DETERMINING THE LOCATION OF A DEFECT IN THE HIGH-SPEED METHOD OF RADIATION FLAW DETECTION USING SCINTILLATION DETECTORS

V. A. VOROB’EV, Yu. D. GAVKALOV

(Presented by the Section of Physical and Technical Sciences of the Second Scientific Session of Higher Educational Institutions of Western Siberia.)

At the present time, among nondestructive methods for inspecting industrial large-size products, the role of generators of high-energy electromagnetic radiation—betatrons—is increasing. The developed radiation-flaw-detection installations provide automation of inspection and high detectability of defects: cracks, cavities, etc. [1].

However, these installations do not make it possible to determine the shape and depth of occurrence of defects. The radiographic methods used for this purpose are laborious and do not ensure continuous-flow inspection.

In the present article a method is proposed for determining the depth of occurrence of a defect with the aid of a scintillation flaw detector, which increases the value of the method of flaw detection by the bremsstrahlung radiation of a betatron.

The basic scheme for transilluminating a part by the bremsstrahlung radiation of a betatron is shown in Fig. 1.

Fig. 1. Basic scheme for transilluminating a part in radiation flaw detection:
1—betatron, 2—working beam, 3—part, 4—variable collimator, 5—scintillation detector, 6—detector shielding, 7—recording system.

The intensity of radiation that has passed through a layer of material of thickness \(t\) is equal to

\[ I(t)=B(t)I^{0}(t), \tag{1} \]

where \(I^{0}(t)\) is the intensity of the primary radiation (narrow beam) after a layer of thickness \(t\),
\(B(t)\) is a coefficient taking into account the intensity of radiation scattered by the part after a layer of thickness \(t\).

A defect in the part under investigation may be regarded as a change in its thickness by an amount \(dt\).

If the defect is located on the surface of the specimen in front of the detector, i.e., has coordinate \(x=t\), then the relative change in the intensity of the radiation incident on the detector, for a narrow beam and for radiation with allowance for scattered radiation (wide beam), is determined by the differential attenuation equations:

\[ \left[\frac{dI(t)}{I(t)}\right]_{y}=-\mu(t)_{y}\,dt, \tag{2} \]

\[ \left[\frac{dI(t)}{I(t)}\right]_{\mathrm{sh}}=-\mu(t)_{\mathrm{sh}}\,dt . \tag{3} \]

where \(\mu(t)_{\mathrm{u}}\) and \(\mu(t)_{\mathrm{sh}}\) are the effective attenuation coefficients of the narrow and wide beams, respectively.

From equations (2) and (3), denoting

\[ \left[\frac{dI}{I}\right]_{\mathrm{u}}=\varepsilon_{\mathrm{u}}, \qquad \left[\frac{dI}{I}\right]_{\mathrm{sh}}=\varepsilon_{\mathrm{sh}}, \]

we have

\[ \varepsilon_{\mathrm{sh}}=\frac{\mu(t)_{\mathrm{sh}}}{\mu(t)_{\mathrm{u}}}\,\varepsilon_{\mathrm{u}} . \tag{4} \]

In the case of a defect with coordinate \(x=0\), the change in the intensity of the wide beam is equal to

\[ dI(t)_{\mathrm{sh}}=-I^0\mu_{\mathrm{sh}}\,dt, \tag{5} \]

with \(\mu_{\mathrm{sh}}=\mu_{\mathrm{u}}\).

According to equations (1) and (2), we have

\[ \varepsilon_{\mathrm{sh}}=\frac{\varepsilon_{\mathrm{u}}}{B(t)} . \tag{6} \]

It has been calculated, for example, for steel and copper under bremsstrahlung from a betatron with maximum energy up to \(30\ \mathrm{MeV}\), that the coefficients \(\mu(t)_{\mathrm{sh}}>\mu(t)_{\mathrm{u}}\) and \(B(t)>1\) for \(t>0\). Consequently, \(\varepsilon_{\mathrm{sh}}>\varepsilon_{\mathrm{u}}\) when the defect is located on the surface of the part in front of the detector \((x=t)\), and \(\varepsilon_{\mathrm{sh}}<\varepsilon_{\mathrm{u}}\) when the defect is located on the surface of the part at the point where the radiation beam is incident \((x=0)\). It is this difference that is proposed for use in determining the coordinate of the defect.

Denoting

\[ \frac{\mu_{\mathrm{u}}}{\mu_{\mathrm{sh}}}=B^{c(t)}, \]

one can obtain, from (4) and (6), an equation for any value of \(x\) in the interval \(0\leq x\leq t\):

\[ \varepsilon_{\mathrm{sh}}=\varepsilon_{\mathrm{u}}B^{\frac{x}{t}(1+c)-1}, \tag{7} \]

or

\[ x=\frac{t\left(\dfrac{\ln|\varepsilon_{\mathrm{sh}}/\varepsilon_{\mathrm{u}}|}{\ln B}+1\right)}{1+c}. \tag{8} \]

In expression (8), the quantities \(\varepsilon_{\mathrm{u}}\) and \(\varepsilon_{\mathrm{sh}}\) are measured with the narrow and wide diameter of the collimator aperture in front of the detector. The coefficients \(c\) and \(B\) can be determined theoretically. However, theoretical calculations are complicated, and therefore, for practical use of the proposed method, equation (8) may be represented in the form

\[ x=t\cdot F\left(\frac{\varepsilon_{\mathrm{sh}}}{\varepsilon_{\mathrm{u}}}\right), \tag{9} \]

where the function \(F\) is determined experimentally by simulating a defect at various depths in the part.

The function \(F\) is monotonic, and for its graphical representation it is sufficient to determine the values at several points.

The proposed method for determining the depth at which a defect lies is most effective in continuous inspection of large industrial products of simple shape.

REFERENCES

1. Nondestructive Methods for Inspecting Materials and Products. Collection of articles edited by S. T. Nazarov, Moscow, 1964.