The Effect of Test Specimen Size on Dynamic Young’s Modulus Measurements of Graphite

1. The Effect of Test Specimen Size on Dynamic Young’s Modulus Measurements of Graphite A Tzelepi ASTM Symposium on Graphite Testing for Nuclear Applications: The Significance of Test Specimen Volume and Geometry and the Statistical Significance of Test Specimen Population 19-20 September 2013, Seattle

2. Overview of presentation Basic principles of ASTM standard C769-09 Deviations from the basic principles of this standard Experimental considerations related to C769-09 Signal analysis Transducer frequency Applying C769-09 on small specimens Applying C769-09 on irradiated small specimens Thoughts on new ASTM standards Conclusions

3. Basic principles where: υ = group velocity of sound waves l = sample length Tt = the total time lapse To = the delay time Cii = the longitudinal elasticity modulus (the subscript refers to the direction of the tensile stress and strain) ρ = the sample density E = the Young’s modulus σ = the Poisson’s ratio (1)

4. Assumptions • Samples are homogeneous and isotropic • Signal wavelength is sufficiently small to provide the required level of timing accuracy, yet it has to be sufficiently large to be representative of the bulk material and not be affected by frequency dependent attenuation in graphite • Specimen lateral dimensions are much larger than the wavelength of the transmitted pulse so that: • the specimen can be considered as an infinite medium and dispersion of the propagated pulse is minimal and, • Young’s modulus can be calculated from the sonic velocity

5. Phase and group velocity Phase Velocity – Phase velocity refers to the velocity of a single frequency (infinite) sinusoidal wave

6. Phase and group velocity Group Velocity – In real life, there are no infinite sinusoidal waves. Waves, wave packets, pulses or signals contain components with a range of frequencies. The group velocity of a wave packet or signal is essentially the velocity with which the envelope or the energy of the wave propagates through a medium.

7. Deviations from the basic principles of C769-09 Anisotropy Eq. 1 should only be applied to isotropic graphite. An example: the corresponding formula for an extruded needle coke graphite, Young’s modulus across the grain (wave propagation in the z-direction):

8. Deviations from the basic principles of C769-09 Inhomogeneity Discontinuities within the specimen  wave scattering and attenuation  different effect for each of the frequency components in the transmitted signal  distortion of the received signal  it cannot be directly correlated to the initial transmitted signal The apparent ToF depends on the part of the signal used for timing. It is well established that frequency dependent attenuation affects the apparent group velocity measurements .

9. Deviations from the basic principles of C769-09

10. Deviations from the basic principles of C769-09

11. Deviations from the basic principles of C769-09 Inhomogeneity The degree of inhomogeneity varies with graphite grade. The microstructural features that are likely to affect ultrasound wave propagation are the grain and pore sizes, the absolute values of which are not easily determined. It is unlikely that ultrasound propagation with a typical wavelength in the order of a few millimetres will be affected by inhomogenity through small thicknesses (< 30mm) of superfine or ultrafine grain, dense graphites.

12. Deviations from the basic principles of C769-09 Inhomogeneity Extensive literature review with the aim of identifying a solution for the attenuation of sound waves in other solids there is no analytical solution for calculating the attenuation of a material with a high scatterer concentration, which is the case with radiolytically oxidised graphite. Although not quantifiable, the user must be aware of this uncertainty and, most importantly, of the fact that the effect on the accuracy and reproducibility of the test can differ for different experimental set-ups or different specimens.

13. Experimental Considerations Signal Analysis Distortion Transmitted and received signal are different  The various timing markers (onset, peaks, etc) change by different amounts  The value of the measured transit time and wave velocity depend on the timing method Advantages of the 4peak average: Reduces the effect of frequency dependent parameters Determining the pulse onset is difficult Leading edge of the pulse is a superposition of the high frequency components of the signal more prone to timing errors due to attenuation

14. Experimental Considerations Signal Analysis Studies in highly attenuative media (glass beads, quartz sand, etc) (Molyneux and Schmitt, 2000) Differences between phase and group velocities and apparent velocities measured by common timing methods, such as the onset, the first peak, the zero cross-over and the wave packet maximum The latter three timing methods were in agreement (within 3%) with the real ultrasonic group velocity whereas the onset timing method showed a discrepancy of ~12% Each method is self consistent This implies that wave speed measurements made with a particular timing method at different laboratories will agree even though they may all be in error.

15. Experimental Considerations Signal Analysis No timing method or other type of signal analysis, including cross-correlation and pulse-echo methods, is immune to the attenuation and dispersion effects FFT is not sensitive to pulse distortion but is difficult to implement accurately on a noisy signal

16. Experimental Considerations Transducer Frequency (1.25MHz) 6mm of PCEA 12.190μs 11.400μs T 12.590μs 11.795μs f = 1 / (12.190 - 11.400) = 1.27MHz

17. Experimental Considerations Transducer Frequency (1.25MHz) 100mm of PCEA 50.340μs 49.185μs T 49.745μs 51.005μs f = 1 / (50.340 - 49.185) = 0.87MHz

18. Experimental Considerations Transducer Frequency For graphite specimens, the transducer frequency must be low enough (large λ), so that it is not attenuated through the range of specimen thicknesses to be investigated. This also ensures that λ >> grain size so that the measurement is representative of the bulk material. . This also imposes a restriction on the specimen length. Large wavelengths  low frequency  reduced timing accuracy In other words, for a given accuracy, the total ToF needs to be larger so the specimen needs to be longer.

19. Basic principles of ASTM standard C769-09 Deviations from the basic principles of this standard Experimental considerations related to C769-09 Signal analysis Transducer frequency Applying C769-09 on small specimens Applying C769-09 on irradiated small specimens Thoughts on new ASTM standards Conclusions

20. Specimen Lateral Dimensions (1) When D/λ < 10, two issues must be considered: relationship between the measured group velocity and DYM signal distortion due to dispersion The ultrasonic velocity method yields the group velocity and its relation to the DYM depends on the specimen diameter Dispersion: each frequency component propagates at its own phase velocity, while the energy of the wave propagates at the group velocity. For sufficiently small D, the phase and group velocities are the same and are independent of transverse dimension and independent of Poisson’s ratio. For infinitely large D, the phase and group velocities are the same and dependent on Poisson’s ratio.

21. At intermediate sizes: several modes of ultrasonic wave propagation combine the phase velocity is sensitive to transverse sample dimension, due to resonance effects the phase velocity is not equal to the group velocity. The difficulty in obtaining a correction for the group velocity as measured from the ultrasonic wave transit time is that analytical solutions consider the propagation of pure sine waves and consequently yield the phase velocity. Specimen Lateral Dimensions (2)

22. Specimen Lateral Dimensions Numerical analysis: FE code “Impact” Propagation in the z-direction, infinite dimension in y-direction Thickness, h, in x-direction was chosen such that λ ≈ h Pulsecentre frequency of 0.34 Mhz (Ω = 0.75) Material properties of Y = 7.5 GPa, ρ = 1g/cm3, σ = 0.4 υp = 3660 m/s (for an infinite medium, h >> λ) A high value of Poisson’s ratio, was chosen, because, at σ = 0.4, phase velocities differ more from the expected value for a large sample, i.e ~0.449 υp Specimen Lateral Dimensions (3)

23. Specimen Lateral Dimensions (4) z-displacements in the material at 6.5μs from the start of the pulse

24. Specimen Lateral Dimensions (5) • Wave propagation in the sample: displacement in the z-direction is plotted against z, the direction of wave propagation Centre of the sample, x = 0 6.5μs from the start of the pulse • • 4.3μs from the start of the pulse Edge of the sample, x = h • • 6.6mm offset 6.3mm offset

25. Specimen Lateral Dimensions (6) • Clearly, the wave shape at the centre of the sample (x = 0) changes considerably with time. • To align the first peaks of the pulses, an offset of 5.0mm is required, which is quite different from the offset required to align the troughs (6.3mm). • If the pulse is timed at the edge of the sample, it appears to have travelled ~5.0mm between 4.3μs and 6.5μs so the apparent wave speed is ~2.3mm/μs. • If the pulse is timed at the middle of the sample, it appears to have travelled ~6.3mm between 4.3μs and 6.5μs so the apparent wave speed is ~3.0mm/μs. • A speed of 2.3mm/μs is indeed much less than υp, the speed expected in an infinite medium, which is 3.66mm/μs, although not as low as the phase velocity at the pulse centre frequency ~0.449 υp.

26. Specimen Lateral Dimensions (7) Variation of x-averaged z-displacement with time -2.1µs - 4µs z = 0 z = 6mm z = 12mm

27. Specimen Lateral Dimensions (8) The shape of the wave changes as it propagates, so the apparent wave speed depends on the point on the waveform that is used for timing and on the sample thickness. The shape change is particularly obvious at z = 12mm, where the z-displacement remains negative at the first peak, so a zero crossing between the first trough and peak cannot be used to time the pulse. Aligning on the first peak, the apparent speed of propagation based on x-averaged z-displacement is between ~2.8 and 3mm/μs. The above differences are purely the effect of geometric dispersion. Attenuation has not been taken into account.

28. Specimen Length (1) Maximum specimen length depends on the graphite grade (frequency dependent attenuation). However, smaller specimen lengths  smaller transit times measured  inaccuracies in the timing methods become more important. Two experimental studies 1a. Hard-faced, 1MHz transducers Ø19x5mm velocity=-6%parent Ø19x15mm Ø19x8mm velocity=-2%parent

29. Specimen Length (2) 1b. Rubber-tipped, 1.25MHz transducers Ø19x7mm velocity=-0.4%parent Ø19x15mm Ø19x7mm velocity=-2%parent Ø19x4mm velocity=-3.9%parent Ø19x15mm Ø19x4mm velocity=-4.1%parent Ø19x4mm velocity=-5.3%parent

30. Specimen Length (3) 2. Hard-faced transducers with a range of frequencies and with a range of liquid and solid couplants • Specimen lengths ranging from 12 to 80mm • Specimen diameters either 12 or 19mm • For a transducer frequency of 1MHz using a liquid couplant, the study concludes that there is no length effect.

31. Applying C769-09 on irradiated small samples (1) Magnox PGA graphite from 9 reactor installed sets

32. Applying C769-09 on irradiated small samples (2) Analysis of the DYM results using ANOVA mean value was significantly different, at the 95% confidence level, between specimens of dimensions Ø24 × 16mm and Ø12 × 6mm for both orientations the DYM value measured parallel to the grain direction was found to decrease by 30% the DYM value measured perpendicular was decreased by 19% The larger apparent decrease for the parallel values is expected due to the larger wavelength or smaller transit time for these specimens.

33. Thoughts on new ASTM standards Current ASTM standards for Sonic resonance or Impulse Excitation More accurate than ToF methods because the measurement involves standing waves The disadvantage of the specific resonance methods is the sample size and geometry requirement. Resonant Ultrasound Spectroscopy (RUS) “The RUS approach has the advantage of simplicity in that no gluing, clamping, or painstaking alignment of the specimen is required since it is held by contact force. Both large and small samples are readily accommodated in RUS” (Wang and Lakes, 2002). Potentially obtain all the elastic moduli Cijkl of a single specimen of an anisotropic material. Not limited to isotropic material, no size/coupling effects.

34. Thoughts on new ASTM standards RUS – Basic principles

35. The most important features of this experimental setup are the following: Because RUS relies on free-surface boundary conditions, weak coupling is ensured by clamping the sample on its corners or edges. The use of a lock-in amplifier. Lock-in amplifiers are used to detect and measure very small AC signals — all the way down to a few nanovolts. Accurate measurements may be made even when the small signal is obscured by noise sources many thousands of times larger. Thoughts on new ASTM standards

36. Thoughts on new ASTM standards RUS is applied successfully on small, non-uniform samples of other materials with high levels of anisotropy. Practical implementation of RUS is straightforward RUS can provide accurate and reproducible Young’s modulus and Poisson’s ratio values on graphite cubes and cylinders. Although further work is required to fully prove the technique, it is considered very promising for carrying out routine measurements of Young’s modulus and/or Poisson’s ratio of irradiated graphite samples.

37. Conclusions (1) • Discussion on assumptions inherent in the basic principles of the ultrasonic velocity test method for obtaining a value of DYM. • The first assumption in this test method is that graphite is an isotropic and homogeneous material. • The second assumption in this test method is that the specimen can be considered an infinite medium, i.e. the specimen lateral dimensions are much larger than the wavelength through the specimen. • Experimental and theoretical work carried out to address these and understand size effects on as-manufactured and irradiated graphite.

38. Conclusions (2) • Isotropy and homogeneity • The degree of isotropy and homogeneity depends on graphite grade. • For anisotropic graphite, the derived Young’s modulus depends on all Poisson’s ratios and hence the formula given in the ASTM standard can only be used for isotropic graphite. • For non-homogeneous material, frequency dependent attenuation can significantly distort the signal leading to erroneous or inconsistent measurements. • It is strongly recommended that the transducer frequency is carefully selected for the range of Young’s moduli or longitudinal velocities and the range of specimen lengths under investigation. • It is strongly recommended that the selection of the signal analysis method also takes into account other material intrinsic properties, such as scattering and attenuation.

39. Conclusions (3) • Small specimens • Although the analysis represents an extreme case, it shows that dispersion causes considerable distortion of the propagated pulse. • The pulse distortion is severe enough that the apparent wave speed depends considerably on sample length and on whether the centre or edge of the sample contributes most to the electrical signal produced by the receiving transducer. • Frequency dependent attenuation of ultrasound in graphite was already known to distort the pulse shape; the effects found here are additional sources of pulse distortion.

40. Conclusions (4) • Discrepancies in measured velocity values between laboratories on the same specimens are generally below 5%. • Although consistency does not ensure the accuracy of the measurements, the experimental results show that the effects discussed in this paper contribute an uncertainty of ±10% discrepancy in modulus on virgin graphites. • However, graphite elastic and attenuation properties change significantly after exposure in a reactor environment. • It is recommended that extreme care is taken when comparing DYM data from different facilities with different experimental setups.

41. Acknowledgement The majority of the work reviewed in the accompanying paper is not available in the open literature and so many of the source documents cannot be cited. The author would like to acknowledge the contributions from internal documents authored by John Payne, Tim Shaw and Bill Ellis of the UK National Nuclear Laboratory and Matthew Brown of EDF Energy. The author would also like to acknowledge EDF Energy and Magnox Limited support in funding some parts of this work. Thank you for your attention.