Philippa L. Moore and Henryk G. Pisarski
Paper presented at ISOPE-2012. The 22nd International Ocean and Polar Engineering Conference Rodos Palace Hotel, Rhodes (Rodos), Greece, June 17-22, 2012.
The accuracy of a range of methods to determine CTOD (crack tip opening displacement) for single edge notched tension (SENT) specimens is validated against physical measurements of CTOD taken from silicone notch replicas taken from the specimens. A range of crack lengths was used to investigate the influence of crack length on CTOD. Both numerical modelling and silicone crack infiltration methods agreed fairly well with the double-clip method to determine CTOD, giving confidence that the double-clip method gives conservative estimates of CTOD for SENT specimens. However, it is shown that the double clip method should only be employed when a/W>0.1. Recommendations are also made for alternatives to DNV-OS-F101 in order to calculate CTOD from J.
|Original crack length (mm)
|Plastic area under the force versus displacement graph (Nmm)
|Specimen thickness (mm)
|Net specimen thickness after side grooving (mm)
|Young's modulus (MPa)
|Length of SENT specimen 'daylight' between the grips (mm)
|J integral (J/mm2)
|Elastic stress intensity factor (MPa√m)
|Constraint parameter according to ASTM E1290-02
|Strain hardening parameter according to ASTM E1290-02
|Plastic part of the clip gauge displacement (mm)
|SENT specimen width (mm)
|Height of the clip gauge above the crack mouth (mm)
|Crack tip opening displacement, or CTOD (mm)
|Flow stress, the average of yield and UTS (MPa)
|Yield strength (MPa)
|Ultimate tensile strength (MPa)
There is an increasing trend in the offshore pipeline industry to use tension-loaded fracture mechanics specimens (single edge notched tension; SE(T) or SENT specimens) instead of the standard bend SENB design, so as to better replicate the crack-tip constraint conditions experienced in pipeline girth welds. In the US there is an increasing tendency to express R-curves in terms of crack tip opening displacement (CTOD or δ) instead of J. CTOD can be determined indirectly from J, as given by a formula in [DNV-OS-F101 (2010)]; this conservative estimation procedure, is, however, considered to be rather crude and not properly validated for SENT specimens. [Shen (2009)] offers a revision to that approach developed specifically for SENT specimens, while [Moreira & Donato (2010)] offer a method to calculate CTOD directly from SENT test parameters. There is also an established formula for determining CTOD from a SENT specimen double clip gauge [DNV, 2000 and ExxonMobil, 2010]. There is a need for work to validate these various methods for determining CTOD for SENT specimens [Pisarski, 2010]. These and other methods for determining CTOD for SENT specimens are compared and evaluated in this report.
A set of SENT tests was carried out to provide the reference data for the evaluation of CTOD. Parent material that is representative of offshore pipelines (API 5L X65) was selected, with a thickness of 23mm. The SENT specimens were 2BxB (where B is the material thickness in cross section), and surface notched. All tests were carried out at room temperature. The specimens were tested using wedge/hydraulic grips such that the ratio between the day light between the grips, H, and the specimen width, W, was 10. The SENT testing was carried out in accordance with DNV-RP-F108 as far as possible to generate multiple-specimen CTOD and J R-curves. Notching and fatigue pre-cracking was carried out in accordance with BS 7448 Parts 1 and 4.
Three different sets of six specimens were tested with different nominal crack length to specimen width (a/W) ratios of 0.1, 0.3 and 0.5. For each set, six specimens were tested to different levels of tearing with complete unloading to generate data points for the multiple-specimen R-curve.
Two specimens from each set of six also had CTOD measured by producing replicas of the specimen notches (including the fatigue crack) using the silicone rubber infiltration method, to enable a direct comparison to be made between the CTOD estimation equations and actual measurements. The silicone injection system consisted of a Microset 50ml dispensing gun used with a syringe needle attachment and nozzle along with a 50ml Microset 101RF Cartridge of silicone rubber. The black silicone rubber replicas were then sectioned in two locations in the middle part of each crack tip and mounted so that measurements of the CTOD could be made from the notch cross sections.
Finite element modelling
Finite element analysis was carried out on numerical models of three different SENT specimen geometries to match the specimens that were mechanically tested. The finite element models were prepared and analysed using the finite element software package Abaqus v. 6.10.1. The finite element analyses carried out were used to produce load versus CMOD curves and to determine values of CTOD.
The SENT specimens were modelled with one-quarter geometry in Abaqus, exploiting the specimen symmetry. A sharp crack was employed, and the model consisted of three solid, deformable parts, assembled together by tie constraints (Fig.1). This subdivision of the geometry allows the mesh to be fine in the region near the crack-tip and coarse farther away (Fig.2). Inside the innermost semi-circular partition, 15-node, quadratic, wedge elements C3D15 were used. In the remaining half-annular regions, a radially symmetric mesh of quadratic brick elements was generated. For the remainder of the domain, 20-node, quadratic brick, reduced integration elements C3D20R were employed.
Fig 1. Quarter SENT specimen geometry with the three distinct parts coloured differently
Fig 2. SENT specimen model showing mesh size in different regions
The smoothed parent metal stress strain curve, derived from the experimental data, was used to generate a table of yield stress versus plastic strain behavior (Fig.3). These data were then used to define an isotropic material in Abaqus with Young's modulus 207000 MPa, Poisson's ratio of 0.3 and plastic behaviour as illustrated in Fig.3.
Fig 3.Stress-strain experimental data and smoothed data used in FEA
CTOD from Double Clip. Older versions of the DNV F101 standard from 2000 provided equations for calculating the plastic component of CTOD directly from a pair of clip gauges mounted above the notch (Fig.4), known as the double clip method:
Fig 4. An example of a double clip gauge arrangement at the crack mouth of a fracture toughness test specimen
The elastic component of CTOD is calculated from the elastic stress intensity factor, KI, at the subject load. The second term represents the plastic component of CTOD and is derived by extrapolating the plastic component of the readings obtained from the pair of clip gauges. Vp1 and Vp2 are the plastic parts of the clip gauge displacements for clips at gauge heights above the crack mouth of z1 and z2 respectively. The ExxonMobil procedure for SENT specimens [ExxonMobil, 2010]) also uses this double-clip approach to calculate CTOD but ignores the elastic contribution (the first term in the formula). In these tests TWI used a double clip with the lower clip at a height of 2.4mm from the crack mouth and the upper clip 10mm above the lower clip.
CTOD from J - DNV-OS-F101. [DNV-OS-F101 (2010)] gives a formula for calculating CTOD from J:
Where m is a constraint parameter, N is the strain hardening parameter, a is the crack length and W is the specimen width.
This formula was originally intended for bend specimens, but it is now implicit for tension specimens too, although no references to validation for tension specimens is given in the DNV standard. The standard does state that it is a conservative method for determining CTOD and should not be used the other way around (i.e. not for estimating a value of J from CTOD).
CTOD from J - Shen & Tyson, 2009. [Shen and Tyson (2009)] offer a revision to the approach used in DNV F101 to calculate CTOD from J. Their method also uses Eq. 2, but gives equations to calculate m specifically for SENT specimens. It is dependent on both N, and the ratio of the load, P, to the reference load, PY (Eq. 5). For elastic-plastic materials the tensile properties are described (Eqs. 7 and 8) to allow N to be determined from the material stress-stain curve.
Where σflow is the flow stress, BN is the specimen net thickness of side-grooved specimens. The equations for m are then given by:
CTOD calculated using η from Moreira & Donato, 2010. [Moreira and Donato, 2010] give a method for direct calculation of CTOD using the fracture mechanics test parameters (Eq. 16) and give specific η factors for calculating CTOD as well as those for J. The solutions include parameters for weld strength mismatch and weld width, which make it of particular interest for the assessment of weld specimens. The H/W ratio does not affect the results significantly, but the set of polynomial parameters for H/W=10 were used here.
KI is given by equations (Eqs. 17 and 18). The parameters of m and η are calculated from the equations (Eqs. 19 and 20), which have been simplified from those given in the original reference by assuming that the weld width equals zero and overmatch equals one for the parent metal specimens in this work. Only the equation for η for displacement measured using CMOD is shown, although an alternative for when load line displacement is used is given in the reference.
The specimens notched to a nominal a/W ratio of 0.1 had actual values ranging from 0.091 to 0.12. The specimens with nominal a/W of 0.3 measured crack length to width ratios from 0.346 to 0.349, while the specimens with nominal ratio of 0.5 were actually from 0.532 to 0.563. DNV-RP-F108 permitted values of 0.2 ≤ a/W ≤ 0.5, so the shallowest and deepest notched specimens were outside this range. Most of the shallowest notched specimens also had invalid crack shapes to BS 7448 Part 4 (an example is shown in Fig.5). The crack shape clauses in BS 7448 Parts 1 and 4 are intended for BxB or Bx2B bend specimens, rather than 2BxB SENT specimens. The validity of these clauses for SENT specimens is the subject of ongoing research [Malpas, 2012].
Fig 5. Fracture face from SENT specimen nominally notched to a/W of 0.1, showing a crack shape invalid to BS 7448 Part 4
Fig 6. Illustration of how two measurements of displacement at each clip gauge in a double clip can be used to determine the CTOD at the crack tip, by assuming similar triangles, and a fixed point of rotation ahead of the crack tip
Using the double clip method to calculate CTOD assumes that there is a given point of rotation for the specimen and the crack faces remain parallel to the points of attachment of the clips. CTOD can be obtained by extrapolating the two clip gauge readings to the crack tip assuming similar triangles (Fig.6). The point of rotation was determined for the SENT tests, as a distance from the specimen surface. The average point of rotation for a/W of 0.3 and 0.5 was 45mm (with a standard deviation of 9mm). This means that under tension the level of rotation is only slight, and hinges around a point 25mm outside the specimen (for bend specimens, the point of rotation would be within the remaining ligament). For the a/W = 0.1 specimens the distance to the point of rotation was highly scattered, and negative in many cases. Values ranged from -73mm to +101mm for the six specimens, meaning that the point of rotation was not consistently ahead of the crack, and the double clip method to estimate CTOD would not be considered to be accurate for these shallow notched specimens.
In addition to CTOD, J was estimated from CMOD in accordance with the procedure described in [DNV F108 (2006)] and J resistance curves derived. R-curves of the form y = m + l(Δa)x as given in BS 7448 Part 4 were fitted to the lower bound of the data points, both for the values of J and for the values of CTOD, assuming the double clip method. The multiple specimens R-curves produced from each set of six specimens are plotted in Fig.7 as J-R-curves and in Fig.8 as CTOD R-curves. In Fig.8 equivalent values of tearing and CTOD measured from the notch replicas are also shown for comparison, but not included as data points for the R-curve fitting. The individual fitted equations are as follows:
Fig 7. J R-curves determined for the three sets of SENT specimens, showing the data points and the best curve fit
Fig 8. CTOD R-curves (using CTOD determined from the double clip), showing the data points and the best curve fit. Equivalent measurements of crack growth and CTOD taken from the notch replicas are also shown
The shapes of the three R-curves for each crack depth to width ratio are slightly different, but the results confirm that the SENT multiple specimen R-curves are fairly insensitive to crack depth to width ratio, when plotted as both CTOD and J. The scatter was greatest in the specimens with a/W ratios of only 0.1, reflecting the difficulties in achieving a satisfactory fatigue crack shape with such a shallow crack, and the large variation in points of rotation (which affects the estimation of CTOD from the double clip gauges). The R-curve plotted for a/W of 0.1 was lower relative to the a/W of 0.3 and 0.5 when plotted as J compared to CTOD from double clip.
The silicone replicas of the notches were sectioned across the notch front in two places, and both slices were mounted for measurement of CTOD from the perpendicular cross sections. The value of CTOD was measured across the points of transition between the end of the pre-crack and the cracking during the test (shown as line AA on Fig.9). The amount of crack growth in each specimen was also measured as the perpendicular line to the notch tip to line AA (shown as line BB on Fig.9).
Fig 9. A cross section through one of the CTOD specimen notch replicas, showing the measurement for CTOD (A-A), and to determine the amount of tearing (B-B)
Analysis of CTOD methods
The CTOD results derived from double clip obtained for the specimens with a/W ratio of 0.1 were scattered. For specimens, such as shown in Fig.5, with an uneven fatigue crack front shape, the results from the silicone crack infiltration method were dependent on where along the crack front it was sectioned. The FEA model showed greatest difference between the model and measured values of CTOD for a/W of 0.1, despite being able to match the J values fairly well. The results for a/W of 0.1 have been included in this analysis, but more weight has been given to the results from specimens with a/W of 0.3 and 0.5.
When the values of CTOD and Δa measured from the silicone notch replicas were plotted along with the experimental data and R-curves, the points were consistently below the R-curves determined from the tests, with the largest difference shown by the series with nominal a/W of 0.1. This reflects the fact that the replica measurements of tearing are taken at the location of maximum tearing in the middle of the specimen, whereas the test results average the tearing across the specimen crack front. This will effectively shift the notch replica measurements to the right of their equivalent test results. Nevertheless, the data points taken from the notch replicas also bear out the relative independence of SENT fracture toughness on crack depth ratio in the range 0.1 to 0.5.
The values of CTOD obtained from all the different estimation methods were compared to the values of CTOD measured from the silicone rubber notch replicas. Fig.10 shows this comparison plotted against the measured initial a/W ratios for the two specimens from each set of six that had silicone replicas made. The SENT test data used for these comparisons had measured levels of crack extension of between 0.3 and 1.8mm at the end of test. The methods which most closely matched the physical measurements taken from the notch replicas were the double clip method, finite element modelling, and the Shen & Tyson equation for CTOD from J. For specimens with nominal a/W of 0.1 the Shen & Tyson formula CTOD is under-estimated, indicating that its validity may be limited for very shallow notched SENT specimens. The shallowest notched specimens also showed some scatter in the double clip method due to inconsistent points of rotation.
Fig 10. Comparison of CTOD values from all the assessed evaluation methods plotted relative to the actual CTOD values measured from silicone notch replicas
Fig.11 shows a comparison of the three equations for calculating CTOD for SENT specimens, with data points calculated for each SENT specimen of the sets of six with nominal a/W of 0.3 and 0.5, plotted against the CTOD from the double-clip, relative to the line of unity. The Shen & Tyson equation matched most closely the double clip method for a/W of 0.3 and 0.5. The [DNV (2010)] and the [Moreira & Donato] methods had less scatter with a/W ratio, but both consistently under-estimated the CTOD relative to the double-clip method, with the DNV method being the most over-conservative. This reflects the fact that its method of calculating CTOD from J uses equations developed for SENB rather than SENT specimens and is therefore not an accurate method to determine CTOD values for SENT specimens.
Fig 11. Comparison of the equations for calculating CTOD from J for SENT specimens with double clip method, with data points calculated for each individual SENT specimen with a/W of 0.3 or 0.5
Despite the [Moreira & Donato] method appearing over-conservative for these specimens, the method was developed for welds, and it may prove to be less over-conservative when it takes account of weld width and strength overmatching, which the other methods do not. This would be an area for further investigation.
Calculating the CTOD directly from the double clip assumes a point of rotation ahead of the crack tip in the SENT specimen as the crack opens. It is possible for the location of the point of rotation to vary considerably in an SENT specimen, compared to an SENB specimen where the point of rotation is necessarily constrained to within the remaining ligament ahead of the crack front. Any variation in the point of rotation will affect the scatter in the measured results, and is a concern with SENT specimens. This has been shown by the very large variation in the distance to the point of rotation for the shallowest notched SENT specimens (a/W of 0.1), compared to a more consistent rotation point for the a/W of 0.3 and 0.5 specimens.
Discussion & conclusions
Using silicone rubber crack infiltration allows direct measurement of CTOD to be made from replicas of the SENT specimens notch, although the replica method is not very practical for routine testing. FEA models also give a reliable way to determine CTOD, but require too much analytical processing to be practical for determining CTOD for every fracture mechanics test. These methods have been used to compare the effectiveness of other simpler methods for calculating CTOD that have been published.
Ignoring the scattered results for a/W of 0.1; for a/W ratios of 0.3 and 0.5 both the FEA model and the crack infiltration methods agreed fairly well with the double-clip method, giving confidence that the double-clip method can give reasonably accurate values of CTOD for SENT specimens.
It is concluded that the double-clip method is a viable alternative method for determining CTOD for a/W in the range 0.3 to 0.5.
At a/W ratios of 0.3 to 0.5 the equation for calculating CTOD from J for SENT specimens given by [Shen & Tyson] offers the best alternative method to calculate CTOD from J compared to the over-conservative approach given in the current [DNV OS F101] standard.
The authors gratefully acknowledge the assistance provided by to our TWI colleagues Jerry Godden, David Seaman and Phil Robinson for their work in carrying out the SENT tests described here, and thanks also to Tyler London who carried out the numerical modelling for this work.
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