ˇTable of Contents
ˇMaterials Characterization and testing
Use of Barkhausen effect in Measurement of Residual Stresses in Steel after Heat Treatment and Grinding
J. Grum, P. Zerovnik
Faculty of Mechanical Engineering, Akerceva 6, 1000 Ljubljana, Slovenia
Faculty of Electrical Engineering, Trzaka 25, 1000 Ljubljana, Slovenia
For on-line monitoring of the state of the material analysed, various non-destructive methods exist, among them the micromagnetic method, with which a ferromagnetic material is being magnetised by an alternating current, while the Barkhausen noise generated is monitored. A suitable experimental set-up was composed. By means of a measuring coil or Hall's probe, the changes in the induced voltage in magnetisation, which are due to various influences of the analysed material, were detected. Further processing of the captured voltage signals was carried out on samples being in different states, and calibration curves were determined. A final decision on the state of the material was obtained from the calibration curves. On the basis of the micromagnetic parameter obtained, the parameter of surface integrity searched for can be determined.
The paper deals with determination of residual stresses in samples of heat-treatment steel C45E which were hardened and tempered at three different temperatures and eventually flat ground. The assessment of the efficiency of determination of residual stresses by the micromagnetic method based on the Barkhausen noise was carried out by means of measurement of residual stresses with the relaxation method. Comparative through-thickness measurements showed that the micromagnetic method was suitable for determination of residual stresses since it gives a real-time variation of residual stresses in a thin surface layer of the material concerned in a very short time.
The physical principle behind the micromagnetic method based on the Barkhausen noise is that every ferromagnetic material being magnetised will consist of small magnetic domains. Because of an external magnetic field, movement of Bloch walls of magnetic, i.e. Weiss, domains occurs, which produces changes in their size. The changes of size of the magnetic domains having the same orientation produces abrupt increase in magnetic flux density, which is reflected in induced voltage shocks in the measuring coil as a time-varying voltage signal. Ferromagnetic materials may show different microstructure states or may be subjected to various external mechanical stresses, which is reflected in the process of directing of magnetic-domain growth, i.e., in the voltage signal. The effects of complementary influences in the material such as microstructure, microhardness, residual stresses and dislocation density, produce the differences in the captured Barkhausen-noise (BN) voltage signals. Various methods of further processing of the captured BN voltage signals permit us to establish relations between the micromagnetic parameters obtained with the state of the analysed ferromagnetic material. Individual characteristics are determined on the basis of calibration curves which indicate a relationship between the known state of the material and the selected characteristic of the captured voltage signal.
The calibration curves are determined by changing external mechanical loads applied to the samples with known properties, i.e., etalons. The external loads applied to the etalons, which may be uniaxial or biaxial, produce various stress conditions in the elastic domain of the material. Uniaxial calibration curves are those which are obtained by taking into account uniaxial stress conditions and mostly used for characterisation of residual stresses [1,2]. Lately some authors proposed a biaxial calibration curve elaborated on the basis of biaxially stressed etalons . A comparison of experimentally obtained biaxial mechanical loads, i.e., stresses, which were determined on the basis of the captured magnetic BN signals, and of the calculated stress conditions with different external biaxial loads applied to the etalon showed that deviations are very small. These small differences between the calculated mechanical stresses and the measured ones, i.e., those determined from the BN voltage signal, indicate good reliability of the micromagnetic method when applied to determination of the size and variation of load stresses applied to etalons. The latter include also residual stresses in the unstressed condition and exist also when external mechanical loads applied to the etalon vary. That is to say that the micromagnetic method permits a similar determination of the size and variation of residual stresses in the thin surface layer of the material which have a decisive influence on the life of machine parts and products. Numerous researchers studied the influence of dislocation density on the changes of amplitude values of the captured voltage signals. They found that an increase in dislocation intensity produces an increase in the number of outbursts due to orientation of magnetic domains, which affects the size and variation of the amplitude values of the BN voltage signal .
2.0 EXPERIMENTAL PROCEDURE
2.1 MATERIAL SELECTION AND SAMPLE PREPARATION
Residual stresses were determined for heat-treatment structural carbon steel C45E. This steel is often used in the hardened and tempered state and/or surface hardened state for production of structural parts which are, during their operation, subjected to major loads. According to the manufacturer's catalogue, the steel contains 0.42 to 0.50 % of carbon and 0.50 to 0.80 % of manganese. The tensile strength after hardening and tempering ranges between 590 and 740 MPa, and, consequently, steel hardness between 224 and 612 HV0.2.
From bar-shaped steel having f
50x200 mm in size, two sets of samples having dimensions of 40x200x10 mm were prepared by means of face milling. They were heat treated and ground. The samples were heated and superheated to the austenitising temperature Ta of 860 °C, then quenched in water, strongly tempered at three different temperatures, i.e. Tp1 = 220 °C, Tp2 = 400 °C, and Tp3 = 700 °C. The present study will show different microstructures obtained after heat treatment in terms of the size and variation of residual stresses. Changes in steel microstructure and hardness were produced by different temperatures of high tempering after hardening. After hardening of steel C45E, a structure of tetragonal martensite is obtained. At lower temperatures of high tempering, i.e., around 200 °C, this martensite transforms into cubic or tempered martensite. At higher temperatures of high tempering, i.e., around 700 °C, martensite disintegrates into a very fine pearlitic microstructure, which is uniform across the entire sample cross-section. The fine pearlite formed consists of fine coagulated cementite particles which are inserted in the ferrite matrix. The size and distribution of cementite in the ferrite matrix determine steel hardness after the heat treatment performed.
3.0 DETERMINATION OF RESIDUAL STRESSES ON THE BASIS OF THE BN VOLTAGE SIGNAL
In the case when the searched-for parameter of the surface integrity does not vary across the material cross-section, the method of power frequency spectrum including the signal variance is used for processing the captured voltage signals. The calculated value of variance with individual frequencies of the BN voltage signal depends on the frequency characteristic of the band-pass filter, magnetisation parameters and the state of the material analysed. Our interest was focused on residual stresses through the specimen thickness due to heat treatment and/or machining. It was decided to use spectrum power with the given analysing frequency to process the captured voltage signals.
An advantage of further processing of voltage signals by analysing the signal power with the given frequency is that we are not limited by the lower cut-off frequency of the band-pass Butterworth filter. In the case when the frequency response of the band-pass filter ranges between 0.7 and 20.5 kHz, the maximum theoretically calculated depth of sensing micromagnetic changes is conditioned by the lower cut-off frequency. The depth of sensing of micromagnetic changes is always the same because the method of the power frequency spectrum including the calculation of variance with individual frequencies comprises the entire frequency spectrum of the filter. In the case when the spectrum power is monitored with the given analysing frequencies, the theoretically calculated depth of sensing of micromagnetic changes, however, varies in dependence of the frequency at which the spectrum is monitored. Thus high analysing frequencies reduce the theoretically calculated depth of measurement whereas low frequencies increase it.
|Sensing depth d(mm)
|QUENCHING AND TEMPERING CONDITION: Th = 8600C|
Tt3 = 7000C, HV=224
|QUENCHING AND TEMPERING CONDITION: Th = 8600C|
Tt1 = 2200C, HV=612
|Table 1: Theoretically calculated depth of sensing as a function of analysing frequency with two different states of steel C45E.|
Since our interest is focused on the size and variation of residual stresses in the thin surface layer of the specimen, which are due to heat treatment and machining, it is the depth of sensing of micromagnetic changes which is important with the micromagnetic method based on the Barkhausen noise. Suominen and Tiitto  and Vohringer  described the dependence of the depth of Barkhausen emission, i.e. the theoretically calculated depth of sensing, and the selected analysing frequency by an equation.
Fig 1: Calibration procedure for the experimental set-up with etalons and measurement of the unknown stressed condition.|
The NDT micromagnetic method described and designed for measurement of residual stresses is a comparative one; therefore, in the first phase, calibrating measurement had to be carried out. This means that stress calibration curves determining the dependence between the signal power with the given analysing frequency and the stress condition in the etalon were to be determined. The initial measurements at the etalons were made in an unstressed condition presuming that there are no residual stresses in the etalons. Then the etalons were gradually subjected to tensile loads at a tensile testing machine and additionally to compressive loads. After each application of load, a voltage signal was captured and processed. After etalon calibration at the experimental set-up, stress calibration curves were obtained which indicate the dependence between the signal power with the given analysing frequency and the residual stress obtained at the etalon after loading. The calibration procedure is shown in Fig. 1, above. The following findings can be stated:
- There are etalons in the unstressed condition. At variously heat-treated samples in the unstressed condition, different values of signal power are obtained with the given analysing frequency.
- The same etalons are then subjected to tensile loads, which produces different residual tensile stresses, which result in higher values of the signal power with the given analysing frequency.
- The same etalons are then subjected to bending. In the compression zone the signal powers are established for the given analysing frequency.
- When measuring an unknown stressed condition of the material or unknown samples, a suitable calibration curve determined on the basis of a preliminary measured material hardness after heat treatment should be selected (measurement procedure is shown in Fig. 1, below).
- A suitable calibration curve having been selected, measurement is carried out at the samples with an unknown stressed condition. After measurement, the signal power with the given analysing frequency, i.e., with a certain depth, is calculated. By means of the calibration curve, the corresponding residual stress in the material is determined.
Fig 2: Power-spectrum intensity with the given analysing frequencies as a function of tensile and compressive stresses.|
Fig. 2 shows stress calibration curves plotted for the etalons and indicating the dependence between spectrum intensity with the given analysing frequencies and the residual stress. The figure shows only the calibration curves elaborated at the hardened etalons tempered at the highest temperature Tp3 of 700 °C.
4.0 COMPARISON OF RESIDUAL STRESSES DETERMINED WITH THE MICROMAGNETIC AND RELAXATION METHODS
A comparison of variations of residual stresses determined with the relaxation method and the micromagnetic method based on the magnetic BN signal are shown in Figs. 3 and 4. Fig. 3 shows the variation of residual stresses at the hardened samples which were tempered at the temperature Tp1 of 220 °C and then finely ground. The highest values of residual tensile stresses measured with the relaxation method amount on the average to 420 MPa. The tensile stresses then decrease rather quickly. In the depth of 280 m
m they change into a compressive stress state. A considerably lower residual tensile stress is, however, obtained at the samples which were tempered at the temperature Tp3 of 700 °C. Fig. 4 shows that the maximum tensile stress, which on the average amounts to 190 MPa, is to be found in the direction of sample grinding and in the depth of 35 m
Fig 3: Comparison of variation of residual stresses measured with the micromagnetic method and the relaxation method at the same samples.|
Fig 4: Comparison of variation of residual stresses measured with the micromagnetic method and the relaxation method at the same samples.|
The comparison of the measured values of residual stresses at the samples treated under the same conditions of heat treatment and machining indicates that the deviations between the two methods of through-thickness determination of residual stresses differ. The differences in the stresses measured at four different measurement depths amount to 5 to 30% with regard to the size of the stress measured with the relaxation method. Regarding the residual stress measured with the relaxation method it should be mentioned that the results of measurements with the micromagnetic method based on the Barkhausen noise represent average values of residual stresses which were determined theoretically on the basis of the theoretically calculated depth of sensing of micromagnetic changes.
For determination of the stress condition in the material, the comparative way of measurement, including determination of the stress calibration curve in the first phase, was used. Processing of the captured voltage signals was accomplished with the method of power frequency spectrum, with which the frequency composition of a signal is determined. The spectrum power was monitored with the given frequency. The variation of stress calibration curves indicated a linear dependence between the spectrum power with the given frequency and the mechanical stress in the material. Higher values of tensile as well as compressive residual stresses, however, do not indicate a linear dependence. This indicates that no significant changes are obtained in the captured BN voltage signals.
The variation of residual stresses was determined at four different depths which are conditioned by the analysing frequency and amounted, in our case, to 20.5 kHz, 40 kHz, 100 kHz, and 200 kHz respectively. For individual analysing frequencies fa, theoretical depths of sensing of micromagnetic changes were calculated. From the calibration curve based on the spectrum power measured with the given frequency, the corresponding residual stress was then determined.
The efficiency of prediction of residual stresses in the material by means of the micromagnetic method was verified by means of the relaxation method based on a continuous electrochemical taking-away of the stressed material layer. The samples for both methods were equally heat treated and machined. In the thin surface layer, residual stresses generated due to heat treatment and grinding of the material.
The comparison of the results of measurement of residual stresses obtained with the two methods indicate deviations which are different in different depths of measurement. The greatest difference may be observed in the depth of 50 m
m where it amounts on the average to 30%. The differences in the results of measurement then decrease. Thus in the depth of 100 m
m they amount to only 5%. Then they increase with the increase in depth. The reasons for stronger deviations in smaller depths can be related to the fact that with the micromagnetic method the mean value of a residual stress is measured to the analysed depth.
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