Absolute stress measurement of structural steel members with ultrasonic shear-wave spectral analysis method

Li, Zuohua; He, Jianping; Teng, Jun; Qin, Huang; Wang, Ying

doi:10.1177/1475921717746952

Cited by 30 publications

(26 citation statements)

References 40 publications

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“…The echo signals are collected by the ultrasonic generator and displayed on the oscilloscope. More details of the shear‐wave spectrum method can be found in Li et al…”

Section: Experimental Studiessupporting

confidence: 93%

“…After the two shear‐wave modes with interference effects are reflected from the steel‐member rear side, they return to the shear‐wave transceiver probe. The theoretical expression of the received shear‐wave echo spectrum can be written in the following form:

(||, U ((), f)) = (||, F ((), f)) \times \sqrt{1 + \frac{1}{2} {[2 {sin}^{2} (θ + \frac{π}{4}) - 1]}^{2} ((), cos 2 italicπf normalΔ t - 1)},

φ ((),, θ, f) = \sqrt{1 + \frac{1}{2} {[2 {sin}^{2} (θ + \frac{π}{4}) - 1]}^{2} ((), cos 2 italicπfΔt - 1)},

where | U ( f )| is the spectrum of the shear‐wave echo when the steel member is under a stressed condition; | F ( f )| is the reference spectrum of the shear‐wave echo when the steel member is under a zero‐stress condition; φ ( θ , f ) is defined as the interference factor; θ is the shear‐wave polarisation angle, that is, the angle between the shear‐wave particle vibration and the stress direction; f is the shear‐wave frequency; and Δ t is the TOF difference of two separated shear‐wave modes.…”

Section: Theorymentioning

confidence: 70%

“…Hughes and Kelly derived an expression for the velocity of an ultrasonic wave in a stressed solid using Murnaghan's theory of finite deformations and third‐order terms in the strain–energy expression . According to the acoustoelastic effect, the relationship between the shear‐wave velocity and stress can be expressed as follows:

ρ {v_{italicSki}}^{2} = μ - \frac{σ_{j}}{3 λ + 2 μ} ((), m - 2 λ - \frac{λ + μ}{2 μ} n),

ρ {v_{italicSkj}}^{2} = μ - \frac{σ_{j}}{3 λ + 2 μ} ((), λ + 2 μ + m + \frac{λn}{4 μ}),

where σ j is the steel‐member uniaxial stress in the j direction, v Ski and v Skj are the shear‐wave velocities when the propagation is in the k direction and the particle‐vibrations are in the i direction and j direction, respectively, ρ 0 is the material density, and l , m , and n are Murnaghan constants. For isotropic solids, there are three independent third‐order elastic constants, which are usually expressed as Murnaghan constants.…”

Section: Theorymentioning

confidence: 99%

“…By combining Equations , , and and considering the initial acoustic anisotropy of the steel member, we obtain the following formulas:

σ_{j} = \frac{κ}{f^{*}} - γ, ((), N_{2} = 1),

κ = \frac{1}{4 \cdot N_{3} \cdot t_{S 0}} \cdot \frac{- 8 μ^{2}}{4 μ + n}, ((), N_{3} = 1, 2, 3 \dots),

γ = \frac{‐ 8 μ^{2}}{4 μ + n} α,

where t S 0 is the shear‐wave TOF when its travel path is L S in a free‐stressed steel member; N 3 is the round‐trip time of the shear waves; α reflects the steel‐member initial acoustic anisotropy and the specimen‐transducer coupling condition; and κ and γ contain information on the steel‐member material properties, dimensions, and initial acoustic anisotropy and should be fitted using the uniaxial tensile test. Thus, by detecting the characteristic frequency that corresponds to the minimum value in the shear‐wave spectrum, the steel‐member absolute stress can be obtained for the uniaxial stress state.…”

Section: Theorymentioning

confidence: 99%

“…Blinka and Sachse investigated the shear‐wave echo power spectrum, and their experimental results showed that the shear‐wave spectrum changed with the stress. The ultrasonic shear‐wave capability for absolute stress measurement was recently confirmed by Li et al, who investigated the shear‐wave interference effect and found that the inverse of the first characteristic frequency in the shear‐wave amplitude spectrum linearly changed with the uniaxial stress. On this basis, the absolute stresses of steel members were tested, and the results were verified at the laboratory scale.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of the L cr wave TOF and shear‐wave spectrum methods for the uniaxial absolute stress evaluation of steel members

Teng

et al. 2019

Struct Control Health Monit

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The absolute stress of steel members is a key parameter for determining the performance of steel structures. Compared with other nondestructive evaluation methods, ultrasonic methods, which correlate material stress with ultrasonic velocity, have received the greatest amount of research attention. In this study, we investigated the measurement of the absolute stress distribution of steel members using two ultrasonic methods: a longitudinal critically refracted (Lcr) wave method and a shear wave method. The Lcr wave is generated from the longitudinal wave mode conversion and exhibits the greatest sensitivity to stress. The shear waves are generated by the birefringence effect, and their synthesis signal spectrum exhibits a minimum that varies with stress. A comparison of the two absolute stress evaluation methods is performed. Specifically, four steel members with identical dimensions and materials are used to investigate the discreteness of the calibrated parameters. The uniaxial absolute stress distributions of two steel members with variable cross sections are measured using the two methods and verified using the traditional strain gauge method. The results show that the uniaxial stress distributions of the two steel members can be evaluated by both the Lcr wave time-of-flight method and the shear-wave spectrum method, although the latter is more accurate for the measurement of stress distribution. Furthermore, the measurement principles, parametric calibrations, sensitivity, accuracy, and repeatability of the two methods are compared, and their applicability is discussed. KEYWORDS acoustoelastic effect, birefringence effect, Lcr wave TOF method, nondestructive stress measurement, shear-wave spectrum method, steel members, uniaxial absolute stress

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“…The echo signals are collected by the ultrasonic generator and displayed on the oscilloscope. More details of the shear‐wave spectrum method can be found in Li et al…”

Section: Experimental Studiessupporting

confidence: 93%

(||, U ((), f)) = (||, F ((), f)) \times \sqrt{1 + \frac{1}{2} {[2 {sin}^{2} (θ + \frac{π}{4}) - 1]}^{2} ((), cos 2 italicπf normalΔ t - 1)},

φ ((),, θ, f) = \sqrt{1 + \frac{1}{2} {[2 {sin}^{2} (θ + \frac{π}{4}) - 1]}^{2} ((), cos 2 italicπfΔt - 1)},

Section: Theorymentioning

confidence: 70%

ρ {v_{italicSki}}^{2} = μ - \frac{σ_{j}}{3 λ + 2 μ} ((), m - 2 λ - \frac{λ + μ}{2 μ} n),

ρ {v_{italicSkj}}^{2} = μ - \frac{σ_{j}}{3 λ + 2 μ} ((), λ + 2 μ + m + \frac{λn}{4 μ}),

Section: Theorymentioning

confidence: 99%

“…By combining Equations , , and and considering the initial acoustic anisotropy of the steel member, we obtain the following formulas:

σ_{j} = \frac{κ}{f^{*}} - γ, ((), N_{2} = 1),

κ = \frac{1}{4 \cdot N_{3} \cdot t_{S 0}} \cdot \frac{- 8 μ^{2}}{4 μ + n}, ((), N_{3} = 1, 2, 3 \dots),

γ = \frac{‐ 8 μ^{2}}{4 μ + n} α,

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Comparison of the L cr wave TOF and shear‐wave spectrum methods for the uniaxial absolute stress evaluation of steel members

Teng

et al. 2019

Struct Control Health Monit

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Measurement of the stress of steel members using the ultrasonic phase spectrum

Liu

et al. 2022

Structural Contr & Hlth

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Summary The stress state of steel members is an important indicator in evaluating structural safety. The ultrasonic time‐of‐flight method of measuring the stress of steel members based on acoustoelastic theory has been fully developed. However, the time difference is hard to be measured. The present paper proposes a new method of measuring the uniaxial stress of steel members using the phase spectrum of the ultrasonic transverse wave. The effect of interference of the two wave components generated by shear‐wave birefringence under uniaxial stress is investigated. It is found that the derivative curve of the phase spectrum of the pulse‐echo comprising the two wave components reaches a maximum periodically, and the frequency corresponding to the maxima is sensitive to stress and relatively easy to be measured. On this basis, a theoretical formula for the measurement of the uniaxial stress of steel members based on the phase spectrum is derived. Results of calibration tests show a good linear relationship between the stress and the reciprocal of the first response frequency corresponding to the maximum of the derivative curve of the phase spectrum. The uniaxial stress can then be measured by obtaining the first response frequency of the phase spectrum of the in‐service structural steel member. In addition, the effects of the thickness of steel members and the sampling rate of the oscilloscope on the uniaxial stress measurement are investigated. The present paper also illustrates the correspondence between the amplitude spectrum method and phase spectrum method.

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