Nondestructive Testing Residual Stress Using Ultrasonic Critical Refracted Longitudinal Wave

Nondestructive Testing Residual Stress Using Ultrasonic Critical Refracted Longitudinal Wave

Available online at www.sciencedirect.com ScienceDirect Physics Procedia 70 (2015) 594 – 598 2015 International Congress on Ultrasonics, 2015 ICU Me...

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Available online at www.sciencedirect.com

ScienceDirect Physics Procedia 70 (2015) 594 – 598

2015 International Congress on Ultrasonics, 2015 ICU Metz

Nondestructive Testing Residual Stress Using Ultrasonic Critical Refracted Longitudinal Wave Chunguang Xu*, Wentao Song, Qinxue Pan, Huanxin Li, Shuai Liu Beijing Institute of Technology, 5th South Zhongguancun Street, Haidian District, 100081, Beijing, China

Abstract Residual stress has significant impacts on the performance of the mechanical components, especially on its strength, fatigue life and corrosion resistance and dimensional stability. Based on theory of acoustoelasticity, the testing principle of ultrasonic LCR wave method is analyzed. The testing system of residual stress is build. The method of calibration of stress coefficient is proposed in order to improve the detection precision. At last, through experiments and applications on residual stress testing of oil pipeline weld joint, vehicle’s torsion shaft, glass and ceramics, gear tooth root, and so on, the result show that it deserved to be studied deeply on application and popularization of ultrasonic LCR wave method. Keywords: Residual stress; Ultrasonic; Nondestructive testing

1. Introduction The engineering properties of materials and structural components, notably fatigue life, distortion, dimensional stability, corrosion resistance, and brittle fracture can be considerably influenced by residual stresses [1]. Such effects usually bring to considerable expenditure in repairs and restoration of parts, equipment, and structures. Accordingly, residual stresses analysis is a compulsory stage in the design of parts and structural elements and in the estimation of their reliability under real service conditions [2]. Residual stresses occur in many manufactured structures and components. Different methods have been developed to measure residual stress for different types of components in order to obtain reliable assessment. The different residual stresses measurement methods are classified to destructive, semi destructive and non-destructive techniques depends on their application and the availabilities of those techniques [3].

* Corresponding author. Tel.: +86-10-68914283; fax: +86-10-68912714. E-mail address: [email protected]

1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ICU 2015 doi:10.1016/j.phpro.2015.08.030

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Determination of the stress state, as well as its magnitude and its depth, which extends inside the material, has been traditionally done by diffraction techniques such as X-ray or synchrotron radiation [4,5]. More recently, a nondestructive method which shows promise for sub-surface stress measurement uses acoustic transducer as an ultrasonic strain gauge [6,7]. This paper based on theory of acoustoelasticity, the testing principle of ultrasonic LCR wave method is analyzed. Further, the testing system of residual stress is build. in order to improve the detection precision, the method of calibration of stress coefficient is proposed. At last, the experimental and applied study of ultrasonic LCR wave method is carried out. 2. Principle of residual stress testing method 2.1. The testing theory of acoustoelasticity Acoustoelasticity theory is one of the main bases of ultrasonic stress testing. Acoustoelasticity theory is based on the finite deformation of continuum mechanics to study the relationship between the elastic solid stress state and the macroscopic elastic wave velocity. Based on the four basic assumptions of acoustoelasticity, the elastic wave equation (acoustoelasticity equation) in stress medium under initial coordinates can be obtained [8]. wuK º w ª i « G IK t JL  CIJKL » wX J ¬ wX L ¼

Ui

w 2uI wt 2

(1)

Where G IK is Kronecker delta function, U i is the density of the solid in the loading condition, uI is the dynamic displacement, X J is the particle position vector, CIJKL is the equivalent stiffness, which depends on the material i is the Cauchy stress shown in the initial coordinates under the constant and the initial displacement field and t JL solid loading state. In the case of homogeneous deformation and the solid is isotropic, Eq. (1) can be analytically expressed. Therefore, the equation for the ultrasonic propagation velocity and stress in solid can established in Cartesian coordinates [9]. For the longitudinal wave which propagates along the stress direction:

U0V 2

O  2P 

V

ªO  P º 4O  10P  4m  O  2l » « 3O  2P ¬ P ¼

(2)

In Eq. (2), O and P are the Lame elastic constants; l , m, n are the Murnaghan elastic constants; the elastic constants of different materials are shown in Table 1 [10]. U 0 is the density of the solid before deformation; V is the stress applied in one direction (tensile stress is positive and compressive stress is negative); V is the velocities of the longitudinal wave. Table 1. Lame and Murnaghan constants of the materials, unit (Gpa). Material

O

P

l

m

n

Steel (1045)

120

79

-179

-496

-628

Aluminium (6061)

62

26

-201

-305

-300

Copper (99.9%)

104

46

-542f30

-372f5

-401f5

2.2. The testing principle of ultrasonic LCR wave method When a longitudinal wave propagates from a medium in which the wave velocity is slower to a medium in which the wave velocity is faster, according to the Snell law, there is an incidence angle that makes the refraction angle of

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the longitudinal wave equal to 90o. A longitudinal wave with a refraction angle equal to 90o is called the critically refracted longitudinal wave (LCR wave). The angle of incidence is the first critical angle. We obtain the relationship between the longitudinal wave velocity that propagates along the stress direction and the stress, as shown in Eq. (2). In the actual detection, the distance between the transmitting and receiving transducer is fixed, and we can reflect the change of the sound velocity by calculating the change of the sound time and then determine the acoustic elastic effect. From Eq. (2), we can obtain the relationship between the stress variation and the changing time of sound propagation: dV K

K ˜ dt or 'V

K ˜ 't

 (3)

2V0 (3O  2 P ) 4O  10P  4m 2l  3O  10P  4m ( )L  P O  2P

(4)

Where, K is stress coefficient of measured component, the unit is MPa/ns; 't is the time variation under the condition of stress; L is the distance between the transmitting and receiving transducer, V0 is the longitudinal wave velocity under the condition of zero stress. Taking 6061 aluminium alloy for example, the velocity of LCR wave in zero stress 6061 aluminium alloy is 6.32km/s. From the Table 1, we can obtain Lame and Murnaghan constants of 6061 aluminium alloy are O 62GPa , P 26GPa , l 201GPa , m 305GPa , n 300GPa . When we choose the distance of transducers L 30mm , the stress coefficient of 6061 aluminium alloy can be calculate by Eq. (4) is K 4.15 (MP/ns) . 3. Testing of residual stress

3.1. Overview of the testing system The residual stress testing system based on the principle of ultrasonic LCR wave method. It mainly includes specialized ultrasonic transducers, ultrasonic transceiver, temperature sensor and transmitter, automatic scan device, trigger and data collector, portable industrial control computer and corresponding algorithm software, calibration block, and so on.

3.2. Calibration of the stress coefficient It is necessary to calibrate the detector before testing residual stress. In a laboratory environment, calibration can be carried out by a tension and compression testing machine. It is based on the principle that a tension and compression testing machine can provide standard stress value. Before tensile test, it needs to prepare zero stress specimens. In order to relax the residual stress in the specimen, annealing treatment or vibration aging treatment should be done to the specimen. The metallurgical composition and texture as well as the surface roughness of the specimen material should be the same as those of the material to be tested. Shape and size of the specimen should be meet the requirements of tensile samples of ISO 6892-1:2009 [11]. The surface roughness of calibration region should less than Ra 10Pm. Carry out the tensile test according to the method defined in ISO 6892-1:2009 with ambient temperature at 22f 2ć. Measure stress and transit time increment 'V and 't at least 8 point in the elastic stress range of the material, repeat tensile test at least 5 times and take the average of measured stress and transit time increment as calibration data. Fig. 1 shows an example calibration data, the relationship between transit time increment 't and stress increment 'V . linear fitting method should be used to process the stress and transit time data to obtain the fitting line. The reciprocal of the fitting line slope is the calibrated stress coefficient K . From Fig. 1, we can obtain the stress coefficient K of 6061 aluminium alloy after calibration is 4.52 (MPa/ns).

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Fig. 1. Relationships between tensile stress and transit time. (Test conditions are as follows: the frequency of transducers are 5MHz, the transit distance between transducers is 30mm, the material of the specimen is 6061 aluminium alloy and environment temperature is 23ć).

4. Experiments and applications Ultrasonic LCR wave method has the characteristics of high resolution, high penetration, nondestructive and no harm to the human body, and that it is the most promising technology in the development of residual stress testing. Using the ultrasonic detector, we carried out experiment research on residual stress testing of oil pipeline weld joint. The material of pipeline is X70 steel and welding procedure is manual arc welding. We tested residual stress around straight weld joint in a section of pipeline. In order to verify the accuracy of the test results, a hydrostatic test has been carried out. From the Fig. 2, it is observed that the blasting area is consistent with the dangerous area evaluated by ultrasonic LCR wave method. area of stress concentration

testing stress direction straight weld joint the blasting area probe

0

4700

4860

4980 (mm)

Fig. 2. Hydrostatic experimental verification.

In addition, we also carried out application research on residual stress testing of high pressure pipe, vehicle driving shaft, vehicle shell weld joint, aviation turbine disk, blade of aviation engine, aluminum alloy plates, highspeed railway track, component with coating layer, glass and ceramics, circuit board, gear tooth root, bearing, thin pipe or tube, fiber composites, and so on. The states of residual stress distribution in those mechanical components we tested are match with the actual results. Up to now, there already have been more than 20 corporations in China using the ultrasonic detector to nondestructive testing residual stress. 5. Conclusions Based on theory of acoustoelasticity, the testing principle of ultrasonic LCR wave method is analyzed. The testing system of residual stress is build. The calibration of stress coefficient is the important parts in the system because of related to the accuracy of the test results. Usually, the stress coefficient of different materials can calculate by Eq. (4)

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in this paper. However, it is better to obtain stress coefficient by experimental method to reduce the influence of different metallurgical composition and texture. The residual stress in oil pipeline welds joint and many other mechanical components are tested. Through experiments and applications, it is verified that the accuracy, practicability and universally application fields of the ultrasonic LCR wave method. Acknowledgements The authors acknowledge National Natural Science Foundation of China (Grant No. 51275042) for financial support. References [1] Totten, G. E., Howes, M., Inoue, T., 2002. Handbook of Residual Stress and Deformation of Steel. ASM International Publishers, USA, pp. 417-444. [2] Jacomino, J. L., Burgos, J. S., Cruz, A. C., et al, 2010. Use of Explosives in the Reduction of Residual Stresses in the Heated Zone of Welded Joints. Welding International 24, 920-925. [3] Rossini, N. S., Dassisti, M., Benyounis, K. Y., et al, 2012. Methods of Measuring Residual Stresses in Components. Materials and Design 35, 572–588. [4] Epp, J., Hirsch, T., 2010. Residual Stress State Characterization of Machined Components by X-ray Diffraction and Multiparameter Micromagnetic Methods. Experimental Mechanics 50, 195-204. [5] Wang, Q., Ozaki, K., Ishikawa, H., et al, 2006. Indentation Method to Measure the Residual Stress Induced by Ion Implantation. Nuclear Instruments and Methods in Physics Research B 242, 88–92. [6] Yashar, J., Mehdi, A. N., et al, 2012. Residual Stress Evaluation in Dissimilar Welded Joints Using Finite Element Simulation and the LCR Ultrasonic Wave. Russian Journal of Nondestructive Testing 48, 541–552. [7] Song, W. T., Pan, Q. X., Xu, C. G., et al, 2013. Benchmark of residual stress for ultrasonic nondestructive testing. 2013 Far East Forum on Nondestructive Evaluation/Testing: New Technology, & Application, 73-76. [8] Bray, D. E., Junghans, P., 1995. Application of the Lcr Ultrasonic Technique for Evaluation of Post-weld Heat Treatment in Steel Plates. NDT&E International 28, 235-242. [9] Rose, J. L., 1999. Ultrasonic Waves in Solid Media. Cambridge: Cambridge University Press. [10] Viktor, H., 1997. Structural and Residual Stress Analysis by Nondestructive Methods. Netherlands: Elsevier Press, 1997. [11] ISO 6892-1:2009. Metallic materials -- Tensile testing -- Part 1: Method of test at room temperature.