Comparative study on the characteristics of magnetic memory signals for welding and non-welding steels with different materials under tension-compression fatigue

Abstract

Metal magnetic memory (MMM) testing method has been proved to be a valid approach to monitor early damage and predict fatigue life, but there is no systematic description and comparison about the characteristics of MMM signals for welding and non-welding specimens with different materials under tension-compression fatigue. Thus, the fatigue tests for Q345B and Q345qC welding and non-welding specimens were carried out and the MMM testing was done synchronously. Then, based on the normal components of MMM signals, H _p(y), and its variations, ΔH _p(y), the slope of ΔH _p(y) fitting curves, K _C, and the average of ΔH _p(y) signals on the whole testing line, ΔH _p(y)_ave, were extracted as the characteristic parameters for Q345B and Q345qC non-welding specimens, respectively. Additionally, the gradient of “peak–vale” on H _p(y) signals curves, k, and the average of H _p(y) signals in the scope of welding zone, H _p(y)_ave, were extracted as the characteristic parameters for Q345B and Q345qC welding specimens, respectively. Some conclusions can be drawn by comparison: the variation laws of H _p(y) signals with cyclic loads are related to the material. The characteristic parameters for welding and non-welding specimens with the same material have a certain similarity. Then, the failure of non-welding steel can be warned early by K _C or ΔH _p(y)_ave when the fatigue life has 20% left, but the damage degree of welding specimen should begin to be valued highly once the k or H _p(y)_ave is decreasing. Finally, the fatigue life of welding and non-welding specimens with different materials can be evaluated effectively by using corresponding magnetic characteristic parameters.

Keywords

Metal magnetic memory (MMM) testing fatigue life magnetic characteristic parameter Q345B and Q345qC steel weldments

1. Introduction

Fatigue is one of the most common materials degradation mechanisms in the industry that occurs when material experiences repeated or cyclic stresses for a long duration of time [1]. However, welding, as a widely-utilized joining method for steel structures, will decrease fatigue performance of structures because slag inclusions, incomplete fusion, gas pores, undercuts at weld toes [2]. Even though the maximum stress level does not exceed the yield stress in case of high cycle fatigue (HCF), the fatigue damage increases with applied cycles in a cumulative manner which may lead to fracture suddenly without any warning [3]. Therefore, to avoid that the fatigue damage process ends in a sudden fracture, it is vital to assess the material degradation preferably in a nondestructive fashion [4].

At present, some traditional nondestructive testing (NDT) techniques, such as ultrasonic testing (UT), eddy current testing (ECT) and magnetic particle testing (MT), have been proved to be the reliable measuring techniques for detecting macroscopic defects. However, these traditional NDT techniques are incapable of determining mechanical degradation and early damage of objects under test [5]. As a novel magnetic testing method [6,7], metal magnetic memory (MMM) testing can diagnose early damages in ferromagnetic materials without smearing couplant, cleaning the specimen surface entirely and applying a strong external magnetic field [8]. Critically, compared with traditional NDT techniques, MMM technique can realize an early prediction of possible damage position, and then perform early diagnosis of ferromagnetic components, based on the comprehensive analysis of the maximum stress concentration positions and the damage sources [9,10].

The essence of MMM can be explained by magneto-mechanical effect [11]. The magnetic field on the component surface varies when ferromagnetic materials are subjected to stress in the presence of the geomagnetic field. These anomalies in magnetic fields, in turns, an indication of local changes in the stress the state of a component [12]. Therefore, previous studies reported that the normal component of magnetic memory signals and its variable gradient can be used to evaluate the degree of damages of materials in the elastic and plastic deformation stages [13,14].

Up to now, it has been proved that the MMM technique can not only predict fatigue life but also can be adopted for welding detection [15,16]. Wherein, establishing the quantitative relationship between fatigue damage and MMM signals is one of the vital problems in MMM testing. Scholars have therefore performed much experimental researches about fatigue damage characterization based on MMM technique. Ren et al. [17] performed the tension-tension fatigue test of 45 steel with crack and found that the average of the absolute values of the leakage magnetic field could be used to differentiate the different damage stages of components clearly and reflect the degree of fatigue damage. Wang et al. [18] tested 0.45% C notch steel under tension-compression fatigue and found that the gradient of H _p(y) curves between the two abnormal peaks and the maximal values of H _p(x) curves exhibited consistent tendency in the whole fatigue life and could be used to differentiate the different stages of fatigue. Li et al. [19] carried out the tension-tension fatigue tests of a center cracked specimen and the results indicated that the peak value of the tangential component and the maximum gradient value of the normal component increased with fatigue crack length, which was possible to evaluate the fatigue damage degree of ferromagnetic components. Huang et al. [20] demonstrated that the maximum gradient, K _max, was a potentially useful indicator to monitor the fatigue crack propagation of weldments through dynamic bending fatigue tests of Q235 center-notched welding specimens. Ni et al. [21] established the relationship between the area of gradient curve K _n for loading cycles of n and damage through three-point bending fatigue test for single edge notched 35CrMoA specimen, and then provided a new idea for predicting fatigue life with MMM testing results.

Through the above researches, the degree of fatigue damage at stress concentration region for the specimen with a prefabricated notch can be reflected effectively based on the characteristic parameters of magnetic memory signal. Virtually, the fatigue damage accumulates constantly with the increase of cyclic load for the welding and non-welding specimen without the prefabricated notch. Meanwhile, under cyclic stress and geomagnetic field, the variation of magnetization in ferromagnetic material causes the changing of the magnetic field on the surface of specimen. Therefore, the fatigue life of welding and non-welding specimen evaluated by MMM technique still need to be studied. Furthermore, as an important factor, the chemical composition of ferromagnetic material does affect magnetic memory signals [22,23]. Thus, the relationship between fatigue life and magnetic memory signals for welding and non-welding specimens with different materials needs further contrastive analysis.

Therefore, the tension-compression fatigue tests for Q345B and Q345qC welding and non-welding steels were carried out. Synchronously, the magnetic memory signals on the surface of specimen were collected under different cyclic loads. Then, the variation laws of magnetic memory signals for different specimens were analyzed and compared. And some different characteristic parameters were determined to estimate the fatigue damage of specimen under cyclic loads.

2. Experiment

2.1. Specimen preparation

The tested materials are Q345B steel and Q345qC steel, which are widely used in the engineering field of construction and bridge, respectively, due to its excellent mechanical properties. The chemical compositions of Q345B and Q345qC steel are listed in Tables 1 and 2. According to the standard of Metallic materials–Tensile testing–Method of test at ambient temperature (GB/T 228.1–2010) and Metallic materials–Fatigue testing–Axial-force-controlled method (GB/T 26077–2010), six flat samples were cut from two Q345B and Q345qC steel plate with a thickness of 14 mm, respectively. Its shape and dimensions are shown in Fig. 1. Classification and the serial number of specimens are shown in Table 3. Wherein, the sheet specimen with V-grooved weld was fabricated in CO₂ gas shielded welding, as shown in Fig. 1(b) and (d). Weld wire ATLANTIC CHW-50C was selected according to the standard GB/T 8110 EP49–1.

Table 1
Chemical composition of Q345B steel (wt%)

Material C Si Mn P S Mo Nb V Ti CEV

Q345B 0.16 0.14 1.46 0.10 0.006 0.004 0.002 0.004 0.031 0.42

Material	C	Si	Mn	P	S	Mo	Nb	V	Ti	CEV
Q345B	0.16	0.14	1.46	0.10	0.006	0.004	0.002	0.004	0.031	0.42

Table 2

Chemical composition of Q345qC (wt%)

Material	C	Si	Mn	P	S	Cr	AIt
Q345qC	0.14	0.29	1.46	0.015	0.003	0.04	0.03
Material	Mo	Ti	Cu	Nb	Ni	V	Ceq
Q345qC	0.014	0.003	0.03	0.025	10	0.002	0.4

Fig. 1.

Specimen shape and testing points position (Unit: mm).

Table 3

Classification and serial number of specimens

Specimens		Monotonic tension	High cycle fatigue
			Stage 1	Stage 2
Q345B	Non-weld	J-1	PJ-1	PJ-2
	Weld	JH-1	PJH-1	PJH-2
Q345qC	Non-weld	Q-1	PQ-1	PQ-2
	Weld	QH-2	PQH-1	PQH-2

Fig. 2.

Testing machine for monotonic tension.

Fig. 3.

Stress-strain curves of different specimens.

2.2. Specimen properties

Monotonic tension tests for specimens J-1, JH-1, Q-1, and QH-1 were performed on the CSS-WAW300D1 electro-hydraulic servo testing machine (as shown in Fig. 2), whose loading velocity is 0.05 mm/s. The stress-strain curves for four specimens were obtained as shown in Fig. 3. The mechanical properties for different specimens were listed in Table 4. Wherein E is Young’s modulus; ϵ_y is yield strain; σ_y is yield strength; σ_u is ultimate strength; A is elongation rate.

Table 4
Mechanical properties of different specimens

Specimens E / GPa ϵ_y, % σ_y/ MPa σ_u/ MPa A, %

J-1 203 0.14 385 535 34.00

JH-1 193 0.20 346 450 10.00

Q-1 203 0.18 430 550 40.00

QH-1 205 0.28 430 535 36.00

Specimens	E / GPa	ϵ_y, %	σ_y/ MPa	σ_u/ MPa	A, %
J-1	203	0.14	385	535	34.00
JH-1	193	0.20	346	450	10.00
Q-1	203	0.18	430	550	40.00
QH-1	205	0.28	430	535	36.00

2.3. Instrument and method for fatigue test

Fatigue tests were carried out at room temperature with the MTS 250kN electro-hydraulic servo fatigue testing machine (see Fig. 4), whose displacement range and the limit value of load are ±80 mm and 250 kN, respectively. According to the standard of GB/T 26077–2010, the loading method controlled by force were used in fatigue test. Tension-compression cyclic loads with a constant amplitude (sinusoidal waveform) were performed, with the stress ratio R = −1, as shown in Fig. 5. The maximum load is 78.4 kN (i.e. the maximum tensile stress at 280 MPa, the maximum compressive stress at −280 MPa) and load frequency is 7 Hz.

Fig. 4.

HCF testing machine.

Fig. 5.

The waveform of cycle load.

Firstly, specimens PJ-1, PJH-1, PQ-1, and PQH-1 were loaded until the occurrence of fracture. For one thing, the number of cycles to fracture for different specimens were got. For another thing, the rational cyclic times for collecting magnetic memory signals were determined.

Before tension-compression fatigue test, specimens PJ-2, PJH-2, PQ-2, and PQH-2 were demagnetized by using a home-made demagnetization machine CFW-2000 (see Fig. 6) to eliminate machining magnetization. Each specimen was put on the non-ferromagnetic platform along the south-north direction, and the initial MMM signals of each testing line on the surface of specimen were measured. Then, when loaded to a predetermined cyclic number, the specimens were taken off from the grip holders carefully and the MMM signals were measured the same way as that of initial signals.

Fig. 6.

Demagnetization machine.

EMS-2003 intelligent MMM detector with a Hall pencil-type probe was served to collect the MMM signals, whose measuring range and sensitivity were ±1000 A/m and 1 A/m, respectively. Figure 7 shows the MMM testing instrument and collecting signals by the probe. The probe was normalized before each testing for reducing signal interference caused by the environmental magnetic field. Moreover, the probe was placed vertically on the surface of specimen with a constant lift-off during testing. Three testing lines (i.e. 1-1’, 2-2’ and 3-3’) were arranged on the upper surface of the specimen (see Fig. 1). Testing line 1-1’ and 3-3’ is 3 mm away from the edge of specimen. The distance of adjacent testing lines is 7 mm. Fifteen testing points are on each testing line and the uniform distance interval among the testing point is 5 mm. The H _p(y) signals on each testing point were measured three times and the mean values of H _p(y) signals were calculated to reduce the random error.

Fig. 7.

Collecting magnetic memory signal.

3. Results

3.1. Non-welding specimen

The results of fatigue tests indicate that the numbers of cycle to failure for Q345B and Q345qC non-welding specimens are 17465 c and 82428 c, respectively. Fracture appearance for different specimens is shown in Fig. 8. It can be seen that no obvious necking and extension occur at the position of fracture, which belongs to typical brittle failure. In addition, the fatigue life of Q345qC steel is about 4.7 times than that of Q345B steel, so the fatigue performance of Q345qC steel is better.

Fig. 8.

Fracture appearance of non-welding specimens.

Only nine testing points within the scope of 50 mm at the middle of the specimen were chosen to analyze because the six testing points at both ends of the testing line exceeded the effective tension-compression range for the specimen. To compare the variation tendency of H _p(y) signals curves for different specimens clearly, the variation of H _p(y) signals curves with cyclic times were divided into three stages: initial stage; loading stage; ultimate failure.

Figures 9, 10 and 11 show the variation laws of H _p(y) signals curves on three testing lines for Q345B specimen under different stages. It can be seen that the variation tendencies of H _p(y) signals curves on three testing lines are similar at the same stage. In the initial stage, the values of H _p(y) signals are ranged from 5 A/m to 35 A/m and exhibit linear diminution approximatively along the testing line.

Fig. 9.

Variation laws of H _p(y) signal on testing line 1-1’ for Q345B non-welding specimen.

Fig. 10.

Variation laws of H _p(y) signal on testing line 2-2’ for Q345B non-welding specimen.

Fig. 11.

Variation laws of H _p(y) signal on testing line 3-3’ for Q345B non-welding specimen.

In the loading stage, all of H _p(y) signals curves appear obvious counterclockwise rotation compared with that in the initial stage. However, with the increase of cyclic times, the H _p(y) signals curves tend to stable gradually and the regularities of that become more unified, which agrees with the experimental phenomenon (see Fig. (6) in Ref. [24]). Compared with the beginning of loading (less than 7000 c), the variation of H _p(y) signals curves are relatively stable along the direction of testing line at the late of loading (more than 10000 c). It can be explained as follows by the Jiles-Atherton magneto-mechanical constitutive model which can be well used to describe the magneto-mechanical coupling effect of ferromagnetic components under applied stress and geomagnetic field [25,26].

According to the Jiles-Atherton model [27,28], the relationship between magnetization M and stress σ in specimen after one cycle can be gotten by Eq. (1). $\begin{eqnarray}\displaystyle \frac{\text{d}M}{\text{d}{\sigma}}=\frac{{\sigma}}{E{\xi}}(M_{an}-M)+c\frac{\text{d}M_{an}}{\text{d}{\sigma}} & & \displaystyle\end{eqnarray}$ (1) where E is Young’s modulus; 𝜉 is a coefficient related to the energy density; c is a constant which describes the flexibility of magnetic domain; M _an is the anhysteretic magnetization which can be expressed by using the Langevin function in Eq. (2). $\begin{eqnarray}\displaystyle M_{an}=M_{s}\left[\coth \left(\frac{H_{\mathit{eff}}}{a}\right)-\frac{a}{H_{\mathit{eff}}}\right] & & \displaystyle\end{eqnarray}$ (2) where M _s is the saturation magnetization; a is a coefficient scaling the effective magnetic field; H _eff is the effective fields of ferromagnetic materials which can be obtained by Eq. (3). $\begin{eqnarray}\displaystyle H_{\mathit{eff}}=H+{\alpha}M_{an}+\frac{3{\sigma}}{{\mu}_{0}}[({\gamma}_{1}+{\gamma}_{1}^{\prime }{\sigma})M_{an}+2({\gamma}_{2}+{\gamma}_{2}^{\prime }{\sigma})M_{an}^{3}] & & \displaystyle\end{eqnarray}$ (3) where H is the environment magnetic field; 𝛼 is the mean field coefficient representing the self-coupling of the magnetization; μ₀ is the vacuum magnetic permeability; 𝛾₁, ${\gamma}_{1}^{\prime }$ , 𝛾₂ and ${\gamma}_{2}^{\prime }$ are the fitting coefficients of magnetostrictive strain in terms of magnetization.

According to the literature [29], the model parameters are given M _s = 1.7 × 10⁶ A∕m; a = 1000; 𝛼 = 0.001; μ₀ = 4π × 10⁻⁷ H∕m; 𝛾₁ = 7 × 10⁻¹⁸ A⁻² m²; 𝛾₁ ^′ = −1 × 10⁻²⁵ A⁻² m² Pa⁻¹; 𝛾₂ = −3.3 × 10⁻³⁰ A⁻⁴ m⁴; 𝛾₂ ^′ = 2.1 × 10⁻³⁸ A⁻⁴ m⁴ Pa⁻¹; E = 2.10 × 10¹¹ Pa; 𝜉 = 2000 Pa; c = 0.1. Thus, the variation law of magnetization M and stress σ can be obtained by the above formulas, as shown in Fig. 12.

Fig. 12.

The relationship between magnetization and stress [25,26].

Figure 12 shows that magnetization M cannot return to the virgin state after cyclic loading, and the irreversible magnetization ΔM _σ will be generated in the specimen. Under cyclic load Δσ and geomagnetic field, the irreversible magnetization ΔM _σ accumulates constantly with the increase of cyclic times [30], as shown in Fig. 13. However, according to the results of theoretical analysis in Ref. [31] and the experimental phenomenon in Ref. [32], if the cyclic load Δσ is relatively high, the rate of convergence for the magnetization process will become quicker. The irreversible magnetization reaches saturation after a few cyclic times so that the H _p(y) signals curves tend towards stability. After specimen failure, H _p(y) signals curves have a little clockwise rotation.

Fig. 13.

The magneto-elastic effect under cyclic load [28].

Figures 14, 15 and 16 show the variation laws of H _p(y) signals curves on three testing lines for Q345qC steel under different stages. The variation tendencies of H _p(y) signals curves on three testing lines for Q345qC steel are similar at the same stage. In the initial stage without applied load, the values of H _p(y) signals are almost in the range of −5 A/m to 10 A/m and exhibit linear increase approximatively along the testing line.

Fig. 14.

Variation laws of H _p(y) signal on testing line 1-1’ for Q345qC non-welding specimen.

Fig. 15.

Variation laws of H _p(y) signal on testing line 2-2’ for Q345qC non-welding specimen.

Fig. 16.

Variation laws of H _p(y) signal on testing line 3-3’ for Q345qC non-welding specimen.

In the loading stage, the H _p(y) signals tend to relatively steady and have not changed much under different cyclic times. However, the values of H _p(y) signals on three testing lines decrease obviously when the specimen is approaching failure. After specimen failure, the H _p(y) signals curve appears some fluctuations and its values decrease further.

Through comparing the variation laws of H _p(y) signals curves for two steels of different materials, it can be found that all of the H _p(y) signals curves change linearly basically along the testing line under different stages. Different from Q345B steel, the H _p(y) signals curves for Q345qC steel do not appear obvious rotational phenomenon from the initial stage to the ultimate failure and only the values of H _p(y) signals have some changes. It implies that the variation laws of H _p(y) signals curves with cyclic load for different materials exist some differences.

3.2. Welding specimen

The results of fatigue tests indicate that the numbers of cycle to failure for Q345B and Q345qC welding specimens are 5066 c and 26928 c, respectively. Fracture appearance for different specimens is shown in Fig. 17. It can be seen that the position of fracture for welding specimen is at the welding joint. Similar to the non-welding specimen, no obvious necking and extension occur at the position of fracture, which also belongs to typical brittle failure. In addition, the fatigue life of all welding specimens decreases by almost 70% compared with the smooth specimens. It means that welding quality plays a vital role to affect the fatigue performance of material.

Fig. 17.

Fracture appearance of welding specimens.

The H _p(y) signals curves on three testing lines for welding specimens still were analyzed by three stages. The variation laws of H _p(y) signals curves on three testing lines for Q345B welding specimen at different stages are shown in Figs 18, 19 and 20.

Fig. 18.

Variation laws of H _p(y) signal on testing line 1-1’ for Q345B welding specimen.

Fig. 19.

Variation laws of H _p(y) signal on testing line 2-2’ for Q345B welding specimen.

Fig. 20.

Variation laws of H _p(y) signal on testing line 3-3’ for Q345B welding specimen.

Figures 18, 19 and 20 indicate that the variation laws of H _p(y) signals curves on three testing lines for Q345B welding specimen are similar at the same stage. Obvious mutation of H _p(y) signals curves appears at the position of welding joint (i.e. the scope of −10 mm ∼ 10 mm), which is termed as “peak-vale” phenomenon. In the initial stage without applied loads, the values of H _p(y) signals on three testing lines have an increasing trend and appear a slight fluctuation.

In the loading stage, the variation tendencies of H _p(y) signals curves on three testing lines are same under different cyclic times. The H _p(y) signals on three testing lines increase about 25 A/m sharply at the scope of −10 mm to 0 mm while decrease a little and trend to stable gradually at the scope of 0 mm to 20 mm. After specimen failure, the polarity of “peak-vale” on the H _p(y) signals curves reverses.

Compared with the non-welding specimen, because the material property and the cross-sectional shape for welding specimen change obviously at the butt-welding joint, the distribution of magnetic induction lines is affected dramatically, as shown in Fig. 21. The welding zone can be assumed as a “bump” defect. Under the geomagnetic field (the direction from left to right) and the load, magnetization M which is consistent with the direction of geomagnetic field is generated in the specimen on account of the magneto-mechanical coupling effect. Correspondingly, the magnetic induction lines form a closed loop at the butt-welding joint. And a small inverse magnetic field which is opposite to the direction of the geomagnetic field generate appears on the surface of the welding area [33]. Hence, the above phenomenon of “peak” and “vale” on H _p(y) signals curves at the butt-welding joint can be explained by the magnetic charge model which can realise simulation of MMM signal because it is in essence a magnetic flux leakage (MFL) signal [34,35].

Fig. 21.

The distribution of magnetic induction lines.

The 1-D magnetic charge model for V-shape butt-welding joint was established, as schematically represented in Fig. 22. Suppose that the relative permeability of materials is a constant, the magnetic field intensity H at the point P (x _p, y _p) can be expressed as [36]: $\begin{eqnarray}\displaystyle \mathbf{H}(\mathbf{r})=\mathbf{H}_{a}(\mathbf{r})+\frac{1}{4{\pi}}\int _{S}\frac{\mathbf{n}\cdot \mathbf{M}(\mathbf{s})}{|\mathbf{r}-\mathbf{s}|^{3}}(\mathbf{r}-\mathbf{s})\text{d}S(\mathbf{s}) & & \displaystyle\end{eqnarray}$ (4) where r is the position vector; H _a is the externally applied magnetic field intensity, which equals the geomagnetic field with an amplitude of 40 A/m in MMM; S is the surface area of ferromagnet; s is the position vector of an arbitrary point inside or on the surface of ferromagnet; n ⋅ M(s) is the surface magnetic charge.

Fig. 22.

Representation of 1-D magnetic charge model for V-shape butt-welding joint.

The above magnetic charge model assumes that the uniform geomagnetic field is along the x-direction and the surface of the welding area is an arc centered on point O with radius $R=\sqrt{t^{2}+a^{2}}$ . Two magnetic charge areas have the same magnetic charge density 𝜌_m and opposite magnetic pole. Hence, the normal component of magnetic field intensity H can be rewritten as: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \hspace{-25.0pt}H_{p}(y)=-\frac{{\rho}_{m}}{4{\pi}}\int _{0}^{\arctan \left(\frac{t}{a}\right)}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \hspace{-10.0pt}\frac{\left(y_{p}-\sin \left({\theta}+\arctan \left({\displaystyle \frac{t}{a}}\right)\right)\sqrt{t^{2}+a^{2}}+t\right)\sqrt{t^{2}+a^{2}}}{\left|\left(x_{p}+\cos \left({\theta}+\arctan \left({\displaystyle \frac{t}{a}}\right)\right)\sqrt{t^{2}+a^{2}}\right)^{2}+\left(y_{p}-\sin \left({\theta}+\arctan \left({\displaystyle \frac{t}{a}}\right)\right)\sqrt{t^{2}+a^{2}}+t\right)^{2}\right|^{3/2}}\text{d}{\theta}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \hspace{-10.0pt}+∼\frac{{\rho}_{m}}{4{\pi}}\int _{0}^{\arctan \left(\frac{t}{a}\right)}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \hspace{-10.0pt}\frac{\left(y_{p}-\sin \left({\theta}+\arctan \left({\displaystyle \frac{t}{a}}\right)\right)\sqrt{t^{2}+a^{2}}+t\right)\sqrt{t^{2}+a^{2}}}{\left|\left(x_{p}-\cos \left({\theta}+\arctan \left({\displaystyle \frac{t}{a}}\right)\right)\sqrt{t^{2}+a^{2}}\right)^{2}+\left(y_{p}-\sin \left({\theta}+\arctan \left({\displaystyle \frac{t}{a}}\right)\right)\sqrt{t^{2}+a^{2}}+t\right)^{2}\right|^{3/2}}\text{d}{\theta}.\end{eqnarray}$ (5)

The parameters t and a are taken as 14 mm and 7.9 mm as the same with the size of specimen, respectively. Accordingly, the normalized H _p(y) signals at the butt-welding joint can be calculated by Eq. (5), as presented in Fig. 23. In accordance with the Q345B welding specimen, the obvious “peak-vale” phenomenon appears on the H _p(y) signals curves. It means that the experimental phenomenon fits the results of theoretical model to some extent.

Fig. 23.

The normalized H _p(y) signals for welding specimen calculated by 1-D magnetic charge model.

Analogously, the variation laws of H _p(y) signals curves on three testing lines for Q345qC welding specimen at different stages are shown in Figs 24, 25 and 26. Figures 24, 25 and 26 show that except for the initial stage, the variation laws of H _p(y) signals curves on three testing lines for Q345qC welding specimen are similar at the same stage. In the initial stage, the variation tendencies of H _p(y) signals curves on three testing lines have some differences, but the maximums of all H _p(y) signals curves appear at the left edge of welding joint (i.e. the position of −5 mm).

Fig. 24.

Variation laws of H _p(y) signal on testing line 1-1’ for Q345qC welding specimen.

Fig. 25.

Variation laws of H _p(y) signal on testing line 2-2’ for Q345qC welding specimen.

Fig. 26.

Variation laws of H _p(y) signal on testing line 3-3’ for Q345qC welding specimen.

In the loading stage, the H _p(y) signals curves on three testing lines present a similar variation trend during the fatigue process. As a whole, the values of H _p(y) signals increase gradually along the direction of testing lines. However, an evident positive peak of H _p(y) signals appears at the left edge of welding joint (i.e. the position of −5 mm), which can be termed as “peak” phenomenon. After specimen failure, the “peak” phenomenon on H _p(y) signals curves becomes more obvious and the value of that increases dramatically.

The above results show that after cyclic loading, the H _p(y) signals curves for Q345B welding specimen appears the “peak-vale” phenomenon at the welding zone, but the Q345qC welding specimen only has the “peak” phenomenon. The reason may be the influence of welding quality and experimental conditions. Additionally, different from the Q345B welding specimen, Q345qC welding specimen does not exhibit the reversal of “peak-vale” after specimen failure.

4. Discussion

To further realize the fatigue life evaluation based on the MMM technology, the corresponding magnetic characteristic parameters were extracted by analyzing the variation laws of H _p(y) signals curves for welding and non-welding specimens with different materials under different cyclic times.

4.1. Non-welding specimen

In order to reflect the variation of MMM signals caused by cyclic loads more clearly, the H _p(y) signals variations, ΔH _p(y), can be calculated by means of subtracting the H _p(y) signals of corresponding position in the initial stage, as shown in Eq. (6). The variation laws of ΔH _p(y) signals curves for Q345B and Q345qC non-welding specimens are shown in Figs 27 and 28, respectively. $\begin{eqnarray}\displaystyle {\rm\Delta}H_{p}(y)=H_{p}(y)-H_{p}(y)_{0} & & \displaystyle\end{eqnarray}$ (6) where H _p(y)₀ is the H _p(y) signals in the initial stage.

Fig. 27.

Variation laws of ΔH _p(y) signals curves for Q345B non-welding specimen.

Fig. 28.

Variation laws of ΔH _p(y) signals curves for Q345qC non-welding specimen.

The ΔH _p(y) signals curves for the Q345B non-welding specimen have good linearity. Given that the linear magnetic signals are observed easily, thus, the ΔH _p(y) signals curves on three testing lines under different cyclic times were fitted linearly. The fitting results are shown in Table 5, wherein K _C is the slope of fitting curves and R ² is the correlation coefficient. Table 5 shows that the fitting results meet the accuracy requirement because the R ² for three testing lines all exceeds 95%. Thus, taken K _C as a characteristic parameter, the relationship between K _C and fatigue life was studied.

Table 5

The fitting results of ΔH _p(y) signals curves on three testing lines under different cyclic times

Circles / c	Testing line 1-1’		Testing line 2-2’		Testing line 3-3’
	K _C	R ²	K _C	R ²	K _C	R ²
1000	0.8900	0.94971	0.8401	0.98643	0.9267	0.98905
4000	0.6755	0.95493	0.6145	0.97001	0.7278	0.95839
7000	0.6322	0.96227	0.5745	0.97509	0.7300	0.97820
10000	0.6456	0.97071	0.6912	0.99086	0.7367	0.98352
13000	0.6900	0.96741	0.6801	0.97464	0.8544	0.97365
16000	0.5867	0.95363	0.6434	0.96765	0.6667	0.98016
17465	0.4867	0.94268	0.3656	0.93546	0.5022	0.96398

After subtracting the H _p(y) signals in initial stage, the ΔH _p(y) signals curves for Q345qC non-welding specimen appear a slight fluctuation and do not have good linearity like Q345B non-welding specimen. However, the ΔH _p(y) signals curves on three testing lines for Q345qC non-welding specimen have a downtrend as a whole with the increase of cyclic times. Hence, the average of ΔH _p(y) signals on the whole testing line, ΔH _p(y)_ave, as a characteristic parameter, was used to evaluate the fatigue damage of Q345qC non-welding specimen. ΔH _p(y)_ave can be defined as follows. $\begin{eqnarray}\displaystyle {\rm\Delta}H_{p}(y)_{ave}=\frac{1}{n}\mathop{\sum }_{i=1}^{n}[{\rm\Delta}H_{p}(y)]_{i} & & \displaystyle\end{eqnarray}$ (7) where n is the numbers of testing points; [ΔH _p(y)]_i is the value of ΔH _p(y) signals at the testing point i.

As shown in Fig. 29, the slope of ΔH _p(y) fitting curve, K _C, and the average of ΔH _p(y) signals, ΔH _p(y)_ave, for Q345B and Q345qC non-welding specimens are extracted, respectively.

Fig. 29.

The magnetic characteristic parameters for non-welding specimen.

According to Miner’s linear accumulative damage theory [37], the normalized life n∕N can be used to reflect the fatigue life. Thus, the relationship between the slope K _C and the normalized life n∕N for Q345B non-welding specimen was plotted, as shown in Fig. 30. Figure 30 shows that the overall variation tendency of K _C with n∕N decreases sharply at first, then becomes stable and decreases drastically again at last. At the beginning (i.e. n∕N is in the range from 5.7% to 22.9%), the slope K _C decreases obviously and its values have a 25% drop. Then, while n∕N rises from 22.9% to 74.4%, the K _C-n∕N curves for three testing lines tend to stable. When D exceeds 75%, the slope K _C decreases again. After specimen failure, the value of slope K _C declines under 0.5.

Fig. 30.

The relationship between slope K _C and normalized life n∕N for Q345B non-welding specimen.

The relationships between ΔH _p(y)_ave and n∕N on three testing lines for Q345qC non-welding specimen can be got, as shown in Fig. 31. Figure 31 shows that the variation laws of ΔH _p(y)_ave with n∕N on the three testing lines are similar. As n∕N increases, the variation tendency of ΔH _p(y)_ave fluctuates slightly at first, then becomes stable and decreases sharply again at last. At the beginning (i.e. n∕N is in the range from 14.6% to 36.4%), the values of ΔH _p(y)_ave fluctuate as a little amplitude of 2 A/m. During n∕N rises from 36.4% to 80%, the ΔH _p(y)_ave-n∕N curves for three testing lines tend to stable. When n∕N exceeds 80%, the ΔH _p(y)_ave curves decrease constantly again until specimen failure.

Fig. 31.

The relationships between the average ΔH _p(y)_ave and normalized life n∕N for Q345qC non-welding specimen.

4.2. Welding specimen

In contrast with the non-welding specimen, the H _p(y) signals curves for Q345B and Q345qC welding specimen do not have good linearity. And the obvious “peak” and “vale” phenomenon in welding zone will become irregular after subtracting the H _p(y) signals in the initial stage. Thus, as shown in Fig. 32, based on H _p(y) signals curves of Q345B and Q345qC welding specimen, the gradient of “peak-vale” on H _p(y) signals curves, k, and the average of H _p(y) signals in welding zone, H _p(y)_ave, was extracted as the characteristic parameters of Q345B and Q345qC welding specimen, respectively. k and H _p(y)_ave are defined as shown in Eqs (8) and (9). $\begin{eqnarray}\displaystyle & & \displaystyle k=\frac{H_{p}(y)|_{p}-H_{p}(y)|_{v}}{{\rm\Delta}L_{p-v}}\end{eqnarray}$ (8) $\begin{eqnarray}\displaystyle & & \displaystyle H_{p}(y)_{ave}=\mathop{\sum }_{i=1}^{n}H_{p}(y)_{i}\end{eqnarray}$ (9) where H _p(y)|_p is the value of H _p(y) signals at position of “peak”; H _p(y)|_v is the value of H _p(y) signals at position of “vale”; ΔL _p−v is the distance between the “peak-vale”; n is the numbers of testing points in the welding zone; H _p(y)_i is the value of H _p(y) signals at the testing point i.

Fig. 32.

The magnetic characteristic parameters for welding specimen.

Figure 33 indicates that the variation laws of k with n∕N are similar on the three testing lines. While n∕N rises from 0% to 59.2%, the k-n∕N curves fluctuate largely. After n∕N exceeds 59.2%, the k on three testing lines decreases gradually with the increase of n∕N, and its values are down about 0.42 A ⋅ m⁻¹ ⋅ mm⁻¹ when specimen approaches failure (i.e. n∕N reaches 98.7%). Finally, the k increases after specimen failure but the amplitude is little.

Fig. 33.

The relationships between the gradient k and the normalized life n∕N on three testing lines for Q345B welding specimen.

Figure 34 demonstrates that the variation laws of H _p(y)_ave with n∕N are similar on the three testing lines and the values of H _p(y)_ave have a slight growth once the fatigue damage generates. While n∕N rises from 14.9% to 81.7%, the H _p(y)_ave decreases slowly and its values reach the minimum at last. When n∕N exceeds 81.7% and the specimen approaches failure, the H _p(y)_ave increases drastically. After specimen failure, the values of H _p(y)_ave on three testing lines are about 1.8 times than that in the initial stage.

Fig. 34.

The relationships between the average H _p(y)_ave and the normalized life n∕N on three testing lines for Q345qC welding specimen.

5. Comparison of magnetic characteristic parameters

The above results illustrate that the corresponding magnetic characteristic parameters should be determined for the life evaluation of welding and non-welding specimens with different materials. The rate of change and the average for H _p(y) signals are useful for the fatigue life evaluation of Q345B and Q345qC steel, respectively. It implies that the characteristic parameters for the welding and non-welding specimens with the same material have a certain similarity.

Meanwhile, the variation trend of characteristic parameters can be mainly classified into the following four status by the above analysis: (1) Increase status; (2) Decrease status; (3) Fluctuation status; (4) Stabilization status. Thus, during the fatigue accumulation, the magnetic characteristic parameters for different specimens were further compared in the histogram Fig. 35.

Fig. 35.

Comparison of magnetic characteristic parameters varying with normalized life.

As shown in Fig. 35, the characteristic parameters K _C for Q345B non-welding specimen and the characteristic parameters ΔH _p(y)_ave for Q345qC non-welding specimen are relative stabilization when the n∕N is in the range from 37% to 70%. And the K _C and the ΔH _p(y)_ave decrease obviously once the n∕N reaches about 80%. It demonstrates that the failure of non-welding steel can be warned early by K _C or ΔH _p(y)_ave when the fatigue life has 20% left.

In contrast, the characteristic parameters k for Q345B welding specimen and the characteristic parameters H _p(y)_ave for Q345qC welding specimen decrease at first, and then increase obviously when specimen approaches failure. The failure of Q345B and Q345qC welding steel can be warned early by k and H _p(y)_ave when the fatigue life has 1.3% and 18% left, respectively. On account of the differences in welding quality for different welding specimen, the discreteness of method by using the variation of k and H _p(y)_ave to forecast the specimen failure is larger. Thus, it should begin to attach importance to the safety of welding specimen once the characteristic parameter k or H _p(y)_ave is decreasing.

Although some magnetic characteristic parameters have a certain fluctuation at the beginning of damage accumulation, the characteristic parameters of magnetic memory signal (i.e. K _C, ΔH _p(y)_ave, k, and H _p(y)_ave) still can be used for the characterization of fatigue damage process. Hence, it is feasible to evaluate the fatigue life of welding and non-welding steels with different materials using the magnetic memory technique.

6. Conclusion

In this paper, the tension-compression fatigue tests for Q345B and Q345qC welding and non-welding specimens were carried out and the MMM testing was done in this process. Based on the normal component of magnetic memory signals, H _p(y), and its variations, ΔH _p(y), the slope of ΔH _p(y) fitting curves, K _C, and the average of ΔH _p(y) signals on the whole testing line, ΔH _p(y)_ave, were extracted as the characteristic parameters for Q345B and Q345qC non-welding specimens, respectively. Additionally, the gradient between “peak” and “vale” on H _p(y) signals curves, k, and the average of H _p(y) signals in the welding zone, H _p(y)_ave, were extracted as the characteristic parameters for Q345B and Q345qC welding specimens, respectively. The following conclusions can be drawn by comparison:

The H _p(y) signals curves for Q345qC non-welding specimen do not present obvious rotational phenomenon like the Q345B non-welding specimen. It indicates that the variation laws of H _p(y) signals curves with cyclic loads for different ferromagnetic materials have some differences.

Q345B welding specimen appears the “peak-vale” phenomenon at the welding zone, but the Q345qC welding specimen only has the “peak” phenomenon and does not exhibit the reversal of “peak-value” after specimen failure. It indicated that the variation laws of H _p(y) signals curves with cyclic loads for Q345B and Q345qC welding specimens are quite different.

The fatigue life of welding and non-welding specimens with different materials can be evaluated effectively by using corresponding magnetic characteristic parameters. Remarkably, the characteristic parameters for welding and non-welding specimens with the same material have a certain similarity.

The failure of non-welding steel can be warned early by K _C or ΔH _p(y)_ave when the fatigue life has 20% left. In contrast, due to the larger discreteness of welding quality, the damage degree of welding specimen should begin to be valued highly once the k or H _p(y)_ave is decreasing.

Footnotes

Acknowledgements

The authors are grateful for the financial support received from the National Nature Science Foundation of China (Grant Nos. 51878548 and 51578449), the Key Project of Natural Science Foundation Research Plan of Shaanxi Province (Grant No. 2018JZ5013).

Conflict of interest

The authors declared that they have no conflicts of interest in this work.

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Comparative study on the characteristics of magnetic memory signals for welding and non-welding steels with different materials under tension-compression fatigue

Abstract

Keywords

1. Introduction

2. Experiment

2.1. Specimen preparation

Table 1 Chemical composition of Q345B steel (wt%) Material C Si Mn P S Mo Nb V Ti CEV Q345B 0.16 0.14 1.46 0.10 0.006 0.004 0.002 0.004 0.031 0.42

Table 4 Mechanical properties of different specimens Specimens E / GPa ϵ y , % σ y / MPa σ u / MPa A, % J-1 203 0.14 385 535 34.00 JH-1 193 0.20 346 450 10.00 Q-1 203 0.18 430 550 40.00 QH-1 205 0.28 430 535 36.00

3.1. Non-welding specimen

4.1. Non-welding specimen

Footnotes

Acknowledgements

Conflict of interest

References

Table 1
Chemical composition of Q345B steel (wt%)

Material C Si Mn P S Mo Nb V Ti CEV

Q345B 0.16 0.14 1.46 0.10 0.006 0.004 0.002 0.004 0.031 0.42

Table 4
Mechanical properties of different specimens

Specimens E / GPa ϵ_y, % σ_y/ MPa σ_u/ MPa A, %

J-1 203 0.14 385 535 34.00

JH-1 193 0.20 346 450 10.00

Q-1 203 0.18 430 550 40.00

QH-1 205 0.28 430 535 36.00