RU2590224C1 - Method of estimating bending stress in elements of structures - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to diagnostics of technical state of metal structures, while in operating condition. On controlled section of sample (analogue) of element (or on operating element) in absence of external bending force and at application of external bending force (within limits of elastic properties of element) each time is magnetised in order to create symmetric magnetic field relative to axle (axes) of symmetry of element cross section geometric shape. Value of magnetic field induction is measured in characteristic points on boundaries of element cross sections, symmetrical to each other relative to axle (axes) of symmetry of element cross sections. Mean difference of absolute values of magnetic induction is determined in characteristic points on controlled section. At experimental dependence of bending force (or average tension in material) from mean difference of absolute values of magnetic induction in characteristic points on the monitored section of the sample (analogue of element or on operating element) analytical relationship is found. On controlled section of structural member in working state, symmetric magnetic field relative to geometrical figure section element is created, value of magnetic field induction is measured in specific points of sections, average absolute difference values of magnetic induction is determined in similar characteristic points and at earlier obtained analytical relationship, average estimated value of tension in material on controlled element section in working structure is found.

EFFECT: possibility to provide rapid evaluation of bending stresses in material of structure elements in working condition, by means of simple mobile equipment.

1 cl, 10 dwg, 1 tbl

Description

The invention relates to the field of diagnostics of the technical condition of metal structures in working condition.

Modern technical diagnostics of structural materials focuses on methods and means of measuring and evaluating residual and working internal stresses. Analysis of methods for monitoring and evaluating the stress-strain state of the elements of working steel structures shows that the effectiveness of various methods remains low when used directly on equipment [1-5]. In particular, unsuitability for control of long pipelines and structures, large-sized products; does not take into account changes in the structure of the metal the impossibility of assessing the deep layers of the metal for most control methods; it is necessary to build graphs based on tests of prefabricated samples, which, as a rule, do not reflect the actual energy state of the equipment; preparation of the controlled surface and objects of control is required; the difficulty of determining the position of the control sensors in relation to the direction of action of maximum stresses and strains that determine the reliability of the equipment. It follows that the solution of the problem of experimental control and assessment of the real stress state of structural elements at the stages of production and their further operation is currently relevant.

The proposed method solves the problem of assessing bending stresses in elements having an axis having a symmetrical cross-sectional shape, various kinds of structures during their operation, made of a homogeneous ferromagnetic material.

The problem is solved using the results of patents [6-8]. The controlled section of the extended element is magnetized by creating a symmetric magnetic field relative to the axis (axes) of symmetry of the geometric shape of the element’s cross section along its length. With the homogeneity of the material of the structural element and the absence of mechanical stresses in it, the magnetic induction at the characteristic points of the sections of the element that are symmetrical about the axis (axes) on the surface of the element will be the same in magnitude. When mechanical stresses appear on a controlled section of an element in its sections, according to the Villari effect [9, 10], non-symmetry appears in the pictures of the magnetic field of the sections. After measuring and finding the difference between the absolute values of the magnetic induction at the characteristic points of the cross sections in the control area, an assessment of its stress state is made.

When developing the proposed method, an experiment was carried out with a rectangular steel profile when it was bent, as a result of which an analytical relationship was obtained between the average tension in the material of the profile and the average difference in the absolute values of the magnetic induction at the characteristic points of the cross sections in a controlled area with elastic deformation of the profile, which essentially similar to Hooke's law [9, 10]. Brief results of the experiment are as follows. A defect-free steel rectangular profile has been used for a long time as a laboratory sample in the CM1 universal measuring complex for “Material Resistance”. Steel profile (overlay) with dimensions of 92 × 35 × 788 mm consists of a central part (rectangular profile) with dimensions of 92 × 5.2 × 232 mm and peripheral parts (I-beam), steel grade ST45, FIG. 1-3. During the experiments, the magnetizing system MSN14 and the defectoscopic magnetometer MF-23IM were used. The sample was fixed at the ends, a bending force F = F ₁ + F _{7 was} applied on top of the sample, which is divided into two equal forces F ₁ and F ₇ concentrated in the region of the first and seventh sections at a distance of 125 mm from the center of the profile each, forces are applied throughout the width of the upper edge of the profile, FIG. 1 and FIG. 2. The test central portion of the sample is divided into seven sections: the center is indicated by number 4, three sections to the left and to the right of the center through 40 mm each. Characteristic points from B ₁ to B ₈ are marked along the perimeter of the sections on the sample, FIG. 3. The force F during testing of the sample varied within its elastic properties.

Before the experiments, the absence of residual magnetization of the sample was established. During testing, the sample was magnetized in a controlled area in order to create an axisymmetric picture of the magnetic field relative to the symmetry axes of a rectangular section, FIG. 3. In the controlled area of the sample, the magnetic induction values were measured at the characteristic points of the cross sections in the absence of an external bending force F = 0, as well as when two bending forces were applied, F = 1.5 kN and F = 3 kN. The distribution curves of the magnetic induction along the length of the controlled section at pairwise symmetric points B ₁ and B ₂ , B ₃ and B ₄ , B ₅ and B ₆ practically coincide in value with each other in each section. In FIG. 5 shows graphs of the distribution of magnetic induction at points 7 and 8 that are pairwise symmetric with respect to the smaller axis of symmetry of the section, which differ in each section from each other. In this case, the graphs of the change in induction at the characteristic points B ₁ , B ₂ and B ₇ practically coincide with each other, as well as the graphs of the distribution of induction at the characteristic points B ₅ , B ₆ and B ₈ , which belong to the upper and lower faces of the profile, respectively. The directly opposite signs at the induction at the characteristic points of these faces correspond to two magnetic poles formed as a result of magnetization of the controlled section of the profile. In FIG. 6 shows graphs of the distribution of modules (absolute values) | B ₇ | and | In ₈ | in a controlled area of the sample. In what follows, we will consider the difference in the magnetic induction moduli at characteristic points 7 and 8, as the middle representatives of the upper and lower faces of the profile, respectively.

Graphs of the difference in the modules of these values ΔВ ₇₈ = | В ₇ | - | В ₈ | along the length of the test section are shown in FIG. 7 at F = 0 and in FIG. 8 when applying an external bending force F ≠ 0. The analysis of the graphs of the distribution of induction at zero bending force F = 0 shown in FIG. 4-7 shows that in the studied section of the profile in the metal there is a residual tension, while its distribution is uneven. So, in areas of the second, third, fifth and sixth sections, the tension in the metal is increased in comparison with the rest of the sections. In this case, the zones of increased voltage are not symmetrical and are shifted towards the lower edge of the sample (B _{8 is} greater than B ₇ modulo), which is well reflected in the graphs of FIG. 5 and FIG. 6, as well as a plot of ΔB ₇₈ , FIG. 7. Since the prototype profile is mounted uniformly in the CM1 laboratory unit, the lower part of the profile is constantly stretched during experiments, and the upper one is compressed. Under ideal conditions, the boundary of these multidirectional stresses in the sample should pass along the midline along the sample and coincide in cross section with a horizontal line of symmetry. In FIG. 4 graphs 3 and 4 of induction B ₃ and B ₄ at characteristic points lying on the horizontal axis of symmetry of the section of the profile deviate from the zero axis towards the zone of increased residual voltage, i.e. to the bottom of the sample. The average value of the difference in magnetic induction ΔВ ₇₈ in the controlled section of the sample is -1.26 mT. Thus, due to the prolonged use of the sample for its intended purpose, the initial (residual) internal stresses in it were revealed in the laboratory setup, while there were no visible signs of sample deformation.

After applying an external bending force with values of F = 1.5 kN and F = 3 kN, the distribution of magnetic induction along the length of the sample at characteristic points becomes different from its similar distribution at F = 0.

In the graphs of FIG. Figure 8 shows the redistribution of internal stress along the length of the controlled section of the profile depending on the applied value of the bending force F, taking into account the residual tension in this section. From the graphs of FIG. 8 of the distribution of the difference of the magnetic induction modules at two characteristic points of the section of the profile 7 and 8 along the length of the sample ΔВ ₇₈ = | В ₇ | - | В ₈ | (curve 1 - at F = 0 kN; curve 2 - at F = 1.5 kN; curve 3 - at F = 3 kN) it follows that the average value of ΔВ ₇₈ in the experimental section of the profile is, respectively, -1.26 ; -1.63 and -2.13 mT increases in absolute value as increasing bending force is applied.

We find the analytical relationship between the value of the bending force F and the average increment of the difference in the absolute values of the induction ΔВ ₇₈ , and also make an estimate of the equivalent bending force F ₀ , which led to the average residual stress in the controlled section of the profile. We use the following relations:

where δВ ₇₈ is the increment of the average difference of the module | ΔВ ₇₈ | in relation to the initial average difference of the induction module | ΔВ ₇₈ (0) |; ΔВ ₇₈ (0) is the average difference between the induction modules at characteristic points 7 and 8 in the absence of an external bending force F = 0.

Let us introduce the relative increment of the average difference between the induction modules at the characteristic points ΔВ * ₇₈ to estimate the average increments | ΔВ ₇₈ | in relation to the initial increment | ΔВ ₇₈ (0) | when changing external bending force:

The experimental data and the entered indicators will be placed in table 1.

According to the data of the fourth column of Table 1, it follows that the relative increment of the average difference between the induction modules at the characteristic points ΔВ * ₇₈ in percentage terms is quite significant and is 29% and 69% for F = 1.5 kN and F = 3 kN, respectively, which says sufficient information content of the introduced indicators (1) and (2).

In FIG. 9 shows a graph of the dependence of the external bending force F on δB ₇₈ , constructed according to the table. one.

Experimental curve F (δB ₇₈ ) of FIG. 9 is close to a linear dependence and can be used to determine the external bending force by incrementing the average modulus difference δB ₇₈ .

In FIG. 10 shows a graph of the dependence of the bending force F on the average difference of the magnetic induction ΔВ ₇₈ , constructed according to the table. one.

We approximate the experimental dependence F (ΔB ₇₈ ) (Fig. 10) by a linear function:

where the force F ₀ is the equivalent of the average bending force that led the symmetric magnetic field of the unloaded profile (without internal stresses in the considered section of the profile) to the non-symmetry of the magnetic field at characteristic points 7 and 8, making the average difference in magnetic induction ΔВ ₇₈ (0), unequal zero; K is the coefficient of proportionality.

For two points of the experimental curve (Fig. 10) with the coordinates of the points (ΔВ ₇₈ ; F): t. 1 - (-1.26; 0) and t. 2 - (-2.13; 3) we compose a system of linear equations and we solve it with respect to F ₀ and K:

F ₀ = -4.34 kN = -4.34-10 ³ N and K = -3.45 kN / mTl = -3.45 · 10 ⁶ N / T.

Then the dependence (4) takes the form:

It follows that the average residual tension in the sample will be proportional to the equivalent bending force F ₀ = 4.34 kN applied in the vertical plane of the sample in the same direction. Note that in the horizontal plane of the sample, no residual tension is observed, according to the experimental curves at zero external bending force F = 0, FIG. 4. From the graphs (Fig. 4) it follows that the differences in magnetic induction at the corresponding characteristic pairwise symmetric points of the cross sections of the sample along its length ΔB ₁₂ = ΔB ₁ -ΔB ₂ , ΔB ₃₄ = ΔB ₃ -ΔB ₄ and ΔB ₅₆ = ΔB ₅ - ΔB _{6 are} practically zero. The graphs of these experimental curves show traces of the three planes of the distribution of the residual tension in the sample material along its length.

We estimate the average tension in the steel of the sample in its controlled area. Using the approximating function (4), we find the average total bending force F * participating in the creation of tension in the sample material

The average normal tension σ * in the considered section of the profile will be found by definition:

In view of (6), expression (7) can be rewritten in the form:

where in expressions (6) and (7) it is indicated: S is the cross-sectional area of the profile in the controlled area of the sample; k = K / S is the coefficient of proportionality between the average tension and the average increment of the difference of the induction modules at characteristic points 7 and 8 in the controlled portion of the sample.

For experimental data with a cross-sectional area of the tested part of the profile S = 288 · 10 ^-6 m ² , the coefficient k will take the value:

and the average normal tension σ * in the considered section of the sample, according to (8), will be determined by the dependence:

Since the upper layers in each section of the sample are compressed, and the lower ones are stretched, we take the average tension of the upper and lower layers to be equal in absolute value to σ, then, taking into account expression (8), we can write:

In expression (11), we write the difference in magnetic induction at characteristic points 7 and 8. Since the magnetic field is created axisymmetric with respect to the geometric shape of the cross section and the sample material is isomorphic, for the values of induction at the characteristic points of the cross sections of the sample, the following expressions are valid:

Here B ₀ is the value of the induction modulus corresponding to a symmetric magnetic field in the absence of bending stresses at characteristic points; ΔВ is the absolute increment of induction, according to the Villari effect [9]. Then the difference in magnetic induction at characteristic points 7 and 8 in accordance with (1), (12) and (13) is written

where the “-" sign indicates the direction of bending of the sample. From the obtained expressions (12) - (14) it follows that the absolute value of B ₀ associated with the magnitude of the magnetizing field does not play a role in the magnitude of the difference in induction at the selected characteristic points ΔB ₇₈ .

We rewrite expression (11) with allowance for (14) for their modules:

The resulting dependence (15) is similar to Hooke's law [9]:

where E is the elastic modulus (Young's modulus), ε is the relative linear deformation.

By analogy with Hooke's law (16) in expression (15), the coefficient k is called the modulus of magnetic elasticity, and the absolute increment of magnetic induction ΔB is called magnetic deformation, since it is an increment of magnetic induction, which causes a distortion of the symmetry of the magnetic field at characteristic points associated with the internal voltage in the cross sections of the sample.

We equate the tension in the expressions (15) and (16):

From the solution of equation (17) we find the dependence of the relative linear strain ε on the magnetic strain ΔB:

- отношение модуля магнитной упругости k к модулю Юнга Е служит коэффициентом пропорциональности между линейной и магнитной деформациями.here $$\frac{k}{E}$$

- the ratio of the modulus of magnetic elasticity k to the Young's modulus E serves as a proportionality coefficient between linear and magnetic strains.

Given expression (15), the relative linear deformation can be expressed in terms of the average difference of the magnetic inductions at the characteristic points ΔВ ₇₈ :

, модуля упругости Юнга для стали $$E=\mathrm{2,1}\cdot {10}^{11}\frac{{\rm H}}{м2}$$

и ΔВ₇₈=2,13·10^-3 Тл при F=3 кН из табл. 1, с учетом внутреннего напряжения, найдем относительную линейную деформацию:Using relation (19), the value of the modulus of magnetic elasticity (9) $$k=11979\cdot {10}^6\frac{{\rm H}}{\text{T m2}}$$

Young's modulus of elasticity for steel $$E=2.1\cdot {10}^{\mathrm{eleven}}\frac{\mathrm{<figure-callout\; id="2"\; label="{\rm H}\; m"\; filenames="00000023.png,00000024.png"\; state="\{\{state\}\}">{\rm H}\; </figure-callout>}}{m}$$

and ΔB ₇₈ = 2.13 · 10 ^-3 T at F = 3 kN from table. 1, taking into account the internal stress, we find the relative linear deformation:

The obtained value of the relative linear strain in expression (20) shows sufficient sensitivity of the developed method. Thus, expressions (15), (18), and (19) make it possible to use the existing apparatus of the theory of elasticity [9] to analyze the bending stresses of structural elements without disassembling and breaking them.

Based on the foregoing, the proposed method for assessing bending stresses in the elements of the working structures made of a homogeneous ferromagnetic material having a symmetrical cross-sectional shape, is that according to the sample (analogue) of the structural element (or on the current working structural element, if possible) with different values of the external bending force within the elastic properties of the element determines the analytical dependence between the average tension and the average absolute difference of the magnetic induction and at the characteristic points of the cross sections in the controlled area. The obtained analytical dependence is subsequently used to assess bending stresses on structural members in working condition. To this end, a symmetric magnetic field is created in the controlled portion of the structural element in working condition with respect to the geometric shape of the element’s cross section, the magnetic field induction is measured at the characteristic points of the cross sections, the average difference between the absolute values of the magnetic induction at the required characteristic points and the previously obtained analytical dependence is determined is the average estimated value of tension in a controlled area of the element.

The technical result of the implementation of the method lies in the possibility of providing an operational assessment of bending stresses in the material of structural elements in working condition using simple mobile technical means.

Information sources

1. Non-destructive testing in industry. Magnetic control. / Gorbash V.G., Delendik M.N., Pavlenko P.N. Nondestructive testing and diagnostics. 2011, No. 2.

2. Aleshin N.P. Physical methods of non-destructive testing of welded joints: a training manual. - M.: Mechanical Engineering, 2006. - 368 p.

3. Shur EA Rail damage. - M .: Intex, 2012 .-- 192 p.

4. Non-destructive testing: Reference: In 8 t. / Under the total. ed. V.V. Klyueva. T. 4: In 3 book. Prince 1. V.A. Anisimov, B.I. Katorgin, A.N. Kutsenko et al. Acoustic strain gauge. Prince 2. G.S. Shelikhov. Magnetic particle inspection method. Prince 3. M.V. Owls. Capillary control. - 2nd ed., Rev. - M.: Mechanical Engineering, 2006. - 736 p.: Ill.

5. Non-destructive testing: Reference: In 8 t. / Under the total. ed. V.V. Klyueva. T. 6: In 3 book. Prince 1. V.V. Klyuev, V.F. Muzhitsky, E.S. Gorkunov, V.E. Shcherbinin. Magnetic control methods. Prince 2. V.N. Filinov, A.A. Ketkovich, M.V. Owls. Optical control. Prince 3. V.I. Matveev. Radio wave control. - 2nd ed., Rev. - M.: Mechanical Engineering, 2006. - 848 p.: Ill.

6. Pat. No. 2441227, Russian Federation, RU 2441227 C1, IPC G01N 27/72 (2006.1). The method of magnetic inspection of products in tension. / Stepanov A.P., Milovanov A.I., Stepanov M.A. Applicant and patent holder Irkut. state unt-t paths communicated. - No. 2010121417/28, declared 05/26/2010, publ. 01/27/2012. Bull. Number 3. - 3 p.

7. Pat. No. 2452943. Russian Federation, RU 2452943 C1, IPC G01N 27/82 (2006.1). A method for detecting bending stresses. / Stepanov A.P., Stepanov M.A., Milovanov A.I., Salomatov V.N. Applicant and patent holder Irkut. state unt-t paths communicated. - No. 2010142042/28, declared 10/13/2010, publ. 06/10/2012. Bull. No. 16. - 5 sec.

8. Pat. No. 2455634. Russian Federation, RU 2455634 C1, IPC G01N 27/80 (2006.1). A method for evaluating the safety factor of products during operation. / Stepanov A.P., Stepanov M.A., Milovanov A.I., Milovanova E.A., Salomatov V.N. Applicant and patent holder Irkut. state unt-t paths communicated. - No. 2010145975/28, declared 11/10/2010, publ. 07/10/2012. Bull. No. 19. - 5 sec.

9. Physical encyclopedia, http://allphvsics.ru.

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Claims (1)

A method for evaluating bending stresses in structural members made of a homogeneous ferromagnetic material and having a symmetrical cross-sectional shape during its operation, characterized in that in the controlled area of the specimen (analog) of the element (or in the active element) in the absence of external bending force and when applied external bending force (within the elastic properties of the element) magnetization is carried out each time, in order to create a symmetric magnetic field relative to the axis (axes) of symmetry of the geometry eskoy shape of the cross section of the element; the magnitude of the magnetic field induction is measured at characteristic points at the boundaries of the cross-sections of the element symmetrical to each other with respect to the axis (axes) of symmetry of the sections of the element; the average difference between the absolute values of the magnetic induction at characteristic points in the controlled area is determined; then, according to the experimental dependence of the bending force (or average tension in the material) on the average difference of the absolute values of the magnetic induction at the characteristic points on the controlled area of the sample (analog) of the element (or on the active element) is an analytical dependence; a symmetric magnetic field is created in the controlled portion of the structural element in working condition with respect to the geometric shape of the element’s cross section, the magnitude of the magnetic field induction is measured at the characteristic points of the cross sections, the average difference in the absolute values of the magnetic induction at the same characteristic points is determined and, from the previously obtained analytical dependence, is the average estimated value of the tension in the material on the controlled area of the element of the current structure.

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