Advances in Materials Science and Engineering

Volume 2015, Article ID 457384, 8 pages

http://dx.doi.org/10.1155/2015/457384

## Properties of GH4169 Superalloy Characterized by Nonlinear Ultrasonic Waves

^{1}School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China^{2}College of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China

Received 26 December 2014; Revised 28 January 2015; Accepted 28 January 2015

Academic Editor: Jainagesh A. Sekhar

Copyright © 2015 Hongjuan Yan et al. 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 nonlinear wave motion equation is solved by the perturbation method. The nonlinear ultrasonic coefficients *β* and *δ* are related to the fundamental and harmonic amplitudes. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing and bending fatigue testing of GH4169 superalloy. The results show that the curves of nonlinear ultrasonic parameters as a function of tensile stress or fatigue life are approximately saddle. There are two stages in relationship curves of relative nonlinear coefficients *β*′ and *δ*′ versus stress and fatigue life. The relative nonlinear coefficients *β*′ and *δ*′ increase with tensile stress when tensile stress is lower than 65.8% of the yield strength, and they decrease with tensile stress when tensile stress is higher than 65.8% of the yield strength. The nonlinear coefficients have the extreme values at 53.3% of fatigue life. For the second order relative nonlinear coefficient *β*′, there is good agreement between the experimental data and the comprehensive model. For the third order relative nonlinear coefficient *δ*′, however, the experiment data does not accord with the theoretical model.

#### 1. Introduction

GH4169 superalloy has good integrate performance in 253~400°C. It is manufactured as complex components and widely used in aerospace, nuclear energy, petroleum industry, and extrusion dies. Under the tensile loading and the cyclic loading, the metal structural components gradually occur as plastic deformation and induce the damages. They induce the components to crack or fracture.

Fatigue is one of damage mechanisms of components. According to statistics, more than 90% of the parts failures result from fatigue damages. The fatigue life of structural components can be divided into three stages as follows: early dislocation generation and lattice deformation, microcrack formation, and fracture failure. For structural components, the first and second stages are 80%~90% in fatigue life. Therefore, the detection of early fatigue damage is critical to evaluation of component life [1–3]. The ultrasonic method is believed to be the most promising nondestructive testing technique compared with other destructive and nondestructive testing. Many researches show that the linear ultrasonic parameters such as ultrasonic velocity and attenuation are effective in detection and evaluation in second stage and third stage of fatigue life [4–6]. But the ultrasonic linear parameters are not sensitive to nonlinear behavior and early fatigue state in metal components [5–8]. Therefore it is a focus issue that the nonlinear ultrasonic parameters evaluate the early fatigue state or stress in metal components and predict the fatigue life.

In 1755, Euler proposed the concept of nonlinear acoustic. Researchers such as Lagrange (1760) [9], Stokes (1848) [10], and Rayleigh (1910) [11] studied the theory of nonlinear acoustic [9]. In the 1960s, researchers began to study the phenomenon of nonlinear acoustic in solid [12]. In 1963, Hikata et al. observed that the harmonic waves appeared in aluminum. And Breazeale et al. detected third order elastic constants of single crystal aluminum and copper in 1963 and 1968 [13, 14]. Buck et al. studied the acoustic harmonic generation at unbonded interfaces and fatigue cracks [15]. Nagy used nonlinear ultrasonic waves to assess fatigue damage in plastics [16]. Kim et al. used nonlinear ultrasonic waves to characterize fatigue damage in a nickel-base superalloy [17]. Metya et al. studied the generation of second harmonic wave in grade maraging steel [18]. Shui et al. used nonlinear longitudinal waves to evaluate plastic damage in metal materials [19]. Ruiz et al. used nonlinear acoustic parameter to assess early detection of thermal degradation of mechanical properties in 2205 duplex stainless steel [20]. Punnose et al. used nonlinear ultrasonic waves to evaluate fatigue in austenitic stainless steel in low cycle regime [21]. The results show that the second order nonlinear coefficient is related to the fatigue life or fatigue damage of materials. But few researchers studied the relationship of the third order nonlinear coefficient versus stress or fatigue life.

The one-dimensional nonlinear ultrasonic wave motion equation is solved by perturbation method. During tensile testing and bending fatigue testing, the relationships of nonlinear ultrasonic parameters and tensile stress or fatigue cycles are studied. The nonlinear ultrasonic testing system is used to detect the received signal. RETIC advanced measurement system generates a tone burst signal and receives the signal propagated in GH4169 superalloy plate. The received signals are transformed by FFT. The fundamental and harmonic amplitudes are obtained, and the parameters are calculated. The relationship curves of nonlinear parameters as the functions of tensile stress or fatigue life are obtained to detect or predict stress or fatigue life of GH4169 superalloy.

#### 2. Nonlinear Acoustic Properties

##### 2.1. Nonlinear Acoustic Wave Theory

When one-dimensional longitudinal wave propagates in nonlinear medium, the wave motion equation is as follows [22]: where is the displacement along direction, is the density of medium, and is the positive stress along direction. The perturbation method is used to solve (1). The solution is where is the circular frequency and is the wave number. If the amplitude of and are, respectively, assumed as and , they can be obtained: With the fixed frequency and the fixed propagation distance, the nonlinear coefficients and are, respectively, proportional to and . In the measurements, the relative nonlinear parameters can be defined as The and are the functions of propagation distance . The relationship of and is a good linearity for propagation distance in the far field. In current experiments, is measured over [23]. And in the optimized distance, and are measured over stress and fatigue life.

##### 2.2. Dislocation Model for Second Order Nonlinear Coefficient

Nonlinearity of solid material mainly comes from two aspects: nonharmonic property of particles interaction force of the material and internal microdefects of the material, such as crystal dislocation, lattice slip, and microcrack. Many researches show that the ultrasonic nonlinearity induced by dislocations is the main factor leading to the variation of ultrasonic nonlinearity. Cantrell et al. promoted two dislocation models [15, 24, 25].

Hikata et al. [12], Buck et al. [15], and Cantrell [24] proposed the dislocation monopole model (shown in Figure 1). The generation of the second harmonic wave depends on the motion of the dislocation between the dislocation pinning points. The nonlinear acoustic coefficient is written as [24] where is the dislocation density, is Burgers vector, and are, respectively, the second or third order elastic coefficients, is shear modulus, is the transform coefficient from shear strain to principle strain, and is the transform coefficient from shear stress to principle stress.