Determination of elastic constants of Inconel-625 superalloy, using laser-based ultrasonic
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This paper deals with the determination of the elastic constants of Inconel-625 from the analysis of laser-generated ultrasonic bulk waves. A pulsed Nd/YAG laser (1064 nm) is used for ultrasonic generation in a thick stepped Inconel-625 sample, and a He–Ne laser is used for heterodyne detection of the laser-generated signals. Ultrasonic signals obtained at epicenter and at off-epicenter position of the detection points are analyzed using wavelet transforms. Here, the identification of pressure as well as shear waves and the estimation of their velocities are done successfully. From the estimated velocities, the elastic constants (Young’s modulus, shear modulus, bulk modulus, Lames constant and Poisson’s ratio) are calculated. The agreement of these constants with the standard values confirms the identification of shear waves at off-epicenter position. The work presented in this paper brings out the applicability of the study of laser-generated bulk waves for the determination of elastic constants of any bulk material.
KeywordsLaser-based ultrasonics (LBU) Wavelet transforms Pressure waves Shear waves Elastic constants Inconel
Inconel alloys possess several properties making them well suited for engineering applications in extreme environments. Inconel is very resistant to oxidation and corrosion, when heated it forms a thick passivating oxide layer, protecting it from further attack. Inconel retains its strength over a wide range of temperatures. This makes it particularly attractive in high-temperature applications where aluminum and steel would soften. It is a high-performance alloy. Inconel has wide application in the areas of aerospace industry, jet engines and turbine blades, etc. Determination of internal structure and material properties of an object without actually destructing or damaging the material is achieved using nondestructive evaluation (NDE) techniques.
The several NDE techniques available are being discussed here in brief. Radiographic inspection (X-ray and gamma-ray) involves penetration of gamma- or X-ray radiation on materials and products to detect defects or examine internal or hidden features. In acoustic emission testing, a localized external force is applied to the part being tested. The resulting stress waves in turn generate short-lived, high-frequency elastic waves that are detected by sensors that have been attached to the part surface. Ultrasonic inspection uses the same principle as is used in naval SONAR and fish finders. Ultra-high-frequency sound is introduced into the part being inspected and by measuring the returning time of reflected wave, the distance to the reflector (the indication with the different acoustic impedance) can be determined. Neutron radiography uses an intense beam of low-energy neutrons as a penetrating medium. Neutrons generated by linear accelerators, betatrons or other sources penetrate most metallic materials, rendering them transparent, but are attenuated by most organic materials (including water, due to its high hydrogen content) which allows those materials to be seen within the component being inspected. Magnetic particle testing (MT) uses one or more magnetic fields to locate surface and near-surface discontinuities in ferromagnetic materials. This produces a visible indication of defect on the surface of the material.
Among the several NDE techniques available, laser-based ultrasonic (LBU) is gaining importance in the recent times. In LBU, a high-intensity laser beam is used to generate ultrasound in the test object. One of the biggest advantages of LBU technique is that generation and detection of the ultrasound can be made at a distance, without any physical contact with the surface of the component to be inspected and furthermore no coupling medium is required. However, laser generation of ultrasound has the disadvantage of simultaneous generation of different waves such as shear and longitudinal bulk waves as well as Rayleigh and Lamb waves, thus complicating the process of signal analysis.
Scruby and Drain  discussed the mechanisms of generating various ultrasonic waves with lasers and detection by using variety of laser interferometers. Laser irradiation of bulk samples leads to the generation of pressure (longitudinal) and shear (transverse) waves, while it leads to the generation of Lamb waves in thin plates. Scruby et al.  carried out the quantitative studies on thermally generated elastic waves in laser-irradiated metals. Wavelet analysis and the properties of different wavelets are explained by Daubechies  in her work. Georgiou  discussed tissue characterization using the continuous wavelet transform in his work. Singhal et al.  discussed recent studies in aluminum using LBU and presented bulk wave signal analysis using wavelet transforms, while Pramila et al.  presented the frequency analysis of laser-generated pressure waves in aluminum. Pramila et al.  in their recent work studied pressure wave behavior using LBU in Inconel superalloy using wavelet transforms. Zhang et al.  measured the shear wave velocities in metals using specially designed speckle interferometer. Ultrasonic velocity studies and laser processing of Inconel are reported by Kumar et al.  and Bugayev et al. , respectively. Apart from LBU, there are other NDE methods available for characterization of Inconel 625 which have their own merits and demerits. Rai et al.  studied the microstructures in Inconel 625 by employing X-ray diffraction peak broadening method, another NDE method for the characterization of microstructures in Inconel 625.
The present work deals with laser-generated bulk waves both shear and pressure, in Inconel-625 and their analysis using wavelet transforms. Inconel-625 is also prominently known for its unique combination of yield strength, tensile strength, fatigue strength, creep strength and excellent weldability. Inconel 625 is a nickel–chromium–molybdenum alloy with an addition of niobium that acts with the molybdenum to stiffen the alloy’s matrix and thereby provide high strength without a strengthening heat treatment. The alloy resists a wide range of severely corrosive environments and is especially resistant to pitting and crevice corrosion. It has been widely used in chemical processing, aerospace and marine engineering, pollution control equipment and nuclear reactors.
Fabrication of nickel-based superalloy components could be done in two ways first, they can be made as an integrated casting, and second, the parts can be joined to form the final assembly. Components made from nickel-based superalloy when exposed to harsh operating environments such as high temperatures, oxidizing and reducing conditions for longer periods give rise to cracks that propagate through the surface irregularities and cause failure of the parts. Thus, it becomes important to measure elastic constants of Inconel 625.
In the present work, the elastic constants of Inconel 625 have been calculated using wavelet transforms. The wavelet transforms are generated using MATLAB software. Results thus obtained are used for the estimation of elastic constants.
The signals are amplified and digitized using a digital oscilloscope. Recorded waveforms on the oscilloscope are transferred to a computer over an USB/ethernet interface for subsequent storage and analysis.
However, if the ultrasonic signal is picked up at off-epicenter position as shown in Fig. 3b, with the probe beam normal to the surface, the heterodyne will be able to pick up the components of vibrational amplitudes of both pressure wave and shear (horizontal) wave.
Laser-generated ultrasonic signals for Inconel stepped sample are recorded repeatedly in the epicenter as well as five off-epicentral directions (10°, 20°, 30°, 40°,50°).
Results and discussion
The recorded ultrasonic signals are analyzed using wavelet transforms . The details of the analysis are given in the following subsections.
Pressure wave velocity estimation
The temporal behavior of frequency 10.97 MHz component is shown by the coefficient line in (Fig. 4). It is evident from (Fig. 4) that continuous wavelet transforms give good time–frequency localization as seen by the variation in color representing how dominant a particular frequency component is at a particular time . Among bulk waves, pressure wave is known to be having highest velocity so the groups of waves that arrive earliest are identified as the pressure waves. The temporal and spectral behaviors of pressure wave are studied and the results are reported. In this paper, pressure wave velocity and critical angle for Inconel are reported 5823 m/s and 30°, respectively. At the critical angle, the pressure wave signal is found to be of minimum intensity.
Shear wave velocity estimation
Determination of elastic constants
Elastic constants of Inconel-625
Name of elastic constant
Formula for elastic constant
Calculated value (× 1011 dynes/cm2) OR (× 1010 N/m2)
Standard value (× 1011 dynes/cm2) OR (× 1010 N/m2)
Y = D C 2 2 (4 − 3 k2)/(1 − k2)
η = D C 2 2
B = D C 2 2 (k2 − 4/3)
λ = D C 2 2 (k2 − 2)
σ = (2 − k2)/(2 − 2 k2)
Using these relations, the elastic constants are calculated and are given in the third column of Table 1.
The standard values of these constants are given in column 4 .
One can see from above table that the values of elastic constants obtained in the present work are in good agreement with the standard values for Inconel. This agreement confirms that the bulk wave signal identified as shear wave in the present work is actually shear wave.
In the present paper, results of wavelet analysis of LBU signals obtained for stepped sample of Inconel are presented. Identification of pressure as well as shear waves and their velocity estimation is done successfully [9, 10].
Accurate match of estimated and standard values of elastic constants confirms the assumed presence of shear waves at off-epicentral position. The technique may be employed for the characterization of different materials in terms of elastic constants.
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