Defects detection on the welded reinforcing steel with self-shielded wires by vibration tests

. The aim of this paper is the development and validation of a vibroacustic technique to welding defects detection, especially for welded reinforcing structures. In welded structures subjected to dynamic cyclic loads may appear and propagate fatigue cracks due to local structural damage. These cracks may initiate due to the technological parameters used in welding process, or due to environmental operating conditions. By the means of Finite Element Method (FEM), the natural frequencies and shape modes of more welded steel specimens are determined. The analysis is carried out in undamaged condition as well as damaged one, after artificially induced damages. The experimental measurement of the vibroacustic response is carried out by using a condenser microphone, which is suitable for high-fidelity acoustic measurements in the frequency range of 20 – 20.000 Hz. The vibration responses of the welded specimens, in free-free conditions, are carried out using algorithms b ased on Fast Fourier Transform (FFT), and Prony’s series. The results are compared to modal parameters estimated using FE Analysis.

grade is as follows: maximum 0.22% C; maximum 0.55% Si; than 1.6% Mn; maximum 0.045% S; maximum 0.045% P and 0.06% Ti or Nb maximum. Preparation of the ends of bars and choice of joints form were made according to norm SREN 438/1-2012 [5] for concrete steel bars with a diameter greater than 16 mm. The norm is applicable for welding weldable steel bars and concrete that can transmit loads. The legislation specified requirements for materials, design and construction, welded joints, and quality requirements. Welding processes are given which can realize concrete reinforcement welded steel.
To obtain the samples was chosen arc welding process together with or without the root, and in the process of arc welding fittings was chosen tubular wire welding with self protection. Butt welding fittings concrete can be done without root support if the diameter of the steel bar is more than 16 mm, respectively with root support if bar diameter is greater than 12mm.

Resonant vibration tests
In the following, the samples consist of welded reinforcing steel, shall be considered circularly bars, having a constant section, and no subject to external tensions. To study the free vibration of these bars can consider different boundary conditions. The best known cases in the literature are: freefree conditions.

Free-free vibration of welded reinforcing steel bars
Vibratory motion of the bar is governed by a differential equation with partial derivate Euler-Bernoulli as in Meirovitch [6]: where : E is Young's modulus, I is the geometric moment of inertia of the cross-sectional area, A is the area of this section, and ρ is material density. With v(x, t) was noted the transverse deflection of the bar at a distance x from the end. To determine the transverse vibrations of the specimen must be known boundary conditions. In the physical model developed was assumed a free-free bar.
In table 1 are calculated the characteristic equation and the first five solutions on the free-free boundary conditions for the flexural vibration. In this table was noted: where λ is: and r =1,2.....5, represent the number of the natural mode. From (3) there are obtained the natural frequencies: where, X r are the routs of the characteristic equation Euler -Bernoulli, table I. If the cross area and geometric moment of inertia are modified by surface defect, the natural frequencies becomes where [ΔK] is stiffness structural modification matrix and [M] is mass matrix, L. Bereteu [7].

Finite Element Analysis
To validate the shape of vibration modes of the sample and correlation with resonance frequencies experimentally obtained is necessary to make a modal analysis. The modal parameters are obtained by Finite Element Analysis using ANSYS.The shape and size of the sample are given in Fig.2.

Experimental setup
The experimental stand for non-contact measurement of free vibrations of the sample is shown in Fig. 2. and it is composed by: the sample 1, which is the mechanical structure to be analyzed; impulsive mini hammer 2; brackets to support the sample 3; elastic threads for support of the structure in boundary conditions with the free ends 4; the acoustic sensor one condenser microphone 5, and the computer that has embedded and acquisitions plate 6.

Numerical results
The sizes mechanical characteristics of the PC 52 steel bar analyzed by ANSYS software are: L=310 mm, ϕ = 16 mm, ρ = 7850kg/m 3 and E 1 =200GPa. The frequencies and the shape modes of the sample without any defect are given in table 2, and the frequencies and the shape modes of the sample with surface defect are given in the table 3.

Experimental results
To determine the resonance frequencies of reinforcing bars without any surface defect and with induced surface defect, Fast Fourier Analysis are required for two signals. Signal acquired for reinforcing bar without surface defect is shown in Fig. 3.   Fig. 3. Experimental acquired signal A similar signal is obtained for a bar with surface defect induced. The two signals are processed using Fast Fourier Transform method, S.W.Park [8] and Prony's series method, D.J. Trudnowski [9]. The Fourier Frequency Spectrum in 0 Hz to 4000 Hz for without defect bar in the Fig. 4 is presented. A similar spectrum, but with changes in natural frequencies, it was obtained for surface defect induced bar.
To characterize weld quality depending on the method used to determine the resonant frequencies three indicators are introduced. The first indicator shows the relative deviation of the resonance frequencies of the bar where f FEM is the r-th mode frequency of the bar without defect and f rFEM and Prony Method Indicator (PMI) as where the frequencies marked with an apostrophe ( ' ) are denoted bar modes frequencies with surface defects, and without ( ' ) the frequencies of the undamaged bar.

Conclusions
The results obtained in this work show that the signals and data analysis method for free vibration of the samples can be considered between nondestructive methods that can be used to determine the quality of the welding. The changing of resonance frequencies through structural modifications as a consequence of welding defects obtained in experiments come to validate the numerical results obtained on modal analysis by FEM, and the results obtained by applying the formulas (5). There is a good convergence of results obtained by the two methods of experimental analysis of signals: Prony's Series Method and Fast Fourier Transform Method, compared with numerical method (FEM). It finds that the three indicators give a weak sensitivity for a surface defect, especially for first resonant frequency of vibration. However, the sensitivity is double or even triple for higher frequencies mode of vibration. The best stability is given for high resonance frequencies of the modes by FFT Indicator.