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 . 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 : , 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 . 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) 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  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  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 , 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: . 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. . 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). . 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).
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