Advances in Hole-Drilling Residual Stress Measurements
G.S.Schajer
Received:21August 2008/Accepted:27January 2009#Society for Experimental Mechanics 2009
Abstract Residual stress measurements by hole-drilling have developed greatly in both sophistication and scope since the pioneering work of Mathar in the 1930s.Advances have been made in measurement technology to give measured data superior in both quality and quantity,and in analytical capability to give detailed residual stress results from tho data.On the technology side,the u of multiple strain gauges,Moiré,Holographic Interferometry and Digital Image Correlation all provide prolific sources of high quality data.In addition,modern analytical techniques using inver methods provide effective ways of extracting reliable residual stress results from the mass of available data.This paper describes recent advances in both the measurement and analytical areas,and indicates some promising directions for future developments.
战狼下载Keywords Residual stress measurements .Hole-drilling .Strain gauges .Full-field optical measurements .Inver calculations
Introduction
桃树下的小白兔The hole-drilling method is a widely ud technique for measuring residual stress.It has the advantages of good accuracy and reliability,standardized test procedures,and
convenient practical implementation.The damage caud to the specimen is localized to the small drilled hole,and is often tolerable or repairable.For this reason,the method is sometimes described as “mi-destructive ”.
The modern hole-drilling method has its roots in the pioneering work of Mathar in the 1930s [1].It involves:1.drilling a small hole in the specimen in the area of
interest,
around the hole,and
ptical techniques such as Moiré,Holographic Inter-ferometry,and Digital Image Correlation.The early empirical stress computation procedures have been super-ded by finite element calibrations and inver calculations to accommodate the character and quantity of the newly available measured data.Procedural steps 2and 3described above,deformation measurement and stress computation,have greatly developed in sophistication and scope in recent years.This paper reviews the advances and suggests some promising directions for future developments.
Strain Gauge Measurements
Strain gauges were introduced for hole-drilling residual stress measurements in the 1950s and ,[2,3].Development of the measurement procedures has continued
Experimental Mechanics
DOI
10.1007/s11340-009-9228-7
胯骨疼自我疗法
Keynote paper,prented at the SEM XI International Congress &Exposition on Experimental and Applied Mechanics.Orlando,FL.June 2–5,2008.
G.S.Schajer (*,SEM member)
Department of Mechanical Engineering,University of British Columbia,Vancouver,Canada
e-mail:
初中网课schajer@mech.ubc.ca
apace since then,leading to the introduction of ASTM Standard Test Method E837in1981,veral subquent updates[4],and an extensive literature, e.g.,[5–7].A variant procedure,the Ring-Core method[8,9]has also been developed.Esntially,it is an“inside-out”version of the hole-drilling method.Hole-drilling involves cutting stresd material from the central area with the strains measured in the surrounding material,while the ring-core method has the rotte at the center with the surrounding stresd material being removed.The two methods are identical mathematically,and differ only in the numerical values ud for the calibration constants.Hole-drilling is the more commo
nly ud procedure becau of its ea of u and lesr specimen damage.
The strain gauge hole-drilling method has en develop-ments in all three procedural steps identified in the Introduction.The first step,the practical mechanics of drilling a hole,is now well established[4,5,7,10].The cond step,the measurement of the surface strains,is strongly influenced by the geometry of the strain gauge rotte that is ud.The standard Rendler and Vigness design[3]shown in Fig.1(a)is the most widely ud style,and is suitable for general-purpo u.The three strain gauges that compri the rotte are just sufficient to evaluate the three in-plane residual stressσx,σy andτxy. Several other rotte geometries have been propod over the years for specialized applications,for example an8-gauge design[11]to improve measurement accuracy, 12-gauge[12]and6-gauge[13]designs to provide thermal compensation and incread nsitivity,and4-gauge[14]and9-gauge[15]designs to allow consideration of plastic deformations.All the variant designs involve incread measurement complexity and rotte cost,and only the 6-gauge design is available commercially.
An alternative measurement approach is to replace traditional resistance-type strain gauges with optical strain gauges bad on interferometric techniques[16,17].The interferometric strain gauges are very small and can make very localized measurements.Strain gauge rottes[18]have been dev
eloped and successfully applied to hole-drilling and ring-core residual stress measurements[19,20].
Uniform Stress Measurements
For the third procedural step of hole-drilling measurements, the computation of the residual stress,two basic cas are of interest.The first ca occurs when the in-plane stress do not vary with depth from the specimen surface (“uniform stress”).Here,the three in-plane residual stress can be identified from three strain reliefs measured as the hole is directly drilled from zero to full depth.Such measurements u the minimum required strain data,and so,any measurement noi proportionally corrupts the computed residual stress.This is a concern becau, while the drilling relieves all the stress in the drilled hole,it relieves only about one third of the residual stress at the strain gauge locations around the hole.Thus,the measured strains tend to be small,causing the relative effect of noi to be large.The Ring Core method relieves all the residual stress,thus giving larger measured strains and a smaller relative effect of measurement noi.
A practical way to improve measurement accuracy is to make strain measurements at a ries of small depth increments as the hole is drilled from zero to full depth [21].All measured strain data can be considered,outliers identified and removed,and an averaging method ud to minimize the effect 小流域综合治理
of measurement noi.The u of eight hole depth increments is specified in ASTM E837 [4],and is an effective procedure for improving measure-ment quality[22].
惊讶的反义词Stress Profiling
In addition to their possible u for data averaging,strain measurements at a quence of hole depth increments also provide the ability to determine the variation of residual stress with depth.This process is often called“stress profiling,”and is the cond ca of interest when doing hole-drilling measurements.For this ca,it is assumed that the variation of the in-plane stressσx,σy andτxy occurs only in the depth direction,with no variation in the in-plane
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directions.Given the proximity to the free surface,the out-of-plane stress are assumed to be zero.
Early methods for evaluating the stress profiles[23,24] relied on experimental calibrations of the strain vs.stress relationships.Of necessity,the methods were approximate becau the experimental calibrations could not provide all the detailed calibration data needed.The subquent development of finite element calculations provided the needed detailed calibrations[25].They enabled the intro-duction of more accurate and reliable stress computation methods,notably the Integral and Power Series methods [26,27].In addition,the finite element calculations pro-vided greater accuracy and consistency.The features are particularly significant becau the stress profile calcula-tions are very nsitive to small calibration errors.Detailed modeling of the strain gauges is necessary to achieve accurate results;it is not sufficient to assume that the strain nsitivity is uniform within each strain gauge area[28].
Although much more complex and error nsitive than uniform stress evaluations,stress profiling hole-drilling measurements are now widely ud.The ASTM Standard Test Method E837[4]has recently been revid to include a standardized procedure to evaluate residual stress vs.depth profiles.
Optical Techniques
In recent years,veral optical techniques have been introduced for evaluating residual stress by the hole-drilling method.The techniques have the advantage of providing full-field data,which are uful for data averaging, error checking and extraction of detailed information. Effectively,having full-field optical data is like having multi-element strain gauge rottes of the type shown in Fig.1,but with many thousands of available gauges.In many ways,the optical techniques are complementary to the strain gauge technique,each approach having somewhat opposite advantages and disadvantages.Table1lists some features of strain gauge and optical measurements.MoiréInterferometry
Moiréinterferometry[29–35]provides a nsitive tech-nique for measuring the small surface displacements that occur during hole drilling.Figure2schematically shows a typical optical arrangement[33].Light from a single coherent lar source is split into two symmetric beams that illuminate the specimen surface.A diffraction grating consisting of finely ruled lines,typically600–1,200lines/ mm,is replicated or made directly on the specimen surface. Diffraction of the light beams creates a“virtual grating”, giving interference fringes consisting of light and dark lines.Figure3shows an example hole-drilling measure-ment[32].Each light or dark line reprents a contour line of in-plane surface displacement,in the x-direction in Fig.2.For typical optical arrangements,the in-plane di
splacement increment between fringe lines is about 0.5μm.The vertical lines are“carrier fringes”that are deliberately induced by slightly rotating one illumination beam.They correspond to a hypothetical uniform tensile or compressive strain in the x direction,and are added to enable the sign(tension or compression)of the surface displacements to be identified.The added strains are mathematically removed during the stress calculation.
The Moirétechnique exemplifies the features of optical measurements summarized in Table1.The full-field character of the measurements gives both an opportunity and a challenge.Potentially,large numbers of measurements can be obtained by extracting many individual points from within the field of view.Points clo to the hole provide the most uful information.The associated challenge is to extract the data at tho points efficiently,preferably with minimal human interaction,and to u the data within a compact and efficient numerical scheme to evaluate the corresponding residual stress.
A video image consisting of light and dark fringes,such as Fig.3,is difficult to interpret automatically.Fringe counting and interpolation can be challenging for complex fringe patterns,particularly in the prence of measurement noi.Automatic interpretation of light intensity data from
Table1Features of strain gauge and optical measurements
Strain gauge measurements Optical measurements而君幸于赵王翻译
Moderate equipment cost,high per-measurement cost High equipment cost,moderate per-measurement cost
Significant preparation and measurement time Preparation and measurement time can be short
Small number of very accurate and reliable measurements Large number of moderately accurate measurements available for averaging Stress calculations are relatively compact Stress calculations often quite large
Modest capabilities for data averaging and lf-consistency
checking
Extensive capabilities for data averaging and lf-consistency checking Relatively rugged,suitable for field u Less rugged,more suited to lab u
Sensitive to hole-eccentricity errors Hole center can be identified accurately
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fringe patterns can be difficult becau any given light intensity could correspond to one of two possible pha angles.In addition,pha angle determination near the peaks of the light or dark fringes is nsitive to measure-ment noi becau of the near zero slopes of the intensity vs.pha relationship in the areas.To address this issue,“pha-stepping”Moirétechniques[29,30]have been introduced,where the lengths of the optical paths are stepped using piezo actuators,with optical images mea-sured at each step.Typically,four images are measured at 90°pha intervals.The optical pha at each image pixel can be determined from the pixel intensities in t of stepped images[36].The pha is determined modulo2π, so“unwrapping”[37]is needed to place the pha angles of all the pixels in correct quence of fringe order.Ya et al.
[35]describe an impressive apparatus for hole-drilling residual stress evaluations using pha-stepping Moirémeasurements.
The availability of“excess”data provides the possibility to improve stress evaluation accuracy and reliability by data averaging,and to be able to identify errors,outliers or additional features.This can be done visually,for example, the vertical non-symmetry of the fringes in Fig.3shows that the residual stress are non-uniform within plane. Alternatively,non-conforming data can be revealed by evaluating the“residuals”,i.e.,the difference between the actual measurements and the expected measurements bad on the evaluated stress.
Moirémeasurements have the advantage of making u-ful measurements very near to the hole boundaries,much nearer than could be made by strain gauges.When using an attached diffraction grating,some minor delamination of the grating near the hole edge can limit the cloness of available measurements.The surface preparation to attach or form the diffraction grating on the surface is burdensome but not prohibitive.
Holographic Interferometry
Holographic interferometry[36,38,39]provides a further important method for measuring the surface displacements around a drilled hole.It has veral similarities to the Moirémethod and also involves measuring the interference pattern that is created when mixing two coherent light beams.
Holographic interferometry using the classical photo-graphic technique[40–43]provides a direct method to make hole-drilling residual stress measurements.A variant technique us a video camera in place of photographic film to avoid the need for photographic processing[44–46].A further variant us Electronic Speckle Pattern Interferom-etry(ESPI).This is an attractive alternative approach becau it is relatively straightforward to implement and can produce“live”fringe patterns by image subtraction [47–50].Stepping the reference beam using a piezoelectric pha shifter enables the local pha to be determined at each measured pixel[36,39,50,51].This is a very signifi-cant feature becau it enables the evaluation of pha change throughout the obrved area and greatly facilitates residual stress evaluations using full-field data instead of a few fringe values at lected points.
Figure4shows a typical ESPI arrangement[50].The light from a coherent lar source is divided into two beams,one of which illuminates the specimen surface and is subquently imaged by a CCD camera,while the
cond Fig.3Moiréfringe pattern created by hole drilling(from Nicoletto [32
])
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feeds directly to the CCD camera where it creates an interference pattern on the CCD surface.The measured speckle pattern appears to be random noi,but each pixel in the image has a consistent pha relationship between the illumination/object and reference beams.A piezo actuator steps the reference beam at 90°intervals to create a t of four images,from which the pha angle at each pixel can
be determined.This is the same technique as ud for pha-stepping Moiré.
The surface deformations caud by hole drilling change the pha angle of the illumination/object beam at each pixel.The pha changes indicate the surface displace-ment in the direction of the “nsitivity vector,”which for the arrangement in Fig.4is in the direction of the bictor of the illumination and object beams.Figure 5(a)shows an example fringe pattern created by hole drilling.O
nly the area within the two dashed circles is typically ud for the computation,the central area being too noisy,and the exterior area containing minimal deformations.
好热图片Developments in hole-drilling residual stress measure-ments using ESPI parallel tho using Moirémeasurements.Several different ESPI arrangements can be ud,each with different capabilities.The arrangement shown in Fig.4measures surface displacements in the direction of the indicated “nsitivity vector ”.An optical arrangement similar to that shown in Fig.3is also uful for ESPI measurements [48,51].In this ca,the measured quantity is the in-plane displacement.Some further variations are possible,for example,the interesting radial in-plane arrangement in [52].Shearography is another important class of ESPI mea-surements [53,54].A Michelson interferometer is ud to prent two images of the specimen to a CCD camera,one image slightly shifted (“sheared ”)relative to the other.The two images interfere in the same way as the two beams shown in Fig.4,one of them acting as the illumination/object beam and the other as the reference beam.The resulting pha measurements give the differences in out-of-plane displacements of the paired points in the sheared images.The displacement differences in turn equal the mean surface slope between paired points,from which the residual stress can be identified when doing hole-drilling measurements [55–57].Shearography measurements tend to be more stable than displacement measurements becau they are innsitive to rigid-body motions.However
the
Fig.4Schematic arrangement ud for ESPI measurements (from Steinzig [50
])
Fig.5ESPI hole-drilling measurements.(a )experimental data,(b )theoretical data,(c )misfit
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inherent subtractions cau a tendency for the measured pha changes to be smaller.
A significant feature of ESPI is that it can work with a plain specimen surface,without attachment of the diffrac-tion grating needed for Moirémeasurements.This makes it possible to do ESPI measurements rapidly,and potentially to u the method as an industrial quality control tool.It also explicitly determines the pha at each point within the image area,as done with pha-stepped Moirémeasure-ments.As with all the optical methods,ESPI equipment is delicate and expensive compared to strain gauge equip-ment,but the per-measurement cost is relatively low becau no strain gauges need to be attached.Digital Image Correlation
Digital Image Correlation [58–60]is a versatile optical technique for measuring surface displacements in two or three dimensions.Figure 6shows the arrangement ud for 2-D displacement measurements.The technique involves painting a textured pattern on the specimen surface and imaging the region of interest using a high-resolution digital camera.In some cas,for example,wood,the specimen may have sufficient natural texture not to require the addition of paint.The camera,which is t perpendic-ular to the surface,records images of the textured surface before and after deformation.The local details within the two images are then mathematically correlated,and their relative displacements determined.The algorithms ud for doing this have beco
me quite sophisticated,and with a well-calibrated optical system,displacements of ±0.02pixel can be resolved.
The 3-D technique involves imaging the region of interest with two cameras and using stereoscopic imaging to determine deformations in three dimensions [60].The
equipment is more complex than for the 2-D technique,and careful tup and calibration are required.Both the 2-D and 3-D techniques are less nsitive to environmental dis-turbances than Moiréor ESPI,and so are more suited to field u.
Digital Image Correlation has been successfully applied to residual stress measurements using hole-drilling.Both large [61]and small [62]specimens have been investigated.The challenge has been to find ways of using the available deformation data effectively.In principle,1-D data are sufficient,and the u of some lected points can give reasonable residual stress results.As with computations with the other optical techniques,the residual stress evaluation benefits from the inclusion of a wider range of data,both in terms of number and type of data.The 2-D technique can evaluate two in-plane displacement compo-nents (horizontal and vertical,or radial and circumferential)from one pair of images.The u of such 2-D data can significantly improve the accuracy of the computed residual stress.
Out-of-plane surface deformation data are additionally available using 3-D Digital Image Correlation [60].The additional data can further improve the accuracy of residual stress evaluations from hole-drilling measurements.How-ever,the out-of-plane displacements are much smaller and therefore less influential than the in-plane displacements.Thus,the major benefit is likely obtained by going from 1-D data to 2-D data.The further benefit of using 3-D data has yet to be evaluated in terms of the added cost and complexity of making the 3-D measurements.
Inver Computation of Uniform Stress
A defining characteristic of the hole-drilling method and almost all other destructive methods for measuring residual stress is that they involve removal of stresd material in one area of the specimen and the measurement of defor-mations in a different nearby area [63].This difference in the locations of the target stress and the measured deformations creates a substantial computational challenge,particularly when stress vs.depth profiling is the objective.For the simpler “uniform stress ”ca,a straightforward stress calculation is possible.Minimally,there are just three strain data at the final hole depth and three in-plane stress components are to be determined.Even when data averaging is done using strain data from a ries of hole depth increments [21],the required computation remains fairly straightforward.
The situation becomes more challenging when working with optical data,especially when it is in the form of light and dark fringes.Initial optical measurements for hole drilling ud calculation methods parallel to tho ud
for
Fig.6Schematic arrangement ud for 2-D Digital Image Correlation (from Sutton et al.[60])
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