Paper - NDT.net

11th European Conference on Non-Destructive Testing (ECNDT 2014), October 6-10, 2014, Prague, Czech Republic
Estimation of the Internal Demagnetizing Factor of Cast Iron
Sergey G. Sandomirsky
United machine-building institute of the National academy of sanities of Belarus, Republic of Belarus, Phone:
+33 2651 904905, Fax: +375 17 2842351; e-mail: [email protected]
Abstract
In this paper, the difference in the interrelation between the coercive force Hc and the maximal magnetic
permeability of steels and cast-irons is analyzed. The internal demagnetization coefficient Nin of cast-irons with
different forms of graphite inclusions is estimated. The magnetization of cast-iron is analyzed as magnetization
of a material with a demagnetizing factor equal to Nin. A formula is derived for calculating the Nin of cast-iron in
the state of remanent magnetization on the major hysteresis loop from the Hc and the magnetization of technical
saturation.
Keywords: irons; magnetization; internal demagnetization coefficient; permeability; coercive force; remanent
magnetization.
Introduction.
Magnetic parameters of cast-iron depend on the structure of the metal. This fact allows
to use the results of measuring these parameters for testing structural and strengthening
properties of cast-iron products and determines the importance of studying the magnetization
of cast-iron. The magnetization of cast-iron in a closed magnetic circuit differs from the
magnetization of steel. Non-magnetic graphite inclusions demagnetize the metallic base of
cast-irons. This effect may be characterized by an internal demagnetizations coefficient, Nin.
In the magnetic structures copy, methods are widely used that rely on measuring the remanent
magnetization and the maximal magnetic permeability of the products’ material. Therefore, it
is of a particular interest to determine the Nin of cast-irons on the descending branch of the
major loop of magnetic hysteresis, in the region of the remanent magnetization and on the
major magnetization curve in the region of the maximal magnetic permeability. This talk is
dedicated to a quantitative estimation of changes in the interrelations between the magnetic
parameters of cast-irons compared to these interrelations for steels [1, 2], as well as to an
analysis of feasibility of sorting cast-irons with different structures from each other and from
steels based on the results of magnetic measurements.
Main Part.
Our theoretical analysis is based on the fact that the size and distribution of the
graphite inclusions in cast-irons do not change during a magnetic impact. Therefore, the
inclusions, not taking their demagnetizing influence into account, decrease the magnetization
of cast-irons to an equal degree on all parts of the major hysteresis loop. A change in the
relation of the remanent magnetization Md and the saturation magnetization Ms of cast-irons
compared to this relation (MR/Ms) of the metallic base is determined by the demagnetization
influence of graphite inclusions in cast-iron.
We have analyzed the magnetization of cast-iron as a magnetization of a uniform
magnetizing body with a demagnetization factor Nin (Fig. 1) on the descending branch of the
major loop of the magnetic hysteresis in the region of remanent magnetization [1]. We have
shown that Nin of cast-irons in this region is proportional to the coercive force Нc and a
parameter γ. Nin is also inversely proportional to the magnetization Ms [1]:
,
where γ = (1 − m d mR ) [md (1 − md )] , md = M d M s , m R = M R M s
(1)
.
(2)
Figure 1. The descending branch of the saturation hysteresis loop of a ferromagnetic
material (1) and body (2).
Based on the results of a statistical analysis (Fig. 2, 3) of the relations between the
remanent magnetization MR and Ms of steels and cast-irons with different forms of inclusions,
the values of the parameter γ were determined for high-strength (γ ≈ 0,983) and grey (γ ≈
1,364) cast-irons.
Md , kA/m
Md , kA/m
MS ,kA/m
MS ,kA/m
а).
б).
Figure 2. Dependences of the results of measuring the remanent magnetization Md of
grey (a) and high-strength (b) cast-irons with different structure of the metal matrix on their
the saturation magnetization Ms, and the zero-crossing trend-lines of the statistical analysis of
the data.
It is established that the Nin of a foundry-cast grey cast-iron on the descending branch
of the major hysteresis loop in the region of remanent magnetization is 18 times smaller than
its Nin on the major magnetization curve in a strong field. Based on results of a statistical
analysis of the dependencies of the remanent magnetization of steels and cast-irons on their
Мs, it was established that the remanent magnetization of high-strength cast-iron is 1,32 times,
and of grey cast-iron – 1,49 times smaller than the remanent magnetization of steel with the
same Мs. This result may be used to develop methods for sorting cast-iron products with
different forms of graphite inclusions from steels and from each other.
MR , kA/m
Ms , kA/m
Figure 3. Dependence of the results of measuring the remanent magnetization MR of
steels on their magnetization of technical saturation Ms and the zero-cutting trend-line of their
statistical analysis.
The same methodology was applied to analytically describe the relation of the
maximal magnetic permeability µmt of cast-irons to their Нc, analyze the difference of this
relation for steels and cast-irons, and to estimate the values of µmt of cast-irons with different
structure based on results of measuring their Нc [2]. It is shown that the maximal magnetic
permeability µm of steels may be estimated based on their Нc using a formula (Нc is measured
in kA/m) [3]:
(3)
The correlation coefficient R in the linear regression equation between the calculation
results according to (3) and the experimental results is R ≈ 0,976, the relative error δ of
calculation for many steels is less than ±20%.
For cast-irons, this dependence has the form:
,
(4)
where k is a coefficient, which depends on the shape and size of the graphite
inclusions.
In Fig. 4, the calculations of the dependence µm(Нc) using (3) and the dependency
µmt(Нc) using (4) at k = 1,37 are compared to experimental results for 203 cast-irons with the
magnetic parameters, varying in ranges: 40 ≤ µmt ≤ 2120 and 120 A/m ≤ Нc ≤ 6078 A/m. The
studied cast-irons embrace practically the whole possible for cast-irons interval of variation of
Нc and µmt. In the Figure, for better visualization, the results are presented for cast-irons with
Нc ≤ 1,5 kA/m. The value k = 1,37 ensures the least mean-square deviation between the
calculation results using (4) and the experiment. The obtained data confirm the physically
correct description of the correlation between µmt and Нc by the equation (4) at k = 1,37. R in
the linear regression equation µmt(calculation) = µmt(experiment) is 0,926. The mean-square
error σ of calculation using (4) at k = 1,37 is σ ≈ 130.
A comparison (Fig. 5) of the dependence µm(Нс), calculated using (3), and the
dependence µmt(Нс), calculated using (4) at k = 1,37, has shown [2] that at an equal Нс , the µmt
of cast-irons amounts on average to only 42% from µm of steels.
μmt
НС , A/m
Figure 4.
Dependence of the maximal magnetic permeability µmt of cast-irons on their
Нc. х , +, □, and ○ mark the experimental results respectively for grey, high-strength,
malleable, and white cast-irons; ∆ and ● mark the results of calculation of µmt using formulas
(3) and (4) respectively at k = 1,37.
μmt [experiment]
μmt[calculation using (4)]
Figure 5. Relation between the calculation results using (4) and measurements of the
maximal magnetic permeability µmt of cast-irons.
The difference in relations between the Нс and the maximal magnetic permeability of
steels and cast-irons may be used for sorting steels and cast-iron from each other.
In [2] it was shown that the Nin of cast-irons in their magnetized state that corresponds
to the region of the maximal magnetic permeability µmt on the major magnetization curve,
may be approximated by the value:
.
(5)
An analysis was performed of the differences in coefficients k when calculating µmt
using (5) for cast-irons with different shapes of graphite inclusions. The analysis didn’t reveal
a statistically significant difference in values of k ≈ 1.71 for white (with prevalence of
carbon in a bound state) and grey (with a laminar form of graphite inclusions) cast-irons.
However, for cast-irons with a compact form of graphite inclusions (for high-strength and
malleable cast-irons) the values of k are significantly smaller and are equal, respectively, 1.02
and 0.83. This result may as well be used for development of methods for sorting cast-iron
products with different forms of graphite inclusions from steels and from each other.
Thus, the mean value of the product µmtНс(kA/m) for 117 cast-irons with a laminar
form of inclusions is 265 with σ = 89. For 48 cast-irons with spherical form of inclusions, the
mean value of the product µmt Нс (kA/m) is 351,5 with σ = 115. For 313 different steels, used
for the analysis of the relation between µm and Нс in [3], the mean value of the product µm
Нс (kA/m) is 526.4 with σ = 132.
Conclusions:
1. The internal coefficient Nin of demagnetization of cast-irons on the descending
branch of the major loop of magnetic hysteresis in the region of remanent magnetization is
proportional to the coercive force Нc and the parameter γ, determined according to the
formula (2). Nin is also inversely proportional to the magnetization of technical saturation Ms
of cast-irons. Statistically, the values of γ were determined for high-strength (γ ≈ 0,983) and
grey (γ ≈ 1,364) cast-irons. It was shown, that the Nin of malleable grey cast-iron in this
region of the hysteresis loop is 18 times smaller that its Nin on the major magnetization curve
in a strong field.
2. It is established statistically, that the remanent magnetization of high-strength castiron is 1.32 times, and of grey iron — 1,49 times less than the remanent magnetization of
steels with the same Мs. This may be used to develop methods for sorting cast-iron products
with different form of graphite inclusions from steels and each other.
3. It is verified that the Nin of cast-irons on the major magnetization curve in the region
of µmt may be estimated using formula (5). A statistical analysis was performed of the results
of measuring µmt and Нc of 203 cast-irons with different structures in comparison with the
relation between µm and Нc for steel. It is established that the value of the coefficient k ≈ 1,71
in (5) is the same for white and grey cast-irons. For high-strength cast-iron k ≈ 1,02.
4. The formulas are obtained for estimation of the maximal magnetic permeability µmt
of cast-irons with different form of graphite inclusions based on Нc. It is shown that µmt of
cast-irons may be calculated using the formula (4) based on their coercive force Нc. The
correlation coefficient between the results of calculation of µmt for 203 cast-irons (for which
40 ≤ µmt ≤ 2120 and 120 A/m ≤ Нc ≤ 6078 A/m) using (4) at k = 1.37 m/kA and the results of
measuring µmt is 0.926. The relative calculation error for most cast-irons did not exceed
±40%.
5. It is established that at the same Нc, the maximal magnetic permeability µmt of castirons is (on average, not considering deviations) 42% from the maximal magnetic
permeability µm of steels. The µmt of grey and high-strength cast-irons at equal Нc have
difference, on average, of 34 %. This difference may be used to sort cast-irons from steels, as
well as to sort cast-irons with the laminar and spherical forms of graphite inclusions from
each other.
References:
[1]. Sandomirsky S. G. Estimation of the internal demagnetizing factor of cast iron
from its measured remanent magnetization // Russian Metallurgy (Metally), Vol. 2013, No. 5,
pp. 392 – 397.
[2]. Sandomirsky S. G. Estimation of the maximal magnetic permeability of steels
from their coercive force // Заводская лаборатория. Диагностика материалов (Industrial
laboratory. Diagnostics of materials). 2012. Т.78. № 12. С. 39 – 44. (in Russian).
[3]. Sandomirsky S. G. Estimation of the maximal magnetic permeability of cast-irons
from the coercive force // Заводская лаборатория. Диагностика материалов (Industrial
laboratory. Diagnostics of materials). 2011. Т.77. №3. С. 35 – 38. (in Russian).