·Table of Contents ·Materials Characterization and testing | Evaluation of residual stresses in ferromagnetic steels by means of magnetic and magnetoelastic proceduresA.P. Nichipuruk, E.S. GorkunovionContact |
The present paper discusses the application of magnetic and magnetoelastic methods for evaluating the mean values of internal stresses in various steels which have been subjected either to extension deformation or to overall reduction (hydroextrusion).
For the present investigation, the samples were cut from a low-carbon steel with ~0.1%C (steel grade 1) which was tempered and then subjected to extension deformation and from a low-alloy ferritic-pearlitic steel with ~0.3%C, ~1%Cr, ~1%Mn, ~1%Si (steel grade 2) which was deformed to a large ratio by means of hydroextrusion.
Magnetoelastic tests were performed according to the following procedure: demagnetized samples were extended to a certain ratio, then a magnetic field was applied along the extension axis, thus the elastic dynamic oscillations of low frequency and small amplitude were produced. The amplitude of magnetic flux density induced within the sample was measured by means of a coil which covered the sample. Measurements were conducted under various tensile stresses ranging from zero to 0,6s _{0,2}. The dependence of the detected induction upon the tensile stress has exhibited a specific profile with a maximum [1,2]. In view of some results presented in [1,2] as well as those shown in figs. 1 and 2 (e.g. a certain dislocation density in steel grade 1 and a monotonic variation of the strength of steel grade 2 with the plastic deformation ratio), it may be noted that the tensile stress corresponding to the maximum induction correlates with the mean amplitude of internal stresses in the examined steels subjected to various deformation regimes. However, magnitoplastic tests are not easy to perform by means of standard non-destructive testing procedures. To overcome this difficulty a detailed investigation was carried out to derive 90° domain walls hysteresis parameters directly from the major hysteresis loop.
Fig 1: Internal stresses determined by the magnetoelastic method as a function of the square root of the dislocation density in Grade 1 steel | Fig 2: Internal stresses determined by the magnetoelastic method vs. the plastic strain of the specimens: 1- normalizing; 2- isothermal treatment |
In previous studies [3,4] a model of reversal magnetization in cubic ferromagnetic materials was presented for the case when both natural and induced crystallographic anisotropies coexist in a material, the induced one resulting from the incidental distribution of internal stresses. A mathematical program developed in terms of the model made it possible to analyze the magnetic field dependence of the experimentally measured differential magnetic susceptibility (permeability) c_{d} of the material and enabled us to estimate the critical fields corresponding to irreversible displacements of 180° and 90° domain walls, as well as to determine the dispersion of the Gaussian distribution of these fields and to evaluate the field of the induced anisotropy. The critical field values in samples of both examined steel grades were estimated using the present program.
The field dependence of differential magnetic susceptibility is shown in figs. 3 and 4 by curves obtained from experimental observations and from the data derived theoretically by means of the above mentioned model. All the samples tested, including steel grade 1 samples subjected to extension and annealing under the temperature ranging from 300° to 600° C and steel grade 2 samples subjected to 20, 40 and 60% hydroextrusion, exhibited similar field dependence. A thorough analysis of the data indicates that the variation of the internal stresses in the course of plastic deformation or annealing results in a change in magnetic susceptibility associated mainly with displacements of 90° domain walls. The displacements of this type take place mostly in magnetic fields ranging from saturation magnetization to residual magnetization and further within the bend area of the hysteresis loop, in magnetic field 2 or 3 times as large as the coercive force of the material. When the deformation ratio increases or the annealing temperature decreases, the critical magnetic field value corresponding to the maximum 90° domain walls differential susceptibility is removing towards either negative values (maximum is to the left) or positive values (maximum is to the right).
Fig 3: Field dependence of the differential susceptibility. Grade 1 steel. e = 10%, Tan = 500^{0}C |
Fig 4: Field dependence of the differential susceptibility of a normalized Specimen after 40% strain: points -experiment; 1- total calculated susceptibility; 2- 1800 calculated susceptibility; 3- 90^{0} calculated susceptibility |
The position of maxima associated with critical field values are governed by the induced magnetic anisotropy energy [3,4], the value of which in this particular study should be considered as a function of the magnitude and distribution of residual stresses. As the applied magnetic field varies from -H_{max} to zero, the maximum is observed when the magnetostatic energy declines and becomes as low as the induced anisotropy energy; meanwhile the domains which provide nuclei for the reversal magnetic phase are likely to grow since the reversal magnetic phase exists in fields roughly equal to ± H_{max}. As the magnetic field increases from zero to +H_{max},_{ }the most intensive displacements of 90° domain walls are observed in fields larger than the field of induced magnetic anisotropy. In both cases a discussion was made of the magnetic field values corresponding mostly to the displacements of domain walls, thus the considerations become valid only if the induced anisotropy is substantially lower than the crystallographic one.
Figs. 5 and 6 present the calculated field of the induced anisotropy as a function of the annealing temperature for the strained samples of steel grade 1 and as a function of deformation ratio for steel grade 2 respectively. In both cases the behavior of this parameter corresponds to variations in the strength properties of the examined materials and thus indirectly confirms the correlation between the field of the induced anisotropy and the internal stress rate.
Fig 5: Calculated anisotropy field plotted against the annealing temperature of deformed wire. Grade 1 steel | Fig 6: Calculated anisotropy field vs. plastic strain: 1- normalizing 2- isothermal treatment |
A comparison should be made between the results on evaluating the internal stresses obtained by two different methods, viz. on the basis of the field dependence of differential magnetic susceptibility and by means of magnetoelastic examination of steel grade 2. Assuming that magnetic anisotropy is induced mostly by internal stresses, it can be stated that the energy of magnetic anisotropy is equal to magnetoelastic energy E_{me} = 1.5 l_{100}s_{0i} , where l_{100} is the magnetostriction constant for iron; s_{0i} is the mean value of internal stresses. On the other hand, from the obtained mean values of the induced anisotropy field H_{a}, the anisotropy energy can be determined as E_{a} = H_{a}M_{s}, where M_{s} is saturation magnetization of the examined samples. After equating E_{me} with E_{a} and substituting all the known constants for the material, it becomes possible to estimate values of s _{0i }and to compare them with s _{0} shown in Fig. 2. The following table presents both parameters for the samples with different deformation ratio.
From the comparison of the data, it may be stated that s _{0} and s _{0i }are in quite good agreement taking into consideration some obvious approximations involved in s _{0i } estimation as well as making allowance for rather significant instrumental error in s _{0 }measurements. It is obvious that a better agreement in s _{0 }and s _{0i } values will be reached in samples with higher residual stresses, otherwise in samples with relatively low residual stresses grain boundaries and carbide inclusions are likely to make a substantial contribution to the induced anisotropy.
Normalization | Isothermal treatment | |
e, % | 0 20 40 60 | 0 20 40 60 |
s_{0}, MPa | 88 160 220 260 | 50 140 200 236 |
s_{0i}, MPa | 139 181 212 263 | 126 191 237 294 |
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