Measuring the Crack Growth Rate (da/dt) of a Fatigue Crack Using Phased Array Ultrasonics
TWI Ltd, Granta Park, Great Abington, Cambridge CB21 6AL, UK
TWI Member Publication, 28th November 2013
This paper presents the measurement of the growth rate of a fatigue crack in a standard notched specimen using ultrasonic phased array technology. The real-time measurement of the crack size allows establishment of the growth rate. This information is valuable in understanding behaviour of materials, components and the models such as Paris’ Law used to predict the lifetimes of engineering structures. The information presented in this paper was collected in a laboratory fatigue test and work is now ongoing to generate the instrumentation to measure the growth rate of a natural crack initiated during the simulated fatigue testing of a full size component.
Establishing the growth rate of cracks during failure is a key part of assessing the integrity of the structure. Fracture models based on Paris’ Law aim to predict the rate of growth of a crack during fatigue failure over the number of fatigue cycles – ie da/dN. This can typically be approximated during resonance fatigue testing by measuring the size of a crack through non-destructive testing (NDT) methods by stopping the test and taking a measurement.
The ability to establish the rate of crack growth as a function of time – ie da/dt – during the fatigue fracture failure of a component will allow an added sophistication to the assessment of a structure’s integrity. This will have to be monitored and measured while the tests are underway as an online/condition monitoring technique. It is thought that actual propagation rate of a crack in different materials and under different loading scenarios may give greater insight into the modes of failure as well as opening the possibility to provide more information towards the integrity of structures.
As part of several current projects underway in TWI it is proposed to implement and trial the measurement instrumentation to achieve this goal. This exploratory project was aimed at optimising the instrumentation which will monitor a known crack in the component online (live) during a test. The aim was to essentially collect an ultrasonic video of a crack as it grows to failure, and by establishing the frame rate it was possible to get the value for da/dt. The key was to establish this recording frame rate such that it was within the speed of the crack growth and setting the ultrasonic instrumentation fast enough to capture the fast fracture point at failure.
The methodology generated in this exploratory project is being prepared for implementation during the fatigue testing of a full scale component in TWI.
The verification test setup was simple. A standard fatigue test specimen with a starter notch was fabricated. The test specimen was 290mm long, 29mm wide and 15mm deep. The notch was 3mm deep leaving a 12mm ligament at the outset of the experiment. The notch was generated by electro-discharge machining (EDM) with a width of 0.3mm. A 10MHz linear array probe containing 32 elements at a pitch of 0.3mm was placed on a Rexolite wedge to generate shear waves at angles from 40 to 85º. Figure 1 shows the design of the test specimen and Figure 2 shows the ultrasonic phased array technique setup. Figure 2 also shows two geometric features of the notch which can be clearly identified in the ultrasonic signal data in Results.
Figure 3 shows the design of the probe connection on the fatigue test specimen. It was clear that given the likely vibrations during the fatigue testing the ability of the probe to remain attached to the specimen would be an issue. Equally it was not possible to mechanically connect the probe to the specimen (eg using screws) as the screw holes will have implications for the validity of the test and possibility of damage taking place in the vicinity of the screw threading. Small powerful rare earth magnets were selected to generate sufficient force to keep the probe attached to the specimen during the test. Figure 4 shows the test items to include the probe, the reference specimen and two test specimens. The first of the specimens was statically loaded to failure to establish the yield strength of the material which was then used to calculate the appropriate stress range for the fatigue test. The criteria was to ensure that the component failed within 20 minutes leading to a stress range between 5kN to 0.85 of yield at a sinusoidal 9Hz frequency.
Figure 5 shows the test setup with the ultrasonic probe in position to monitor the notch and the fatigue testing machine (INSTRON). The ultrasonic data was collected using a Zetec DYNARAY array controller which was able to achieve refresh rates in excess of 20Hz. A software package called CamStudio was used to generate the video using CODECs that allow control of the frame rate and the precision of the data. CamStudio is licenced for commercial use under GNU GPL. Figure 6 shows the data collected and shows the signals from the notch corner and tip – compare to Figure 2 to understand the corresponding ultrasonic image area.
The video of the test showing the growth and failure due to a fatigue crack can be found here. The sensitivity of the ultrasonic system was set high enough to be able to detect the weak diffraction signals emanating from fatigue cracks in the pulse-echo mode – evident from the saturated signals from both the corner and tip echoes of the starter notch as shown in Figure 6. Note that the time value recorded as 0 seconds in Figure 6 was after a loading duration of approximately 7 minutes into the test, close to when the fatigue crack was initiated. The first live, measurable indication of a crack tip emanating from the starter notch was identified at a time of 129s as shown in Figure 7.
It can be seen and noted clearly on the video that the nature of the crack tip growth leads to moments in time when the crack tip cannot be seen – ie no signal is generated by the crack tip to be detected in the pulse-echo mode. For example at a time of 334s, clearly after when a crack was initiated, no indication of a tip is available in the image area – see Figure 8. The diffraction mechanism at the local crack tip level is highly dependent on the local orientation of the tip and, as the crack tip propagates, there are times when no signal will be detected. This poses a limitation on ultrasonic testing for such weak reflectors but without an exhaustive search for the tip from all different angles and all available inspection surfaces (which in practice will take a long time and be an expensive effort), this limitation must be accepted and factored into any testing and monitoring regimes. Figure 9 shows the presence of a typical crack visible on the edge of the specimen, ahead of the notch tip; the actual crack depth at the centre of the specimen at this point in time was closer to the failure point, illustrating the usefulness of the method using ultrasonics which is able to interrogate inside materials.
The data presented can be plotted on a graph of crack height (a) from the original position of the notch tip (see Figures 2 and 6) against the time. This result provides valuable insight into the nature of the material and the variable rate of the crack growth, presenting valuable input to failure models.
The following conclusions draw together the findings in this paper:
- A phased array ultrasonic technique was successfully developed to monitor in real-time the failure of a notched standard fatigue specimen.
- The data allowed the plotting of the size of the crack at specific times during the fatigue test and the gradient of this plot gives the growth rate of the crack at any given time during its propagation towards failure.
- The video frame rate and the repetition frequency of the instrument determine the precision with which the growth rate can be captured. It is possible to set these parameters to measure growth rate even at the fast fracture period at the end.
- The instrumentation has been optimised for application to a scenario where a full scale component is fatigue tested to failure in the large testing facilities of TWI.
The author will like to thank Mark Tinkler of TWI for implementing the fatigue testing and Emilie Soileux of TWI for successfully performing the calculations to allow the notched specimen to fail within the elected time period of 20minutes.