Table of Contents ECNDT '98 Session: Nuclear Industry  Characterization of Nodular Cast Iron Properties by Harmonic Analysis of Eddy Current SignalsFeiste, K. L., Fetter Marques, P. , Reichert, Ch., Reimche, W., Stegemann,D.Institute of Nuclear Engeneering and Nondestructive Testing, University of Hanover Rebello, A. J. M. , Krüger, E. S. Laboratory of Nondestructive Testing  LABOEND/COPPE, Federal University of Rio de Janeiro Corresponding Author Contact: Ch.Reichert, Hannover Germany, Phone: ++49 511 762 8085, Fax: ++49 511 762 2741, nhkpreic@mbox.ikph.unihannover.de 
TABLE OF CONTENTS 
Frequency domain evaluation of eddy current signals (harmonic analysis) in ferromagnetic materials has been introduced in the last years as an industrial tool for materials characterization and proved to be a reliable and cost effective alternative to traditional techniques of quality control (metalography, mechanical tests, etc.). In this paper the harmonic analysis is applied to nodular cast iron samples characterization to evaluate the technique performance in predicting their metallurgical and mechanical properties. The samples were first charcterized metalographically and by mechanical tests to a quantitative determination of their microstructural parameters (graphite nodules and pearlite/ferrite ratio of the matrix) and their mechanical properties (tensile strength, yield strength and hardness) respectively. This mechanical and metallurgical parameters were found to have a very good correlation with the harmonic analysis parameters measured in the same samples, showing reliable industrial applicability of the technique.
The main characteristics of the harmonic analysis system are the high measuring velocity and the high accuracy of measuring values which can be compared to destructive testing methods.
Increasing quality requirements and low production costs demand additionally a quality assurance during the production of semifinished products. Due to this, the importance of process integrated nondestructive testing, which offers additionally the possibility of nondestructive material characterization, increased progressively the last years.
Mechanical properties of casted iron result from influencing parameters like the graphite form and the microstrucure of the material /1,2/ which is mainly influenced by the alloy composition and heat treatment.
Some foundries produce materials with a wide range of specifications which means, to obtain the requiered properties it is necessary to vary the influencing paramenters continously. Other foundries, specialized in the production of one particular class of ductil iron, are using similar charges of materials where the material composition is closely controlled.
The proved relations between mechanical properties and measurable physical quantities were the reason for the development of nondetructive testing systems such as the harmonic analysis system
Fig. 1: Nodular cast iron with ferrite structure Fig. 2: Nodular cast iron with pearlite structure 
This paper concerns specificly nodular cast iron materials, where only the microstructure of the material is varied.
The test samples were first analyzed referring their chemical compositions, their mechanical properties (tensile strength, yield strength and hardness) and their metallurgical properties (pearlite/ferrite content and graphite form). The nondestructive testing method used in this investigations will be described in the next chapture.
Figure 1 and 2 show the results of the metallurgical analysis made by the Laboratory of NonDestructive Testing at the University of Rio de Janeiro (COPPE/UFRJ). The metallurgical structure shown in figure 1 and 2 give examples for nodular cast iron normed by the ENJS1050 with a minimum tensile strength of 500 N/mm² (figure 1) and nodular cast iron normed by the ENJS1070 with a minimum tensile strength of 700 N/mm².
The probes were etched to stress the differences of the crystallographic microstructure inside the material. The pictures show that the quantity of nodular graphite (black) does not vary significantly but the proportion of pearlite (dark gray) and ferrite (light gray) is changing. Using digital image processing it is possible to determine the quantity of each part.
Figure 3 show the linear correlation between the results of destructive testing and metallurgical analysis. The pearlite content increases proportional to the hardness values of the material. The proportion of pearlite also influences the magnetic properties of the material, which effects directly the form of the hysteresis loop, shown in figure 4. Casted iron with a high content of pearlite needs more energy to be magnetized than casted iron with a high content of ferrite.
Fig. 3: Influence of the pearlite quantity to the material hardness  Fig. 4: Influence of the crystallographic microstructure to the hysteresis loop 
A suitable nondestructive testing principle for an indirect characterization of nodular cast iron is the harmonic analysis of eddy current signals. This magneticinductive method determines electromagnetic measurable values of cast iron which are closely connected to the mechanical characteristics of the material (fig.5).
Fig. 5: Indirect determination of mechanical material properties 
The course of the hysteresis loop is defined by different effects as e.g. reversible and irreversible dislocations of Blochwalls or rotary movements of elementary magnets out of their crystallographicaly prefered direction. In principle the Blochwalls need low energy levels to shift through an ideal crystal lattice, but inside a real crystal lattice there are different kinds of obstacles, depending on the material composition, which make the movement of the Blochwalls more difficult and as a matter of this finally influence the form of the hysteresis loop.
The harmonic analysis of eddy current signals is based on the fact that a primary electromagnetic field caused by a sending coil is influenced by a secondary electromagnetic field in opposite direction which results from the induction of eddy currents inside of the material and the magnetical behaviour of the material. Changes of magnetic properties influence the signals in their amplitude and phase shifting.
For ferromagnetic materials the measuring signal depence on the form of the hysteresis loop which is dependent on the measuring frequency and the magnetic field intensity. Higher harmonic parts of the receiving signal and phase shifting are caused by the nonlinearity of the hysteresis loop (fig.6).
Fig. 6: Origin of harmonics 
Fig. 7: Measuring system 
Figure 7 shows the measuring system which were employed for the material characterization of nodular cast iron. The system consists of a personal computer, an amplification unit and a measuring sensor system. The integrated eddy current plugin card produces a sinusoidal signal which is sent through the sending coil and produce a magnetic field. The eddy currents inside the material, caused by this primary magnetic field, induces a secondary magnetic field with opposite direction. A second coil (receiving coil) is receiving a signal which results from the primary field superimposed by the secondary field. This receiving signal can be measured by tension indication on the receiving coil after lowpass filtration, amplification and digitalization. The last step is the analysis of this signal in the frequency domain.
Fig. 8: Number of measuring values and number of regression dimensions in dependence on time 
Fig. 9: Automatic detection of regression dimension 
The calibration system is based on multifrequency measurements of eddy currents (harmonic analysis algorithm) in combination with a multidimensional regression analysis. This method could be applied successfuly on determination of characteristic properties from different ferromagnetic materials /3/.
By means of variation of measuring parameters like e.g. frequency and magnetic field intensity the amount of measuring values can be influenced. In the present case four combinations of frequencies with five measuring values of each combination (first, third, fifth, seventhharmonic and phase shifting) were used. That means an amount of 20 measuring values for each test sample.
For industrial applications there are nondestructive testing systems needed wich are easy to handle, robust and easy to calibrate, which means a automatizated calibration. Due to this, there was developed an algorithm called JackKnife test which enables to determine the best calibration that means the combination of measuring values with the highest correlation coefficient to the calibration values.
Therefore, the algorithm correlates the measuring values with the mechanical properties and calculates every possible combination, where:

with:  c= number of combinations 
n= number of measuring values  
k= dimension of regression 
For a 8dimensional calibration with 20 measuring values (four combinations of frequencies, five values each frequency) the number of possible combinations is:
 combinations 
The necessary time for this calibration using a 120 Mhz PC is about 50 minutes, which is not acceptable, but the time for calibration also depends on the quantity of properties to calculate.
Figure 8 shows how the calculation time for calibration depends on the number of measuring values and dimension of regression. Therefore the JackKnife test can be optimized in two points concerning the calibration time:
The precision of the harmonic analysis is demonstrated in the following examples, refering the determination of mechanical properties of nodular cast iron. It is shown in the figures 10 to 12. The results of nondestructive determination of material properties using harmonic analsis are compared to the characteristic values determined by destructive testing methods.
Analyzing the obtained results there were calculated statistical parameters like e.g.:
Using a 4dimensional regression the obtained correlation coefficient for the calibration of tensile strength was 99% (fig.10). The calculated root mean square deviation was 1.8 N/mm^{2}, the relative deviation 9%. For the calibration of yield strength there was made a 6dimensional regression. The obtained correlation coefficient was 98% (fig.11) with a root mean square deviation of 1.4 N/mm^{2} and a relative deviation of 6%. Using a 7dimensional regression for the calibration of hardness, the obtained correlation coefficient was 97% (fig. 12), with a root mean square deviation of 2.0 HB30 and a relative deviation of 9%.
Fig. 10: Calibration for tensile strength using 4dimensional regression  Fig. 11: Calibration for yield strength using 6dimensional regression  Fig. 12: Calibration for hardness using 7dimensional regression 
The harmonic analysis of eddy current signals could be employed efficiently for the determination of mechanical properties of nodular cast iron. The results of this nondestructive testing method for tensile strength, yield strength and hardness represent a comparable accuracy to destructive testing methods. One important advantage of the automatic calibration method applied to the harmonic analysis of eddy current signals is the high calibration velocity which amounts to 1 minute. Another advantage of the system is the short measuring time using harmonic analysis for nondestructive testing. The determination of one characteristic value for material properties can be realized in less than 2 seconds. Therefore the presented measuring system is suitable for the employment in online inspection systems.
The authors thank the scientific bilateral project between Brazil and Germany supported by the CNPq, KFA and DLR to realize the presented investigations in nondestructive testing.
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