1. Introduction
Residual stresses are the result of internal or built-in strains in materials that persist in the absence or after the removal of external mechanical or thermal loading. The loading may be intentional or unintentional and occur during the fabrication and manufacturing process as well as the use of a material during its lifetime [
1].
Residual stresses generally extend throughout the bulk of the material and reflect a balance between tensile and compressive stresses forming a nonuniform 3D profile mathematically described by a stress tensor. Their effect is similar to that of external mechanical loading, with the difference that the latter is generally known or can be determined in a straightforward manner. They may, therefore, be responsible for material or structure failure even in the absence of apparent external loading. Residual stresses are ultimately the result of lattice irregularities and dislocations related to the composition as well as the history of a material. In materials used in construction, such as steels, their monitoring, evaluation, and control, during the fabrication process, will contribute to zero defect manufacturing while, during their lifetime, it will optimize maintenance and prevent critical fatigue.
Typical steel fabrication and manufacturing technologies include casting, rolling, molding, bending, welding, heat treatment, which all induce residual stresses. For example, welding is a highly dynamic process during which the materials undergo phase transformations because of the high temperatures and subsequent cooling applied. During welding, the heat energy disperses inside the material, primarily via conduction, and causes random internal permanent strains [
2]. Three welding zones are distinguished, based on the effect the welding has on its microstructure and related residual stresses: (1) the fusion zone (FZ) which is the result of a temperature induced phase transformation whose texture depends on the material’s composition and the method of welding applied; it is characterized by high residual stresses due to inhomogeneously distributed elastically or plastically deformed regions [
2]; (2) the heat affected zone (HAZ) which is characterized by stress relief and microstructural characteristics similar to annealed materials; (3) the base metal (BM) whose stress profile is unaffected by the welding. The residual stresses, induced during the welding process, typically do not exceed the base material’s yield point but it is possible that they extend even up to the ultimate tensile strength [
3]. The balance of tensile and compressive stresses is important for the quality and performance of the weld. Tensile residual stresses are thought to be harmful as they assist crack propagation and stress corrosion cracking while compressive residual stresses, within the elastic deformation range, increase wear and corrosion resistance can prevent crack initiation and propagation [
4,
5].
Several techniques, some of them standardized, have been proposed for the monitoring or determination of residual stresses, such as the hole-drilling method, diffractometry, ultrasonics and nonlinear acoustics [
2,
3,
4,
5,
6]. Some of them operate in the bulk while others only on the surface of the material. The lowest uncertainty, approximately 1%, is offered by X-ray diffraction (XRD) for surface strains [
7] and neutron diffraction (ND) for bulk strains.
The magnetic properties of most steel grades and their inherent link to the atomic structure and microstructure have led to the emergence of magnetic non-destructive testing applications. Several studies [
7,
8,
9,
10,
11,
12,
13,
14] have established the relationship between magnetic parameters and material properties such as hardness, yield, residual stress, and deformation state etc. The magnetic Barkhausen noise [
15,
16,
17,
18,
19], the magneto-acoustic emission [
15,
20], the magnetic memory method [
21], and the magnetic adaptive method [
22] have long been studied by several laboratories. Magnetic methods are applied to the surface or the bulk of the material depending on the setup and sensors used. Though their potential in residual stress monitoring has been recognized, their sensitivity to the experimental setup, the high level of uncertainty, and the lack of metrics for calibration have so far prevented their standardization.
In this work, we focus on a recently proposed magnetic non-destructive method for determining residual stresses, which has been successfully applied to welds. The method has shown uncertainties comparable to those attained with diffraction methods while at the same time offering a calibration method for each steels’ grade examined [
23,
24,
25]. The magnetic parameter used is the maximum value of the differential magnetic permeability,
measured after unloading from various tensile and compressive stress levels applied within the elastic region of the material. The plotting of the magnetic parameter against residual stress results in the Magnetic Stress Calibration (MASC) curve, which is characteristic for a given steel grade. Residual stresses in any given structure made of that steel grade can then be determined using a simple permeability measurement. The method does not depend on the sensor or arrangement being used as long as the same is used for both the MASC curve determination and the residual stress evaluation.
We present results on three different samples of welded steels, namely non-oriented electrical, low carbon hypoeutectoid and low-alloyed hypoeutectoid steel samples prepared using Gas Tungsten Arc Welding (GTAW). The MASC curve for each sample has been obtained in the laboratory using extra low frequency ac magnetometry, to minimize eddy current losses in the magnetic measurements, and a calibrated, load cell controlled, apparatus to apply tensile and compressive stresses within the elastic region of the material. In this work, we only show results on bulk magnetic measurements but it is possible to measure the magnetic parameter, , either on the surface or in the bulk. The MASC curves thus obtained were used to determine the residual stresses along the three welds. Next, we evaluated local strains on the same samples, using the stress-strain curve of each steel grade and XRD (Bruker D8 diffractometer, Analytical Instruments SA, Athens, Greece), in the Bragg–Brentano set-up, for surface stresses or ND for bulk. After the magnetic and diffraction measurements, the microstructure of the welded samples was studied with Scanning Electron Microscopy (SEM) (JSM 6100 type, N. Asteriadis SA, Athens, Greece). Finally, in order to establish the uncertainty level of the new method, was measured at the same points where residual stresses, , had been determined by diffractometry. The resulting curve was successfully compared to the one obtained in the laboratory, which underlines the superiority of the new method to existing ones with respect to accuracy, efficiency, cost, and ease of use.
2. Materials and Method
The three ferromagnetic steel grades chosen for this study are: a cold rolled non-oriented electrical steel (NOES), a low carbon hypoeutectoid steel (AISI 1008) and a low alloyed hypoeutectoid steel (AISI 4130). The alloys differ in both magnetic and mechanical properties. The chemical composition of the alloys is reported in
Table 1.
Rectangular samples were cut from the as-received materials. The dimensions of the samples are listed in
Table 2. Both the oxide and the coating layer were cleaned in a 5% HCl and 95% distilled water solution.
A single pass square butt joint automated weld was made along the rolling direction (RD) of the rolled sheets, using the GTAW process (
Figure 1) according to AWS C5.5 [
26]. Argon, at a flow rate of 10 L/min, was used as a shielding gas. The welding parameters for the weld joints are given below in
Table 3.
For the results shown here, we first obtain the MASC curve for each steel grade, in the laboratory. The methodology for obtaining these MASC curves is the following: Each sample of ferromagnetic steel, similar to the base materials of the welds, is subjected to successive stresses levels, both tensile and compressive, in the elastic deformation range of the material and below the Villari point, to ensure that only residual stresses are induced. The stresses may be induced in a controlled manner using a device that allows the control of the level of stress, via a load cell, and its rate of change, e.g., an INSTRON machine (300DX type) (Analytical Instruments SA, Athens, Greece). At each stress level, the sample is unloaded and
is measured. Its peak value,
, is plotted against the applied stress level [
23].
The magnetic parameter,
, is measured using ac magnetometry (NTUA in-house instrument, Athens, Greece), along the rolling direction, of the unloaded pre-strained samples. A programmable function generator connected to a power amplifier generates the low frequency (0.5 Hz) sinusoidal current fed to the excitation coil of a yoke-shaped sensor forming a closed magnetic circuit with the sample. The sample is magnetized by the excitation field,
, and the resulting time-varying magnetization induces a sinusoidal output voltage
, at the ends of a sensing coil, according to Faradays’ law. It is easily shown that
is proportional to
. If the material is enclosed by the sensing coil, we measure the bulk permeability; if it is perpendicular to it, we measure the surface permeability. Here we report on bulk permeability measurements. The value we record is the peak value of the output voltage,
, which is proportional to
, and which occurs at a field close to the coercivity of the material. Because the sensor is not calibrated against a standard steel sample, we report the measured
values and not
values. The proportionality constant between
and
can be roughly estimated from the excitation field and sensing coil parameters resulting in the following approximate
values: 56, 1.5 and 1.7 mWb/Am, for NOES, AISI1008 and AISI4130 respectively. Each measurement is repeated six times. Plotting
vs.
we obtain the MASC curve of a given material (
Figure 2). The MASC curves shown in
Figure 2 correspond to bulk permeability measurements.
Once the MASC curve for each steel grade is determined, we proceed with the measurement of permeability on the welded samples. It is important that the same sensor is used for these measurements, as well. The measurements have been carried out at regular intervals of 0.5 mm parallel and perpendicular to the weld direction starting from 15 mm away from the weld edges at each side of the weld specimen to include all three welding regions, namely the BM, the HAZ and the FZ, and to avoid edge effects due to cutting [
23]. Then, using the permeability measurements and the corresponding MASC curve we can determine the residual stress levels at each point of measurement.
To investigate the effectiveness and efficiency of our method, we compared the residual stress profiles thus obtained against diffraction measurements. XRD is used in the Bragg–Brentano set-up (XRD-BB) in order to determine the average of local surface microstrains in the area of measurement, which are correlated with surface permeability measurements. ND measurements provide the reference measurements for bulk permeability. The uncertainty of XRD-BB can be brought down to 1–5% [
27] by appropriate control of the photonic excitation as well as optimization of the counts averaging method. Similar techniques have been applied for the ND measurements shown here. XRD measurements were carried out using Cr-Kα radiation X-ray tube, operating with a target current of 5 mA at 30 kV. ND measurements were carried out at the Nuclear Station Rez near Prague (Nuclear Station Rez near Prague, Rez, Czech Republic), with an accuracy of 5%, along the (110) crystallographic plane of the ferrite. The experimental procedure is discussed in detail in [
23,
24,
25]. The corresponding residual stresses are calculated using Young’s modulus and Poisson’s ratio of each steel grade. Young’s moduli,
, have been determined from the gradient of the linear portion (elastic region) of the stress-strain curves. They have been found to be 210 GPa, 225.5 GPa, and 225 GPa for NOES, AISI 1008 and AISI 4130 respectively; the Poisson’s ratio,
, was taken equal to 0.28.
Finally, microstructural characterization using SEM is carried out in order to investigate changes in microstructure in all three welding zones: BM, HAZ, FZ. Metallographic samples were extracted from the welded plates and polished with 800 to 2400 grit SiC paper followed by 3 μm and 1 μm diamond paste suspension to obtain mirror finish, and etching using 2% Nital solution.
3. Results
Figure 2 illustrates the bulk MASC curves for the three steel grades examined. Compressive (negative) and tensile (positive) residual stress values in MPa are plotted on the horizontal axis. The sensor’s peak output voltage,
, corresponding to
measured at each given stress level, is plotted on the vertical axis (in arbitrary units because the sensor is uncalibrated.)
All three curves follow a similar sigmoidal trend.
increases with tensile and decreases with compressive stress. Since all three steels have positive magnetostriction, the results are in line with the Le Chatelier equilibrium principle: the magnetization along the stress direction increases, if the signs of magnetostriction and applied stress are the same, and vice versa. No hysteretic effects have been observed and this contributes to a lower uncertainty of the measurement [
23,
24,
25].
Τhe curves were normalized using yield stress, σY, as a proxy. The yield stress values used were 200 ΜPa for NOES, 214 ΜPa for AISI 1008 and 280 ΜPa for AISI 4130.
The use of a normalized curve greatly facilitates the determination of the residual stress value at the under-examination region of each welding sample. It simplifies the mapping of the stress profile as it allows the evaluation of residual stresses with respect to the fractional deviation from the unstressed state (zero point).
To determine the normalized magnetic permeability and stress values,
and
respectively, the following formulas are used:
where (
,
) is the
th point on the MASC curve, (
,
) is the point corresponding to the maximum tensile stress point, and (
,
) is the point corresponding to the maximum compressive stress point (
Figure 2).
Figure 3 shows the normalized calibration curves of the three aforementioned steel grades as well as the MASC curve of a high alloyed steel. All normalized curves seem to collapse into one which suggests the existence of a universal curve.
Figure 4 presents the distribution of residual stress values on either side of the FZ centerline, as determined via XRD, ND, and bulk magnetic permeability measurements for all three types of steel. The permeability values shown correspond to measurements across the weld, in the middle of each sample; i.e., at 60 mm from the edge for the NOES sample and at 100 mm form the edge for the other two steel grades.
As already mentioned, MASC curves are obtained for the elastic region only. To determine stresses outside the MASC curve range, extrapolation is used. The extent of the validity of this approach is currently under study.
The profiles of the residual stresses measured using diffraction techniques exhibit similar trends as well as differences, which are attributed to the difference in volume of inspection and penetration depth in each case. The XRD measurements are sensitive to surface conditions with an assumed penetration depth in the order of 20 μm, while for the ND measurements, the residual stress value is the average over an effective penetration depth of 5 mm. For NOES and AISI 4130 samples (
Figure 4a,c), XRD measurements reveal a tensile bell-shaped stress profile that increases sharply around the weld line and tends to zero exponentially moving away from the weld line. ND measurements show high tensile and compressive stresses in the FZ and compressive stresses in the HAZ, which tend to zero away from the weld line. In the case of AISI 1008 (
Figure 4b), the bell-shape profile was inversed possibly due to the difference in the heat dissipation profile in this steel grade, as a result of the welding procedure. In all cases, stress, tensile or compressive, gradually tends to zero as the BM region is approached.
With known
and
, Equations (1) and (2) have been used to determine residual stress values
, from permeability measurements and the normalized curve of
Figure 3. The stress profiles thus obtained are similar to the ND curves. This is strong evidence for the validity of our method since the MASC curves used for the stress profile determination were based on bulk permeability measurements. Significant deviations are observed near the centerline where the microstructural changes due to welding are dramatic. FZ is of higher complexity than the other two regions and requires further study.
The microstructural studies of the base metal and welded joints samples were performed using SEM on the above welded samples. The metallographic evaluation showed that the BM of the NOES welded sample consisted of a single-phase ferrite matrix (
Figure 5a).
Figure 5b illustrates the microstructure in the heat affected zone which consists of an almost completely recrystallized elongated ferrite structure with a quite homogeneous grain size distribution, which is in line with the lower stresses measured there. Dendrite groups of α-ferrite developed in the FZ (
Figure 5c) during the solidification process, which make the microstructure highly inhomogeneous. The stress profile in that region is quite complex as is the microstructure and tests the limits of our method.
The BM of the AISI 1008 welded sample has shown predominantly equiaxed proeutectoid ferrite grains (α-Fe) and low volume fraction of banded-structured pearlite (P) (
Figure 6a). The HAZ microstructure comprised finer pearlite and uniformly distributed carbides in polygonal ferrite grains (
Figure 6b). On the other hand, the FZ is comprised of acicular ferrite (AF) and Widmanstätten ferrite (WF) as parallel ferrite laths, thermodynamically unstable bainite (B) and cementite (Fe
3C) (
Figure 6c).
Figure 7 illustrates the microstructural complexity developed at the weld joints of AISI 4130 welded sample. The microstructure of the BM consists mainly of ferrite grains (α-Fe) with regions of martensite-austenite (MA) constitutes and presumably granular bainite (GB) (
Figure 7a). The martensite is characterized by an absence of carbide precipitation, whereas an extensive carbide precipitation was observed on the bainitic structure. The diverse constituents of the multiphase HAZ are shown in
Figure 7b. A continuous network of polygonal ferrite grains is observed with the remaining part of the structure consisting of degenerated pearlite (DP), acicular platelets of bainite (B) arranged in the form of islands within a ferrite matrix. A full martensitic structure is the dominant microstructure of the FZ as illustrated in
Figure 7c.
Author Contributions
Conceptualization, E.H.; Methodology, E.H. and P.V.; Software, P.V.; Validation, A.K. and P.T.; Formal Analysis, P.V. and A.K.; Data Curation, P.V.; Investigation, P.V.; Writing-Original Draft Preparation, P.V.; Writing-Review & Editing, A.K., P.T. and E.H.; Visualization, P.V.; Supervision, E.H.; Project Administration, E.H.
Acknowledgments
Acknowledgements are due to the researchers of the nuclear station Rez near Prague and Peter Svec, Slovak Academy of Sciences.
Conflicts of Interest
The authors declare no conflict of interest.
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Figure 1.
Dimensions of the (a) non-oriented electrical steel (NOES); (b) low carbon hypoeutectoid steel (AISI) 1008 and low alloyed hypoeutectoid steel (AISI) 4130 welded samples. (WD: Welding direction, RD: Rolling Direction).
Figure 2.
Magnetic Stress Calibration (MASC) curves for (a) NOES; (b) AISI 1008 and (c) AISI 4130 steel. The black marks with the error bars indicate the measured permeability values at each residual stress level while the red line is a fitted curve.
Figure 3.
Normalized maximum differential permeability vs. normalized stress for the examined steel grades.
Figure 4.
Residual stress profiles using X-ray diffraction (XRD), neutron diffraction (ND) and magnetic techniques (top) and optical images (bottom) of the Gas Tungsten Arc Welding (GTAW) welded (a) NOES, (b) AISI 1008 and (c) AISI 4130 steel samples (WD: welding direction, RD: rolling direction).
Figure 5.
Scanning Electron Microscope (SEM) metallographic images from (a) base metal; (b) heat affected zone and (c) fusion zone of the NOES welded sample (marked phases: α-Fe: ferrite).
Figure 6.
SEM metallographic images from (a) base metal; (b) heat affected zone and (c) fusion zone of the AISI 1008 welded sample. (Marked phases: P: pearlite, AF: acicular ferrite, WF: Widmanstätten ferrite, B: bainite, Fe3C: cementite).
Figure 7.
SEM metallographic images from (a) base metal; (b) heat affected zone and (c) fusion zone of the AISI 4130 welded sample. (Marked phases: α-Fe: ferrite, GB: granular bainite, B: bainite, DP: degenerated pearlite).
Figure 8.
Maximum differential permeability measurements vs. residual stress determined by ND in GTAW welded (a) NOES, (b) AISI 1008 and (c) AISI 4130 steel.
Figure 9.
MASC curves obtained at the laboratory are compared against the difference ∆μ (blue marks) between permeability measured on unwelded samples in the lab and permeability measured across GTAW welds for comparable levels of residual stress on samples of: (a) NOES, (b) AISI 1008 and (c) AISI 4130 steel.
Table 1.
Chemical composition in weight percent of the selected ferromagnetic steels.
Impurities | NOES | AISI 1008 | AISI 4130 |
---|
C | 0.002 | 0.060 | 0.30 |
Si | 2.20 | 0.180 | 0.26 |
Mn | 0.15 | 0.530 | 0.55 |
Cr | - | 0.014 | 0.95 |
Mo | - | 0.015 | 0.15 |
Al | 0.30 | - | - |
Cu | - | 0.050 | - |
Ni | - | 0.020 | - |
S | 0.00005 | 0.014 | 0.021 |
P | 0.00005 | 0.030 | 0.021 |
Fe | in balance | in balance | in balance |
Table 2.
Dimensions of ferromagnetic steel samples before welding.
Dimensions | NOES | AISI 1008 | AISI 4130 |
---|
Length (mm) | 60 | 80 | 80 |
Width (mm) | 120 | 200 | 200 |
Thickness (mm) | 0.28 | 15 | 15 |
Table 3.
Welding parameters for weld joints.
Parameters | NOES | AISI 1008 | AISI 4130 |
---|
Welding process | GTAW | GTAW | GTAW |
Current (A) | 85 | 92 | 92 |
Voltage (V) | 15 | 15 | 15 |
Speed (mm·s−1) | 4,1 | 3,1 | 3,1 |
No. of passes | 1 | 1 | 1 |
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