is debate on eta factors to obtain J from crack mouth opening displacement (CMOD) [8] and, more fundamentally, on the definition of CTOD [9]. This paper focuses on crack extension measurement in singlespecimen SENT testing. Different methods exist, of which the unloading compliance (UC; e.g. [10e12]) and potential drop (PD) techniques [13e15] have received most attention, and other techniques (e.g. normalization [16], optical deformation analysis [13,17]) are mentioned. This paper focuses on potential drop measurements of crack growth. PD techniques can be based on either a direct current (DCPD) or an alternating current (ACPD). DCPD is typically preferred because of its simplicity: a constant current source injects a high electrical current into the specimen, and an

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accurate volt meter captures the voltage drop across the notch. In contrast, the electronics for ACPD are far more complex as secondary pick-up voltages have to be filtered out (which requires input current typically in the kHz range). Also, the skin effect on which ACPD is based, restricts its use to the measurement of surface-breaking defects [18]. Finally, the capacitance effect over the crack flanges (which is influenced by the distance between both crack faces) [15] and a strong effect of strain on magnetic permeability and electric conductivity [19] influence the relation between potential drop and crack extension, thus complicating the ability to size growing cracks (especially when adopting higher alternating current frequencies). The single-specimen SENT test was first standardized in 2014 by the British Standards Institute (BSI Group) and published as BS 8571 [20]. The development of the standard is comprehensively described in Ref. [21]. BS 8571 mentions UC and DCPD as suitable methods for crack growth characterization. However, prescriptive guidance on the application of these methods is missing. Instead, references are provided to a list of papers that can be used as a basis. This is appropriate for UC testing, for which fully documented procedures are available (including test procedure requirements and conversion of compliance to crack size). Given as examples are the CANMET single-specimen J-R test procedure reported in 2009 [10], and procedures developed in the framework of round robins for SENT testing organized by CANMET and BMT [22,23]. In sheer contrast, the use of potential drop methods is far less documented which limits its application. This is clearly reflected in Zhu's recent review of fracture toughness test methods for ductile materials in low-constraint conditions [1], which summarized the vast majority of relevant literature related to SENT resistance curve testing. Whereas this review paper has multiple paragraphs devoted to unloading compliance testing, the potential drop method was only briefly mentioned once to be an equivalent alternative to UC testing, and referred to research performed at Ghent University [24]. CANMET's round robin test procedure (discussed in Ref. [22]) explicitly recommends UC over DCPD testing. BMT's round robin test procedure is not biased towards any of both methods. However, its guidance for DCPD test parameters (to a large extent based on ExxonMobil's SENT procedure [7]) is less explicit than that for UC testing. Hereby, reference [23] reported that 12 out of 15 participants adopted UC for crack growth measurement, whereas only 3 participants performed DCPD. Despite its limited popularity, recent research at Emc2 preferred the DCPD technique over UC, as the latter approach was found to provide more scattered crack growth predictions and anomalies such as a negative crack growth estimation [14]. This outcome is likely assisted by ample experience with DCPD monitoring as shown in Ref. [15]. Moreover, DCPD assisted SENT testing involves a potential economic advantage, since the DCPD assisted test series are performed faster than UC assisted testing (which requires a time consuming and tedious sequence of unloading/reloading cycles). Further, DCPD typically provides more resistance curve data points than UC assisted testing and may be better suited to tests performed in environmental chambers or furnaces. Finally, DCPD may be used for tests at various rates of loading, whereas UC is more restrictive in this respect [15]. This paper reports on Soete Laboratory's experience with (and guidance towards) crack extension measurements in singlespecimen SENT tests by means of DCPD. First, the test procedure is discussed (section 2). Section 3 discusses an experimental database and numerical (finite element) model which have been used to evaluate the test procedure. Section 4 validates the soundness of the transfer function between potential drop and crack extension, discusses the sensitivity of crack extension to potential drop measurement and provides a robustness analysis with respect to

unavoidable variations in testing conditions. Finally, section 5 provides a comparison between crack growth predictions obtained by UC and DCPD. 2. UGent SENT test procedure 2.1. General aspects The test specimens considered in this paper have a square (B x B) cross section and daylight grip length (H) to width (W ¼ B) ratio of ten (Fig. 1 [24]). Specimens were notched with a fine saw blade, producing a notch width at the tip of 150 mm. No fatigue precracking was performed. The initial notch depth is denoted as a0 (not to be confused with the crack depth a at any moment during the test). To overcome the anticipated crack tunnelling, the majority of reported specimens had V-shaped side grooves machined at both sides of the test specimens, with a root radius of 0.5 ± 0.2 mm and an opening angle of 45 (in agreement with existing procedures for SENB [25] and SENT testing (e.g. Refs. [7,10])). Through these side grooves, the cross-sectional area was reduced by 15% for all specimens (BN ¼ net thickness ¼ 0.85 B). This value was chosen in accordance with CANMET's round robin test procedure [10]. The variety of tested specimen configurations is discussed in more detail in section 3.1. In combination with the crack growth measurements, the crack mouth opening displacement (CMOD) and crack tip opening displacement (CTOD) were calculated using a double clip gauge method [6]. Hereto, two miniature knife blocks are bolted onto the test specimen using two screws each (self tapping, type #2-56 x 3/ 16” Phillips Pan Head Thread Cutting Screw), whose center is located 4.5 mm from the notched section. The centreline distance between both screws is 6.0 mm. The clip gauges used for evaluating the opening displacement are located 2.0 and 8.0 mm above the specimen surface. The adopted double clip gauge assembly is common for SENT testing and a graphical representation is provided in test procedures and standards such as BS 8571 [20]. The SENT specimens were tested using hydraulic test setups with a capacity of either 150 kN (typical) or 1 MN (when required) and were rigidly clamped at both ends using hydraulic clamps. A constant displacement rate of either 0.01 mm/s or 0.005 mm/s was applied. Both values are sufficiently low to ensure quasi-static conditions according to existing procedures. Some specimens were monotonically loaded; others were periodically unloaded and reloaded to allow for an UC analysis. To obtain sufficient crack growth, the tests were continued beyond the maximum load until the load dropped below 80% of its maximum observed value. The following signals were captured: tensile load, actuator displacement, readings from both clip gauges, potential drop crossing the notch, reference potential drop. After testing, specimens were heat tinted (for instance, at 220  C for two hours) and fractured in a brittle manner after cooling in a bath of liquid nitrogen. Initial notch depth and final crack depth were measured using the nine-points average method.

Fig. 1. Schematic representation of SENT specimen [24].

Please cite this article in press as: K. Van Minnebruggen, et al., Crack growth characterization in single-edge notched tension testing by means of direct current potential drop measurement, International Journal of Pressure Vessels and Piping (2017), http://dx.doi.org/10.1016/ j.ijpvp.2017.06.009

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2.2. Determination of crack size from DCPD To evaluate the crack extension, the potential drop across the crack was measured during the tests according to the schematic overview shown in Fig. 2. For the specimens reported in this paper, a constant current Is of either 25 or 50 A was applied depending on specimen thickness, representing a current density per unit noncracked cross sectional area ranging between 0.1 and 0.2 A/mm2. Notably, all specimens were made out of high-strength low alloy steel. Other materials (such as stainless steels) may require less current for similar potential drop values, due to a lower conductivity (or vice versa). Current input and output pins were located at a normalized distance of four times the specimen width (Dpin ¼ 4W) from the cracked section. The pins (M5 rods made out of copper plated steel) were stud welded to the specimen. A power source with a constant supplied current up to 150 A for voltages not exceeding 20 V was applied. This voltage limitation is irrelevant for SENT testing, as the applied voltage (including specimen resistance, cable resistance and voltage losses across contacts) typically ranged between 0.2 and 0.6 V. The current source is additionally characterized by a low ripple and noise of 75 mA (root mean square error). The potential drop over the notched section is a function of cross sectional dimensions B and W, (relative) notch depth a/W, applied current Ia, material conductivity Cm and probe positioning. As the goal is to transfer potential drop to notch depth, it is important to rule out any undesired effects of the other involved parameters (current density, conductivity, probe positioning). Although the delivered current Is is constant under abovementioned conditions, the effectively applied current Ia through the cracked cross section can vary because the specimen is not electrically isolated from the test setup (i.e., there is a variable current leakage Is e Ia). To compensate for this discrepancy and potential changes in material conductivity during the test (e.g. due to temperature variations), preference is given to the dual probe technique in which the potential drop of interest is compared to a reference measurement, which also accounts for changes in Ia and Cm. Successful applications of this technique have been reported for the analysis of crack growth in small scale fracture toughness tests as well as full scale tests [26e28]. The dual probe technique has particularly been adopted for the tests discussed in this paper, as these were conducted in a large test hall where small fluctuations of temperature (i.e., material resistivity) and air flow (e.g. by opening an access gate) are hard to avoid. Noteworthy, normalization of one measured signal against another adds to the statistical uncertainty of the result. This increase in uncertainty is not considered problematic as resistance curves with satisfactorily low

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scatter were obtained based on the dual probe technique (see Figs. 4 and 5 further in the paper). Other research institutes have opted to electrically isolate the specimen from the test rig instead (e.g. [14,15]). This eliminates the need for a reference measurement, provided the test can be performed in a controlled environment. A fixed probe positioning strategy is followed (and further discussed in section 4.2). Specifically, two reference probes are positioned remote from the cracked area. These are located at two and three times the specimen width from the cracked section (Dmeas,2 ¼ 2W; Dmeas,3 ¼ W). The probes consist of two wires that are rigidly connected to the specimen using small self-tapping screws (type #2-56 x 3/16” Phillips Pan Head Thread Cutting Screw). The voltage between the probes, denoted as Vref, is measured using a dual channel nano volt meter which has an accuracy better than 0.01% of the measured signal, provided an appropriate measurement range is selected. The second voltage measured is the potential drop across the crack, referred to as V. To this end, two probes are positioned 4.5 mm from the cracked section (2Dmeas,1 ¼ 9.0 mm). This fixed location coincides with the mounting holes of the knife blocks used for evaluating the CTOD and CMOD. The self-tapping screws used for attaching these knife blocks also connect the measurement probes. The intimate contact between screws and specimen (due to self-tapping) ensures a proper transfer of voltage to the probes. Both probes are positioned diagonally to each other, which is a typical measure to reduce the effects of non-uniform crack extension (e.g. [29]). The transversal distance between both probes (Dh on Fig. 2) is 6.0 mm, the centreline distance between knife block mounting screws. Notably, using self-tapping screws for probe connection was preferred over spot welding since, in our experience, the latter approach posed stronger challenges in terms of positioning accuracy. Both abovementioned measured signals, Vref and V, are measured at constant CMOD intervals of 0.04 mm throughout the test. These measurements coincide with the onset of the unloading cycles for tests where UC was performed simultaneously [24]. Vref and V are then used to obtain crack growth by adopting a procedure which was introduced in Ref. [13]. Under theoretical conditions, the normalized potential drop V/Vref is independent of current leakage in the mechanical grips and uniform temperature changes. To convert this normalized potential drop to a physical crack size, an analytical expression originally described by Johnson in 1965 is used [30]:

vðaÞ ¼ vða0 Þ

cosh1





cosh1

coshðpDmeas;1 =2WÞ cosðpa=2WÞ coshðpDmeas;1 =2WÞ cosðpa0 =2WÞ

 

(1)

where v (-) represents the normalized potential drop V/Vref. Notably, in our test database, orders of magnitude of initial V (at a0) and Vref are comparable, yielding initial v values in the order of unity. Equation (1) is easily turned into the following solution for relative crack depth a/W as a function of v(a)/v(a0):

0 a 2 1 @ ¼ cos W p

Fig. 2. Schematic of potential drop instrumentation for SENT specimen.

1    cosh pDmeas;1 2W

A coshðpDmeas;1 =2WÞ vðaÞ 1 cosh vða0 Þ cosh cosðpa0 =2WÞ

(2)

Although developed for center cracked tensile (CCT) specimens, the abovementioned analytical solution can also be applied to other configurations including compact tension (CT), single edge notched bend (SENB) testing [31], and SENT testing. Reality is more complex since plasticity effects give rise to a

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linear increase of (normalized) potential drop (Fig. 3, stage II). This increase is described by means of a so-called ‘plasticity line’. Notably, literature commonly refers to the ‘blunting line’. This wording is somewhat debatable as effects other than blunting (such as the plastic deformation of the crack ligament, change in material resistivity upon plastic deformation) also contribute to the increase of potential drop. Such effects continue to take place after the onset of tearing, whereas crack tip blunting is halted. The plasticity line is typically fit by means of regression over the linear trajectory prior to initiation and subsequently compensated for in the potential drop analysis. To this end, v(a) in Eqs. (1) and (2) is substituted by v(a) e (vblunt e v(a0)). As a consequence, DCPD analysis merely calculates the contribution of ductile tearing (Dapd) to total crack growth Dat,pd. Obtaining the latter requires a correction term Dab to incorporate blunting:

Dat;pd ¼ Dab þ Dapd

(3)

Dab is typically expressed as a certain fraction of the CTOD at crack initiation, di. Different procedures advise different proportionality factors (for instance, Dab ¼ di/1.4 as suggested by ASTM E1820 [25], or di/2). The presented data have been processed using the relation Dab ¼ di/2, as for instance advised in ExxonMobil's SENT test procedure [7]. This correction applies to points beyond crack initiation. Note that di/2 represents a constant value, which reflects the idea that blunting seizes to intensify beyond crack initiation. Prior to crack initiation, a linear CTODeDa response is assumed, having a slope 2. An investigation on the calculation of Dab is beyond the scope of this paper, but we wish to point out that the influence of the proportionality factor should not be underestimated. For instance, considering a CTOD at crack initiation of 1 mm, using either 1.4 or 2.0 as a proportionality factor yields a difference of around 0.2 mm in predicted total crack growth. As a remark, the procedure above requires knowledge of CTOD to calculate crack growth from blunting. CTOD values may not be readily available in SENT testing designed for J-R curve determination (i.e., instrumented by means of one clip gauge to obtain CMOD). In such case, other procedures suggest to calculate Dab on the basis of the J-value at initiation, Ji. For instance, ASTM E1820 (addressing high-constraint fracture toughness tests) stipulates that Dab ¼ Ji/(2sy), sy representing the material's yield strength. An alternative approach is to calculate di from Ji using a J-to-CTOD conversion formula, and use the obtained value to calculate blunting crack extension. Note that using the method above, the predicted crack length does not depend on the applied current nor is it affected by

material conductivity. It is uniquely obtained from its initial value a0, specimen geometry (W), measurement probe position (Dmeas,1) and the normalized potential drop signal. A case study is provided in Figs. 4 and 5. Fig. 4(a) shows the measured normalized voltage signal, before and after compensation for blunting. Then, the Johnson equation and blunting correction are applied to obtain Dat,pd in Fig. 4(b). The finally obtained CTOD resistance curve is plotted in Fig. 5 and its final value Dat,pd,f compared against the physical final crack extension Da9p, obtained using the nine-points average method. 3. Materials and methodology 3.1. Experimental dataset A database of 101 SENT test results of different projects has been collected to evaluate the DCPD procedure outlined above. A wide range of variables is covered as detailed below. Numbers between brackets represent numbers of SENT specimens corresponding to a certain configuration.  Relative initial notch depth a0/W between 0.2 and 0.6;  BxB cross section between 12  12 mm2 and 22  22 mm2;  Tests on base metal (41) as well as girth welds including their HAZs (60);  Weld mismatch level on the basis of flow strength (defined as the average between yield strength and ultimate tensile strength) between 0% and 33%;  API 5L pipe grades from X65 to X80;  Yield-to-tensile ratios Y/T of base material between 0.82 and 0.92;  Traditional SENT specimens (70) and specimens containing a tilted notch to evaluate spiral weld defects (31) [32]. The tilted aspect of the notch refers to its appearance at the crack mouth surface, thus producing a mixed mode (I and III) loading. Notch tilt angles up to 40 were tested (0 representing a traditional straight notch);  Side grooved (67) and plane sided (34) specimens. Notably, 31 plane sided specimens contained a tilted notch, for which crack tunnelling was observed to be far less pronounced (thus eliminating the necessity for side grooves). All welded specimens were side grooved.  The majority of tests were performed at room temperature, while a minority was performed at temperatures down to 40  C. Thirty-nine tests were additionally executed with an unloading/ reloading strategy to allow for UC analysis. These tests are used to compare DCPD with UC in section 5. 3.2. Finite element model A static electrical finite element (FE) model has been developed for two purposes:  to evaluate the validity of the Johnson equation (Eq. (1)) for three-dimensional plain sided or side grooved SENT specimens.  to determine the minimum required distance of current input and output pins to eliminate the influence of their position on measured potential drop.

Fig. 3. Schematic representation of normalized potential drop as a function of CMOD.

The model was introduced in Ref. [3], and essential features are summarized hereafter. The model has been developed using the commercial FE software package ABAQUS (version 6.11 and further) on the basis of a parametric Python script. The mesh consists out of

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Fig. 4. Case study of data postprocessing: (a) subtracting the linear plasticity line from raw data; (b) adding a blunting correction to crack growth.

distributions near the current pin and the notched section, separated by a region in which cross sections show a highly uniform potential. Since the adopted model is purely electrical, no mechanical load is applied and the analysis is based on an undeformed specimen. This may reduce its accuracy for specimens where the reduction of ligament cross section due to plastic collapse is significant compared to that due to crack extension [33]. A similar statement applies for the Johnson equation.

4. Results and discussion 4.1. Validation of Johnson equation

Fig. 5. Case study of data postprocessing (continued): CTOD resistance curve and comparison with measured final crack extension.

linear brick elements with a reduced integration scheme, and has been optimized in terms of balance between numerical accuracy and computational time. Electrical current is input and output in accordance with experimental practice; a similar statement applies to the virtual measurement of potential drop, which agrees with experimental voltage probe positions. A voltage ground is introduced at the notched section, implying that voltages are positive at one end of the specimen, and negative at the other. Homogeneous material properties are defined in terms of material conductivity Cm, expressed in (U.mm)1. A longitudinally oriented symmetry plane is implemented. Thus, only half of the specimen is modelled to reduce computational time. Side grooves can be introduced by means of nodal coordinate transformations applied to a plain sided specimen. A blunted crack with initial tip radius according to experimental practice is introduced. The crack tip is surrounded by a regular spider web mesh to enhance the generic character of the mesh, which is also suitable for a computational fracture mechanics analysis. Fig. 6 shows an example model mesh. Fig. 7 shows an example prediction of voltage distributions, represented as a contour plot of equipotential lines and taken at the longitudinal symmetry plane. Clearly visible are complex two-dimensional voltage

A representative set of SENT configurations has been simulated using the FE model presented in section 3.2, in order to evaluate the Johnson equation. As the rationale behind a reference voltage measurement is irrelevant to finite element modelling, it is not considered and normalized potential drop v is replaced with the actual potential drop across the notch V. Fig. 8 shows an example validation. Both plain sided and side grooved (total width reduction of 15%, i.e., BN ¼ 0.85 B) specimens were simulated for a configuration with W ¼ 8 mm, 2Dmeas,1 ¼ 9 mm and various relative notch depths a/W ranging from 0.25 to 0.75. Considering 0.25 as the initial relative notch depth a0/W, a relative crack growth Da/W up to 0.5 is covered (final crack depth a/W ¼ 0.75). As the crack grows, the potential drop increases as indicated by the ordinate values in the figure (relative to the potential drop of the initial notch). The Johnson equation accurately predicts the simulated potential drop values for both plain sided and side grooved SENT specimens. Simulated data differ from Eq. (1) by less than 2% of the actual value. Hence, the transfer of DCPD voltage output to crack growth in (side grooved) SENT specimens does not require the use of electrical finite element modelling, but may be based on the Johnson equation instead. Notably, this statement only applies to ‘traditional’ SENT specimens (as opposed to specimens having a tilted notch). Note that the above may inversely serve as a validation of the finite element model based on the Johnson equation. This justifies the use of electrical FE modelling for more complex configurations for which no analytical solution is available. For instance, the modelling approach has been successfully adopted for the DCPD analysis of SENT specimens having a tilted notch (which forms part of the test database reported in this paper, see section 3.1) [32] and

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Fig. 6. Mesh of a SENT finite element model with electrical current pins [3].

Fig. 7. Equipotential lines at one end of a SENT specimen.

output pins first, two strategies can be followed (Fig. 9, adopted from Ref. [34]). On the one hand, current pins can be placed close to the surface defect (left figure), as to tune the potential distribution around the notched section. As a concrete effect, the potential drop crossing the notched section will be increased for a given notch depth (similarly reported in Ref. [35] for CT specimens), thus increasing crack sizing accuracy. It is to be noted that Johnson's equation would be invalid for this configuration. On the other hand, current pins can be placed far from the surface defect (right figure), as to create a front of uniform potential which approaches the notched section. For reasons of robustness, the latter approach deserves preference and is adopted in the presented procedure, since the potential distribution surrounding the notch is only marginally influenced by the exact position of the current pins. A minimum required pin distance Dpin has been calculated from an arbitrarily defined uniformity requirement for the potential field remote from the notched section. Specifically, it was stated that Dpin should be so that there is a cross section for which the standard deviation of its electric potential does not exceed 1% of its average value. In other words, the notched cross section does not ‘feel’ the presence of the current pins (and vice versa) both are separated by a uniform potential field. This criterion was evaluated using the finite element model described in section 3.2. A full-factorial parametric study was performed covering different material conductivities Cm (1000, 2000, 4000, 8000, 16000 (Umm)1), currents Is (10, 20, 30, 40, 50 A) and specimen thicknesses W (10, 15, 20, 25, 30 mm). Notably, common conductivity values for low alloy steels

Fig. 8. The Johnson equation accurately calculates potential drop for plain sided and side grooved SENT specimens. Configuration shown: W ¼ 8 mm, 2Dmeas,1 ¼ 9 mm, a0/ W ¼ 0.25.

surface notched curved wide plate specimens [3]. 4.2. Effects of current pin and voltage probe positioning The positioning of current pins and voltage probes is an important attention point with respect to the sensitivity and robustness of the analysis procedure. Focussing on current input/

Fig. 9. Different philosophies for current pin positioning. The right setup deserves preference from a robustness point of view. Image taken from Ref. [34].

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are between 2000 and 8000 (Umm)1; values between 1000 and 2000 (Umm)1 are rather representative for stainless steels. The parametric study led to the following criterion for minimum required pin distance (using the dimensions mentioned above):


1=4 Dpin Is > 18 W Cm W

(4)

Ohm's law of electrical resistance allows to understand that the ratio between brackets indicates the order of magnitude of the voltage drop along the specimen, noting that the specimen resistance is proportional to the inverse of material conductivity and to length divided by cross sectional area W2, whereby length scales linearly with W. For realistic combinations of parameters (i.e., giving rise to common voltage drops along the specimen as discussed in section 2.2), a pin distance Dpin equal to 4W is more than sufficient to achieve the uniformity criterion set forward, and this distance was chosen for all experiments. Second, attention is given to the effects of measurement probe positioning (Dmeas,1, Dmeas,2 and Dmeas,3). Starting with the reference potential probes, Dmeas,2 was chosen sufficiently large to avoid that crack growth would influence Vref. This is achieved by positioning the probes in a region which is separated by the notched section by means of a cross section of ‘uniform potential’ as defined in the analysis that led to Eq. (4). A distance Dmeas,2 ¼ 2W was found sufficient to meet this aim. Then, the distance Dmeas,3 between both reference measurement probes was chosen sufficiently large to obtain Vref values similar to the potential drop across the notch. This limits the influence of measurement errors (which would be larger for smaller values of Vref) on the normalized potential drop, yet allows to measure Vref using the same voltmeter measurement range as for V. It appeared that Dmeas,3 ¼ W is suitable to meet this purpose for the reported SENT test database. Further focussing on the probes for measuring V(a), 2Dmeas,1 is fixed at 9.0 mm regardless of SENT specimen dimensions (due to its connection with the clip gauge knife blocks). In other words, Dmeas,1/W is variable and takes values between 0.15 and 0.5 for common thickness values (assuming W between 9 and 30 mm). The following analyses will consider results within this range. Two aspects are discussed: sensitivity of potential drop to increase in crack depth, and robustness of crack size prediction with respect to probe positioning errors. First, it is beneficial to have a large sensitivity of potential drop to an increase in crack depth (or, equivalently, a small sensitivity of crack depth to changes in potential drop). This promotes the distinctive ability of the measurement and reduces the sensitivity of crack growth measurements to voltage measurement scatter. The expression of interest is V(a)/V(a0) as a function of Da/W and can be calculated using Johnson's equation, whereby a0/W and Dmeas,1/W are considered as constants (Fig. 10). The analysis is performed for a0/W ¼ 0.2 (left graph) and 0.5 (right graph), which represent the limits of allowable initial notch depth according to BS 8571 [20]. Data for a0/W ¼ 0.2 are plotted up to Da/W ¼ 0.4, representing a final relative crack depth of 0.6; the analysis for a0/ W ¼ 0.5 is stopped at Da/W ¼ 0.3, which corresponds with a final relative crack depth of 0.8. The abovementioned range of interest for Dmeas,1/W is bounded by vertical dashed lines. Notably, curves of similar shapes were observed for compact tension (CT) specimens in Ref. [35]. A sensitivity analysis is performed by translating Fig. 10 into Fig. 11, which introduces a sensitivity parameter s ¼ v(V(a)/V(a0))/ v(a/W). Every 0.01 increase in a/W (or Da/W) corresponds with an increase in V(a)/V(a0) of s percent. The increase in absolute voltage (which should be sufficiently high compared to the voltage scatter) then depends on its initial value V(a0). Higher values for s are

7

preferred. It is observed that:  Observed sensitivity values within the range of tested thickness values (i.e., between the dashed vertical lines) are between 1 and 7. Accordingly, 0.01 increase in a/W results in 1e7% increase of V(a)/V(a0) depending on the exact conditions.  The sensitivity of the voltage signal to crack growth increases as Dmeas,1/W is decreased (in other words, as specimen thickness W increases). Hence, thicker SENT specimens require a lower current density to produce an equal crack sizing scatter in terms of a/W, which may be helpful with respect to the limited capacity of the current source.  The sensitivity of the voltage signal progressively increases as the crack grows. In other words, crack sizing scatter is expected largest near initiation and decreases as the resistance curve is progressing.  Larger initial notch depths tend to decrease the sensitivity for low Dmeas,1/W values and vice versa. For very shallow initial notches, the potential benefit of positioning voltage probes closer to the notch is more pronounced than for deep notches. Note that the analysis above applies to dimensionless crack depth (a/W), and interpretations change when sensitivity is expressed as the increase of V(a)/V(a0) per absolute increase of crack depth a. Consider for example the case where a0/W ¼ 0.2 for two width values: W ¼ 9 mm or W ¼ 30 mm. Voltage sensitivities s (with respect to Da/W) of 0.95 and 3.55 are respectively obtained from Fig. 11. As a result, the first 0.1 mm of crack growth (Da/W ¼ 1/ 90 for W ¼ 9 mm, and Da/W ¼ 1/300 for W ¼ 30 mm) yields an increase of V(a)/V(a0) by 0.011 and 0.012, respectively. In this example, the sensitivity of potential drop (relative to its initial value) to absolute crack growth is not strongly dependent on W. Second, it is beneficial to have a large robustness with respect to unavoidable probe positioning errors. Hereto, a robustness parameter r is defined as [v(a/W)/v(Dmeas,1/W)]1 for fixed values of voltage measurement V(a)/V(a0) and initial crack depth a0/W. Regardless of W, every millimetre of probe positioning error corresponds with an absolute crack sizing error (in millimetre) equal to 1/r. Larger values for r are preferred. Robustness parameter curves are plotted in Fig. 12 for the same configurations considered earlier. Since the measured crack depth is no longer necessarily its correct value in this analysis, V(a) is simply denoted as V (the measured potential drop). The following is observed:  For the considered range of Dmeas,1/W (between 0.15 and 0.50), robustness tends to decrease as the crack grows from its initial notch. This is reflected in a decreasing robustness parameter as V/V(a0) increases. In other words, probe positioning errors (in terms of absolute crack depth) become more pronounced as the resistance curve progresses.  Deeply notched SENT specimens are more robust to probe positioning errors (i.e., show higher values for r) than shallow notched specimens.  Robustness is lowest in the range of considered probe positions. As an example, for a0/W ¼ 0.2 and V/V(a0) ¼ 2.00, the lowest observed robustness parameter is around 1.25, indicating that every ‘millimetre of probe positioning error’ is associated with a ‘crack depth sizing error of 1/1.25 or 0.8 mm’. This observation implies that accurate probe positioning should be a point of attention for the sake of measurement accuracy. With proper attention to this aspect, accurate potential drop measurements can be achieved as shown in Section 5. Notably, combining Figs. 11 and 12, it appears that the optimal potential probe positions are directly adjacent to the notch faces

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Fig. 10. Graphical representation of the Johnson equation for various levels of a0/W, Da/W and Dmeas,1/W.

Fig. 11. Sensitivity analysis of potential drop with respect to a/W, derived from Fig. 10.

Fig. 12. Robustness analysis of a/W measurement with respect to probe position Dmeas,1/W.

(highest sensitivity and robustness). However, this positioning strategy is obstructed by the presence of the dual clip gauge knife blocks. Within our range of dimensions tested, these blocks consumed (near to) the entire specimen width, eliminating (or strongly limiting) the available space for probe spot welding.

Noteworthy, we do not advise against probe positioning adjacent to the notch faces provided it is practically feasible to do so. In this respect, thicker specimens may more easily allow for probe attachment near the notch faces, thus increasing the robustness of the measurement. It should be borne in mind, though, that the gain

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in terms of sensitivity would be limited (Fig. 11), and the absolute value of potential drop would be less. This may yield larger effects of ripple noise. Overall, the adopted probe positioning strategy appears sound, given the satisfactory crack sizing accuracies obtained in our test database (see following sections). 4.3. Crack sizing accuracy of DCPD technique Fig. 13 compares DCPD predictions of final crack extension

Dat,pd,f against actual values Da9p, measured using the nine-point

average method. Also shown are lines of ±15% error relative to Da9p. A first distinction is made between straight notched specimens (to which the presented test procedure applies) and specimens with a tilted notch (with a devoted but similar test procedure). Further distinction is made between base metal and weld specimens. Overall, a good agreement is observed. The measurement error, when defined as Dat,pd,f e Da9p, has an average value of 0.08 mm and standard deviation of 0.28 mm. Closer analysis reveals that the errors are similar for straight and tilted notched specimens, but different for base metal specimens (average error 0.04 mm; standard deviation 0.22 mm) and weld specimens (average error 0.17 mm; standard deviation 0.28 mm). The presence of a weld tends to underestimate crack size and increase its prediction scatter. The difference is statistically significant as indicated by a two-tailed t-test (null hypothesis: both distributions have an equal average; alternative hypothesis: different average). This test reveals a p-value of less than 0.001, which clearly allows to reject the null hypothesis. The crack sizing accuracy of the DCPD technique is further discussed in the following section. 5. Comparison with unloading compliance A significant portion of tests described in section 3.1 (39 out of 101, all of which contained a straight notch) was executed with an unloading/reloading strategy. This dataset enables a comparison of crack sizing accuracy of DCPD against the more commonly documented UC methodology, and is focused on in this section. Fig. 14(a) plots the UC measurements of final crack extension against physical nine-point measurement values. Similar to Fig. 13, lines of ±15% error relative to Da9p are shown. UC clearly has the ability to size crack extension with a reasonable accuracy as the datapoints are

9

located near the dashed 1:1 line. UC and DCPD predictions of final crack extension are compared in Fig. 14(b), which indicates that both predictions are generally comparable. Both methods predict similar crack extensions, the average difference between values obtained by DCPD and UC being as little as 0.01 mm. Nonetheless, scatter is present. The maximum observed difference between both methods' predictions is 0.52 mm (UC predicting a larger crack extension), and the standard deviation of differences is 0.17 mm. To qualify the performance of the UC and DCPD methods in a more objective manner, their predictive abilities have been compared with accuracy requirements for crack extension measurements (high constraint) resistance curve testing in ASTM E1820 [25]. This standard prescribes that the calculated final crack extension should not differ from its actual value Da9p (obtained by the nine-point method) by more than 0.15Da9p or 0.03(W e a0) (whichever is smaller), for the measurement to be valid. Fig. 15 plots measured errors against their allowable absolute value according to ASTM E1820. Positive measurement errors represent an overestimation of physical crack extension and vice versa. It is observed that both UC and DCPD have a strong ability to produce valid crack extension measurements, as most data points are located in the area between the slanted dashed lines. Invalid measurements (2 points out of 39 beyond validity limit for DCPD; 4 points out of 39 beyond validity limit for UC) tended to underestimate the physical final crack extension. Analysis of the data presented in Fig. 15 reveals that, on average, UC measurements of final crack extension are somewhat closer to their physical value than DCPD measurements (average error for DCPD and UC respectively 0.074 and 0.055 mm). The scatter in measurement error is somewhat lower for DCPD (standard deviation of error for DCPD and UC respectively 0.139 and 0.164 mm). The largest error is observed for DCPD (underestimation of physical crack extension by 0.51 mm). However, the statistical significance of this comparison can be questioned given the limited size of the test database and the large degree of scatter present. A two-tailed t-test was performed to confirm the significance of different average measurement errors (null hypothesis: equal average; alternative hypothesis: different average). Assuming two normally distributed independent data sets indicates a p-value of 0.59, which is insufficiently significant to reject the null hypothesis. In conclusion, the presented dataset does not allow to confirm (nor does it reject) Hioe et al.’s statement regarding increased scatter of UC over DCPD measurements [14]. What remains, however, is the essential statement that both methods easily allow to meet the accuracy criteria set forward by ASTM E1820 according to Fig. 15. In a search for factors influencing the accuracy of crack extension measurement by unloading compliance and direct current potential drop, reference [24] considered possible effects of  The presence of natural weld flaws;  Initial crack size;  Crack front straightness.

Fig. 13. Comparison between predicted final crack extensions and actual values measured using the nine-point average method.

For a detailed discussion, the reader is referred to the abovementioned paper. In summary, effects of initial crack size and crack front straightness were found to be non-significant for the investigated set of test data. In contrast, natural flaws pose challenges with respect to measurement accuracy in welded SENT specimens. For instance, the specimen showing the largest error in predicted final crack size for both UC and DCPD was characterized by a clear presence of weld porosities in the fracture surface (Fig. 16 [24]). The exact influence of natural weld flaws (and potential non-validity of test results in their presence) is not quantified and further research on this matter is ongoing.

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Fig. 14. Comparisons between final crack extensions: (a) measured versus UC; (b) DCPD versus UC. Size of dataset: 39 tests.

grooves, which strongly promotes in-plane crack growth), but has been observed in other studies on (plain sided) specimens [36]. 6. Conclusions This paper has presented and evaluated a procedure to measure crack growth during SENT testing by means of direct current potential drop. Having shown the successful application of DCPD for the reported test database, this paper is aimed to contribute to a more prescriptive description of DCPD analysis in revised SENT test procedures or standards. The following major points deserve to be recalled.

Fig. 15. Comparison of measured predictive errors against allowable error according to ASTM E1820 [25].

Fig. 16. Natural flaws observed in the fracture surfaces of a welded SENT specimen [24].

Notably, an additional effect deserving further attention is the effect of out-of-plane tearing on the accuracy of the DCPD measurements. Crack path deviation was not observed in the tests reported in this study (mostly due to the common presence of side

 The effect of undesired changes in current and material resistivity (i.e., temperature) can be eliminated by normalizing the potential drop across the notch against a reference voltage measurement remote from the notch (dual probe technique).  The Johnson equation (which expresses the relation between potential drop increase and relative crack depth) is valid for plane sided as well as side grooved square-sectioned SENT specimens.  A minimum required distance between current input and output pins and notched section is set forward, motivated by the desire to surround the notched section with regions of uniform potential drop.  In our practice, probe positioning is coupled with the mounting of knife blocks for double clip gauge assembly. This restriction results in potential drop measurements which are sensitive to crack extension, but also have a limited robustness with respect to probe positioning errors. Resulting crack sizing errors are kept within acceptable limits by means of accurate probe positioning.  Despite the abovementioned limited robustness, crack growth estimations can be achieved with an accuracy similar to that of unloading compliance analysis. The majority of reported tests showed an acceptable final crack sizing error when adopting the according criterion for high constraint resistance curve testing from ASTM E1820. SENT specimens sampling weld metal produce larger crack sizing errors than specimens sampling base metal. When unacceptable, a major factor of influence proved to be the presence of natural weld flaws. Acknowledgments The authors would like to acknowledge the financial supports of

Please cite this article in press as: K. Van Minnebruggen, et al., Crack growth characterization in single-edge notched tension testing by means of direct current potential drop measurement, International Journal of Pressure Vessels and Piping (2017), http://dx.doi.org/10.1016/ j.ijpvp.2017.06.009

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IWT Vlaanderen (grant nrs. SB-091512 and SB-093512), Arcelor Mittal R&D Ghent (Belgium)/OCAS NV and the EU Research Fund for Coal and Steel (RFCS; project abbreviation SBD-SPipe; grant agreement number RFSR-CT-2013-00025), all of which led to the production of test results reported in this paper.

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Please cite this article in press as: K. Van Minnebruggen, et al., Crack growth characterization in single-edge notched tension testing by means of direct current potential drop measurement, International Journal of Pressure Vessels and Piping (2017), http://dx.doi.org/10.1016/ j.ijpvp.2017.06.009