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BACKGROUND OF STRESSED STATE MAGNETIC INSPECTION
OF STEEL PARTS BY METAL STRESS INDICATORS
OF STEEL PARTS BY METAL STRESS INDICATORS
An operation of
IN01m и IN02 the metal stress indicators is based on the dependence of magnetic parameter of steel object to be inspected – the residual magnetization of metal
J_{r} on the mechanical strain σ.
When steel object inspected is magnetized locally by constant magnetic field to technically saturated state (figure 1) and after the magnetic field action was switched off the metal would remain in the magnetized state, which is characterized quantitatively by residual magnetization J_{r}.
Fig.1. A magnetization of steel part metal J under local action of constant magnetic field
H
O_{13} – is initial magnetization of metal in the Earth magnetic field;
H_{S}
– is strength of the magnetic field required to magnetize the metal to highest possible value J_{S},
called as magnetization of the metal saturated;
J_{r} – is residual magnetization of metal on the local area of steel part after the magnetic field action was switched off;
H_{C}
– is coercive force of metal
Recently in the academic communities the discussions about the behavior of residual magnetization dependence on mechanical strain of metal are inflames: when steel specimens caused to the tensile testing the linearity of one was observed experimentally in one case, however reverse dependence was observed in second. When the metal is deformed simultaneously on two or more directions the residual magnetization is depended on mechanical strain applied not uniquely.
It is obvious, that the understanding of experimental results obtained is fundamentally impossible without the adequate physical model. Lets build this physical model needed supposing the two conditions which cause the residual magnetization of metal to behave as two different physical parameters.
Condition I. When an elementary volume of the metal already loaded constantly is magnetized, the following ratio would be hold between its general magnetic parameters:
_{}, (1)
where are
χ –
is magnetic susceptibility of metal, λ_{S} – is magnetostriction of the saturated metal, J_{S} – is magnetization of the metal saturated, σ – is mechanical strain, μ_{0 }– is the magnetic constant.
For the right triangle OJ_{r}H_{C} on the figure 1 the geometry equation _{}is true. Insertion of one into the formula (1) will result to the following expression:
_{}. (2)
The formula (2) obtained includes the two parameters are depending on mechanical strain of metal: J_{r}
and Н_{С}. In order to exclude last one of recent form the formula (2) we can use the symbolic relation between coercive force and residual magnetization of the metal is known:
_{}, (3)
where are
J_{r}_{0} – is residual magnetization of metal without another mechanical strain (idealσ = 0). Inserting expression (3) into (2) and keeping in the mind that for constructional steels is usually J_{r} <<
J_{S} (see to the figure 1), obtain the dependence of residual magnetization on the mechanical strain of the metal, caused to constant loading:
_{}. (4)
The residual magnetic field strength of metal, measured by metal stress indicators, is directly proportional to residual magnetization, herewith the value of one is also depends on the shape of surface inspected: H_{r}(s) = J_{r}(s)·TF(x, y, z).
A topographic factor TF(x, y, z), describing the surface of metal inspected is always remain constant, so the H_{r}(s) dependence is looks as following:
_{}. (5)
In general the σ parameter would be considered as an effective mechanical strain of metal, which is determined by theory of the durability and strength of materials through components of principal strains and Poisson ratios:
_{}. (6)
In the case of linear (oneaxial) stressed state of metal (σ_{y} = 0 σ_{z} = 0) an effective
strain is equal to the one component of principal strains:_{}.
On the figure 2 an experimental dependences of residual magnetic field strength of metal presented are obtained in linear (oneaxial) loading of steel specimens made from constructional steel, widely used in the industry, which are in agreement with symbolic expression (5).
Fig.2. Dependences of residual magnetic field strength of steel part already under load on the mechanical strain of metal
1 – St372 specimen (DIN), 2 – RSt372, 3 – 9MnSi5, 4 – St523G
In the case of plane (twoaxial) stressed state of metal σ_{z} = 0 an effective
strain is looked as _{}, so the expression (5) will be reduced to following:
_{}. (7)
An expression (7) obtained could explain that the behavior of residual magnetic field dependence H_{r} on the components of principal strains σ_{x} и σ_{y} is determined by relation between their signs:
– If the components of principal strains σ_{x} and σ_{y}
иare in opposite signs then the sign before Poisson ratio in the formula (7) would be positive, so the dependence H_{r}(σ_{x}, σ_{y}) would have unique, however nonlinear behavior (see the figure 3,
σ_{x}_{ }/σ_{y} < 0);
– If the components of principal strains σ_{x} and σ_{y}
are in one sign then the sign before Poisson ratio in the formula (7) would be negative, so the dependence H_{r}(σ_{x}, σ_{y}) would have not unique (see the figure 3, σ_{x} /σ_{y} > 0).
σ_{x}_{ }/σ_{y} < 0 
σ_{x} /σ_{y} > 0 
Fig.3. The influence of relation between signs of
σ_{x} and σ_{y} the plane stressed state components of metal to residual magnetic field H_{r} dependence on ones
1 – σ_{y} = 0 MPa, 2 – 40 MPa, 3 – 80 MPa, 4 – 120 MPa
Condition II. When an elementary volume of the metal preliminarily magnetized to technical saturation is caused to loading, the demagnetization of one would occur due to magnetoelastic effect. So the residual magnetic field strength of metal while the metal is in elastic state would be changing on reverse dependence:
_{}, (8)
where is
σ in general would be considered as an effective strain of metal (6), which is in the case of linear (oneaxial) stressed state of metal (_{y} = 0 _{z} = 0) equal to the one component of principal strains: _{}.
On the figure 4 the residual magnetic field strength of metal changing under linear (oneaxial) loading of preliminarily magnetized steel specimens, made from constructional steel, widely used in the industry, which are in agreement with symbolic expression (8).
In the case of plane (twoaxial) stressed state of metal _{z} = 0 an effective
strain is looked as _{}, so the expression (8) will be reduced to following:
_{}. (9)
Fig.4. A behavior of the residual magnetic field strength when preliminarily magnetized steel part is loaded by constant monotonically increased force
1 – St372 specimen (DIN), 2 – RSt372, 3 – 9MnSi5, 4 – St523G
An expression (9) obtained could explain that the behavior of residual magnetic field dependence H_{r} of the metal preliminarily magnetized on the components of principal strains σ_{x} and σ_{y} is determined by relation between their signs (see to the figure 5).
σ_{x}_{ }/σ_{y} < 0
σ_{x} /σ_{y} > 0

Fig.5. The influence of relation between signs of σ_{x} and σ_{y} the plane stressed state components of metal to behavior of residual magnetic field H_{r} change in twoaxial loading of metal preliminarily magnetized
1 – σ_{y} = 0 MPa, 2 – 40 MPa, 3 – 80 MPa, 4 – 120 MPa
So, creating the different initial conditions in the practice we can to observe how the residual magnetic field strength of metal H_{r} measured by the metal stress indicators IN01m and IN02 behaves as two different physical parameters:
1. When steel part already loaded constantly is magnetized, the residual magnetic field strength H_{r} would depend linearly on effective value of mechanical strain of the metal σ_{eq}; so this dependence on the components of principal strains σ_{x} and σ_{y} is determined by relation between their signs.
2. When steel part preliminarily magnetized to technical saturation is caused to loading, the residual magnetic field strength H_{r} while the metal is in elastic state would be changing on reverse dependence.
Fig.6. The strain gage bench of «Spector» SciTech LLC for experimental investigation of twoaxial strain state of metal
1 – the cruciform steel specimen investigated, 2 – power screws, 3 – strain gages assemblies, 4 – conditioning and measuring unit
Recently the specialists of «Spector» SciTech LLC are carrying out the experimental investigation to approve the theoretical dependences of residual magnetic field strength H_{r} on the components of principal strains σ_{x} и σ_{y} obtained in the strain gage bench shown on the figure 6 which is created especially for this purpose.