PSI - Issue 64

Rui-Xin Jia et al. / Procedia Structural Integrity 64 (2024) 799–806 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Since the creation of prestressing technology, rebar has been widely used as the main vertical prestressing member in prestressed concrete continuous box girders. Such members are in a hidden state during service, and there is an unavoidable loss of prestress due to the coupling of multiple factors such as the initial tensioning process and the environment. These problems can lead to cracking of the top and bottom plates of box girders and severe cracking of the web thus affecting the safe use of the whole structure (Tao et al,2012; Ruan et al,2012). Therefore, how to effectively use non-destructive testing methods to detect the vertical prestressing of such members has become an urgent problem to be solved. Non-destructive testing of stress levels based on the guided wave acoustoelastic effect is a new technique that has been developed recently. It mainly utilizes the relationship that exists between the group velocity of the propagating ultrasonic guided waves and the stress, and inverts the stress level by measuring the value of the change in the group velocity of the guided waves (Chaki et al,2009). Traditional stress identification methods, resistance and fiber optic strain gauge measurements (Deng et al,2007), magnetic leakage (Krause et al,1996) strain methods (Zhong et al,2009) and ultrasonic methods (Zhong et al,2019) all have limitations. This method is able to obtain the absolute stress of the member, and the ultrasonic guided wave has the advantages of wide measurement range and high detection efficiency. In this technical context, many researchers have verified the feasibility and accuracy of the method by means of different prestressed members (Chen et al,2021; Zhu et al,2022; Lu et al,2022). But they often don't take into account the complexity of working conditions, such as outsourced concrete and mortar. Group speed is difficult to observe under complex working conditions, and many problems arise when the acoustoelastic effect is then used for detection. The first wave speed can be regarded as the fastest cluster of waves in the propagation of the guided wave, which can be observed regardless of the complexity of the working conditions. Therefore, in this paper, the first wave speed is used for the experimental study of rebars. Firstly, the acoustic elasticity of round rods is theoretically analysed, and then the tension and ultrasonic tests are carried out on the rebar ones. The change law between the first wave speed and tension is analysed, and the effects of different outer mortar layers and excitation voltage are considered. The results of the study may provide guidance for stress measurements on similar prestressed members in service. 2. Theoretical background 2.1. Dispersion curve At present, there are well-established modal analytical solutions for hollow tubes, cylinders and flat plates. The dispersion curves cannot be obtained by analytical solution for such complex geometrical sections as rebars, which can be considered as cylinders with equal diameters. The longitudinal waveguide modes in cylindrical members can be obtained by solving the Navier fluctuation equation (Datta et al,1996). Solving the propagation characteristics of guided waves in a cylinder is the prerequisite and basis for the study of ultrasonic guided waves in rebars. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 1 1 1 1 2 4 0 o k J r J r k r J r k J r J r a + − −  − =           (1)    ; ρ is the density of the material, λ and μ are the 2nd order elastic constants, ω is the circular frequency, k is the wave number, J is the Bessel function, c L and c T are the longitudinal and transverse wave speeds in the material, respectively. The displacement of any point can be written as Eqs.(2). ( ) ( ) ( ) ( ) ( ) ( ) 2 cos sin cos k r r i k t i k t r u U r n e u U r n e u U r n e         − − = = = (2) Where, r is the radius r =10mm, 2 = − L c k   , 2 2 . / 2 2 − T c k   , 2 2 2 / = 2 T c / =   , ( ) 2 L c 2 / = +