ULTRASONIC NDE MODELLING FOR PREDICTION OF FLAW RESPONSE IN POLYCRYSTALLINE METALS

Abstract

Testing of material or acomponent or a product is an integral and the most important constituent of the quality assurance programme of any industry. Unlike destructive testing, non destructive testing (NDT), as the name suggests does not impair the product or component being tested in any manner. Besides that with this specific procedure the serviceability of materials or components is not impaired by the testing process. Additionally, testing during the manufacturing processes is also facilitated by NDT procedures which are needed to increase the reliability of products in service and maintenance of systems to avoid premature failure of the products. Avariety of NDT methods are followed in the industries. The choice of the specific method depends on many factors including availability, accessibility and suitability based on analysis and past experience. Ultrasonic testing (UT) is one of the most widely used methods of non destructive testing and evaluation of industrial materials and components. This testing method has applications to polymers, plastics, composites and ceramics. Prime uses of ultrasonic testing are the detection and characterization of internal flaws and wall thickness measurements. In recent years, ultrasonic testing has been employed to determine physical properties, elastic constants and microstructure including grain size, phases etc . Ultrasonic testing utilizes high frequency acoustic waves generated by piezoelectric transducers. Frequencies from 1to 10 MHz are typically used, although lower or higher ranges are sometimes required for certain applications. In the present research work, the modelling of ultrasonic NDT is considered with an aim to predict and validate the ultrasound signal received by the transducer. The present ultrasonic NDE modelling concentrates on pulse echo testing method only. In a typical pulse echo testing, each component ofNDE system is modelled as aLinear Time-Shift Invariant (LTI) system. The net effect of the LTI system is to transform input voltage used to excite the system into the output-voltage response measured from the flaw .This transformation involves anumber of physical processes. In this process, the ultrasound generated by the transducer must propagate to the flaw and then from the flaw to the receiving transducer, generating a propagation delay. In addition to this delay, other factors like material attenuation which causes aloss of amplitude of the signal and beam diffraction effects which changes the shape of the traveling pulse and the xv transmission losses are also considered. Once the incident wave reaches the flaw, it is scattered in all directions and these scattered waves are afunction ofthe flaw properties. Again the effects oftransmission loss, beam diffraction and averaging ofthe scattered waves are considered when they are picked up by the receiving transducer. The receiving transducer reconverts these mechanical pulses into electrical pulses which are amplified at the receiver and finally the observed output voltage is obtained. The mathematical modelling of the above physical processes has been termed as ultrasonic NDE modelling. In the present work, modelling offlaw response and grain noise signal and probability of detection of flaws in a polycrystalline material is investigated. Using these results, the probability of detection ofaflaw ofagiven size and shape can be predicted. Apulse echo testing set up using contact transducer is considered. The flaw considered in this work is a spherical void. Flaw response is predicted for the case ofsmall flaws. Different types ofinclusions like a weak scatterer or astrong scatterer are considered. The incident ultrasonic beam is modelled by the well known Multi Gaussian Beam (MGB) technique . The received signal from the flaw is modelled by determining the far field scattering amplitude. The transducer considered in the present study is a circular 1MHz transducer. The main objective ofthe present research work is to predict the flaw response for both a homogeneous isotropic medium and a microscopically inhomogeneous medium. In this case, the effect of ultrasonic attenuation and phase velocity dispersion due to grain scattering is included in the predictions. Hence the wave number kis considered as acomplex quantity. The expected wave propagation constant k=&/vp+ia (co being the angular frequency, v being the phase velocity of the wave and a being the attenuation coefficient) is considered. Both phase velocity and attenuation coefficient depend on the average grain size, single crystal elastic constants and orientation distribution of individual grains. These A: values are computed by using Unified Theory of Stanke and Kino. The flaw response is determined for weak as well as for strong scatterers. The variation of received voltage against the distance of the flaw from the transducer for different sizes ofspherical void has also been investigated. The effect ofvariation ofmean diameter ofthe grains with the received voltage for different domain of interest is also studied. Further, the predicted flaw responses are compared with the grain noise signals which tend to mask the signals from small and subtle defects. Thus, the probability ofdetection ofa flaw of a given shape and size is estimated. xvi The flaw response due to weak scatterers and strong scatterers is determined using approximation techniques like Born approximation and Kirchoff approximation .An extension of Born approximation called Modified Born approximation is also used to predict the flaw response. Low frequency and weak scattering approximation for the calculation of scattering amplitude is referred to as the Born approximation. Although most flaws found in practice are not likely to be weak scatterers, still the Born approximation is found to be very useful in relating the flaw response directly to the flaw geometry. Kirchoff approximation is also called high frequency approximation and in this case the calculation of scattering amplitude can be simplified by making assumptions regarding the scattering process. This is similar to the physical optics approximation employed in the electromagnetic scattering problems. The modified Born approximation is a variation of the conventional Born approximation. The modification as proposed by Schmerr et al. is used to predict the flaw response. The second part of the work is related to the estimation of grain noise signal. The grain noise signals tend to mask the signals from small and subtle defects. Hence reliable ultrasonic testing of such material requires the quantitative knowledge of these scattered signals. This is obtained by determining the average noise spectra which in turn depends on the back scatter coefficient. The back scatter coefficient is determined using the material properties. The average grain noise spectra are obtained for agiven mean diameter of grains and for aflaw of given dimension. The predicted flaw response as obtained by above methods is compared with this grain noise signal so that probability of detection of flaw can be estimated. By all the approximations, the flaw response is predicted for small flaws. The flaw response is predicted for both the near field and the far field. It has been observed that Kirchoff approximation works well for strong scatterers and weak scatrerers goes undetected. On the other XVII hand, it is found that Born approximation can be easily applied for weak scatterers and the flaw response is distorted severely for strong scatterers. Hence when modified Born approximation is applied the response due to both weak and strong scatterers can be predicted. In all these methods, it is observed that the amplitude of the flaw response is reduced significantly for the microscopically inhomogeneous medium when compared with the flaw response in a homogeneous isotropic medium. Also, the received voltage is reduced as the distance from flaw to the transducer is increased and its amplitude is decreased with the increase in mean diameter ofgrains. The results of predicted flaw response using Kirchoff approximation is compared with the grain noise signal and it is found that the flaw of size more than 0.5 mm is likely to be detected when the distance from flaw to the transducer (z) is 10 mm and when z is 14 mm, the flaw of size greater than 1.5 mm can be detected. For the flaw distance of 20 mm, the flaw of size more than 2.5 mm can be detected and for higher values of z>30 mm, the amplitude of predicted flaw response is less than that ofgrain noise signal and hence the flaw goes undetected. Similarly, by comparing the predicted flaw response using Born approximation with the grain noise signal, it is found that the flaw ofsize more than 0.5mm can be detected when the distance zis 10 mm and when zis 14 mm, the flaw ofsize more than 1.5 mm can be detected. For higher values of z (>20mm), the grain noise signal is more than that of the predicted flaw response andhence for these cases the flaw goes undetected. Similar calculations are repeated for modified Born approximation technique. In this case it is found that the flaw ofsize more than 0.5 mm can be detected when the distance z is 10 mm and the flaw ofsize more than 1.5 mm can be detected when zis 14 mm. For higher values of z(>20 mm) the amplitude of predicted flaw response is very much reduced when compared with grain noise signal. Thus, these flaws cannot be detected for higher values ofz. Further, the above calculations of prediction of flaw response and comparison of predicted results with the grain noise signal is repeated for different center frequencies of the transducer like 2MHz, 3MHz and 5MHz. The simulation is carried out for all the above three XVIII approximation techniques. From this comparative study it is concluded that smaller flaws can be detected with higher center frequency ofthe transducer. Finally, it can be concluded that ifthe grain noise signal is more than the predicted flaw response, then the flaw may not be detected from the received signal without the use of complex signal processing methodology.