1. Introduction

Mechanical testing of a material or construct is an essential task in many scientific fields (e.g., material science, mechanical engineering and solid mechanics) and engineering applications. A common implementation of mechanical testing is uniaxial tensile or compressive testing by the use of a Universal Testing Machine (UTM) to determine the ultimate tensile strength, maximum elongation, the elastic limit of the material, and other properties such as elastic modulus, Poisson’s ratio, strain-hardening characteristics. However, to accurately determine these mechanical properties, the surface strains of the loaded specimen must be precisely measured, which could be a challenging task considering the huge diversity in testing materials and testing conditions.

Clip-on mechanical extensometers are popularly used in material testing to measure axial strains of a test specimen with high rigidity like metals or rigid plastics. While providing high-precision strain measurement in many applications [1], these contact devices have the disadvantages of careful manual intervention, less flexibility and limited applicability due to the following reasons [2,3]: (1) Their weight and method of attachment can influence the load-strain response of the test specimen, thus preventing their applications to polymers, biological tissues and soft materials. Also, sufficient tension must be provided to prevent slippage of the knife edges or clip-on wire forms mounted on the specimen, which is prone to initiate premature failure; (2) Many mechanical devices have limited travel and must be removed prior to specimen rupture to prevent any damage to the extensometer assembly; (3) One mechanical extensometer can only measure one-directional (generally axial) strain averaged over the fixed gauge length. Further, common mechanical extensometers designed for use in ambient temperature cannot be used in other environmental conditions (high or low temperature).

To overcome these disadvantages, non-contact video extensometers using a digital video camera and various digital image processing algorithms, including both feature-based [3–8] and intensity-based (or area-based) [9–11] image registration algorithms, have been established. The video extensometers based on feature-based image-processing algorithms measure the surface stains of a specimen by tracking the movements of the geometric features (e.g., centroids, corners) of various artificial marks (e.g., circle dots [3,4], paper strips [5], welded lines [6], heat shrink tubing [7], shoulders [8]), which can be painted, glued, attached or fabricated onto the test sample.

In addition to these feature-based image registration techniques, intensity-based image matching algorithms using digital image correlation (DIC) [9–11] can also be employed. DIC [12–14] is a powerful optical technique widely used in the experimental mechanics community for full-field displacement and strain measurements, and has generally been used as a post-processing technique with higher registration accuracy but heavy computational cost. However, benefiting from recent advancements made on subpixel registration algorithms [15–17], attempts have been made to adopt DIC for real-time displacement and strain mapping. For instance, the authors of this work [18] developed an advance video deflectometer for real-time, remote, multipoint deflection measurement at a rate of 117 fps. Recently, Wu et al. [19] adopted DIC for dynamic strain measurement at a rate of 60 fps. Shao et al. [20] realized real-time 3D deformation monitoring at a frame rate of 10 fps with the aid of parallel computing. Despite these advances, a DIC-based video extensometer, which is capable of measuring both longitudinal and transversal strains with the prominent features of real-time, strong robustness and very high accuracy, has not been reported so far.

In this work, based on the recent progress we made in DIC technique, an advanced video extensometer is proposed for non-contact, real-time, high-accuracy strain measurement for a sample during mechanical testing. To achieve the purpose of real-time, robust and high-accuracy strain measurement using the present video extensometer, innovations are made in the two consecutive stages of DIC measurement, namely image capture and displacement tracking algorithm. Firstly, a “near perfect and ultra-stable” imaging system [21,22] combining the idea of active imaging with a high-quality bilateral telecentric lens is equipped to a video camera, which can continuously capture surface images of a test specimen at a frame rate of 117 fps. The special optical design provides high-fidelity video images with nearly constant image contrast and magnification invariant to the potential variations in ambient lighting and the possible small out-of-plane motions in object surface and/or image plane. Secondly, an efficient and accurate inverse compositional Gauss-Newton (IC-GN) algorithm [17,23] is employed to achieve real-time displacement tracking at defined target points with subpixel accuracy. During the implementation of IC-GN algorithm, a temporal initial guess transfer scheme is used to predict accurate initial guess to avoid time-consuming integer displacement searching. Also, to minimize the bias error in the measured displacements, low-pass pre-filtering of the speckle images using a 5 × 5 pixels Gaussian filter and a high-accuracy intensity interpolation method are jointly used in IC-GN algorithm. In the remainder of this article, the optical design and working principles of the proposed advanced video extensometer are first described. Then, real tensile tests of an aluminum specimen and a carbon fiber filament sample are used to demonstrate the practicality, efficiency and accuracy of the proposed advanced video extensometer.

2. Methods

2.1 Optical design for the advanced video extensometer

A schematic illustration of the established video extensometer for non-contact, real-time, high-accuracy strain measurement is shown in Fig. 1. The system consists of a high-speed area scan monochrome camera (Genie HM1024, Teledyne DALSA, Ontario, Canada), a high-quality bilateral telecentric lens (Xenoplan 1:5, Schneider Optics, Inc., Germany), an optical bandpass filter with a center wavelength of 450 ± 2 nm, a monochromatic source emitting at 450-455nm and a laptop (Thinkpad T440p, Lengend, Intel(R) Core(TM) i7-4700MQ CPU, 2.40GHz main frequency and 8G RAM). The camera allows for a maximum image capture rate of 117 fps in 1024 × 768 pixels resolution with 8-bit quantization, and is connected to the laptop using a Gigabit Ethernet standard LAN wire.

 

Fig. 1 (a) Schematic diagram of the established advanced video extensometer. (b) the bilateral telecentric lens, and (c) the transmission spectrum of the optical bandpass filter.

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To capture high-fidelity digital images of a test object and lay the basis for subsequent high-accuracy strain measurement, a “near perfect and ultra-stable” imaging system, which combines the active imaging with a high-quality bilateral telecentric lens, is established in the proposed advanced video extensometer. Compared with conventional optical imaging systems that use a regular lens and white light illumination, the present imaging system offers the following three distinct advantages.

Firstly, with the unique design and placement of the aperture stop shown in Fig. 1(b), the bilateral telecentric lens is not susceptible to small changes in both the object distance and imaging distance. Thus, compared with the use of a conventional lens, the established imaging system equipped with a bilateral telecentric lens performs much better in minimizing the virtual displacements/strains caused by unavoidable out-of-plane motions (translation and/or rotations) occurred to the specimen surface.

Secondly, the established imaging system using a bilateral telecentric lens presents very low lens distortion, which results in negligible errors in displacement and strain fields due to in-plane motions, as validated in our previous research [21].

Thirdly, to compensate the possible illumination variations presented in the mechanical testing, improvements are also made to illumination and imaging in the proposed video extensometer. A monochromatic ring blue LED lighting emitting at 450-455nm, instead of a common white light source, is adopted for illumination. Also, an optical bandpass filter, with a coupled center wavelength of 450 ± 2 nm and a full-width at half-maximum value of approximately 32 nm, is mounted before the bilateral telecentric lens. Figure 1(c) shows the transmission efficiency curve of the bandpass filter. For the active illuminated monochromatic light, the bandpass filter shows a very high transmission efficiency exceeding 80%. As only very limited portion of ambient light within the bandpass range of the filter can pass through the filter, the ambient light makes negligible contribution to the intensity of recorded image compared with the actively illuminated monochromatic light. The system is therefore capable of acquiring stable video images with almost constant brightness and contrast even though serious changes have been occurred in ambient lighting.

In short, the proposed advanced video extensometer combining the merits of a bilateral telecentric lens and active imaging can be considered to a “near-perfect and ultra-stable” imaging system that can record high-fidelity images of a test specimen without being affected by any small out-of-plane motions occurred between object surface and image plane, ambient light variations as well as lens distortion.

2.2 Working principle of the advanced video extensometer

In order to realize real-time strain measurement and visualization, the live video images of a test sample acquired at a frame rate of 117 fps by the CCD camera must be processed in real time. As indicated in Fig. 2, to simultaneously measure axial and lateral strains of the test specimen, at least four calculation points (i.e., p₁ and p₃, p₂ and p₄) located at the ends of two perpendicular lines with one line along the axial direction and the other along the transversal direction must be tracked. Based on the detected image displacements at these four points, the nominal longitudinal strain and nominal transversal strain are calculated as

 

Fig. 2 The four-point mode for measuring longitudinal and transversal strains

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Based on the measured two normal strains, the Poison’s ratio of a test sample can be estimated as

It is apparent that the efficiency and accuracy of the developed video extensometer strongly depends on the performance of DIC algorithm used. In this section below, the basic principle of the state-of-the-art IC-GN algorithm is described. Some practical issues, which have significant influence on the efficiency and accuracy of IC-GN algorithm, are also provided.

2.3 Real-time and high-accuracy displacement tracking with IC-GN algorithm

The advanced IC-GN algorithm, which was recently introduced into DIC community by the authors of this paper [17], is employed for real-time and high-accuracy displacement/strain determination in the proposed video extensometer. Using the pre-estimated initial guess of displacements at each measurement point, IC-GN algorithm can determine subpixel displacements at these points by optimizing the following robust zero-mean normalized sum of squared difference (ZNSSD) criterion.

The nonlinear ZNSSD correlation criterion given in Eq. (3) can be minimized with respect to $\Delta p$ using Gauss-Newton algorithm. After computing the parameter vector $\Delta p$, the incremental warp $W\left(\xi ;\Delta p\right)$ of the reference subset can be determined. Subsequently, the incremental warp is inverted and composed with the current estimate $W\left(\xi ;p\right)$ to generate the updated warp function of the target subset. In the interest of saving space, more details regarding IC-GN algorithm are not given here. Interested readers are referred to ref [17].

The iteration calculation of the desired deformed parameter vector p is repeated until the pre-set convergence conditions are reached. It has been demonstrated in our previous work [26] that the convergence criteria do have an impact on the accuracy and efficiency of DIC measurement. In this work, the convergence conditions are set to ensure that variations in the norm of the incremental deformation parameter is equal to or less than 0.01 pixels, i.e., $\Vert \Delta p\Vert =\sqrt{{\left(\Delta u\right)}^2+{\left(\Delta v\right)}^2}\le 0.01$ pixels or the maximum number of iteration reaches 5 times [26]. Afterwards, the deformation parameter P of the target subset is determined. It is also worth noting that, to more intuitively indicate the matching quality, the ZNSSD coefficient can be converted to the well-known zero-mean normalized cross-correlation (ZNCC) coefficient, which falls in a range of [-1, 1] with a higher value denoting better matching quality.

Although the accuracy and efficiency of IC-GN algorithm has been well demonstrated in previous works [17,26], the following two practical issues involved in initial guess and subpixel intensity interpolation should be carefully addressed to achieve real-time and high-accuracy displacement tracking with subpixel accuracy.

(1) Initial guess. Note that, as a non-linear local optimization algorithm, IC-GN algorithm requires an initial guess of deformation parameters very close to the true value to determine the subpixel motion of each calculation point. At the initial stage of motion tracking, the initial guess of the displacement vector for each point is set to be zeros. Considering that the incremental displacement of a considered point in the consecutive video frames recorded at a high-frame rate is generally smaller than a pixel, a temporal initial guess transfer scheme using the calculated displacement vectors of calculation points in the previous two frames are used to predict their initial guess of the current frame.

Nevertheless, a simple integer displacement searching performed in the spatial domain can be used to calculate the integer displacement of the point if the final ZNCC value is smaller than the preset threshold (set to be 0.7 in this work).

(2) Intensity interpolation. Also note that, the implementation of IC-GN algorithm requires an intensity interpolation method to reconstruct the subpixel intensities of the target subset. Although recent research [24,25] proves that IC-GN algorithm eliminate the noise-induced bias error, it also has bias error in the measured displacements if a low-accuracy interpolation method is used. We observed that the errors in measured displacements can be further amplified during strain calculation, leading to systematic strain errors that increase linearly with strain level [27]. To eliminate the periodic strain errors, bicubic B-spline interpolation combined with a Gaussian low-pass pre-filtering approach [28] has been incorporated in IC-GN algorithm. As will be demonstrated later, the bias error can be decreased to negligibly small values.

3. Experiments

Two sets of experiments were conducted to validate the practicality, efficiency and accuracy of the proposed advanced video extensometer for real-time, non-contact and high-accuracy strain measurement in material testing.

3.1 Real-time tensile strain measurements of an aluminum sample

In the first test, a dog-bone aluminum specimen measuring 20 mm wide by 2 mm thick was used. The overall length of the specimen was 360 mm, and the distance between the two grips was approximately 280 mm. The specimen was tested in a universal material testing machine (WDW-100A, Jinan Shidai Shijing Yiqi, Co., Ltd., Shangdong Province, China) as illustrated in Fig. 3(a). Before testing, the specimen was sprayed with white and black paints, and then clamped to the upper and lower grippers. After that, the established video extensometer was placed 268 mm (i.e., the working distance of the bilateral telecentric lens used) away from the test sample, with its optical axis approximately normal to the sample surface. Then, by adjusting the illumination intensity of the actively illuminated LED source and the aperture of the bilateral telecentric lens, a clear image of the sample with sufficient contrast was acquired. The initial gauge lengths for the vertical line and horizontal line were specified as 450 pixels (≈14.021 mm), and 380 pixels (≈11.840 mm), respectively, and the subset size defined for correlation analysis was 41 × 41pixels.

 

Fig. 3 (a) The established video extensometer, (b) the reference image of the test aluminum sample, and (c) the pre-assigned load-time curve.

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To demonstrate the accuracy and repeatability of the advanced video extensometer, the highest tensile loading of 3200 N was exerted to the sample. Note that the maximum load was set to 3200 N to keep the strain of the specimen (about 1050 με) within the linear elastic range. Before the start of the tensile test, a tensile load of 200 N was applied to the specimen as an initial load. Then, the specimen was loaded to the maximum load of 3200 N with a loading speed of 50 N/s. After reaching the preset highest load, the sample was loaded and unloaded to 200 N. The same loading procedure shown in Fig. 3(c) was repeated three times. During the loading and unloading process, the video extensometer was used to measure the longitudinal and transversal strains at a speed of 117 fps.

Figure 4(a) plots the axial and transversal strains of the two line as a function of time. As expected, the axial strain increases linearly with the increase of the tensile load, and the transversal strain decrease linearly. The changing trends of these two strains agree with the pre-assigned loading stages. To examine the strain accuracy associated with different interpolation methods, two different interpolation methods (i.e., bicubic convolution interpolation and bicubic B-spline interpolation) were used in combination with Gaussian pre-filtering approach proposed in [28]. A comparison of the measured strains using various interpolation methods is given in Fig. 4. Apparent periodic strain errors in the measured results can be found in Fig. 4(a) and 4(b). We attribute these errors to the systematic errors caused by imperfect intensity interpolation. However, a perfect repeatability in the measured strains can be observed for the three repeating loading periodicities, and the maximum difference in the strains measured at difference period is less than 3 με.

 

Fig. 4 The computed strains versus time using various interpolation methods. (a) bicubic convolution interpolation, (b) 5 × 5 pixels Gaussian pre-filtering and bicubic convolution interpolation, (c) bicubic B-spline interpolation, and (d) 5 × 5 pixels Gaussian pre-filtering and bicubic B-spline interpolation.

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To quantitatively examine the strain accuracy related to various interpolation methods, the strain errors in the first loading stage (ranging from 20 to 80 s) are analyzed as shown in Fig. 5. The strain error is estimated as $\Delta \epsilon =\epsilon -{\epsilon }_a$ with $\epsilon$ denoting the measured longitudinal or transversal directions strains, ${\epsilon }_a$ the actual strain calculated based on the loading force of the material testing machine and the known elastic modulus (70 GPa) and the Poisson’s ratio (0.33) of the aluminum specimen. With the increase in loading force, the amplitude of periodic strain error associated with bicubic convolution interpolation increases obviously. The combined use of Gauss pre-filtering and bicubic convolution interpolation or the sole use of bicubic B-spline interpolation can enhance strain accuracy but cannot fully eliminate the periodic strain errors. Overall, the combined use of Gauss pre-filtering and bicubic B-spline interpolation effectively suppress the strain errors to nearly zeros without discernable periodicity, and the maximum strain errors in longitudinal and transversal directions were estimated as 24 με and 23 με, respectively.

 

Fig. 5 Comparison of the strain errors related to four different interpolation methods: (Left) error in ε_xx, (right) error in ε_yy.

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3.2 Real-time tensile strain and tensile modulus measurements of a carbon fiber multifilament sample

As a typical application example, the established advanced video extensometer was used characterize the mechanical properties of carbon fiber multifilament sample. According to Chinese national standard GB/T 3362-2005 (Test methods for tensile properties of carbon fiber multifilament), the measurement of carbon fiber tensile properties involves three important indicators, namely tensile strength, tensile modulus and elongation at break. Traditionally, the measurement of these three indicators using clip-on extensometer needs to performed on separate tests using two samples. The first sample is used to the measurement of Young’s modulus using clip-on extensometer, since the mechanical devices must be removed prior to specimen rupture to avoid damage. Based on the measured Young’s modulus and the tensile strength as well as the estimated cross-section area of the second sample, the elongation of the carbon fiber multifilament sample can be calculated. By contrast, with the aid of the established video extensometer, all these three parameters can be measured in a single test.

The test carbon fiber multifilament specimen was bought from Toray carbon fiber (Type: T300-3000) with a full length of 250mm. To facilitate the testing machine clamped at both ends of the carbon fiber cardboard stick, the distance between two cardboards is about 150mm. White and black points were premade on the carbon fiber filament. The axial strain of the sample will be tracked by the present video extensometer. The tensile stress-strain relationship and elongation at break of the sample was measured by the video extensometer, based on which the tensile modulus and tensile strength can be estimated. Also, to demonstrate the accuracy of the video extensometer, these experimental obtained values were compared with the reference values provided by the manufacturer.

Before the start of the tensile test, a tensile load of 20 N was applied to the specimen as the initial load. Then the machine was loaded at a speed of 20 N/s to the maximum tensile loading of 1000 N. Meanwhile, the advanced video extensometer was started to measure strain until the sample broke. Two points with a distance of 450 pixels (≈14.021mm) were used to extract the longitudinal strains for the sample subjected tensile loading. Note that the subset size defined for displacement tracking is 41 × 41 pixels, as shown in the bottom left inserted figure in Fig. 6.

 

Fig. 6 Real-time stress-strain curves of the test carbon fiber multifilament sample measured by the established video extensometer. The inserted two pictures show an image of the specimen and its reference image with specified subsets.

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As shown in Fig. 6, the loading force of experimental machine increased linearly as time goes by, and the longitudinal strain value measured by the video extensometer increased accordingly. The strain data appeared abnormal when the specimen was broken. It is observed that, on the breaking moment, the strain was 14980 με and the corresponding loading force was 398 N. The cross-sectional area of the specimen can be estimated based on the provided the carbon fiber volume density of 1.76 kg/m3 and the line density of 198 g/km. Thus, the tensile strength can be estimated as 3.54 Gpa. Taking the linear segment’s stress-strain data from 5 s to 60 s, an elastic modulus of 231 Gpa was calculated with least squares fitting.

Table 1 summarizes the elastic modulus and maximum elongation of the sample measured by the established advanced video extensometer. In contrast to the corresponding reference values provided by the producer, the relative percentage errors are found to be 1.7% and 0.1% respectively. In addition to its high accuracy measurements, the proposed video extensometer also demonstrates another apparent advantage by determining all the three mechanical properties in a single testing.

Table 1. Comparison between the Experimental Obtained Mechanical Properties and the Reference Values

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4. On the accuracy, efficiency and applicability of the established advanced video extensometer

As is clear in Eq. (1), the strain accuracy of the established advanced video extensometer depends on two factors. One is the registration accuracy of DIC algorithm, and the other is the specified gauge lengths defined in the reference image. By the combined use of the low-pass pre-filtering approach and high-accuracy bicubic B-spline interpolation method, the bias error in displacement measurement can be suppressed to less than 0.005 pixels, as demonstrated in our previous paper [28]. Thus, if a gauge length of 500 pixels is used, the strain error is estimated to be 20 με. Of course the strain error is expected to increase if small gauge lengths were defined.

However, for a small gauge length, different calculation schemes can be used at the expense of increasing computational cost. For example, instead of tracking four discrete points, one can track regularly spaced calculation points defined in two perpendicular lines or a rectangular region. Based on the vertical displacements along a vertical line and the horizontal displacements along a horizontal line or the displacement fields in the ROI, the normal strains can be fitted using linear polynomials. The fitting process can effectively eliminate the strain errors due to bias error in displacement tracking. Using this strain calculation approach, dozens or even hundreds of calculation points should be tracked in the live video images, thus lessening the computational efficiency of the proposed video extensometer. Although not shown here, our experimental results indicate that the proposed video extensometer can achieve a frame rate of 15 fps for approximately 400 calculation points (correspond to a 20 by 20 grid).

Also, it should be emphasized here that, there is no single extensometer that can satisfy all testing need considering the diverse requirements of material testing. The proposed advanced video extensometer using a high-quality bilateral telecentric lens may not be used to specimens subjected to large deformation due the limited field of view (FOV) and fixed working distance of the lens. To measure large tensile strains whose elongation plus the initial gauge length is larger than the FOV, the imaging lens must be changed. In this case, special care should be taken for choosing proper objective lens with minimal lens distortion and least sensitivity to out-of-plane motion of the specimen [30,31]. Otherwise, different correction or compensation methods using an additional non-deformable reference specimen [32] or a dual-reflector imaging approach [11] should be used.

5. Concluding remarks

In this paper, an advanced video extensometer based on the recent progress we made in DIC is developed for non-contact, real-time, high-accuracy strain measurement in material testing. The accuracy and efficiency of the present video extensometer over existing ones are mainly delivered by the two innovations made to both optical imaging and correlation algorithms. Specifically, (1) a “near perfect and ultra-stable” imaging system combining the idea of active imaging and a high-quality bilateral telecentric lens is constructed, which offers strong robustness against to ambient lighting changes and is insensitive to the possible small out-of-plane motions occurred in object surface and/or image plane; (2) An efficient and accurate inverse compositional Gauss-Newton algorithm combined with the use of a temporal initial guess transfer scheme and a high-accuracy intensity interpolation scheme is employed to achieve real-time displacement tracking with subpixel accuracy. The results obtained from real tensile tests of two specimens showed that axial and transversal strains can be measured and plotted at a speed of 117 fps and with a maximum error less than 30 με.

Aside from the prominent advantages of real-time, high accuracy strain measurements with strong robustness over exiting non-contact video extensometers, the proposed advanced video extensometer also provides the following merits over conventional contact-type extensometers such as ease of use with fully automatic operation until the breaking point, wider application scope to various materials, flexible measurement with variable gauge lengths. In particular, it is worth pointing out that the use of the active imaging not only demonstrates strong robustness against ambient variations, but also is insensitive to thermal radiation of hot objects [33]. Thus, the proposed advanced video extensometer is anticipated to be used for real-time strain measurement of high-temperature mechanical testing with the aid of a high-temperature furnace equipped with an optical observation window. Further work on this will be reported in forthcoming works.