**1. Introduction**

Residual stresses are present in almost all materials. They may arise during the manufacturing process or over the life of a material. Their quantification process is essential because their superposition with stresses occurring in the material due to the external loading can lead to material failure. The measurement techniques used for residual stress quantification can be divided into three main groups: non-destructive, semi-destructive, and destructive.

In a production environment, determination of residual stresses in the material is usually based on the standardized hole-drilling strain gauge method allowing identification of in-plane residual stresses near the measured specimen surface made from an isotropic linear-elastic material.

The methodology of residual stresses quantification using the hole-drilling strain gauge method involves several steps:


**Citation:** Pástor, M.; Hagara, M.; Virgala, I.; Kal'avský, A.; Sapietová, A.; Hagarová, L. Design of a Unique Device for Residual Stresses Quantification by the Drilling Method Combining the PhotoStress and Digital Image Correlation. *Materials* **2021**, *14*, 314. https:// doi.org/10.3390/ma14020314

Received: 30 November 2020 Accepted: 7 January 2021 Published: 9 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).


Stresses that remain approximately constant along the depth are defined as uniform stresses. If the stresses vary significantly with depth, they are known as non-uniform stresses. If the residual stress in a thin specimen material is investigated, the uniform stress measurement is specified. Both uniform and non-uniform stress measurements are specified for thick specimens. The accuracy of the results is satisfying if the residual stresses quantified in a thick specimen material do not exceed about 80% of the material yield stress. On the other hand, the residual stresses determined in a thin specimen material are less than approximately 50% of the material yield stress. Experimental measurements described in the following parts of the paper will be applied to the investigation of strains relieved in the area surrounding the hole cut into the thin specimen loaded by uniaxial tension. Due to similarity, the methodology for residual stress quantification performed in a thin specimen, drilling a through-hole as described in detail in ASTM E837-13a standard [1], can be found in Appendix A.

Many commercial devices allow control of the hole or the core milling process and evaluate the results using their own software. Over recent years, some modifications in the milling process have occurred, too, e.g., translational motion of the milling cutter has been replaced by circular motion.

Measurement techniques such as moiré interferometry, electronic speckle pattern interferometry, shearography, photoelasticity as well as digital image correlation belong to the group of non-contact experimental methods, which gradually replace conventional strain gauges used for the strain analysis at a point (or its near surroundings) and provide full-field information about the strain distribution. Some of them have already been adapted for residual stress quantification.

The moiré interferometry (MI) method works on the principle of diffraction grating interferometry, where interference fringes occur after each deformation of the object surface. The grating can be physically attached or just virtually generated on the object surface by two symmetric beams of light transmitted from the same source of coherent laser emission. Key characteristics relating to the use of MI for residual stress analysis are high displacement and spatial resolution, the possibility for micro-scaled measurements and incremental hole-drilling investigation. Ya et al. [2] designed a unique measuring system based on phase-shifted MI combined with the hole-drilling method, and analyzed the residual stresses on an aluminum plate. The use of MI in the determination of residual stresses, e.g., in the AS10OU3NG material with one surface shot-peened [2], composite materials [3], welded titanium alloy plate [4] as well as a uniaxially tensioned plate made from black polymethylmethacrylate [5] suggest the possibility of using this method in a wide range of materials.

Electronic speckle-pattern interferometry (ESPI) is based on the interference of two monochromatic laser beams, i.e., a subject beam reflected from the object surface and a reference beam creating reference speckle-effect on the image plane of the CCD (chargecoupled device) camera. The method does not require to create grid or speckles, has a high displacement resolution [6,7], allows performing measurements outside the laboratory [8], and removes the effect of rigid-body motion [9,10]. Analysis can be done on curved and rough surfaces using the incremental hole-drilling method. A portable measuring system with one symmetrical dual-beam illumination constructed by Viotti et al. [11] is another specially designed device that provides automatic calculation of residual stresses from measured displacements using the least square method. In 2017, Lothhammer et al. [12]

constructed a measuring device designed for the residual stress quantification on the resistance-welded pipes. According to the authors, their device provides a more effective way to quantify the non-uniform stress distribution obtained at the same quality level compared to the conventional techniques.

Digital image correlation (DIC) is based on the comparison of digital images captured during the loading of an analyzed object. It is not as sensitive to ambient vibrations as the MI or ESPI methods, and therefore it is suitable for use in a production environment. In all the following references, specially adapted devices combining DIC and the coreor hole-drilling technique were used to quantify residual stresses. In 2005, one of the first residual stresses measurements using DIC was carried out by McGinnis et al. [13], when the authors investigated steel plates and reached less than 7% error in normal stress, which established the robustness of 3D DIC to capture the expected displacements. In 2006, Nelson et al. [14] calculated the residual stresses from displacements using dimensionless relations derived from numerical analysis, and good correspondence with the results acquired by the holographic method was achieved. In 2008, a hole-drilling device with an integrated camera allowing measurement of displacements on the object surface of 7 × 5.6 mm was developed [15]. The accuracy of the device was tested by the analysis of compression residual stresses simulated on the pipe loaded by the testing machine, whereby the acquired results similarly correspond to the results obtained by strain gauge rosette. In 2017, Baldi and Bertolino [16] developed a low-cost residual stress measuring instrument with integrated digital image correlation (iDIC). Using the proposed approach, the rigid-body motion is easily compensated for and no decorrelation problem results from large translations. The use of 2D iDIC was described in [17], where Baldi carried out measurements on specimens made from orthotropic material. The obtained results confirm that his proposed device is as accurate as previously developed optical techniques, however, its measuring range is significantly larger. In 2017, Rief et al. [18] designed a 3D DIC system connected to the hole-drilling device by a rigid frame ensuring that there was no sideward movement of the drill during the drilling process. The advantage of their device is that it is pre-calibrated since the camera's distance to the object surface is constant. In 2020, Brynk et al. [19] also used a fixed stereo-camera system placed symmetrically to the milling cutter attached to the mechanism allowing its movement in the direction perpendicular to the specimen surface and analyzed residual stresses in the LVM316 steel. The milling process was performed by a stepper motor and steered with an Arduino microcontroller allowing precise drilling of holes to desired depth as well as removing of the drilling head from the cameras' observation field. The current research done by Babaeeian and Mohammadimehr [20] aims to analyze the influence of the time elapsed effect on the levels of quantified residual stresses in composites.

Quantitative comparison of the displacement resolution and disadvantages of the aforementioned methods are shown in Table 1.


**Table 1.** Displacement resolution and disadvantages of the optical methods described.

\* Note: *Z* is the distance from the object to the camera for a typical stereo-camera system.

In this paper, which is an extension of the conference contribution [21], the unique device combines hole-drilling with two optical methods and differs from the devices described previously in that the cameras of the correlation system (used as a tool for the full-field displacement/strain analysis) move with the cutting tool. As the digital image

correlation method is based on the correlation of digital images, it was necessary to verify whether the achieved positioning accuracy of the proposed drilling device was sufficient for reliable strain analysis. To eliminate the human failure factor during the measurement process, control software for adjustment of several parameters was created. The most important parameters adjusted were the shift and velocity of the block to which the milling tool was attached.

The initial testing of the drilling device found undesired mechanical clearances, which could significantly influence the measured data and, therefore, the device's design was improved several times. The results obtained from testing of the optimized prototype showed that the aforementioned technical problem was eliminated.
