Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 6762076, 7 pages

http://dx.doi.org/10.1155/2016/6762076

## The Elastic Constants Measurement of Metal Alloy by Using Ultrasonic Nondestructive Method at Different Temperature

School of Mechatronic Engineering, China University of Mining & Technology, 1 Daxue Road, Xuzhou, Jiangsu 221116, China

Received 8 October 2015; Accepted 13 December 2015

Academic Editor: Jose Merodio

Copyright © 2016 Eryi Hu and Wenjin Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The ultrasonic nondestructive method is introduced into the elastic constants measurement of metal material. The extraction principle of Poisson’s ratio, elastic modulus, and shear modulus is deduced from the ultrasonic propagating equations with two kinds of vibration model of the elastic medium named ultrasonic longitudinal wave and transverse wave, respectively. The ultrasonic propagating velocity is measured by using the digital correlation technique between the ultrasonic original signal and the echo signal from the bottom surface, and then the elastic constants of the metal material are calculated. The feasibility of the correlation algorithm is verified by a simulation procedure. Finally, in order to obtain the stability of the elastic properties of different metal materials in a variable engineering application environment, the elastic constants of two kinds of metal materials in different temperature environment are measured by the proposed ultrasonic method.

#### 1. Introduction

The elastic constants are significant properties of some new metal alloy materials. Furthermore, the stability of the elastic properties at different temperature will affect the engineering application of the material in a terrible environment condition, such as the aerospace spacecraft design and deep ocean resources development. For instance, the basic vibration frequency of some special construction will change corresponding with the environment temperature. Thus, the metal material with a much more steady elastic characteristic is more popular in the engineering design. On the other hand, sometimes the engineers are interested in the elastic constants of a new metal alloy. Particularly in the reverse engineering area, the material property coefficients must be measured without the destruction of the rare sample components. Thus, the nondestructive evaluation approach is very useful in these material characteristic researches.

The ultrasonic wave method can be introduced into the elastic constants measurement of the metal material. Nowadays, many researchers are using ultrasonic nondestructive testing to evaluate the mechanical characteristics on metallic materials, mainly, due to its accuracy, besides being fast and very reliable. As we know, the ultrasonic detection methods are very popular in the medical inspection of the human body for a long time. Several researchers have focused on Young’s modulus of the bone material or carotid artery measurement by using the ultrasonic technique [1–3]. And then this method is also used in the elastic modulus and other geometrical coefficients detection of other materials, such as alumina ceramics [4]. The ultrasonic method is also introduced into the civil engineering area to obtain the rock’s material properties [5–8]. Tavares et al. [9–12] proposed a nondestructive determination method of the elastic properties in shape memory alloy, stainless steel, and plain carbon steel by using ultrasonic measurements. From the previous useful research works, it is found that the detection of the propagating velocity of the ultrasonic wave is the key point in the elastic constants measurement of these different materials [13]. The digital correlation and Fourier transform methods can both be used in the ultrasonic wave flight time extraction; however the precision should be increased by some novel algorithms [14–17].

In this paper, we focus on the elastic constant measurement of metal alloy materials especially in a temperature changing environment. Poisson’s ratio, elastic modulus, and shear modulus will be measured by the ultrasonic wave propagating velocity detection. And then temperature stability of the elastic properties can be provided for the further engineering design application.

#### 2. Principle of the Ultrasonic Measurement Method

As we know, the ultrasonic wave is a kind of elastic waves propagating in the medium with higher frequency. Thus, when the elastic wave is propagating in the isotropic medium without the influence of the volume stress, the wave propagating equation can be expressed as follows: where is the volume strain and denotes the deformation of one point in the elastic medium. When the propagating elastic wave is an ultrasonic longitudinal wave, the deformation in the elastic medium can be defined as , , and . It is meant that the wave propagating equation can be simplified as follows:Thus, the propagating velocity of the ultrasonic longitudinal wave denoted as is expressed as

On the other hand, when the propagating elastic wave is an ultrasonic transverse wave, the deformation in the elastic medium can be defined as , , and . The wave propagating equation can be simplified similarly:Following the same process, the propagating velocity of the ultrasonic transverse wave denoted as is expressed asCombining (3) and (5), the elastic constants of the detected material can be deduced:where is the density of the material, is the ultrasonic longitudinal wave propagating velocity, is the ultrasonic transverse wave propagating velocity, is Poisson’s ratio, is the elastic modulus, and is the shear modulus. From (6), it is found that the elastic constants can be calculated after getting the elastic wave propagating velocities and the material density in a certain experimental environment temperature.

#### 3. Ultrasonic Experimental Measurement System

The schematic diagram of the ultrasonic measurement experimental system is illustrated in Figure 1. The experimental system is constructed by the ultrasonic pulse-receiver, ultrasonic wave transducer, digital oscilloscope, personal computer, detected specimen, and temperature control box. The ultrasonic pulse-receiver is used to excite the ultrasonic transducer and receives the signals reflected from the bottom surface of the detected metal specimen. The type of the ultrasonic pulse-receiver manufactured by Panametrics-NDT is Model 5072PR, and the bandwidth is 35 MHz which is sufficient for this experimental research project. And then, the digital oscilloscope is used for sampling ultrasonic waveform, and the digitized waveforms are stored in the memory of the personal computer. In this experiment, the InfiniiVision 4000X digital oscilloscope is manufactured by Agilent Technologies with 5 GHz maximum sample frequency, so that the single point sampling time period is 0.2 ns. The temperature control box called ZTH100UK(S) is manufactured by Shanghai Zundar. The experimental temperature is controlled by a computer automatically in the range of −70~150°C, and the temperature controlling precision is about ±0.5°C.