The three-dimensional elastic constants of materials can be measured using the

ultrasonic Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies f ...

immersion method. This was pioneered by Zimmer and Cost from the National Physical Laboratory in the 1960s. It has mainly been used for

polymer A polymer (; Greek ''poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and ...

composite materials. Knowledge of the elastic constants can be used to feed back into models of the material's behaviour or that of the composite manufacturing process used.

Immersion technique

The ultrasonic immersion method makes use of a temperature stabilised water bath which has a pair of ultrasonic

transducers A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another. Transducers are often employed at the boundaries of automation, measurement, and contr ...

located on either side of the sample which can be rotated using a

stepper motor A stepper motor, also known as step motor or stepping motor, is a brushless DC electric motor that divides a full rotation into a number of equal steps. The motor's position can be commanded to move and hold at one of these steps without any po ...

. The time of flight of an ultrasonic

pulse In medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the ...

that has been transmitted through the material is measured using an electronic timer that determines the start of the transmitted pulse and the start of the received pulse using threshold detection. This timer is typically accurate to

microsecond A microsecond is a unit of time in the International System of Units (SI) equal to one millionth (0.000001 or 10−6 or ) of a second. Its symbol is μs, sometimes simplified to us when Unicode is not available. A microsecond is equal to 100 ...

or better resolution. By rotating the sample, time of flight measurements can be obtained a range of angles of incidence, typically up to 40 degrees. From the time of flight, the phase velocity can be determined as a function of the angle of incidence of the ultrasonic pulse. Using Christoffel's equations, the measured data can be fitted using a least squares numeric method to determine six of the nine elastic constants. By slicing the composite material and re-arranging the slices, the method can be re-applied to obtain the remaining three constants not found from the original measurements.

References

* Zimmer JE, Cost JR. "Determination of elastic constants of a uni- directional fiber composite using ultrasonic velocity measurements", in Journal of the Acoustical Society of America 47, 795–803 (1970) * Enderby MD, Clarke AR, Patel M, Ogden P, Johnson AA, "An automated ultrasonic immersion technique for the determination of three-dimensional elastic constants of polymer composites", in Ultrasonics, 1998, vol. 36, no 1–5 (8 ref.), pp. 245–249. * Goldmann T, Seiner H, Landa M, "Experimental determination of elastic coefficients of dry bovine bone", in Bulletin of Applied Mechanics 4, 262–275 (2005)

Immersion technique

References

Further reading