PSI - Issue 52

Ben M B Sargeant et al. / Procedia Structural Integrity 52 (2024) 472–479 Ben M B Sargeant , Catrin M Davies and Paul A Hooper / Structural Integrity Procedia 00 (2023) 000 – 000

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2.2.1. Potential Difference Crack Measurement Potential difference was measured across the crack as a method of crack length monitoring. Spot welded voltage probe cables were connected directly to the 24bit National Instruments 9219 Data logger, set to ±125 mV range. Use of a single data logger synchronised load and displacement data from the INSTRON system with PD data. A constant current of 2.0 Amps was passed through the sample. Voltage measured will increase with both strain and crack growth. ASTM E1820 [3] provides a calibration function to relate change in potential drop V , to normalised crack length a /W . These calibration functions are dependent on geometry and initial crack size. The ASTM calibration function (eq.2) is appropriate for the geometry and probe positioning employed in this work. The voltage, V , is normalised by the voltage at initial crack length ( V 0 ) allowing for variation in initial set up. V 0 is identified as the point when potential drop deviates from its initial linear trend; this indicates the commencement of crack growth as all previous changed in V are considered to be due to strain. The ASTM standard also includes corrections for V 0 and a 0 to account for crack tip blunting ( a 0,bl ) and to calibrate to voltage at crack-to-width ratio of 0.5 ( ̅ ) [3]. = [0.2864( ̅ −0.5)] 0.3506 , ℎ ̅= 0 3.4916( 0, ) 2.8523 +0.5 0, = 0 + 2 (2) A crack growth calibration function, considering a straight fronted crack in an SEN(B) geometry, was created with COMSOL Multiphysics® software [6] A fourth order polynomial was used to fit a calibration curve. Initial voltage ( V 0 ) is set to each samples true initial crack length. Eq.3 shows the fit function for an example with a o of 5.1 mm. =−0.0032( 0 ) 4 +0.0509( 0 ) 3 −0.3153( 0 ) 2 +0.9353( 0 )−0.1584 (3) 3. Results and Discussion Experimental data provided histories of load ( P ), load line displacement (LLD) and crack potential difference (PD). A MATLAB script was employed for initial data processing. This script identified test beginning and end points, applied a low pass Butterworth filter to reduce noise and, finally, computed stress intensity factor ( K ), elastic J-integral ( J e ) and plastic J-integral ( J p ) as specified in ASTM E1820. 3.1.1. PD Crack Propagation An example of PD data vs LLD record is shown in Fig. 3. Due to the small sample size a relatively small current was required, to avoid a Joule heating effect. This led to small PD voltage measurements. Though a low signal-to noise-ratio is observed in the PD raw data, the trends can be determined, especially after the application of a low-pass filter. A linear trend line was fitted to the first 2 mm and last 3 mm LLD, where two clear linear trends can be observed, which were extrapolated to identify an intersection, corresponding to V 0 . Changes in PD prior to V 0 are considered to be due to strain effects alone, and that crack growth initiates at V 0 . As the second trendline is linear, crack growth in this sample can be considered linear. 3.1.2. Fracture Surface Fracture surfaces were analysed using image processing software to measure initial and final crack length, averaged through the thickness of the sample. Observation of the fracture surfaces (Fig. 4b) shows a high amount of tunnelling, necking and shearing. This indicates fracture tending towards plane stress behaviour. Crack growth between initial and final crack length is shown vs normalised PD in Fig. 4a, assuming a linear relationship. This trend is compared to the predictions from the ASTM calibration function (eq.2) and the COMSOL based function determined in this work (eq.3). All functions, within the observed voltage range, followed an effectively linear relationship, but underestimated growth. The measured crack growth was 1.32 mm, yet PD measurements using both eq.2 and eq.3 predicted this voltage change to increase crack length by only 0.54 and 0.74 mm, respectfully. This work is likely outside the range of empirical data used to inform the ASTM calibration function Whereas the COMSOL model underestimation is considered to be affected by crack tunnelling, since the