The use of conventional strain gauges evaluation for measurements of residual stresses in welded joints

Residual stresses (RS) can reach significant values in a welded joint, committing the quality of the parts since they affect their resistance to fatigue causing cracks and corrosion under stress. The use of strain gauges positioned in specific zones of welded parts, as a way of mapping the RS values from the welding processes, has a great technological interest. The method proposed in this paper defines strategic positions for strain gauges along ASTM A36 steel plates in butt-welded joints using Gas Tungsten Arc Welding. Helped by a signal conditioner, RS values were collected and registered after welding process. The results are the readings of RS imposed by the welding operation, taking into account thermal process effects and the material properties. Experimental results were compared with numerical analysis, via Finite Element Method which showed the potential use of strain gauges for measuring RS from the welding process.

Welding speed, mm/s y Distance from the weld bead, mm industrial scale. However, one difficulty of this process consists in the possibility of generating residual stresses (RS) that can directly affect the quality of components (service life). According to Jiang and Guan [10], a combination of weld residual stress and external loads has a great effect on a welded product, and the weld deformation can increase the stress concentration when the operating load is applied.
RS are consequences of interactions between time, temperature, deformation and microstructure [12]. Examples of these interactions have been mentioned in the automotive [4] and in the shipping industry [16] using welded parts which are constantly subject to the appearance of RS.
Following this approach, the Finite Element Method (FEM) is a tool, among others, for predicting RS due to structural and metallurgical changes in the material during the welding process [2]. FEM had consolidated its application in welding from the 70s [19] and has been widely used as an evaluation tool for RS measurements [9]. The use of numerical methods may represent an important tool for solving problems in welding which should be compared with experimental methods, increasing the results reliability.
The first analytical formulations applied to welding were proposed around the 40s by Rosenthal [17] which presented models of temperature gradients to predict RS in welded joints. Latter, Masubuchi [13] presented resolution strategies through a specific software that performed finite element thermal analysis. Currently, it is common to find papers that deal specifically with numerical analysis using finite elements applied to welding [1]. Some commercial software can be used for this kind of analysis, such as Abaqus Ò and Nastran Ò which are capable of simulating welding processes but are not intended to be used only for this purpose and depend on the skill and knowledge of the users.
For the specific welding application, there are commercial software designed specifically to simulate thermal process resulting from the welding such as Sysweld Ò and Simufact Ò . Basically, these commercial softwares simulate the welding process, solving temperature distributions and the increments of plastic deformation due to temperature gradients. This kind of software allows users to simulate almost of all industrial welding processes such as electrical resistance welding, laser welding, Gas Metal Arc Welding (GMWA) and Gas Tungsten Arc Welding (GTWA), and also some heat treatments, predicting metallurgical transformations that occur in the material due to non-uniform temperature distributions. All these factors make this specific software attractive as regards the comparison of numerical results with experimental methods for RS prediction in welding.
Techniques for measuring RS can be either semidestructive or destructive and also non-destructive techniques are considered, such as X-ray diffraction, neutron diffraction, ultrasound or magnetic techniques [11]. A usual semi-destructive technique for RS measurement in welding is the hole-drilling method [8]. Through this technique, standard small diameter holes are produced on the material surface close to the welding bead and strain measurements are performed due to the stress relief produced by the holes. The measurements are performed by strain gauges rosettes which are sensors positioned in predefined angles for measurement of deformation helped by electrical voltage signals. Small deformations in the material are mechanically transmitted to the strain gauge which converts these deformations into electrical resistance. The formulation for this conversion depends on the material which is intended to perform the measurement [20].
Conventional strain gauges for measuring RS in welding process is a technique that can be used not only for carrying out the measurement after welding such as the hole-drilling method that beyond that has high costs of investment. The method also aims to perform RS measurements as an option for monitoring the development of stresses during the welding process. It is known that the proposed method has limitations such as high temperatures and magnetic noise. However its advantages due to the simplicity to measure the evolution of RS during the welding cycle are also understood.
The experimental results obtained by conventional strain gauges and compared with numerical analysis results as an aid in understanding the mechanisms of RS arising during the welding process were satisfactory. Considering the experimental and numerical results showed in this paper, it is expected that the proposed method can help to prevent RS problems in industrial components subjected to welding processes.

Numerical model
According Masubuchi [12], the temperature distribution peak in welded zones, specifically in the Heat Affected Zone (HAZ) and in its vicinity, can be determined using Eq. (1).
where T p is the temperature peak at a distance y from the weld bead, T 0 is the initial temperature of the plate, q is the density of base material (BM), C is the specific heat source coefficient, t is the thickness of BM, H is the heat input and T m is the plate melting temperature.
In this case, the heat input is the amount of heat intensity per length unit imposed in the welding joint to reach the melting of materials and may be expressed by Eq. (2).
where V is the electrical voltage imposed to the weld, i is the electric current intensity, vs is the welding speed and g is the coefficient of thermal efficiency in the welding process.
Taking into account, boundary conditions and the geometry of the part to be welded in the simulations, the fundamental heat transfer can be applied for a solid material to determine the temperature along the part, at each instant, by means of Eq. (3).
where x, y and z are three-dimensional coordinates, k T is the material thermal conductivity and q 0 is the heat source. RS are a system in equilibrium in the absence of external forces and thermal gradients. For an element to be in static equilibrium under elastic forces, including inertial forces acting on the plane, the total strain on the plate (e total ) can be decomposed into elastic strain (e e ), thermal strain (e T ) and plastic strain (e P ), according to the Eq. (4).
From the assumption that there is no influence on the external stresses, RS arise in the part only if the distribution of inelastic deformation is irregular. This situation occurs due to the large irregularity in the temperature distributions. The formulation used for thermal and structural analyzes, addressing the mathematical models supported by numerical simulation, can be found in Bezerra et al. [2].

RS evolution in the welding process
In the welded joints, thermal cycles are produced by the heat source and phase transformation causing changes in the material metallurgy. After welding, the final product may present small distortions generated by the temperature variation from the process. In this case, the temperature peak intensity determines zones of metallurgic changes. These changes are caused by thermal cycling, generating RS at the end of the procedure [18]. Figure 1 provides, in a simplified form, a better understanding of stresses evolution during a welding process due to thermal cycles.
In the section AA', Fig. 1 shows that the heat input is not sufficient to change the stresses level. In the section BB', located exactly in the weld bead, the peak temperature reached exceeds the material melting point. This process generates the expansion of the material, which undergoes internal (colder surrounding material) and external constraints (clamps and own structural rigidity) providing elastic compression stresses which grow until the material yield strength. In the section CC', the compressive yield stress decreases in magnitude. At this point, stresses appear in the center of the weld bead due to the material cooling in that region. During the material cooling, the shrinkage of the welded parts undergoes the same internal and external constraints and develops stresses which increase with decreasing of the temperature. These stresses may reach the material yield strength depending on the maximum temperature developed during the thermal cycle. When the material turns back to the room temperature (section DD' in the Fig. 1), RS can occur.

RS measurement by using conventional strain gauges
Because of welding be a process that leads to a non-uniform distribution of temperature which is associated with small plastic deformation, the use of strain gauges along the parts to be welded can be applied to measure parts deformation from the process. In strain gauge transducers, the proportionality between the change in electrical resistance of the sensor and the mechanical strain is defined as the Gauge Factor (GF). The GF value is provided by the sensor manufacturer which is obtained by the Eq. (5).
where dR/R is the electrical resistance range and is the axial deformation of the sensor. Knowing the GF value and the change of electrical resistance measured by the sensors helped by a Wheatstone bridge, small deformations of the material are provided in

Materials and methods
In the experiments, it was used plates with dimensions of 125 9 100 9 6 mm from ASTM A36 steel material. This kind of steel is one of the most used materials in welded joints because it does not need special heat treatments. The main mechanical characteristic of this steel is its yield strength of 250 MPa (min) and the limit resistance of 400-550 MPa. Table 1 shows the chemical characteristics of the material used in the experiments. Prior to the welding process, the plates were normalized (treated at the austenitization temperature, keeping them at this temperature in a specific period of time and then cooled in the air). This heat treatment was aimed to eliminate possible defects from any preceding mechanical process. It was used GTWA process, manual welding, direct DC-polarity, filler metal ER 70S-6 (diameter of 2.5 mm), shielding gas 100 % air, and gas flow 9 l/min. Both plates were previously clamped. Table 2 shows the main data used in the welding process of the plates.
A single butt weld position with partial penetration was used in the experiments because the easy accessibility of the operator with no risk of losing the experiment due to nonconformity during welding and consequently the loss of funds spent for the specimen instrumentation. The parts dimension to be welded were defined based on the experiments performed by other authors as Chang and Teng [3] who used similar process and material established in this paper. The welding procedure has been defined based on the requirements of GTWA process and the geometric characteristics of the joint according to Fig. 2.
For the signal conditioning, a device with 32 channels of outputs was used, allowing a proper configuration for each kind of Wheatstone bridge.
In addition, some procedures were rigorously followed for bonding the strain gauges in the parts, which follow standard steps according to Craig's description [5]. It was observed that bonding and positioning of strain gauges in the part were the most important steps due to sensors misalignment occurrence and risk of bubbles between sensors and the surface of the parts, thus compromising the process of measurement.
In the experiments, unidirectional strain gauges were used with GF = 2.11, sensor base material in polyamide for steel using, electrical resistance of 350 X and wired copper welded terminals [7]. The zone in the plates in which the strain gauges were positioned, closer to the weld bead as possible, was considered critical as result of the sensors failure possibility depending on the temperature peaks imposed by the heat source, thus compromising the tests. To avoid this drawback, previous studies of the strain gauges location were performed, helped by thermocouples. Figure 3 illustrates the strain gauges plates positioning considering the symmetry in both plates as regards of the weld bead.
It was known the RS measurement complexity even in materials free from external forces. It is also known that RS are not directly measured, but the elastic deformation caused by it. These deformations, present at the end of welding processes, were measured in the development of experiments that comprise this paper. After plates reached the room temperature, stresses values were collected.   Figure 4 illustrates the experiment at the end of the welding process with the strain gauges position and its proper connections to the data acquisition system.
6 Results and discussion

Experimental results
As expected, failures occurred in some strain gauges due to the high temperature imposed in the experiments. Even following the procedures suggested by the manufacturer, some sensors failed during the welding process as seen in the Fig. 4 (red cycles). For this reason, strain gauges were placed on both plates symmetrically, consequently they could also serve as a comparison of equidistant points, which theoretically should have the same electrical voltage values. Figure 5 shows, schematically, the position of strain gauges that failed identified by an X and the RS results (MPa) for those that remained functioning after welding process.

Numerical analysis results
For the numerical simulation, the same experimental welding parameters were used. A mesh was generated with isoparametric finite elements with eight nodes each one in a total of 18,352 nodes. The mesh was refined close to the weld bead with elements of 1.5 9 1.5 mm which were increased gradually until to reach 5.0 9 5.0 mm. The material used for the simulations has properties similar to ASTM A36 steel, according to the commercial software library. Dimensions of the welded region were collected as shown in Fig. 6 which illustrate a cross section macrography of the weld bead. Through the Fig. 6, the HAZ and the BM (base material) may be noted as well as the main dimensions used as inputs data for numerical analysis. After the full meshing and input data entered correctly in the commercial software, the numerical simulations with iterations were performed taking into account, the analysis in successive time. Since the objective of this paper is to compare the numerical and experimental results, RS in   Figure 7 shows these simulated RS values for each node only for the left side plate due to the fact that symmetrical values were considered for the right side.  (Fig. 8a) and right side (Fig. 8b) of the welded specimen. Figure 9 represents numerical and experimental results of the longitudinal RS in the line of 62.5 mm (see Figs. 5, 7 for the line position reference) positioned on the left (Fig. 9a) and right side (Fig. 9b) of the welded specimen. Figure 10 represents numerical and experimental results of the longitudinal RS in the line of 95 mm (see Figs. 5, 7 for the line position reference) positioned on the left (Fig. 10a) and right side (Fig. 10b) of the welded specimen.

Numerical and experimental results comparison
It is noted in the Figs. 8, 9 and 10 that some points have been omitted which represent the strain gauges that failed in the experiments. For this reason, the trend lines are closed in the graphical representation to mitigate the impact of these missing values. Although, there is no overlap in any of the points analyzed and differences found around 35 %, the numerical and experimental results showed similar behavior, i.e., when strain gauges were moving away from the weld bead, RS values tend to zero.
Even though all RS measurements were carried out from 30 mm to the center of weld bead and consequently generated in the BM, it should be clarified that strain gauges were positioned due to the maximum temperature without compromising its operation. It should also be emphasized that RS are not restricted to the HAZ and some points in the BM present negative RS values [14]. It was confirmed   Longitudinal stresses are small in points more distant from the center of the weld bead, but not necessarily must, be discarded.
Analyzing the feasibility of the proposed method for measuring RS in welding and taking in consideration some similar work as in Rodriguez et al. [16] in which authors used the ASTM A36 steel in the experiments and holedrilling method for RS measurements. Results obtained by Chang and Teng [3], which also used ASTM A36 steel and GTWA process in their experiments, it was found that it is possible to obtain values of 50 MPa far from the weld bead around 40 mm in a sheet metal plate with thickness of 4.5 mm. Finally, Dong et al. [6] used techniques such as X-ray and neutron diffraction for RS measurement in comparison with the FEM. Therefore, the proposed method for RS measurement by using conventional strain gauge is feasible, but with some restrictions which are presented below: • The ability of the operator for the strain gauges bonding. • A signal conditioning system capable of filtering out the thermal and magnetic noises. • Isolate the effect of temperature during the welding process by using special strain gauges.
The above restrictions have influence on the behavior of RS, taking into account the welding process variables.

Conclusions
This paper aimed to evaluate the use of conventional strain gauges on steel plates to measure RS values from the welding process. For this purpose, finite elements via commercial software were used for predicting RS values and correlate them with those obtained using the experimental method suggested. According to results obtained, it is concluded that: • Higher measured values of longitudinal RS were found at 30 mm from the center of the weld bead. These values were negatives (compressive stresses) and decrease as they become more distant from the weld bead. • By means of conventional strain gauges, RS values up to -3 MPa can be measured not necessarily close to the weld bead. • Conventional strain gauge measurement technique can be used in welding where the effect of temperature does not affect sensors operation. The method is not applied for measurements in regions where the temperature of the weld exceeds the value set by the manufacturer of strain gauges. In this case, it is suggested the use of special sensors. • The sensors functionality during experiments depends on the strain gauge bonding process, signal conditioning system and the possibility to cancel the effect of temperature and magnetic field through specific software. • The discrepancy between values found (around 35 %) in the prediction of finite element analysis and experimental tests can be explained by the factors mentioned above, as the operator's skill, lack of filters and effect of temperature on the sensors.