Ultrasonic Wave Sources

Janez Rus, winter semester 2016/17

The term ultrasonic wave sources describes objects or methods that are used to generate ultrasonic waves. These ultrasonic waves can be used for the nondestructive specimen investigation or for the sensor calibration

Nondestructive testing techniques use signals recorded from piezoelectric sensors in order to detect the ultrasonic waves. That the information about the material or structural can be obtained, all the disturbance effects have to be eliminated from the captured signal. Those disturbance effects are a consequence of the filter effects of the each element of the measuring chain. To eliminate those effects the transfer function of the single chain element needs to be known. The process of determining the transfer function of the sensor is called the sensor calibration. The sensor is generally not equally sensitive for all the input frequencies. At the sensor calibration this frequency-dependent sensitivity of the sensor is investigated. With the calibrated sensor the time history of the absolute amplitude of the recorded waves can be sensed and compared with the measures obtained with different sensors.

On the Fig. 1 the signal transformation is schematically represented. For the sensor calibration the output $//<![CDATA[ \begin{array}{l}s(t)\end{array} //]]>$ as well as the input signal $//<![CDATA[ \begin{array}{l}u(x,t)\end{array} //]]>$ of the sensor needs to be determined. Assuming that the transfer functions of the measuring chain elements after the sensor are known, the output signal $//<![CDATA[ \begin{array}{l}s(t)\end{array} //]]>$ is evident. More problematical is to determine the input signal $//<![CDATA[ \begin{array}{l}u(x,t)\end{array} //]]>$. Firstly the ultrasonic wave source properties and therefore the force time history $//<![CDATA[ \begin{array}{l}f(x,t)\end{array} //]]>$ needs to be specified. It can be either calculated from the relevant theory (e.g. Hertz contact theory) or measured with the reference sensor that needs to be independently calibrated. Secondly the wave propagation inside of the material needs to be calculated with a use of the Green's function $//<![CDATA[ \begin{array}{l}g(x’,x,t)\end{array} //]]>$. With the Green’s function we can from the known ultrasonic wave source location and its force history $//<![CDATA[ \begin{array}{l}f(x’,t)\end{array} //]]>$ calculate the displacement history $//<![CDATA[ \begin{array}{l}u(x’,t)\end{array} //]]>$ at the location of the sensor $//<![CDATA[ \begin{array}{l}x\end{array} //]]>$. We can consider Green's function $//<![CDATA[ \begin{array}{l}g(x’,x,t)\end{array} //]]>$ as a transfer function of the specimen.

For the sensor calibration the Green’s function has to be calculated. For the half pace of infinite whole space it can be determined analytically, while for other specimen shapes the numerical evaluation is necessary. Each of those approaches can deliver us satisfactory results. Bigger problem at the sensor calibration is to determine the input parameters for Green’s function i.e. force history $//<![CDATA[ \begin{array}{l}f(x’,t)\end{array} //]]>$ induced by the source. This is the motivation for the ultrasonic source study. Ultrasonic waves can be generated in many different ways according to the spectral bandwidth that are required for the certain application. Generally shorter pulses derive wider bandwidth, since they have lower impulse amplitude and hence they are suitable just for sensitive-enough ultrasonic-wave sensors. The ultrasonic-wave sources can induce an approximation of two different high-bandwidth functions: the impulse and the step function. The impulse-generative sources are for example a small ball impact, electric sparks, expending plasmas, and laser pulse ^[1]. Laser pulse sources we can be subdivided into ablation-based and light-pressure based. The step-generative sources are pencil lead break (Hsu-Nielsen source), capillary fracture and fracture of small grains ^[2]. The common ultrasonic-wave sources are also piezoelectric actuators. They are practically often the same devices that are also used for the ultrasonic wave detection with a slight modification. Because of the unknown input parameters, that are a consequence of an imperfect coupling between the piezoelectric actuator and the probe material, the piezoelectric actuators are not appropriate for sensor calibration.

Ball Drop

At ball impact calibration method the ball impact is the source of the ultrasonic waves ^[2]. If the sensor needs to be calibrated also at high frequencies the ball's radius needs to be appropriately small – typically around 1 mm. The ball is dropped from the known height. The advantage of the ball drop source is that the force history can be theoretically implemented via Hertz’s theory as follows ^[3], ^[4]:

$//<![CDATA[ \begin{array}{lcl} f(t)=f_{\text{max}}\sin{(\pi t/t_\text{c})}^{2/3} & 0\le|t|\le t_\text{c} \\ f(t)=0 & \text{otherwise} \end{array} //]]>$

The contact time $//<![CDATA[ \begin{array}{l}t_\text{c}\end{array} //]]>$ can be (for the transparent material) measured ^[5] or calculated as

$//<![CDATA[ \begin{array}{l}t_\text{c}=5.0824 \left ( \frac{\rho_1}{E^*} \right )^{2/5}R_1v_0^{-1/5}\end{array} //]]>$.

It depends on the ball radius $//<![CDATA[ \begin{array}{l}R_1\end{array} //]]>$, its mass density $//<![CDATA[ \begin{array}{l}\rho_1\end{array} //]]>$, the approach velocity $//<![CDATA[ \begin{array}{l}v\end{array} //]]>$ and the material constant $//<![CDATA[ \begin{array}{l}1/E^*=(1-\mu_1^2)/E_1+(1-\mu_2^2)/E_2\end{array} //]]>$, with the Young’s moduli $//<![CDATA[ \begin{array}{l}E_1\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}E_2\end{array} //]]>$ (glass cube) and Poisson’s ratios $//<![CDATA[ \begin{array}{l}\mu_1\end{array} //]]>$ (ball), $//<![CDATA[ \begin{array}{l}\mu_2\end{array} //]]>$ (glass cube). The maximal force is expressed as

$//<![CDATA[ \begin{array}{l}F_{\text{max}} =0.61R_1^2\text{ }\rho_1^{3/5}v_0^{6/5}E^{*2/5}\end{array} //]]>$.

For a ball drop ultrasonic wave source the force history is known since it can be calculated from material parameters, ball radius and drop height. Neglecting the air drag the approach velocity can be expressed as: $//<![CDATA[ \begin{array}{l}v_0=\sqrt{2gh}\end{array} //]]>$.

On the Fig. 2 four time instances of the ball drop ultrasonic wave source are shown. The ball is dropped from the height $//<![CDATA[ \begin{array}{l}h\end{array} //]]>$ and has the radius $//<![CDATA[ \begin{array}{l}R_1\end{array} //]]>$ (a). The ball approaches the specimen surface (b) and reaches the speed at the beginning of the contact (c). The ball elastically (often also plastically) deform the specimen. After the impact pressure, shear and Rayleigh ultrasonic waves are released (d). The sensors that we calibrate can be positioned on the same side of the specimen or (by plates) also on the other side - practically often epicentral directly beneath the surface ^[2].

Hsu-Nielson Source – Pencil Lead Brake

Pencil lead brake (named also Hsu-Nielson source by its inventor ^[6]) is a simple and common-used test source of ultrasonic waves. It is standardized under ASTM E976. At this method a pencil lead (usually 2H, 0.5 mm diameter – 0.3 mm alternatively) is broken against the specimen. To ensure the repeatable lead break conditions, the guide ring needs to be firstly leaned on the specimen surface (see Fig. 3). After it the angel between the pencil and the specimen surface is increased (red arrow on Fig. 3) till the critical angle at which the pencil lean brakes. Consequently the force, with which the lean presses on the specimen surface, falls speedily. Compared to the ball drop with this method we try to approach the step change of the force.

The advantages of Hsu-Nielson source are: short step force change, high frequency excitation and good repeatability. The disadvantage is a small excited energy of the source. Alternatively to the Hsu-Nielson source as a step generative source also capillary fracture can be used ^[2]. A short length capillary is laid on its side on the specimen. The capillary is loaded over the force sensor that is placed on the capillary. Hence, we get information about the load force.

Laser Pulse – Light Pressure Source

The ultrasonic wave for sensor calibration can be also induced by a laser pulse ^[1]. The advantages of this source compared to others are a very short temporal distribution and a known spatial intensity profile, which produces a well-determined force impulse. Because the source is laser pulse-based, ultrasonic wave induction can be repeated consistently and rapidly. In ^[1] the laser pulse has energy of 200 mJ and (half-maximum) duration of 17 ns. The specimen was coated with a highly reflective layer with reflectivity over 99.8 % at relevant wavelength. The small amount of light that does pass through the plate is absorbed only insignificantly. The ultrasonic waves are therefore only light-pressure-induced and not thermoelastic or ablation-induced. The light-pressure force impulse can be calculated as $//<![CDATA[ \begin{array}{l}J=2E_\text{L}/c_0\end{array} //]]>$, where the $//<![CDATA[ \begin{array}{l}E_\text{L}\end{array} //]]>$ is a the impulse energy and $//<![CDATA[ \begin{array}{l}c_0\end{array} //]]>$ light speed in vacuum.

Literature

1. Laloš, J. et al: High-Frequency Calibration of Piezoelectric Displacement Sensors Using Elastic Waves Induced by Light Pressure. 2015.
2. McLaskey, G. C. et al: Acoustic Emission Sensor Calibration for Absolute Source Measurements. 2012.
3. Goldsmith, W.: Impact: The Theory and Physical Behaviour of Colliding Solids. 1960.
4. Reed, J.: Energy losses due to elastic wave propagation during an elastic impact. 1985.
5. Požar, T. et al: Optical Detection of Impact Contact Times with a Beam Deflection Probe. 2017.
6. Hsu, N.N. et al: Characterization and calibration of acoustic emission sensors. 1981.