1 Introduction

The evolution of strain/stress is one of the most critical factors involved in welding process due to localized heating and nonuniform cooling. Knowledge about the characteristics of strain during welding is fundamental to understand welding residual stress and distortion [1]. However, researches on the strain and stress in the vicinity of the weld pool have been difficult in nature and the success was limited. There are many contact and noncontact methods to measure the residual stress or distortion, such as mechanical relaxation, X-ray, and neutron diffraction and strain gauge [2]. However, most of these methods are costly due to the requirement of specialized instrument, and some of them are not even capable of in situ strain measurement [3]. Strain gauge is a commonly used technique to measure transient strain, but one strain gauge only measures the strain at a single location and the method is vulnerable to high temperature, although some high strain gauges are used in certain cases [4]. Moire technique is another option to measure dynamic strain around a welding arc; it has been used for many years. Lytel measures dynamic strains during welding of Al alloy using a projected-grating moire technique [5]. Kowalski and Voloshin presented an image analysis enhanced moire interferometry method to study laser weld thermal strain [6]. These researches proved the possibilities of in situ strain measurement during welding by moire techniques. However, the moire pattern preparation is complicated and time-consuming compared to digital image correlation (DIC) method. Most of the existing in situ strain data come from indirect calculation such as simulation but not direct experimental measurement. Experimental measurements of the transient strain or deformation fields around the weld pool have been a challenging task.

DIC is a powerful tool to measure surface displacement and strain. It is used in many areas that include material processing. There are also some researches about the strain measurement on a weld bead after welding. Ref. [7] reported full field strain measurement of resistant spot welds using DIC. Ref. [8] reported the constitutive behavior of laser welds in 304-L stainless steel by DIC. The crack tip opening angle and extension of the strain localization ahead of the crack tip of molten spot weld were measured by DIC [9]. However, the in situ strain measurement during arc weld using DIC remains a major challenge due to the higher temperature and strong arc light. Since the DIC technique usually requires a layer of paint to form a random speckle pattern on the material surface, the high temperature would destroy the speckle. In addition, the strong arc would affect the acquisition of high-quality images. Some researchers have tried the strain measurement during welding using DIC. De Strycker et al. [10, 11] proved the feasibility of transient strain measurement during welding using DIC; the results showed good agreements with that measured by electrical strain gauges. Coules et al. [12] measured the biaxial thermal stress fields caused by arc welding. In their researches, the physical shields were used to protect the measurement area from arc welding. In those experiments, only the far-field strain was measured, usually 20 mm far away from weld centerline. However, the strain field in the vicinity of the weld pool is more of interest than far-field area, because the strain field near the weld pool is more important to better understand the evolution of weld strain/stress.

For the welding of thin sheets, one of the main problems is the distortion after welding. In order to understand how the strain develops and how to prevent welded sheets from distortion, the knowledge of strain evolution during the welding history includes the cooling stage which is very important. Experiences from previous researches not only proved the possibilities of strain measurement using DIC but also showed that only the far-field strain could be measured from the front side of weld. This paper aims to evaluate the in situ strain evolution during tungsten inert gas (TIG) welding of thin stainless steel using three-dimensional (3D) DIC to measure the near-field strain on the backside welding pool.

2 Experiments

Four butt welding experiments were carried out at horizontal position (PC according to ISO/EN) using 1 mm-thick 304 stainless steel plates prepared in the layout shown in Fig. 1. The TIG weld without filler metal was used. The welding heat input was designed to be the same, the welding parameters are shown in Table 1, and all welds had full penetration and were defect-free. Before welding, two thin plates were clamped in special designed fixture, one of which was painted with a high-temperature-resistance speckle pattern. One typical image after welding is shown in Fig. 2. The start arc position is set as origin point. The x-axis is along with the weld line, and the y-axis is along the transverse direction of the weld, as shown in Fig. 2. The T-shaped markers were used to calibrate actual distance of welded specimens. Two CCD cameras were fixed at the backside of weld to capture images during welding history. The camera type is GRAS-50S5M/C with image sensor model ICX2/3”; the maximum frame rate at maximum resolution is 15 fps at 2448HX2048V.

Fig. 1
figure 1

Experimental setup

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Table 1 Welding parameters
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Fig. 2
figure 2

Typical image and coordinates system

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Two stages of image acquisition rate were used—8 fps during the first 100 s and 0.5 fps during the next 500 s. The image snapping time of 600 s ensures the weld cool down to room temperature. Totally, 1050 images are used to calculate strain evolution during welding and cooling history.

3 Results and discussion

The software VIC-3D is used to analyze all images acquired by stereovision system. 3D DIC measures the displacements in x, y, and z directions by the image correlation algorithm; the strains are calculated by the following formula:

$$ {e}_{xx}=\frac{\partial u}{\partial x}+\frac{1}{2}\left\{{\left(\frac{\partial u}{\partial x}\right)}^2\right.+{\left(\frac{\partial v}{\partial x}\right)}^2+\left.{\left(\frac{\partial w}{\partial x}\right)}^2\right\} $$
(1)
$$ {e}_{yy}=\frac{\partial v}{\partial y}+\frac{1}{2}\left\{{\left(\frac{\partial u}{\partial y}\right)}^2\right.+{\left(\frac{\partial v}{\partial y}\right)}^2+\left.{\left(\frac{\partial w}{\partial y}\right)}^2\right\} $$
(2)
$$ {e}_{xy}=\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}+\left\{\left(\frac{\partial u}{\partial x}\right)\left(\frac{\partial u}{\partial y}\right)+\left(\frac{\partial v}{\partial x}\right)\left(\frac{\partial v}{\partial y}\right)+\right.\left.\left(\frac{\partial w}{\partial x}\right)\left(\frac{\partial w}{\partial y}\right)\right\} $$
(3)

where e xx , e yy , and e xy means are the strains in x and y directions and the shear strain on the x-y plain. u, v, and w are the displacements in the x, y, and z directions, respectively.

In order to evaluate strain evolution more clearly, we use the concept of principal strain. Figure 3 shows how strains transform from the given coordinates system to principal directions. Its transformation can be expressed by Formula (4).

$$ {e}_{1,2}=\frac{e_{xx}+{e}_{yy}}{2}\pm \sqrt{{\left(\frac{{e_{xx}-e}_{yy}}{2}\right)}^2+{e_{xy}}^2} $$
(4)
Fig. 3
figure 3

Strains in principal directions

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where e xx , e yy , and e xy are strains in x, y and shear strain calculated by Formulas (1), (2), and (3); e 1 , 2 are the principal strains; and θ p in Fig. 3 is the principal angles. It also illustrates an approximate Mohr’s circle for the given strain state.

Prior to performing the experiments, stereovision system is calibrated using a target with uniformly spaced (6-mm checkboard used here) markers. The calibration is performed following the standard procedures provided by Vic-DIC. The calibration would affect the strain calculation accuracy, and successful calibration means minimum average distance between theoretical and the actual position where the point is found in the camera image.

The effect of position on strain evolution is evaluated according to the methods above. The welding parameters are shown in Table 1. Figure 4 shows the strain evolution at different y-distances from the weld centerline (the definition of x, y as shown in Fig. 2). The shear strains are from y = 6, 10, and 17 mm when x = 95, respectively. The data is an average value of an area 1 × 1 mm at the center (x, y). Principal strain e 1 is calculated by Formula (4). Strain rises to peak value at the same time when the arc goes through the tested position. The peak strain decreases with the increase of distance y due to the lower peak temperature at different positions. From the evolution of principal strain, it shows that residual strain after cooling down to room temperature becomes stable but varies with position. The closer to weld centerline, the more residual principal strain is remained.

Fig. 4
figure 4

Strain evolution with y when x is 95 mm. a e xx . b e yy . c e xy . d e 1

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Similarly, we can get the strain evolution with respect to x. Figure 5 shows the strain evolution when x is 27, 33, 50, 86, and 94 mm, separately with y at 8 mm. The strain peaks of x, y direction, shear strain, and principal strain were similar, but occurred at different time due to the time delay of arc traveling. The residual strain becomes stable after cooling stage but appears a little bit different. For the principal strain, the closer to start arc position, the more residual strain is remained.

Fig. 5
figure 5

Strain evolution with x when y is 8 mm. a e yy . b e xx . c e xy . d e 1

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Welding parameters also affect the strain evolution during welding. The main factor is the heat input. In order to evaluate the strain evolution under different welding parameters with the same heat input, four group welding parameters are designed as shown in Table 1. Three of them, butt1, butt3, and butt 4, are chosen for comparison. Figure 6 shows the strain evolution under different designed welding parameters. The data is acquired at position (x = 95 mm, y = 5 mm). The strains reach peak value at different time due to the different welding speed. For strain e xx , the peak value increases with the decreasing of welding speed. For shear strain e xy and strain e yy at y direction, the change of strain peak is different from strain e xx . The evolution of principal strain shows its peak value decreases with the decreasing of welding speed. However, the decrease is not so obvious, and the peak value decreases by 2% when welding speed decreases three times (from 9.6 to 3.2 mm/s). Thus, we can think that the principal strain remains the same under the same heat input, although the welding parameters changed.

Fig. 6
figure 6

The effect of welding parameters on strain evolution (x = 95 mm, y = 5 mm). a e xx . b e yy . c e xy . d e 1

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Figure 7 shows the principal strain evolution map of different welding parameters at two positions. The transient strains at two positions under two different welding parameters are mapped. With the decreasing of welding speed, the strain field shape becomes wider along transverse direction but the peak value remains similar.

Fig. 7
figure 7

Principal strain maps during welding at 2 positions. a Butt1: e 1 when arc at point 2. b Butt1: e 1 when arc at point 3. c Butt2: e 1 when arc at point 2. d Butt3: e 1 when arc at point 3. e Butt3: e 1 when arc at point 2. f Butt4: e 1 when arc at point 3. g Butt4: e 1 when arc at point 2. h Butt4: e 1 when arc at point 3

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In fact, many factors affect the strain evolution during welding, and the weld distribution is complex. We try to keep experimental conditions the same, such as the clamping pressure, restraint and speckle size, and calculated parameters, but there are still some factors that are not under control, which will affect the calculated accuracy. For example, the thin plates usually are not so stiff, which affect the strain calculation [1].

As a measuring technique, the uncertainties and errors are important. The assessment of digital image correlation measurement errors is full researched from both methodology and results [13–15]. Generally, the spatial resolution (including speckle size), hardware (including cameras), and software (including calculate parameters such as calculation, pixel size) affect the errors; the situation is similar in different applications and fully discussed. Here, we simply discuss the uncertainty considering welding conditions. Besides the common factors that affect the uncertainties, the main error results from the burn out of paint speckles due to the high temperature of the arc. That is why it is very difficult to measure the strain close to the arc center. Little research report the results of welding strain by DIC, usually only the data that 20 mm far away from weld centerline can be detected [7, 8]. In order to verify the repeat accuracy, we do more than ten times repeat experiments. The repeat accuracy is about 95% under the same processing parameters, and the errors mainly come from the speckle quality not from welding experiments or calculation. Some random error is bigger because the speckle is partly burned during welding, which will generate errors when compare the images before and after welding during the DIC calculations. The random error can be smoothed by algorithms. Besides the factors mentioned above, the subset is an important factor to affect strain calculation results. Selection of subset size plays a critical role in achieving high accuracy in DIC. The subset size in DIC is normally selected by testing different subset sizes across the entire image. For the welding technology, we hope to achieve care more on the strain data close to weld center. Big subset size would be helpful to detect data closer to weld center but lost some details because more pixels are used to compare and calculate while little subset size gets the contrary effect. Generally, DIC is not considered for measuring strain below 1/1000. For welding, the strain or deformation decreases quickly with the distance to the weld bead. Farther from the weld bead, the noise is larger and strain calculation has less accuracy, which is also proved by Ref. [8]. The closer to the weld bead, the more creditable the data is, but the high temperature and welding arc made the worse condition when capturing welding images. Fortunately, the backside observation prevents images acquisition from deteriorating by strong arc during welding, which makes it possible to get the strain evolution in the vicinity of the weld pool. Usually, we can get the strain data at 4 mm from the weld centerline, but the data is stable at about 5 mm, which is a big progress in the in situ strain measurement during welding. The relationship between the front and backside strain field is undergoing. We are trying to get strain evolution in the front side, and the simulation also would help to develop the relationship.

4 Conclusions

3D DIC technique through backside observation was successfully applied on in situ strain evaluation during TIG welding of thin stainless steel. It proved to be a useful method for extracting local strain response near the weld pool during welding. One of the highlights of this method is the prevention of the strong welding arc from high-quality image acquisition, which makes strain analysis possible in the vicinity of weld pool. Stable strain data could be acquired at 5 mm from weld centerline. The method provides a quantitative assessment of in situ strain evolution in the vicinity of the weld.