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| Research Activities >> MATERIALS CHARACTERISATION >> |
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Linear Ultrasonic Methods |
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Goniometry based Elastic Constants Measurement |
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As anisotropic materials such as fiber-reinforced composites are widely used for many structural applications, the determination of mechanical properties is critical for ensuring reliable performance. The knowledge of complete elastic stiffness matrix is essential for modeling and evaluating the mechanical behavior of composite materials under severe loading conditions.
The disadvantages of conventionally used techniques are (a) some engineering constants of anisotropic materials are difficult to measure, (b) they are destructive in nature, (c) high costs involved in producing samples of desired shape and size and (d) in-situ measurements are difficult. Ultrasonic techniques are however uniquely qualified for nondestructive measurement of all of the elastic constants of such materials. Elastic constants are determined by measurement of ultrasonic velocities (usually phase or group velocities), which are related to the material properties.
The ultrasonic velocities were measured using two different immersion techniques commonly described in the literature namely; back-reflection and through-transmission techniques. From the measured velocity data, the elastic constants were determined through a simple numerical inversion. The inversion method has been verified by implementing the solution for the corresponding forward problem, and from data measured using contact testing, mechanical testing, rule of mixtures estimation and data provided by the manufacturer. The technique was used to make measurements on both isotropic and transversely isotropic (glass-epoxy and graphite-epoxy) composite materials. Based on the results obtained, the following conclusions can be made:
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Using back-reflection immersion inversion procedure, the elastic constants of isotropic and transversely isotropic medium can be measured with an average accuracy of 1.9% when compared with standard ultrasonic contact testing method. It was determined that results from graphite-epoxy samples compared very well with manufacturer supplied data. |
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Back-reflection technique is better than through transmission technique, particularly for thicker samples, due to the limited width of receiving transducer. |
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Back-reflection experimental setup |
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Velocity vs. incident angle plots for 2.16 mm thick unidirectional Graphite-Epoxy composite in the 1-2 plane. using
back-reflection technique. |
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Slowness curves for 2.16 mm thick unidirectional graphite-epoxy composite
for Wave propagating in anisotropic plane (anisotropic plane). |
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References : S.S.S.Reddy, K. Balasubramaniam, C.V.Krishnamurthy, and M. Shankar, “Ultrasonic goniometry immersion techniques for
the measurement of elastic moduli,” Composite Structures 67 3-17 (2005) |
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Blind Inversion for Material Symmetry Determination |
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The elastic moduli of material can be measured using destructive methods like tensile and compressive tests and non-destructive approaches like ultrasonic methods. Ultrasonic methods have advantages over destructive methods since sample preparation is less cumbersome and, with appropriate fixtures, in-situ measurements can be made on actual components without destroying the samples. In addition, ultrasonic measurements can be performed for different orientations; this means that the number of elastic moduli measured for a single plane can be more than the number of elastic moduli measured using destructive techniques.
The determination of material symmetries and principle plane orientations of anisotropic plates, whose planes of symmetries are not known, were calculated using a Genetic Algorithm (GA) based blind inversion method. Ultrasonic phase velocity profiles were used as input data to the inversion. During each blind inversion, the material was initially assumed to be dependent on 21 elastic constants (general anisotropy). A Genetic Algorithm based method was exploited to identify the “statistically significant” elastic moduli using the coefficients-of-variation (CV) to derive a reduced set of elastic moduli.
The unknown material symmetry and the principle planes (angles between the geometrical coordinates and the material symmetry coordinates) were evaluated using the method proposed by Cowin and Mehrabadi. This procedure was verified using simulated ultrasonic velocity data sets on materials with transversely isotropic, orthotropic, monoclinic and triclinic symmetries. Experimental validation was also performed on a unidirectional graphite-epoxy [0]7s material, a quasi-isotropic graphite-epoxy [0/45/90/-45]7s fiber reinforced composite plate, and plate cut at 45˚ degrees to the fibers from a unidirectional graphite-epoxy composite plate.
This method can be applied in (i) characterizing materials such as chopped fiber composites that have less control over the fiber orientation, the effective material symmetry and principal directions of anisotropy, (ii) characterizing the natural composites such as wood where the symmetry and principal directions may need to be verified, (iii) characterizing metals that have anisotropy due to secondary processes such as rolling and heat treatment, (iv) Characterizing the anisotropy of crystalline materials (both natural and grown), (v) finding the changes in the stiffness tensor induced by elevated temperatures in a composites material, and (vi) in characterizing inhomogeneous anisotropic structures such as functionally graded materials. |
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13.69 |
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3.82 |
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- J. Vishnuvardhan, C. V. Krishnamurthy and K. Balasubramaniam “Determination of Material Symmetries from Ultrasonc Velocity Measurements: A Genetic Algorithm Based Blind Inversion Method” Composite Science and Technology in press available online (2007)
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Transmission Factor Elastic Constants Measurement |
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It is shown that low cost PVDF sensors with large apertures can be effective and can be deployed in a simple manner. The inherent wide band response of these PVDF sensors has been exploited for capturing the transmission spectra needed for the determination of elastic constants. Further, the sharp spectral features obtained from using the PVDF sensor may also in improved measurements of material parameters such as thickness, density, and elastic moduli.
The measured transmission spectra can be inverted to determine the material elastic constants. One of the efficient ways to perform inversion for a multi-parameter set is through the Genetic algorithm (GA) as it has the advantage of providing global optimum without any initial seeding.. Although not included, the reconstructed data for the 2 mm thick Aluminum plate agrees with that of the thicker plate. The results from the reconstruction clearly reflects the feature that the quality of input data from the low cost PVDF sensor performs better than the more expensive paintbrush transducer and significantly better than that from the normal transducer.
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STMR Array based Elastic Constants Reconstruction |
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The reconstruction of all 9 unknown elastic moduli of orthotropic plate structures have been achieved using a Single Transmitter Multiple Receiver (STMR) Compact SHM Array. This method uses the velocity measurement of the fundamental guided Lamb wave modes (S0 and A0), generated from a central transmitter, and received by a sparse array of receivers that encircle the transmitter. The measured velocities are then used in an inversion algorithm based on Genetic Algorithms. A prototype compact STMR array was developed and used in the measurement. Simulated data were used to demonstrate the feasibility of the technique. Experiments were conducted on 3.15 mm graphite-epoxy composite plate using commercial transducers as well as Laser vibrometer based displacement measurement. Experimental Lamb wave velocity data was used to validate the present technique. This technique finds application in the area of material characterization and structural health monitoring (SHM) of anisotropic plate-like structures used in aerospace and automobile components made using fiber reinforced composites.
The advantages in reconstructing the elastic moduli from the Lamb wave velocity data over bulk wave methods are (a) the method can be used as self-calibration for SHM work, (b) the method is in-situ ultrasonic Lamb wave method, (c) no need to immerse the sample as the method uses contact mode (using commercial transducers) or non-contact (using Laser for reception), and (d) sensitive to all non zero components of elastic moduli matrix. Out of nine orthotropic elastic moduli, seven moduli (other than C44 and C55) are taken from the elastic moduli set reconstructed using S0 mode velocities and two moduli (C44 and C55) are taken from the elastic moduli set reconstructed using A0 mode velocities. The maximum error in the effective elastic moduli reconstructed using velocity data measured with Laser based reception is less than 7.5% and the maximum standard deviation is 4.75% from the theoretical elastic moduli. Similarly, the maximum error in the effective elastic moduli reconstructed using velocity data measured with PZT based STMR array is less than 8.5% and the maximum standard deviation is 5% from the theoretical elastic moduli.
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J. Vishnuvardhan, K. Balasubramaniam, and C.V. Krishnamurthy Genetic algorithm based reconstruction of elastic moduli of orthotropic plates using an ultrasonic guided wave STMR SHM array Smart Materials and Structures in press available online (2007)
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Nonlinear Ultrasonic Methods
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Non-linear DC Component Measurement |
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The first ever numerical simulation of the acoustic radiation induced static strain (DC Component) in solids during longitudinal ultrasonic wave propagation was conducted by CNDE. The propagation of an ultrasonic wave through a medium which has accumulated nonlinearities has been simulated using a Mass Spring Lattice Model (MSLM) with a Finite Difference Time Domain (FDTD) approach for materials with second order and third order nonlinearities. The results suggest that an asymmetry in the stress strain relationship of the material arising due to the second order nonlinearity is required for the generation of the DC Component. More importantly, our simulation studies provide the first ever numerical evidence supporting the dependence of the DC Component on the distance of propagation and its independence on the width of the tone burst, thus resolving the controversies in this aspect.
A simplified experimental technique to measure the acoustic radiation induced static strain in solids is proposed. Experiments have been carried out to extract the static displacement component without resorting to electronic filters as in the case of previously reported experimental measurements. This prevents the influence of the filter time response characteristics on the measurement of the static displacement component.
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J. Vishnuvardhan, K. Balasubramaniam, and C.V. Krishnamurthy Genetic algorithm based reconstruction of elastic moduli of orthotropic plates using an ultrasonic guided wave STMR SHM array Smart Materials and Structures in press available online (2007)
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Software Super Heterodyne NLU Technique |
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The response of the material during fatigue cycling has been measured using the IR camera to obtain a master curve that may have the ability to define
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Non-linear Ultrasound for Adhesive Bond Strength |
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Ultrasonic harmonic generation technique is the preferred experimental technique used for nonlinear ultrasonic measurements adhesive bonded structures. This experimental technique involves the measurement of relative strengths of harmonics produced in the received signal when a finite amplitude longitudinal sound wave propagates through a material. The generation of harmonics distorts the signal and the degree of distortion increases strongly with increasing wave amplitude. For given amplitude, the strength of the distortion depends on the intrinsic nonlinearity due to the anharmonicity present in the material which is reflected in the magnitude of the third order elastic coefficients. Any additional nonlinearity observed over the intrinsic nonlineairty is considered to be due to the interaction of mesocopic level defects mentioned earlier. The nonlinear parameter, b is defined and obtained by solving the wave equation using perturbation technique utilizing nonlinear constitutive relation between stress and strain. The nonlinear parameter thus obtained is given by Where A1 is the amplitude of the fundamental frequency, A2 is the amplitude of second harmonics, w and y are the angular frequency of the wave and acoustic velocity in the material. This work explores the possibility of using nonlinear ultrasonics (NLU) to evaluate the quality of adhesive joints made with simulated inclusions. NLU experiments were carried out on aluminum adherends with joints made using a commercially available epoxy and polystyrene resin as adhesives with thin copper wires and calcium carbonate fillers used as inclusions that reduce the bond strength. Results from our study suggest that nonlinearity is very sensitive to the interface strength, as well as to the presence of inclusions in the adhesive. The quality of these joints, are compared in the light of various binding energy relations evaluated in terms of measured amplitudes of harmonics generated, as suggested in the literature [1-3]. Our results show that the maximum in binding force curve (as a function of input amplitudes) at the interface could not be measured. Instead, it was found that relative binding energies of the adhesive with various inclusions can only be obtained qualitatively by comparing the slopes of the binding force curves.
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Non-linear Ultrasound for Plastic Deformation Studies |
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The nonlinear ultrasonic technique is shown to relate to the mesoscopic damage that occurs during controlled plastic deformation studies on Aluminum Alloy AA7175-T7351. Both longitudinal and guided Surface Acoustic Wave (SAW) modes were used in these studies. The long dislocation loops that are developed during plastic deformation was found cause subsequent increase in the amplitude of the nonlinear parameter. A trend of increase in the nonlinear parameter with the increase in plastic strain was observed during the initial stages followed by a slight decrease prior to a second peak indicating near failure condition. The nonlinear data behavior was related to the micro-structural changes during plastic deformation.
The nonlinear ultrasonic measurements in plastically deformed specimens were carried out using longitudinal mode across the specimen (through-the-thickness) at different location within the gage length. Scanning at six locations within the gage length showed that the NLU response was not uniform along the gage length as a peak value was observed in each of the samples. These peak values of the NLU response were not in the same location along the gage length in the different samples. However, the final failure of the samples was observed to occur in the near vicinity of the location of the peak NLU response.
It was observed that A2/A12 is nearly constant up to a certain level of residual plastic deformation and thereafter there is a significant increase in the non-linear parameter response. Near-flat response in the intermediate region of residual plastic deformation could be due to the faster rate of strain hardening of material and the associated obstruction to dislocation movement within the grains.
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Non-linear Ultrasound for Early Fatigue Damage |
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Nonlinear ultrasonic harmonic generation measurements were conducted on the aluminum alloy AA7175-T7351 specimens fatigue cycled at the loading conditions. Six hourglass fatigue specimens were prepared for the fatigue damage studies, of which, a batch of three specimens were fatigue loaded between 88% and 8% of yield strength and the other batch was fatigue loaded between 95% and 10% of yield strength. At periodic intervals of time (approximately every 5% of the fatigue life) the specimens were unloaded, the nonlinear ultrasonic response measured using surface acoustic wave mode, and then reloaded and fatigue cycling was further continued. This procedure was continued till the specimen undergoes failure.
The two surfaces of the specimen show two distinct peaks in the variation of nonlinear parameter (A2/A12) for all the samples, however the percentage of life at which they occur differ slightly. The first one appears at ~40-55% of fatigue life and the latter at ~75-90%. The second peak appears just before a visible crack appears at one of the edges on the hourglass specimen and immediately the magnitude of nonlinear parameter falls after 500 cycles (2% of fatigue life) of fatigue loading. Similar results were obtained in case of fatigue specimens that are loaded to 88% and 95% of yield strength. Results showed that there was an increase of around ~200% in the nonlinear parameter A2/A12 in the fatigue sample when compared to the virgin sample. Cracked surface showed a larger change in nonlinearity over the other surface. It was also observed that the crack appeared on the surface of the specimen where the magnitude of the nonlinear parameter is higher when compared to the other.
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Non-linear Ultrasound for Creep Damage |
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This work, in association with DMRL, Hyderabad, ultrasonic measurements in the linear (velocity) and non-linear domains (second harmonic amplitude) to evaluate creep damage in a near-a IMI-834 titanium alloy, currently being used in the compressor module of aeroengines. The creep damage in this alloy has initiated in the form of microvoids at primary α/ transformed β interface and the volume fraction of voids increase progressively with creep deformation. Good agreement between the results and data obtained from metallographic studies indicated the usefulness of the method for in-service evaluation of creep damage. Non-linear ultrasonic technique was found to be significantly more sensitive, when compared to the linear ultrasonic velocity measurements, for the assessment of creep damage.
Non linear Ultrasonic technique has been used effectively to characterize the damage by investigating the magnitude of higher harmonics caused by the non-linear material behavior. Good agreement between the results and data obtained from metallographic studies indicated the usefulness of the method for in-service evaluation of creep damage. Measurements of both ultrasonic velocity and the non-linear parameter have been carried on interrupted creep tested specimens at a temperature of 873 K and under constant stress of 300 MPa. A 150 % change in the non-linear parameter ‘b’ is observed as a function of creep fraction life as compared to 15 % change in the linear velocity, which clearly proves that ‘b’ is much more sensitive than longitudinal velocity measurements. For quantitative characterization of creep damage one should investigate and identify the non-linear response parameter by experimenting on number of samples and then subjecting it to metallurgical investigations for understanding the mechanisms operative in this alloy.
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Thermal Imaging Methods
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Thermal Response for Plastic Deformation State |
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It is a well known phenomena that when a material is deformed, heat is either released or absorbed. In this work, the behaviour of the material due to the repeated plastic deformation is studied for two material systems viz. Al alloy and Stainless Steel. It was observed that in the elastic region the temperature drops while in the plastic deformation the temperature rises. This behavior gives rise to a measurement of the minimum temperature near the yield point of the material. The increase in temperature in the plastic regime leads to a maximum value of temperature that is also a
characteristic of the material behavior under plastic deformation.
From repeated loading-unloading experiments, it is observed that the minimum temperature value decreases with increasing plastic deformation and the peak temperature value reached increases with increased deformation.
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Thermal Response for Fatigue Damage |
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The response of the material during fatigue cycling has been measured using the IR camera to obtain a master curve that may have the ability to define
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Eddy Current Methods
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Conductivity Profiles using Multi Freq EC |
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When the material is subjected to thermal processing, peening or solidification processes, the conductivity continuously changes as a function of depth. Such variations occur due to factors like change in chemical composition and the stress state of the material crystalline structure. The detection of spatial variations in the structure of the material is possible through the measurement of electrical conductivity profiles.
A method for assessing material conductivity involves measurement of the impedance of coils, driven by a constant amplitude alternating current, above a conductive metallic slab with a plane surface. Multi-frequency inductance data was obtained by using well-characterized eddy current probes. The inversion uses a multi-layer axi-symmetric finite element model as the forward model and the conductivity of each layer is found through interpolation of the inductance-conductivity data generated by the forward model. Skin depth approximation was used to isolate the integral effects of the conductivity variation on the inductance signal. Inverted conductivity profiles of the water jet peened specimens was found to resemble the predicted profiles. Information regarding the shape of residual stress gradients and relative intensities of peening were inferred from the conductivity profiles.
Compressive (tensile) stresses cause an increase (decrease) in the electrical conductivity. Up to 5% increase in conductivity is obtained near the surface of water peened specimens. From the stress profiles of peened samples (Fig. 1), a stress reversal over depth was noted after peening wherein the mode changes from compressive in the top layer to a net tensile stress in the bulk of the material. Analogous to this effect, the conductivity of the specimen also changes its mode with respect to the substrate conductivity at depths of around 120 microns. It is further noted that the reversal depth increases when the peening pressures are increased. The multi-frequency eddy current inversion technique is hence effective for assessing the near surface changes in conductivity due to peening and can be used to gauge information regarding the depth of reversal of residual stresses and relative intensities of peening between different samples.
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| Veeraraghavan Sundarajan, K. Balasubramaniam, N Ramesh Babu, N Rajesh NDT&E, International 38 54-60 (2005) |
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Pulsed Eddy Current Based Depth Profiling |
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Pulsed Eddy Current for Plastic Deformation State |
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Pulsed Eddycurrent Technique was employed to study the PEC response to the microstructural changes during plastic deformation of material systems, specifically Stainless Steel and Aluminum Alloys. The PEC was measured using an inhouse built electronic system with 16 bit DAQ for data collection and archival. The commercial coil based probe was used in the experiments.
The maximum amplitude for the PEC signal was observed to increase with increasing the plastic strain. The increase was significantly more in the plastic region compared to the elastic strain region.
During repeated loading experiments, it was observed that the PEC response is observed only after the previous plastic strain value has been reached. This is similar to the Kaiser Effect that has been reported extensively in the Acoustic Emission studies.
The repeated plastic deformation loading follows a master PEC.vs.Deformation curve demonstrating the memory effect of the material..
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