8th International Symposium on NDT in Aerospace, November 3-5, 2016 Multiphysics Simulation of Guided Wave Propagation under Load Condition Lei QIU1,2, Ramanan SRIDARAN VENKAT2, Christian BOLLER2, Shenfang YUAN1 1 Research Center of Structural Health Monitoring and Prognosis, State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics; Nanjing, China E-mail: [email protected], [email protected] 2 Chair of Non-Destructive Testing and Quality Assurance (LZfPQ), Saarland University; Saarbrücken, Germany; [email protected], [email protected] http://www.ndt.net/?id=20587 Abstract A multiphysics simulation method of Guided Wave (GW) propagation under load condition is proposed. With this method, two key mechanisms of load influence on GW propagation are considered and coupled with each other. The first key mechanism is the acoustoelastic effect which is the main reason of GW phase change. The second key mechanism is the load influence on piezoelectric materials, which results in a change of the GW amplitude. Based on COMSOL multiphysics, a finite element model of GW propagation on an aluminium plate under load condition has been established. The simulation model includes two physical phenomena to be considered represented by simulation modules. The first module is called solid mechanics, which is used to More info about this article: simulate the acoustoelastic effect being combined with the hyperelastic material property. The second module is called electrostatics, which considers the simulation of the piezoelectric effect for GW excitation and response. To simulate the load influence on piezoelectric materials, a non-linear numerical model of the relationship between load and piezoelectric constant d31 is built. The simulation results under uniaxial load are obtained and they are compared with the data obtained from an experiment of load influence on GW. It shows that the variations of phase and amplitude of GW obtained from the simulation match the experimental results well. Keywords: Structural health monitoring, time-varying condition, guided wave, multiphysics simulation, acoustoelastic effect 1. Introduction Real aircraft structures serve under uncertain time-varying conditions such as environmental conditions, load conditions and structural boundary conditions etc. Almost all the damage monitoring features can be directly affected by the time-varying conditions, which leads to low damage monitoring reliability. Among Structural Health Monitoring (SHM) methods, Guided Wave (GW) and piezoelectric sensor based method is a promising one because it is a regional monitoring method and is sensitive to small damage [1]. To deal with the time- varying problem [2], several methods [3-7] such as the environmental compensation method, baseline free method, data normalization method and mixture probability method etc. have been proposed but limitations remain. Thus, for real applications, the problem of reliable damage monitoring under time-varying conditions must be fully studied. Considering that the time-varying conditions are often complicated, and the corresponding experiments are highly costly and time consuming, GW simulation under time- varying conditions is an effective way to study the time-varying problem. Based on the simulation, the GW propagation on complex structure under complicated time-varying conditions can be studied easily and the simulation data can be also used to validate the methods which are aimed to deal with the time-varying problem. Although the simulation of GW propagation has been widely studied [8-11], the GW simulation under time-varying conditions is still rarely reported [12], especially for a simulation method which fully considers the influence of time-varying conditions recorded by piezoelectric sensors adhered on a structure and this under close to real conditions. 1 Among a lot of time-varying factors, the changing load condition is a main factor, which can introduce large variations to the phase and amplitude of a GW signal recorded. In this paper, an efficient method of multiphysics simulation of GW propagation under load condition is proposed. The two key mechanisms of load influence on GW are the acoustoelatstic effect which is the main reason of GW phase change and the load induced influence on piezoelectric materials which results in a change of the GW amplitude [12]. Thus, the two mechanisms are considered and coupled together in this method. Based on COMSOL multiphysics, a finite element model of GW propagation on an aluminum plate under load condition is established. An experiment of load influence on GW is performed to validate the proposed multiphysics simulation method. 2. The Experiment of Load Influence on Guided Wave 2.1 Experimental Setup The experimental system is shown in Figure 1. The structure is 2024 aluminium alloy and its dimension is 400mm×200mm×2mm (length×width×thickness). Two piezoelectric sensors (PZT-5A) are placed on the structure which are numbered as PZT 1 and PZT 2. PZT 1 is used to excite GW and PZT 2 is used to be a GW receiver. The distance between PZT 1 and PZT 2 is 200 mm. The structure is fixed on a static tensile machine which is used to apply a uniaxial tension load to the structure. The eleven levels of load (from 0 MPa to 100 MPa with 10 MPa interval) are applied to the structure. For each load level, the GW excitation and response of the two sensors are performed and controlled by a GW based SHM system which is developed by the authors [13]. The excitation signal is a five-cycle sine burst modulated by Hanning window. The central frequency and amplitude of the excitation signal are 200 kHz and ±70V respectively. The sampling rate of GW signal is 10 Msamples/s. Fig.1. The experiment system of load influence on guided wave. 2.2 Experimental Results The acquired GW signals at all load levels are de-noised by a method [14] based on complex continuous Shannon wavelet transform first. The de-noised GW signals are displaced in Figure 2 (a). The amplitude and phase variation of S0 mode of the GW signals are enlarged to be a better observation as well. There should be noted that in this paper, only S0 mode is considered. The reason will be explained in section 4. Figure 2 (b) gives the quantitative variation of the amplitude and phase. It can be noted that the phase velocity decreases linearly and the amplitude increases non-linearly accompanying with the increasing of the load. For measuring the change in phase velocity, 2 equation (1) is used [14]. The slope of phase velocity change is -0.576m·s-1·MPa-1. For measuring the change in amplitude, equation (2) is used. The change in amplitude is fitted by a mixed exponential equation shown in equation (3) and the parameters are obtained as a = 0.1328, b = 0.0022, c = -0.1328 and d = -0.0476. 0 6 0MPa Experimental result 10MPa Linear fit 5 20MPa -10 30MPa 4 40MPa 50MPa -20 60MPa 3 70MPa Relative Relative amplitude 80MPa 2 -30 90MPa 100MPa 1 1.8 1.85 1.9 1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 -40 Time(s) -5 x 10 15 Phase velocity changes(m/s) -50 10 5 -60 0 20 40 60 80 100 0 External load(MPa) -5 20 Relative Relative amplitude -10 -15 0 1 2 3 4 5 6 7 8 15 Time(s) -5 x 10 0MPa 0.1 10MPa 10 20MPa 0.05 30MPa 40MPa 50MPa 0 Amplitude changes(%) 60MPa 5 70MPa Relative Relative amplitude -0.05 80MPa Experimental result 90MPa Exponential fit -0.1 100MPa 0 0 20 40 60 80 100 2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 Time(s) -5 External load(MPa) x 10 (a) GW signals under all load levels (b) Phase and amplitude variation of GW signals Fig.2. The experimental results of load influence on GW signals. 2 VP Vtp (1) l Amplevel Amp0 Amp 100% (2) Amp0 b load d load Ampfit a e c e (3) Where, Vp is the phase velocity of S0 mode and l is the GW propagation distance. Δt is the time shit of constant phase of GW signal. Amplevel is the GW amplitude at the corresponding load level and Amp0 is the amplitude at level 0. load is the load induced stress (Unit: MPa). 3. The Mechanism of Load Influence on Guided Wave 3.1 Acoustoelastic Effect Acoustoelastic effect refers to the stress-dependence of acoustic bulk wave velocity in solid media [15]. When a structure is stress-free, the longitudinal wave velocity and transverse wave velocity of a non-dispersion elastic wave propagating in a solid structure can be expressed as equation (4) and (5) by using the second order Lame constants and . When the structure is in a stressed condition because of external load, the above two velocities can be expressed as equation (6) and (7) by combining with the third order Murnaghan constants l, m and n. In these two equations, T denotes the external load and K is the bulk modulus. 3 2 0CL 2 (4) 2 0C T (5) T C2 2 2 l 4 m 4 10 0 L (6) 3K Tn Cm2 2 0 L (7) 34K It can be known that the two velocities become to be stress-independence because of the external load, and the relationship between the velocity change and the stress is linear. Although GW is a dispersion and multi-mode wave, the abovementioned equation can be also applicable to describe the acoustoelastic effect of GW because the GW is composed by the two wave components of longitudinal wave and transverse wave [16]. Thus, it is clear that if the load influence on GW phase change needs to be simulated, the acoustoelastic effect should be considered combined with the third order elastic constants.