A Novel Low-Cost DIC-Based Residual Stress Measurement Device
Round 1
Reviewer 1 Report
The reviewed paper deals with the highly actual topic of determining residual stresses by full-field optical methods. From the title as well as, for example, Chapter 2 of the paper, the authors' goal is to create a low-cost prototype of a drilling/measuring device for the purpose of quantifying residual stresses by means of the DIC method. I consider the main contribution of the article to be the creation of a concept of the measuring device as well as sharing all the documentation necessary for the construction of the designed device and the realization of the measurement, thus the presented materials can become a suitable tool for further development in the above mentioned issue. However, for the purpose of publication in Applied Sciences, in my opinion, the paper needs to be significantly modified and improved, e.g., by incorporating the following comments or by answering the questions I raise in the following section of the review:
1) Line 145 - In Figure 1 and 2, respectively, the axes are labelled differently - X and Z in the first case, X and Y in the second.
2) Figure 1 - description b) is in a different font (bold) than required.
3) Lines 264 - 344: These are only a rewrite from ASTM E837-13A describing the calculation of residual stresses from measured relaxed strains in the incremental boring method. If the authors find it necessary to include this section in the paper, it could be included in an appendix.
4) In the supplementary materials, the values of the calibration matrices for the DIC or strain gauge application are given. However, there is no description of what type of rosette they apply to, or how the virtual gauges are defined when using DIC. The same is true for the paper itself, which lacks a description of the strain gauge used and the size or location of the virtual meters (as well as a description of why at these locations) on the evaluated area of the analyzed specimen.
5) Information about the calibration of the correlation system is not given in the paper.
6) In lines 354-355 you state: “This involved drilling two holes to the tensile and compressive stress loaded edges of the control specimen, near points T and C respectively.” What exactly does it mean to set the measurement location using DIC near points T and C? Can you take a photo of the specimen with the strain gauge rosettes applied and a random black and white pattern created?
7) In Figure 8, small areas of a circular nature can be seen with a significant change in the magnitude of the displacement measured at their boundaries. What are these?
8) Lines 158-159 you state: “Beyond these considerations, any inaccuracies within the actuation system were minimised by rigid body compensation, commonly used in DIC application”. In Lines 411-412 can be found: “This error may have been due to incorrect rigid body compensation leading to motion blur in the averaged images …” Why did not you try to fix this issue with rigid body motion?
9) Lines 418-420 you state: “These errors may be due to experimental errors, such as the drill wear, heat and the vibrations induced by the drilling, or minor eccentricity and concentricity errors.” Have you experimentally analyzed the accuracy with which the proposed system is able to return to the desired (reference/drill/measurement) positions and the cylindricity of the holes created by the TUNGSTEN CARBIDE PCB Drill Bit 1.6 mm?
10) Since the analyzed 4-point bending problem is a symmetric problem, the magnitudes of the measured residual stresses obtained at points T and C should theoretically be the same. In your case, however, they differ significantly (according to Figure 11 the difference is about 30% and 20%, respectively), and not only when comparing the results obtained by two different methods. Can you explain why?
11) Can you please add the strain fields obtained by DIC to the article?
12) Can you please add the obtained dependencies Sigmamax and Sigmamin versus hole depth to the article?
Author Response
The reviewed paper deals with the highly actual topic of determining residual stresses by full-field optical methods. From the title as well as, for example, Chapter 2 of the paper, the authors' goal is to create a low-cost prototype of a drilling/measuring device for the purpose of quantifying residual stresses by means of the DIC method. I consider the main contribution of the article to be the creation of a concept of the measuring device as well as sharing all the documentation necessary for the construction of the designed device and the realization of the measurement, thus the presented materials can become a suitable tool for further development in the above mentioned issue.
We are pleased that the main contributions of the article are clear to the reviewer.
However, for the purpose of publication in Applied Sciences, in my opinion, the paper needs to be significantly modified and improved, e.g., by incorporating the following comments or by answering the questions I raise in the following section of the review:
1) Line 145 - In Figure 1 and 2, respectively, the axes are labelled differently - X and Z in the first case, X and Y in the second.
Thank you for highlighting this, we have corrected Figure 1 to the correct axis label of X and Z.
2) Figure 1 - description b) is in a different font (bold) than required.
Thank you for highlighting this, it has been corrected.
3) Lines 264 - 344: These are only a rewrite from ASTM E837-13A describing the calculation of residual stresses from measured relaxed strains in the incremental boring method. If the authors find it necessary to include this section in the paper, it could be included in an appendix.
We included this as it forms the basis of subsequent discussion and this standard may not be available to all readers. However we agree that the nature of this analysis is supplementary and we have therefore moved it to an appendix.
4) In the supplementary materials, the values of the calibration matrices for the DIC or strain gauge application are given. However, there is no description of what type of rosette they apply to, or how the virtual gauges are defined when using DIC. The same is true for the paper itself, which lacks a description of the strain gauge used and the size or location of the virtual meters (as well as a description of why at these locations) on the evaluated area of the analyzed specimen.
We apologise for this oversight and have added the manufacturer name and type of rosette used. Although the virtual strain gauges were shown in Figure 8 we agree that the details of size and location were missing from the text. Accordingly, we have added further details to Figure 8, the manuscript and supplementary materials as follows:
Two Micro-measurements EA-06-062RE-120 general-purpose residual stress-strain gauge rosettes were positioned diagonally within the peak stresses induced by the bending.
This was achieved by implementing virtual extensometers that measured directional displacements relative to the reference image at the same location as that measured by the real strain gauge (Micro-measurements EA-06-062RE-120). The size of these strain gauges were 1.57 × 1.16 mm2 with the closest edge of the gauge being 1.35 mm from the hole center at 0°, 45° and 90° angles relative to the primary axis.
These calibration matrices are for virtual strain gauges located at the locations used in a Micro-measurements EA-06-062RE-120 general-purpose residual stress-strain gauge rosette. These are 1.57 × 1.16 mm2 regions with the closest edge of the gauge being 1.35 mm from the hole center at 0°, 45° and 90° angles relative to the primary axis.
5) Information about the calibration of the correlation system is not given in the paper.
The reviewer is correct about this omission. Accordingly, we have added the following paragraphs to clarify the details of the calibration of the correlation system:
Calibration of the correlation system was performed via both physical data collection and the generation of virtual data sets via image manipulation. In the first case two data sets were collected, the first was based on repeated image collection without drilling which was used to generate a baseline estimate of the error associated with image noise when no movement or strain change was physically induced. The strain estimates resulting from this analysis were better than 10-6, demonstrating that this was likely to be the baseline sensitivity for the device/software. In the second case sequential images were collected as the sample was incrementally rastered in the X direction with a step size of 50 μm to assess the impact of bulk shift. The resulting strain estimates were similarly on the order of 10-6 demonstrating that the software was capable of correcting for bulk drift without outputting artificial strain estimates.
Image manipulation was next used to assess the precision of the DIC measurements by artificially inducing an apparent strain and drift in a speckle pattern image. This was performed by using the software ImageJ to implement a digital zoom of the image from 90% to 110% in increments of 1%. Drift was simulated by incrementally translating the image by 20 pixels in both vertical and horizontal directions, in a step of 2 pixels. It was found that the estimates of strain from the digital zoom were correct within 10-7 and that the digital drift was fully accommodated (strain values of 0). There was therefore confidence that the correlation system was calibrated effectively and that the estimates of strain were likely to be reliable.
6) In lines 354-355 you state: “This involved drilling two holes to the tensile and compressive stress loaded edges of the control specimen, near points T and C respectively.” What exactly does it mean to set the measurement location using DIC near points T and C? Can you take a photo of the specimen with the strain gauge rosettes applied and a random black and white pattern created?
We agree that the precision was lacking in this statement. In order to clarify the exact locations of the patterning and DIC hole drilling locations, we have added these to Figure 5, and have added the following text to the manuscript:
This involved drilling two holes to the tensile and compressive stress loaded edges of the control sample, near points T and C respectively, as shown in Figure 5.
7) In Figure 8, small areas of a circular nature can be seen with a significant change in the magnitude of the displacement measured at their boundaries. What are these?
The reviewer is correct that there are circular artefacts within the displacement field which have a change in displacement magnitude at their edges. A careful review of these regions has revealed that this has arisen from aliasing of individual markers at these locations. Fortunately however, it has been found that the magnitude changes are equal and opposite to each other, and therefore by averaging over the entire region, there has been very little impact on the strain estimates we obtained. We have highlighted this phenomenon in the text as well as a route to minimise this effect going forward:
The images clearly illustrate the effect of strain relief due to the hole drilling, which can be separated from the background noise. However a number of small circular artifacts with a ring of displacement at their edges can also be observed within the displacement field. A careful review of these locations revealed that this has arisen from aliasing of markers. Fortunately the displacement change induced by this effect is equal and opposite on either side of the circle. Therefore the averaging performed over the virtual strain gauges means that this phenomenon has had little to no effect on the strain measurements obtained. This suggests that despite the significant refinement performed to optimize the surface speckle pattern, further improvements are required in terms of the number/size of contrast points.
8) Lines 158-159 you state: “Beyond these considerations, any inaccuracies within the actuation system were minimised by rigid body compensation, commonly used in DIC application”. In Lines 411-412 can be found: “This error may have been due to incorrect rigid body compensation leading to motion blur in the averaged images …” Why did not you try to fix this issue with rigid body motion?
Thank you for highlighting this apparent contradiction. We did indeed use rigid body correction to minimise the impact of this effect. In these first few images however we faced an issue that the sample/drill was ‘bedding in’ such that this initial contact caused lateral shifts in the sample position. This effect stopped once a clear hole had been produced, as the perpendicular forces were then significantly reduced. Despite this, the alignment substantially reduced the apparent error and aligned the images to a precision much less than 1 pixel, however the nature of strain measurements means that even very minor sub-pixel misalignment can cause an apparent strain change. This is what we meant by ‘incorrect rigid body compensation’. We have clarified this in the text as follows:
This was initially unexpected, as the initial strain relief at the surface is expected to be minor. However, upon further investigation it was revealed that this artifact was associated with the ‘bedding in’ of the drill bit and the associated lateral forces as the hole was established. Despite making use of rigid body compensation and imaging averaging error, the sensitive nature of DIC means that even very small sub-pixel offsets can lead to blur in the averaged images
9) Lines 418-420 you state: “These errors may be due to experimental errors, such as the drill wear, heat and the vibrations induced by the drilling, or minor eccentricity and concentricity errors.” Have you experimentally analyzed the accuracy with which the proposed system is able to return to the desired (reference/drill/measurement) positions and the cylindricity of the holes created by the TUNGSTEN CARBIDE PCB Drill Bit 1.6 mm?
Testing of the rig’s ability to return to a reference position was performed by repeatedly imaging a nominally identical location before and after a stage movement and homing (without milling). It was found that the offset of the rig was on the order of several microns (5-15 μm). This was less than the 10’s of micron movement in sample position that was induced during the milling process, and was therefore deemed to be acceptable. We agree that discussion of this was missing from the text and have therefore added:
Stage accuracy was also tested during this process by repeatedly imaging a nominally identical location before and after a stage movement (plus homing). This process revealed that alignment could be reliably achieved to within 15 μm. This is significantly less than the 10’s of microns shift typically induced in the sample during milling and therefore it was deemed to be acceptable for subsequent analysis.
In terms of hole cylindricity, no exhaustive test regime has been performed as this was found to be highly sample dependent. It depends not only upon the material being studied, but also the effectiveness of the mounting system, which in turn depends upon the geometry being studied. However, following the suggestion from the reviewer a quantitative measure of the roundness of the holes milled into the surface of alumnimum sample were analysed from the images collected. This measure was found to decrease from 1 at the start of milling to values of 0.9991 and 0.9987 at full milling depth, for the T and C locations, respectively. This demonstrates that although the profile does become more elliptical, the shape change is very minor. Accordingly we have added the following discussion on this to the text:
It should be noted that the hole drilling methodology is based on the assumption that the hole drilled into the sample is cylindrical in form. Whilst it is clear that the exact shape of the milled hole is highly sample dependent, in particular on material, clamping and therefore geometry), it will also be dependent upon the design of the milling rig. To gain an indication of the performance of the use of the rig on this sample the roundness of the holes on the surface were assessed during the milling process. It was found that this measure decreased from 1 at the start of milling to values of 0.9991 and 0.9987 at the final depth for the T and C location, respectively. This indicates that although the hole does become elliptical this transition is minor, suggesting that this sample was likely well mounted and that the rigidity of the rig was sufficient to prevent significant deviations when milling this aluminum alloy.
10) Since the analyzed 4-point bending problem is a symmetric problem, the magnitudes of the measured residual stresses obtained at points T and C should theoretically be the same. In your case, however, they differ significantly (according to Figure 11 the difference is about 30% and 20%, respectively), and not only when comparing the results obtained by two different methods. Can you explain why?
The reviewer raises a good point here - indeed the symmetric nature of the 4-point bending problem does mean that the magnitudes of the tensile and compressive forces should nominally be equal. We are not fully certain as to the origin of this discrepancy, however feel that it is most likely associated with compressive residual stresses in the surface of the aluminum which were induced during manufacture and were retained after the heat treatment of the bar. Despite this, the focus of the article remains on comparing the results obtained by the two independent techniques applied, which were found to show a reasonable agreement within the error bounds the data was obtained. We agree that some discussion on this point was lacking from the text and have therefore added:
One interesting result that has arisen from this analysis is that the magnitudes of the residual stress estimates obtained at both point T and C tend to be moderately more compressive than the theoretical estimate (by several 10’s of MPa). The likely origin of this discrepancy is the compressive residual surface stresses induced in the surface of the bar by the forging and machining processes. Despite the annealing process applied to the bar, these relatively low magnitude forces appear to have been retained.
11) Can you please add the strain fields obtained by DIC to the article?
Yes, these have been added as Figure 12, in Appendix B.
12) Can you please add the obtained dependencies Sigmamax and Sigmamin versus hole depth to the article?
Yes, the confidence bounds on the stresses have been added to Figure 9 and Figure 10.
Author Response File: 
Author Response.docx
Reviewer 2 Report
In this paper the authors presented a novel low-cost DIC-based residual stress measurement device. The idea using DIC method to measure the local strain field instead of using conventional strain gauge method is new and very interesting. The new device can provide a better and faster measurements, and the method is very interesting. The paper is in general well written. The paper can be published after considering the following comments.
1) the highlights have to be improved. The first two does not provide anything new, but only background knowledge. In introduction, it is not accurate to say that residual stresses are stresses locked into a materials through plastic deformation. For some composites with second phase particles, the residual stresses could just be a result of mismatch elastic strains. Also non-destructive methods using X-rays or neutrons should be mentioned briefly.
2) page 10, line 253. The authors mentioned that the deformation will introduce a residual stress value of 85MPa. It is not clear how this is determined. Is this the elastic stress calculated based on the beam displacement? Is there any plastic deformation in the sample during the test? If not, it sounds strange to call it residual stress. Also if the sample deformed, the stress state will be difficult to estimate, as plastic deformation can release the stress. See e.g. Zhang et al. Acta Mater. 2019, 167, 221-230.
3) Figure 5 caption does not appear correctly. Figure 6, (a)-(c) are missing in the figure. Figure 6c is somehow not understandable.
4) page 11, line 279, qj and tj should be strain in stead of stress. line 281, what is k? line 288, should it be j<=n-3.
5) Figures 7 and 10, it is a bit confusing to use stress depth for x-axis. The stress state should be about the same along the depth. With different drilling depth, only part of the stress is released. It would be better to call it drilling depth instead.
6) In the discussion, the authors mentioned that the test sample is isotropic metal. This is not correct. All metals are elastically anisotropic. Different grain orientations will deformed differently under the same strain state.
7) table 4, second last column, the unit should be removed since it is mentioned in the headline. Page 8, last line, remove 'is provided'.
Author Response
In this paper the authors presented a novel low-cost DIC-based residual stress measurement device. The idea using DIC method to measure the local strain field instead of using conventional strain gauge method is new and very interesting. The new device can provide a better and faster measurements, and the method is very interesting. The paper is in general well written. The paper can be published after considering the following comments.
We would like to thank the reviewer for their kind comments. We are pleased that the aims of the paper have been clearly understood.
1) the highlights have to be improved. The first two does not provide anything new, but only background knowledge. In introduction, it is not accurate to say that residual stresses are stresses locked into a materials through plastic deformation. For some composites with second phase particles, the residual stresses could just be a result of mismatch elastic strains. Also non-destructive methods using X-rays or neutrons should be mentioned briefly.
The reviewer is correct in their assessment, in particular that the first two highlights did not focus sufficiently on the content of the paper. Accordingly we have rewritten the highlights as follows:
Residual stress analysis via existing non-destructive or semi-destructive methods can be costly and time-consuming, and therefore a cheaper and faster methodology is sought.
The paper proposes a novel measurement device that combines hole drilling and digital image correlation to propose a measurement methodology comparable to ASTM E-837-13a.
Cross-validation of the methodology was performed on a test specimen using conventional methods and the results were found to be within +/- 30 MPa.
This device reduces measurement time from 2 hours per point to 45 minutes and the cost of the experiment is reduced from £50 to £1 per measurement.
2) page 10, line 253. The authors mentioned that the deformation will introduce a residual stress value of 85MPa. It is not clear how this is determined. Is this the elastic stress calculated based on the beam displacement? Is there any plastic deformation in the sample during the test? If not, it sounds strange to call it residual stress. Also if the sample deformed, the stress state will be difficult to estimate, as plastic deformation can release the stress. See e.g. Zhang et al. Acta Mater. 2019, 167, 221-230.
We apologise for the lack of clarity here. This value was calculated using Equation 1, which is the standard theoretical estimate for residual stress in a 4-point bend test obtained from beam theory. This is based on the applied load, rather than the displacement (which is assumed to be negligible in this theoretical framework). There is indeed plastic deformation during the loading which generates the residual stress being measured. We agree that excessive deformation of the sample would lead to the approximations being used in our calculations becoming invalid (including the release of stress). This, in addition to being able to test sensitivity of the new method, was one of the primary reasons for selecting a relatively low magnitude residual stress value to measure. Accordingly, clarification on this has been added to the text:
This force, in combination with the specimen dimensions can be used in combination with equation 1 to determine that this corresponds to a residual stress of 85 and -85 MPa at Point T and C, respectively. It should be noted that equation 1 is the standard theoretical estimate for residual stress generated in a 4-point bend test using beam theory. This framework is based on the approximation of negligible deformation of the specimen. Therefore, in order to ensure this estimate remained valid, relatively low magnitude stresses were generated (<100 MPa). It should be noted that the use of low magnitude stresses was also useful to quantify the sensitivity of the method being developed. The estimated values of stress facilitated the validation of the calculations of the force required for plastic deformation and was followed by repeating the same procedure with the armed sample.
3) Figure 5 caption does not appear correctly. Figure 6, (a)-(c) are missing in the figure. Figure 6c is somehow not understandable.
We thank the reviewer for raising these errors. Figure 5’s caption has been reformatted. It appears that the labels (a,b,etc) for all figures were lost during the transition to the journal’s template and these have been added at all relevant locations. We agree with the reviewer that Figure 6c could not be understood from the caption alone. An explanation of this figure was previously included in the text however upon reflection we feel that this does not add additional value to the paper and we have therefore removed this.
4) page 11, line 279, qj and tj should be strain in stead of stress. line 281, what is k? line 288, should it be j<=n-3.
Thank you for highlighting these, we have made the stress/strain corrections and replaced < with ≤ in the relevant locations. Following the reviewers suggestion in 3) we have removed Figure 6c which made reference to k, as it was felt that this did not add additional value. Accordingly, k is no longer present in the text.
5) Figures 7 and 10, it is a bit confusing to use stress depth for x-axis. The stress state should be about the same along the depth. With different drilling depth, only part of the stress is released. It would be better to call it drilling depth instead.
We agree, we have replaced the axis label with drilling depth.
6) In the discussion, the authors mentioned that the test sample is isotropic metal. This is not correct. All metals are elastically anisotropic. Different grain orientations will deformed differently under the same strain state.
The reviewer is correct that the single crystal stiffness of aluminium 6082 is anisotropic. However, the grain size of the sample being investigated is on the order of 1 to 10 micrometres, meaning that there are 106 to 109 grains within the gauge volume being investigated. Although it is true that machining may induce some preferred orientation in these grains, in general their orientation will be close to random. This results in a macroscale response that is very close to isotropic. We agree that the reasoning behind this approximation was missing from the text and have therefore added the following clarification:
As is the case with most metals, the single crystal of the aluminium 6082 alloy used in this study is anisotropic. However, given that the nominal grain size for this material is expected to be between 1 and 10 μm there will be between 106 and 109 grains within the gauge volume. It is possible that some preferred grain orientation has been induced by the manufacturing process, however this is expected to be minimal. Therefore it is believed that the grain orientation will be close to random and that an isotropic approximation for the macroscale behaviour will be a good approximation.
7) table 4, second last column, the unit should be removed since it is mentioned in the headline. Page 8, last line, remove 'is provided'.
Thank you for highlighting these issues. They have been corrected in the manuscript.
Author Response File: Author Response.docx
Reviewer 3 Report
The paper shows a DIC based method to evaluate residual stresses. An experimental comparison to the state-of-the-art methods is provided.
The analysis is quite comprehensive and includes economic considerations that may lead to widespread adoption of the measurement system.
My recommendation is to publish the paper as it is and I am looking forward to reading about further applications of the method.
Author Response
The paper shows a DIC based method to evaluate residual stresses. An experimental comparison to the state-of-the-art methods is provided. The analysis is quite comprehensive and includes economic considerations that may lead to widespread adoption of the measurement system. My recommendation is to publish the paper as it is and I am looking forward to reading about further applications of the method.
We would like to thank the reviewer for their comments. We are pleased to hear they they believe that this methodology has the potential to lead to widespread adoption of the device. We are currently working on 2 subsequent journal papers that make use of the device and are looking forward to sharing these with the academic community in due course.
Author Response File: Author Response.docx
Reviewer 4 Report
The authors present an adaptation of digital image correlation for stress measurements using borehole trepanation.
The authors in the valuation of the device designed by them do not mention the price of the software and the need for computer hardware with sufficient computing power.
The authors did not include the license to sell the device or possibly the cost of installation by a specialist
Please provide the measurement accuracy of the drilling depth.
Why is there no trace of a drilled hole in Figure 8?
There is a lack of inclusion of a figure showing the deformation map at the tested locations.
Stress calculations and conclusions in the paper are done correctly
Author Response
The authors present an adaptation of digital image correlation for stress measurements using borehole trepanation. The authors in the valuation of the device designed by them do not mention the price of the software and the need for computer hardware with sufficient computing power.
We thank the reviewer for raising this oversight. Both of the softwares used (Grbl and NCorr) are free open source packages, meaning that there is no cost associated with this. Neither of these packages are particularly processor intensive and all analysis was achieved on a mid-range laptop (CPU: Intel Core i7-8565U Graphics: Nvidia GeForce MX150 RAM: 4GB) within a few seconds. Accordingly it would be possible to run the required software on a low-spec machine, albeit with a slight extension in time from seconds to a couple of minutes. We agree that these details were lacking from the original manuscript and have therefore added:
One additional factor which should be highlighted is that the software used to control the device (Grbl) and perform the DIC (NCorr) are free, open source packages meaning that there is no cost associated with this aspect of the device. In this study all analysis was performed on a mid-range laptop (CPU: Intel Core i7-8565U Graphics: Nvidia GeForce MX150 RAM: 4GB) within a few seconds. This means that it would be possible to run the required simulations on a low-spec machine within a few minutes, further increasing the accessibility of the approach presented.
The authors did not include the license to sell the device or possibly the cost of installation by a specialist
We apologise for the lack of clarity here, but the intention of our study was to provide the design, assembly drawings, manual, g-code and calibration coefficients freely and open-source. This means that researchers can make use of the device without any additional cost beyond purchasing the components outlined in Table 4. Accordingly there is no cost for installation by a specialist. We appreciated however that this will mean that the interested party would need to invest time into the production and assembly of the device which will incur a cost. It is however the case that staff/student time is a resource which is typically more available to academics, particularly in the developing world who would be one of our key user bases.
The device has a production cost of £350, which is kept minimal for the mass adoption of the device, particularly in developing countries where the cost of residual stress equipment and the associated measurements can be prohibitive. All of the assembly drawings, manual, g-code and calibration coefficients required have been provided for free, in an open source format in the supplementary material of this paper. The ‘self-construct’ nature of the device also overcomes the need for a license or installation cost from a specialist, albeit at the cost of time/effort required to produce and assemble the device.
Please provide the measurement accuracy of the drilling depth.
We agree that the accuracy of drilling depth was missing from the manuscript, and have added this to the text.
Assessment of the drilling depth was performed and determined that this could reliably be achieved within +/- 5 μm. This precision ensures that the approximation of equal depth increments associated with the hole drilling procedure could be reliably used.
Why is there no trace of a drilled hole in Figure 8?
The background image of figure 8 is by default the reference image in NCorr, over which the displacement field is shown and can be incrementally viewed through the dataset. In our case this is the surface prior to milling, meaning that no hole is present. We agree that this was somewhat unclear and have reproduced this figure to show an image of the hole at the depth associated with the displacement field.
There is a lack of inclusion of a figure showing the deformation map at the tested locations.
Although figure 8 of the original text included the displacement field at point T, we agree that the equivalent information for the other location (C) was missing. We have added further clarity to this figure by overlaying the locations of the virtual strain gauges in order to highlight the deformation at these locations.
Stress calculations and conclusions in the paper are done correctly
We thank the reviewer for checking these calculations. We are pleased that they are correctly performed.
Author Response File: Author Response.docx
Reviewer 5 Report
In this paper, the blind hole method for measuring residual stress is improved, that is, the digital image correlation technology is used to replace the strain gauge, which can indeed reduce the error to some extent and has certain value, but there are still some problems in the content reported in this paper:
1. How to avoid the factors that may cause deviation, such as the vibration of the drill bit, so as to ensure that the position of each increment is exactly the same as the initial position, in line 149 on page 5.
2. This paper should provide a set of pictures during drilling, such as the initial speckle patterns, the speckle patterns during drilling and the speckle patterns after drilling.
3. The position of the drill hole in Figure 8 is obviously not circular. Will this affect the accuracy of the results?
4. Ncorr software evaluates that the displacement is affected by the size and distribution of speckle patterns, thus affecting the value of residual stress. If the speckle pattern is not appropriate, the error of residual stress will increase. Therefore, how to evaluate the error caused by the size and distribution of speckle provided in this paper?
5. When the drilling depth is 1mm, the X strain still does not tend to be stable, so using the values here to calculate the stress will make the error very large, in Figure 10.
Author Response
In this paper, the blind hole method for measuring residual stress is improved, that is, the digital image correlation technology is used to replace the strain gauge, which can indeed reduce the error to some extent and has certain value, but there are still some problems in the content reported in this paper:
- How to avoid the factors that may cause deviation, such as the vibration of the drill bit, so as to ensure that the position of each increment is exactly the same as the initial position, in line 149 on page 5.
The reviewer raises a very valid point. There are several routes that can be used to reduce offsets in the milling position:
- Ensure that the sample is held securely
- Design the rig rigidly so that it does not deform during milling / actuation
- Minimise the mass of the drilling rig to reduce the force required by the motors
- Use a reliable, referenced and repeatable actuation system (lead screw, coupling, motor and guides with grease)
All four of these methods were used in our design and we agree that discussion on this factor was missing from the text and have therefore added:
A key challenge that needs to be overcome when performing the hole drilling measurement technique is to ensure that the position of the milling increment is well aligned to the starting point. There are four key methods that can be used to improve the reliability of this process:
- Ensure the sample is held securely. In this study, this has been achieved by designing a range of sample holders specifically tailored to standard shapes/component designs. However this is something that the user needs to keep in mind when performing this type of analysis, meaning that subsequent gripping methods may be required for non-standard geometries.
- Maximize the rigidity of the rig. Flexibility in the rig may lead to deformation of the rig/assembly during the milling/actuation process. Therefore the design was specifically tailored and subsequently optimized in order to reduce deflection during these processes.
- Minimize the mass of the actuated components. Reducing the mass of the milling section of the rig reduces the force required by motors in order to perform movements. Mass refinement was used extensively in the design of these sections of the device to ensure that the rig can be realigned to the highest precision possible.
- Make use of a reliable, references and repeatable actuation system. An extensive design procedure was implemented to maximize this aspect of the design including the selection/use of lead screws, couplings, guides and suitable motors, as well as lubrication grease.
The resulting system was tested to quantify the precision of realignment which was found to be better than 15 microns (as highlighted in response to reviewer 1 point 9). Given that there is likely to be errors in tool shape / flexing at a similar order of magnitude it was decided that this degree of offset was acceptable. This was also clarified in the text:
The resulting system was tested to quantify the alignment offset associated with the design, which was found to be at worst approximately 15 μm. This magnitude offset is on the same order of magnitude as errors in tool shape or the flexing of the drill bit and therefore this was deemed to be acceptable.
- This paper should provide a set of pictures during drilling, such as the initial speckle patterns, the speckle patterns during drilling and the speckle patterns after drilling.
We agree that this was missing from the text and have added the images showing the evolution of the speckle patterns during drilling to the supplementary material.
- The position of the drill hole in Figure 8 is obviously not circular. Will this affect the accuracy of the results?
The author raises a good point here, eccentricity in hole drilling measurements has been the focus of previous studies. This analysis has shown that this effect does indeed affect the accuracy of the results. Measurements of the shape of the ellipsoid have shown for this measurement the eccentricity of +/- 0.05 mm which corresponds to a relative error of 5%. This factor was originally not accounted for in the estimates of confidence bound on the results obtained. Therefore these calculations have been repeated to provide improved estimates of confidence including this phenomenon. Discussion on this was also missing from the text, and we have therefore added:
Another factor which needs to be accounted for in the precision of the DIC measurements is the eccentricity of the hole. Measurement of the shape of the final milled shape provided quantitative estimates of this value of +/- 0.05 mm for both point T and C. The influence of this on the resulting stress/strain estimates have been the focus of previous research [66] [67], which revealed that this value corresponds to a nominal increase in relative error of 5%. Accordingly the confidence limits of the DIC results were modified to account for this effect as shown in Figure 10.
- Ncorr software evaluates that the displacement is affected by the size and distribution of speckle patterns, thus affecting the value of residual stress. If the speckle pattern is not appropriate, the error of residual stress will increase. Therefore, how to evaluate the error caused by the size and distribution of speckle provided in this paper?
The reviewer is correct that the size and distribution of speckle pattern can influence the precision with which strain can be reliably tracked. Indeed, optimization of the speckle pattern is an important part of any method whenever using DIC. This has been the focus of numerous studies and we agree that reference to these studies were lacking from the original paper. We have therefore added:
It should be noted that as is the case for all DIC measurements, the precision of the displacement field estimates are highly dependent upon the quality of the pattern contrast, and density. This has been the focus of numerous previous studies [59] [60] and the good practice guidance outlined in these studies was followed to refine the patterns used in this study.
In order to estimate the error caused by the size and distribution pattern when using DIC, the deviation from the expected relief curves can be used. In other words, the deviation from the expected form of displacement field provides a quantitative estimate of the error induced from the tracking of the speckle pattern. The hole drilling methodology is a well-established method and therefore the form of surface relief is known. Accordingly, by fitting this variation to the displacement field the noise, and associated error on the strain/stress relief estimates can be determined. Given that this methodology is well established within the field we did not discuss this in detail within the original manuscript. However the query from the reviewer reveals that not referring to this standard method was an oversight and we have therefore added:
To estimate the error arising from the size and distribution of DIC particles, the standard approach of determining the deviation from the expected hole drilling relief curves was used [36].
- When the drilling depth is 1mm, the X strain still does not tend to be stable, so using the values here to calculate the stress will make the error very large, in Figure 10.
The reviewer raises another good point here. We believe this phenomenon is associated with incomplete relief of surface stresses induced by the manufacturing process in the heat treatment process. It can be seen that this does indeed lead to an increased error in the average estimates of residual stress. Despite this, we believe that the reasonable match achieved between the conventional and DIC results demonstrates that this is likely to be a real effect associated with the sample, and not with the measurement technique. Discussion on this was limited in the text, and we have therefore added:
In particular, it can be seen that there is a discrepancy between the residual stress values obtained at the surface of the sample, and those at larger depths. Given the close agreement between the two independent measurement techniques, it is likely that this is a real effect that indicates the surface of the test specimen experiences a stress state different to the bulk. This is a common effect in these types of specimen, that arises from the manufacturing process, so is not unexpected. It will however, lead to an increase in the confidence bounds of the average value as shown in figure 10.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Following the comments, the authors have significantly revised the manuscript. After replacement of "Displacement X and Y" by "Strains" in the caption of Figure 12, I recommend to accept the manuscript for publishing in Applied Sciences journal.
Author Response
Following the comments, the authors have significantly revised the manuscript. After replacement of "Displacement X and Y" by "Strains" in the caption of Figure 12, I recommend to accept the manuscript for publishing in Applied Sciences journal.
Thank you for highlighting this minor error. We have changed the caption to:
Figure 12. Strains X and Y at Point C (a) and Point T (b) induced during hole drilling
We are pleased that you feel the manuscript is now suitable for acceptance.
Author Response File: Author Response.docx
Reviewer 5 Report
The author made a good response to the reviewer's comments. The manuscript is suggested to be accepted in the present form.
Author Response
The author made a good response to the reviewer's comments. The manuscript is suggested to be accepted in the present form.
We are pleased to see that the reviewer agrees that the manuscript should be accepted in its current form. Thank you for your feedback.
Author Response File: Author Response.docx
