Comparison in magnetic properties of ferritic stainless steels measured using bar and ring samples

2.1. Sample preparation

The material for the present study is Fe-17Cr ferrite stainless steel. The chemical composition of the steel in our experiments is summarized in Table 1.

The steel had been industrially produced at KangJian Precision Stainless Steel Co. Ltd. The steel was processed by vacuum melting, followed by casting. After the steel ingot was forged and rolled, it was cold-drawn and straightened. Then it was fully annealed at high temperatures for corresponding duration followed by cooling in air, aiming at sufficient re-crystallization to form fine annealing microstructure. Finally, it was polished to form a round bar with a final diameter of 10 mm.

For magnetic measuring, the samples are carefully prepared according to IEC and ASTM standards (IEC 60404-4, ASTM A341/A341M). To obtain the magnetic properties, the magnetization curve and hysteresis loops are determined both by the so-called ring core method and the permeameter method according to IEC 60404-4, thus two series of ferritic stainless steel specimens for magnetic measuring are made all from the product in the fully annealed condition. Bar specimens of 100 mm length were directly cut from the product. Toroidal samples were made in the following procedures: after an 8 mm long bar was cut from the rods perpendicularly to bar-shaped samples, the hole in the sample was machined by an electric discharge machine to form a toroidal shape, which has a considerably smaller influence on the magnetic properties of the samples than mechanical cutting.

The ring-shaped sample was 8 mm long with an outside diameter of 10 mm and an inside diameter of 8 mm for an outside-to-inside diameter ratio of 1.25. Then first a 24-turn detecting (pick-up) coil, and then a 120-turn magnetizing (exciting) coil were each wound directly around their bodies, uniformly along the whole circumference. Double-insulated 18 AWG magnet wire was used for the primary winding; double insulated 28 AWG magnet wire was used for the secondary winding.

The measurements of the DC magnetic properties of the rings and of the bar-shaped samples were performed with the measuring system Permagraph–Remagraph Combination C-750 made by Magnet-Physik Dr. Steingroever GmbH of Germany. The whole system is fully automated. This is a magnetically closed circuit measuring system free from the demagnetization effect, so all information needed to conduct the measurements is determined by the program except the dimension of the sample and the number of primary and secondary turns of the coils. The measurements were all fulfilled in the quasi-static conditions. The quasi-static measurement allows obtaining the magnetic material properties independent from measuring speed. In this paper, the peak value of the DC magnetic field H can be as high as 56 kA/m in the permeameter method, and 20 kA/m in ring core method. The details about the set-up of the measuring systems used in this study can be found in [17].

It is well-known that the accuracy of the results greatly relies on the accurate setting of magnetic flux in the samples. This, in turn, requires an accurate measurement of cross-sectional areas or thicknesses of the samples if their diameter can be accurately obtained. Diameters of the round samples and heights of ring samples are measured precisely using a spiral micrometer with a resolution of 0.01 mm, outer and inner diameters of the ring samples were precisely measured using a vernier micrometer of 0.02 mm in resolution, and the lengths of bar samples are measured using a ruler with a resolution of 0.5 mm.

Though the magnetic property of ferrite stainless steel is not very sensitive to the temperature due to its high Curie temperature, to avoid the influence of temperature change, experiments were done at room temperature of about 23 °C, and the sample temperature is maintained at 23 ± 1 °C. Prior to taking each measurement each ring sample and bar sample together with the permeameter were demagnetized by slowly reducing the magnetizing field to zero.

For the ring sample method, the dimensions of the ring are determined first. Then, and a secondary winding of enough turns are applied, and connected to a flux sensing devices. Finally, a magnetizing winding (the primary coil) with enough turns and current carrying capacity is wound on the sample. The flux sensing device can produce an output voltage to calculate B. Also, a voltage developed across a calibrated low-value resistor in the magnetizing circuit can be used to measure the magnetic field H produced. For the bar sample method, the bar specimen was conducted in a closed magnetic configuration, and H is measured by a C-shaped Rogowski-Chattock potentiometer. The bar sample is clamped in the yoke with a J-coil and a potential coil to measure J and H signals. For automated measuring systems, these two signals can be sampled by computer to give the desired result.

The DC magnetic measuring procedure for the soft magnetic property was to determine both the initial magnetization curve and hysteresis loop (in the four-quadrant) to saturation or to a specified maximum magnetic field strength H _max. Then, μ _r –H curve can also be obtained. In the automatic, computer-controlled measuring system we used, the field strength for the ring sample was calculated from the measured DC magnetizing current flowing through the magnetizing winding and the effective magnetic path length; and for bar sample, H is measured by a c-shaped magnetic potential coil. J of the bar sample was measured by a J-coil, and for the ring sample, J was calculated from the electromagnetic induction law together with the cross-sectional area and turns of the secondary winding coil.

The ring and the bar samples were measured with a near quasi-static speed (controlled dB/dt or dH/dt) to ensure the data obtained are DC properties. In a quasi-static measuring, it is often thought that only the level of the magnetic field or magnetization should be controlled, instead of the sweeping speed, but in most of the computer-controlled automatic measuring systems, the measuring speed needs to be controlled to get DC properties of the material. Also, for various materials, different measuring time should be chosen. In addition, the specimen is demagnetized prior to each measurement. Periodically the specimens were re-measured several times to ensure that no damage or time-dependent magnetic property changes had occurred. After each measurement, the specific data required for the material were: μ _i , μ_max, Br, Hc, J _max and also the very important value for application H _μmax : field where μ _r got its maximum μ_max.

3.1. J-H curve, B-H curve and μ _r -H curve

As we have known, although M and J are constant after saturation is achieved, B will continues to increase with H, because H forms part of B [18,19], as: (1)

Thus, we can get Js or Ms value (J or M is almost constant after saturation is achieved) from J-H and M-H curves, but Bs is not a typical value in magnetization curve, and cannot be obtained directly.

Figure 1 is J-H, B-H and μ _r -H curve of ferrite stainless steel measured in a bar sample, including both the magnetization curves and hysteresis loops. Inset is the enlarged figure. From Fig. 1, we can clearly see that B is not saturated (B is still increasing) even in the field up to 50 kA/m. In lower H, B and J have little difference, but when H is as high as 10 kA/m, the difference between B and J can be clearly seen. As μ₀ = 4π ×10⁻⁷ H/m, when H is 10 kA/m, the difference between B and J will be μ₀ H = 0.01257 T. For permanent magnetic material, the difference will become even higher as H will become bigger [19]. Also can be seen from Fig. 1 that, μ _r -H curve has a maximum, called μ_max, the field where μ _r gets its maximum value μ_max is called H _μmax , these two parameters are very important for soft magnetic material applications.

OPEN IN VIEWER

Fig. 1.

J-H, B-H and μ _r -H curve of ferrite stainless steel measured in a bar sample.

For soft magnetic material, as the difference between B-H and J-H curves (including magnetization curve and hysteresis loop) is small, the difference between H _cJ and H _cB is usually negligible, as can be seen in the inset in Fig. 1, they are usually called Hc instead, regardless of H _cJ and H _cB . So in this paper, they are all called Hc. But the difference may be substantial for permanent magnet materials [18].

3.1.1. Bar samples

A set of minor loops with various field H amplitudes up to 56 kA/m were measured by the permeameter method using a bar sample, as can be seen from Fig. 2. The curves show only some of the field levels to avoid too crowded graphs. They are all tested in a demagnetized state. The speed of measuring is controlled by dB/dt. In order to show the details of the loops, the same figure was also shown on different scales. In the case of a demagnetized initial state, J-H loop starts to develop from around the origin and each J-H loop with a different H _max shows a symmetrical loop, which is centered at the origin as shown in Fig. 2a to Fig. 2d. Furthermore, as can be seen from Fig. 2a to Fig. 2d, when H_max is small, the different loop will have different J _m , Hc and Br value.

OPEN IN VIEWER

Fig. 2.

Magnetization and hysteresis loops at different H_max for bar sample.

A graphical resume of the evolution of the magnetic properties extracted from these hysteresis loops (Br, Hc, μ _r , and H _μmax ) with H were shown in Fig. 3. The details of each figure in the lower magnetic field area were also shown in the inset figures. From these figures we can see that these values will increase with H value, and will get a maximum, and then will keep unchanged when H is further increased, showing saturation characteristic. To get μ _r and H _μmax values, field of 2Hc will high enough; but for Br and Hc values, especially for Js value, H needed is more higher to get a stable value. Overall, if H is higher than approximately 8--10 Hc, these values will keep unchanged.

OPEN IN VIEWER

Fig. 3.

Changes of Br, Hc, H μ m a x and μ _r with H_max for bar sample.

Moreover, if we draw the normal magnetization curve with the data Jm-H, where Jm values are the maximum J value obtained in each H _max , we can see that it is just the initial magnetization curve. As shown in Fig. 4, the initial magnetization curve and normal magnetization curve are practically the same curves, though they have different physical meanings. Moreover, Barkhausen Jumps will only exist in initial magnetization curves and do not exist in normal magnetization curves, because normal curves are connections of the tips of each hysteresis loops, and initial magnetization curves are continuous magnetized curves. In addition, the superposition of the two curves also indicates that the effect of demagnetization before each measurement is quite effective.

OPEN IN VIEWER

Fig. 4.

Difference between normal and initial magnetization curve for bar sample.

3.1.2. Ring samples

A series of loops were also measured using a ring sample, as can be seen from Fig. 5, the details of the loops were also shown with magnifying the coercive force region in different scales. Minor hysteresis loops with various magnetic field amplitude H_max up to 20 kA/m were measured by changing H_max step by step. Before measuring each minor loop, the samples were also demagnetized. As can be seen from Fig. 5, when H_max is small, the different loop will also have different Jm, Hc, and Br value, the situation is just the same as the bar sample. Furthermore, the magnetization curve, the major hysteresis loop and μ _r –H curve were also shown, as can be seen in Fig. 6. It is clearly shown the features of these curves of the ring sample are just the same as those that can be found in the figures of the bar sample (from Fig. 1 to Fig. 4).

OPEN IN VIEWER

Fig. 5.

Magnetization and hysteresis loops at different H_max for ring sample.

OPEN IN VIEWER

Fig. 6.

J-H and μ _r -H curve of the ring sample.

3.1.3. Magnetic Property differences between Bar and ring samples

From these measurements, we found that though the curves of the bar sample and the ring sample are the same in shape, we can get totally different values in the major loops. For comparison, the major loops of both samples are put together, as shown in Fig. 7. The difference between the two kinds of samples can be clearly seen in Fig. 7. Also, from relations between minor-loop parameters, magnetic properties being independent of magnetic field amplitude were obtained and compared (that is from the major loops of the bar sample and the ring sample), the obtained parameters are listed in Table 2.

OPEN IN VIEWER

Fig. 7.

Difference between bar and ring samples.

OPEN IN VIEWER

Table 2

Comparison of ring and bar samples

	Br (T)	Hc (kA/m)	H μmax (kA/m)	μ r	Js (T)
Bar	0.875	0.346	0.440	1060	1.628
Ring	0.415	0.419	0.675	417	1.372

From Fig. 7 and Table 2, we can see that, though bar and ring samples are all cut from the same materials, different shaped samples can obtain quite different results. In addition, Br, μ _r and Js values obtained from the ring sample are smaller than that of the bar sample, whereas Hc and H _μmax values are larger than that of the bar sample. Of course, H _max for the two samples are different. As mentioned above, for the ring sample, due to limited space for the magnetizing coil, in our experiments H_max can only reach 20 kA/m, whereas for the bar sample H _max is as high as 56 kA/m. Because for the ring samples, the saturation can be achieved at magnetic fields larger than ∼10 kA/m, so loop obtained with H _max = 20 kA/m is the major loop, and thus the parameters listed in Table 2 for both samples are all saturation values. Thus the differences that can be seen in Fig. 7 and listed in Table 2 are attractive. For the same product, using bar samples and ring samples, different values of Br, Hc, H _μmax and μ _r are obtained. Furthermore, Js values are also different. Ring sample has larger Hc value, thus lower μ _r value, but smaller Js value.

Bar and ring samples can all be used to evaluate the magnetic property of soft ferritic stainless steel. Furthermore, these two methods are also widely used in applications. In practice, for the same material, there exist noticeable differences between measured magnetic properties of ring samples and bar samples, making the problem obviously more complicated. For bar and ring samples, their minor and major loops and also magnetization curves are all different. Thus, different Br, Hc, Js, μ _max values can be obtained.

The magnetic measurements were all performed at room temperature. Moreover, the influence of temperature on the magnetic property of ferrite stainless steels can be negligible. Furthermore, compared with other soft magnetic alloys, stainless steels have higher resistivity, thus measuring speed will have little influence on measuring results. As a result, these differences should be aroused by other reasons.

In addition, the measurements of the minor and major loops and magnetization curves of bar and ring samples show that the details of sets of loops can be clearly seen, showing that the measuring error is very small, and the repeatability and accuracy of measuring are high enough.

In order to reduce the effect of self-demagnetization, international standards require bars for coercivity measurement to have a length-to-diameter ratio L/D of at least 10:1 [6], also the length needed in IEC 60404-4 for permeameter methods is 100 mm or longer [15].

The influences of the samples (such as length to diameter ratio L/D) on the measured magnetic properties of permanent magnetic materials have been studied in recent years [20,21], but few works has been found on soft magnetic materials. A recent study found that further study is necessary for the permeameter methods, since the performance of permeameter is the sample size and property dependent, at least in the high-H region [22].

In fact, as mentioned above, on account of non-uniformity of the magnetic field H in the sample itself, when the recommended sample is a toroidal sample, just as described in the IEC Standard 60404-4 [15], the ratio of external to internal radius r _o ∕r _i should not exceeding 1.4, but the suggested value is smaller than 1.25. If the ratio approaches the value 1.4, there will be a greater radial variation in the magnetic field strength. Only when the condition r _o ∕r _i <1.4 [15] or even preferably <1.1 has been fulfilled [23], the mean length of the magnetic path is determined as (2) Where r _o is the outer radius of the test specimen, and r _i is the inner radius.

If this ratio is between 1.1 < r _o ∕r _i <1.6 [23], the mean length of magnetic path can be determined as (3)

The ratio r _o ∕r _i higher than 1.6 is not recommended due to significant magnetic field non-uniformity occurred in the sample. Thus it is clear that the ring sample should have a large inner diameter and large strip width (ring height). In our measuring, l is calculated by Eq. (3), and we have found that using Eq. (2) and Eq. (3), there is little influence on the result of our samples.

For bar and ring samples, the only difference in microstructure may be internal stress aroused by sample preparation, as the ring sample is made from the bar. As far as we know that, ferrite stainless steel is not easy to work harden, so mechanical machining can have little influence on the performance of the material, including magnetic properties. Furthermore, in the preparation of ring samples, the material is handled very carefully, and great care is taken to prevent internal stress, heat affected zone and work harden. In addition, circumferential direction wire electrical discharge machining was used to prepare the ring samples to avoid internal stress. Even if the magnetic property of ring samples is changed, Js value will not change because of its structural insensitivity nature.

As we have known, basically, the magnetic property of stainless steel is determined more by their crystal structures than by their compositions. Furthermore, grain orientation is also very crucial to magnetic anisotropy, because this can lead to anisotropy in properties. There are several kinds of anisotropy [7,18,24,25], such as crystal anisotropy (formally called magnetocrystalline anisotropy), shape anisotropy, stress anisotropy, induced Anisotropy, and exchange anisotropy. Texture (preferred grain orientation) can also influence the magnetic properties. It has also been found that texture control will make a significant contribution to improve power density and reduce copper losses in induction motors (Fe-Si) due to the improvement of μ _r together with reducing iron loss [26]. In the materials studied in this paper, perhaps the results can partly be explained in terms of the combined influences of two main anisotropies, namely shape anisotropy and the anisotropy determined by the texture.

It is found that if a suitable metallic alloy is undergone cold rolling, the internal stress produced within the material will align the individual crystal, i.e. by a so-called texture effect [27]. Because many of its preparations require the process of drawing, forging, pulling, rolling after wrought, and because ferrite stainless steel is a composite material, then, this can lead to the development of texture, elongated grains, and directional order. Thus, the material will have strong anisotropic features in the mechanical, magnetic, and other properties. As the anisotropic effect has been found in the mechanical property, the magnetic anisotropic effect must exist in stainless steel straight bars. The detailed analysis will be published later.

The distinguishing feature of the columnar crystal is internal shape anisotropy, which will also influence the magnetic property in different directions. In ring and bar samples, the magnetic field is in different directions: for bar samples, the magnetic field is in the longitudinal (or axial) direction, whereas for ring samples, H is applied around the axial direction. So H direction in ring samples is in the perpendicular direction to the radial direction, or more accurately, in the tangential directions. The methods of fabrication bars of ferrite stainless steel can cause a kind of microstructure that many crystals have a non-random distribution of orientations, they are mostly aligned along the rolling direction, this is often referred to as preferred or special orientations, or textures. Also, the grains are isolated from each other by another small grain of carbide, just like magnetic powder cores [19]. Furthermore, each grain also has shape anisotropy, arising different demagnetizing forces in different directions. If the elongated 𝛼-grains are aligned in axial direction, then H direction is parallel to axial direction in bar samples and is perpendicular to axial direction in ring samples. Thus the magnetic differences in bar and ring samples can be regarded as the effect influenced by internal shape anisotropy of 𝛼-grains. Because in these two directions, the inner demagnetization field is different, the effective field the 𝛼-grains experienced in two samples are also different. When H _app is applied, magnetic field the materials undergoes is H _in , which can be calculated by the following equation [13,18,19,23–25]: (4) where H _app is the applied magnetic field, H _in is the inner magnetic field the material experienced, N _d is the effective demagnetization factor [19]. Then, according to Eq. (4), H _in in ring samples will be smaller than that in bar samples in the same H _app . Compared with magnetization curves of the bar sample, the magnetization curves of the ring sample is sheared, revealing the influence of the of grain shapes [19].

Though the measured difference between the ring samples and bar samples is bigger compared with the similar study in magnetic Barkhausen noise using both kinds of samples [28], the samples are all satisfied with IEC standard. That is to say, according to IEC, the samples all have reasonable sizes. In addition, this phenomenon has been found many times. Thus, the results are surely not the effect of the size deviation of both samples. Furthermore, all samples are carefully prepared, and the dimension of the samples has been measured every time before measuring.

As we have known, Br, Hc, H _μmax and μ _r are all structure-sensitive properties (extrinsic properties), which depend on the anisotropy and the nonlinearity, flux density, frequency, heat treatment, deformation, etc. [18,25]. In addition to shape anisotropy and texture, even that something may be changed during the sample preparation, Js will not change because Js is structure-insensitive property (intrinsic property), just like unique properties as magnetic moment per atom, saturation magnetization Ms, saturation magnetostriction 𝜆 _s , Curie point Tc and to a certain extent anisotropy K₁. For the same material, Js should be the same value, regardless of these changes.

Overall, for both kinds of samples, the demagnetizing field is zero, thus there is no need to compensate for the demagnetization field, as all of the magnetic flux is running through the specimen, in a closed-loop. From the above result, we can see that the sampling process is also very important because transverse, longitudinal (or axial), tangential and radial samples or measuring in different directions can achieve different results for the same material in the same measuring accuracy.

Perhaps the difference is due to the improvement of the production process these years, resulting in even bigger anisotropy effect, such as internal shape anisotropy. So, further studies are needed to explain this phenomenon. Further researches are on progress, e.g., the influence of r _o ∕r _i ratio on the magnetic property of ring samples, the direct observation of the microstructure features of the material, etc. Moreover, if the difference between two kinds of samples will become less when the r _o ∕r _i ratio of ring samples is less than 0.1, or something else, perhaps these standards should be revised for these materials.