# Residual Stress Determination Using Combined Cross Slitting Engineering Essay

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It is well known that residual stress is an important factor to affect performance and life span of engineering structures and components. In the last two decades, there have been increased attempts to apply laser Interferometry to determine displacement generated by hole-drilling method' and hence to determine the residual stresses of materials.

Conventionally Hole-drilling and Electronic Speckle Pattern Interferometry (ESPI) are used to measure residual stresses in metal specimens. But hole-drilling involves removal of the most data-rich part of the specimen, the material within the hole. It is possible to reduce this loss of data-rich material by cutting a narrow slit instead of a circular hole. However the conventional single-slitting method is sensitive only to the stress component perpendicular to the slit direction, and thus has a strong directional bias. Electronic Speckle Pattern Interferometry (ESPI) provides additional opportunities for measuring surface displacements for hole-drilling residual stress evaluations. The non-contact nature of the technique (ESPI) avoids the significant time taken to install strain gages, associated wiring and surface coating. In addition, ESPI provides a much richer, full-field data set than is available from strain gauges. Conventional ESPI has a similar bias because it responds to surface displacements in a specific sensitivity direction. This report presents a novel cross-slitting method with dual-axis ESPI measurements. The proposed method combines the advantages of ESPI and the slitting method. It gathers a rich source of data and overcomes the directional measurement biases.

## INTRODUCTION

In any engineering structure/component safety and reliability depends upon our capability to prevent/ predict the failure of the component or structure [3]. The important factor on which any failure depends is external loading but there are some other factors including unfavourable materials microstructure, pre-existing defects and residual stresses. Unpredicted or Unexpected failure occurs when residual stresses combined with applied stresses. So the residual stresses and their measurements are very important in stress analysis.

By considering the importance of Residual Stress, it is clearly important that the origins of residual stress are recognized, means for predicting their evolution in-service developed, and their influence on failure processes understood. In this way, residual stresses can be incorporated into safe structural integrity assessments, leading either to removal of the part prior to failure, or to corrective reparative action when necessary. There are several methods for determining Residual Stresses' each have some advantages and disadvantages.

The strain gauge hole-drilling method [2, 15] is one of the most widely used techniques for measuring residual stresses. It is practical, reliable and causes relatively small damage to the test specimen. However, the installation of strain gauges and associated wiring is very time consuming. The amount of available data is also limited. For every measurement, only three discrete readings are available, just sufficient to evaluate the three in-plane residual stresses.

The slitting method is chosen as an alternative to the more commonly used hole-drilling method because it involves less material removal and leaves large areas of highly deformed material available to be measured [5]. However, the conventional single-slitting method is sensitive only to the stress component perpendicular to the slit direction, and thus has a strong directional bias.

Electronic Speckle Pattern Interferometry (ESPI) [15] provides additional opportunities for measuring surface displacements for hole-drilling residual stress evaluations. The non-contact nature of the technique avoids the significant time taken to install strain gages, associated wiring and surface coating. In addition, ESPI provides a much richer, full-field data set than is available from strain gauges [7]. However, hole drilling involves removal of the most data-rich part of the specimen, the material within the hole. It is possible to reduce this loss of data-rich material by cutting a narrow slit [2, 5, 6] instead of a circular hole. Significant areas of highly deformed material then remain adjacent to the edges of the slit. However, a single slit can only relieve normal stresses perpendicular to the slit and the shear stresses. Thus, it can only indicate up to two of three in-plane stress components, and so creates a biased estimation. Conventional ESPI has a similar bias [2, 12, 15] because it responds to surface displacements in a specific sensitivity direction.

In this report, We will discuss thoroughly a conventional hole drilling method , single slitting method , a cross-slitting method , Electronic Speckle Pattern Interferometry (ESPI) method and their advantages and limitation .Then the New method which is " CROSS SLITTING COMBINED WITH DUAL -AXIS ESPI" which address both directional biases [2]. In this method Cross slitting is introduced as a means of releasing all in-plane stress components and the dual-axis ESPI system uses diagonal-mirror and shutter devices to provide surface displacement measurements in orthogonal in-plane directions. The combinations of the cross-slit and dual-axis measurement gives isotropic sensitivity to the inplane residual stress components and provide more data and useful information regarding residual stress determination than conventional methods.

## RESIDUAL STRESSESS

Residual stresses are the ones that remain on components and structures after the load has been removed [3, 4] or the stresses which are retained within a body when no external forces are acting. Residual stresses arise because of misfits (incompatibilities) between different regions of the material, component or assembly.

Residual Stresses may result from fabrication processes such as welding and machining, or due to overload localized yielding [3]. Usually these stresses are undesirables because they added to service stresses reducing the structures maximum load. However, in case, when variable loads are expected compression surface residual stresses are sometimes applied to improve fatigue resistance. This way the residual stress assessment assumes a very important role in mechanical design.

Therefore, the prevention and prediction of failure in components/ structures is not only the interest of engineering, but it is essential for the safe execution of our daily lives. When external loadings acting on a material or component are clearly important. Other factors often play a determining role like preexisting defects, unfavorable microstructure and residual stresses. When unexpected failure occurs, it is often because residual stresses have combined critically with the applied stresses, or because they, together with the presence of unknown defects or poor microstructure, have dangerously lowered the stress at which failure will occur.

From the above discussion, it is clear that the origins of residual stress should recognized, means for predicting their evolution in-service and their influence on failure processes should be considered. Therefore, the residual stresses can be incorporated into safe structural integrity assessments of component or structure.

## Methods for Residual stress Determination [3]

There are two basic classifications of methods.

Destructive methods of residual stress measurement.

Non-Destructive methods of residual stress measurement.

## Destructive methods of residual stress measurement

Destructive methods of residual stress measurement rely on the fact that when a cut is introduced the object deforms as the necessary components of tractions due to the residual stress field reduce to zero at the newly formed surface. The most common method for residual stress measurement is the hole-drilling method with strain gauges. This method is most economical and simple technique for residual stress determination [4] .But it has some limitations therefore other methods and the combinations of different methods are used to avoid the limitations or disadvantages [7].

## Non-Destructive methods of residual stress determination

Non destructive methods rely on the fact that no damage done on sample or test specimen. This method can save time, money for the testing and determination of residual stresses. There are several non-destructive techniques, and methods and each have advantages and limitation .But in this report we will discuss Electronic Speckle Pattern Interferometry [10, 13] their merits and demerits and ways to improve this method.

## HOLE DRILLING METHOD

Hole-drilling method is a most common and simple method for determining residual stresses in various materials and structures [3]. This Method involves drilling a shallow hole around which the local surface deformations are measured by a specially designed strain-gauge rosette.

## Strain Gauge Localization Figure 1

The systematic arrangement of strain gauge rosette is shown in figure 1 .For the uniform stress case, the surface strain released after Hole drilling is given by [4]

(1)

In equation 1, aÂ¯ is calibration constant for isotropic stresses, bÂ¯is the calibration constant for shear stresses. They indicate the relieved strains due to unit stresses within the hole depth. They are dimensionless, almost material-independent constants. Use Slight different values of these constants apply for a through thickness hole made in a thin specimen and for a blind hole made in a thick specimen. Now ÆŸ is the angle of strain gage from the x-axis, r is the distance from hole center to strain gage center. Where Ïƒx, Ïƒy and Ï„xy are residual stresses E is Young's modulus and Ê‹ is Poisson's ratio. See figure 2.

## Hole Geometry and Residual Stresses figure 2

Equation (1) shows that three normal strains must be obtained to determine the residual stresses Ïƒx, Ïƒy and Ï„xy. Therefore, three strain gages should be localized at positions with different angle ÆŸ from x-axis, for example ÆŸ = 00, 450 and 900. Substituting ÆŸ with these values in equation 1, we get the following equations.

## Limitations of Hole-Drilling Method

The removal of Data rich material also the installation of strain gauges and associated wiring is very time consuming. The amount of available data is also limited. For every measurement, only three discrete readings are available, just sufficient to evaluate the three in-plane residual stresses [2].

Hole Geometry and Residual Stresses

Fig 2

## SINGLE SLITTING METHOD

The slitting method can be used as an alternative to the more commonly used hole-drilling method because it involves less material removal and leaves large areas of highly deformed material available to be measured [2].

The slitting method is used to determine a residual stress distribution along one direction and can give good results near the surface or through the thickness [5]. A cut is made into the component containing the residual stress [6]. Residual stress normal to the face of the cut is released and the resulting strain is measured by surface mounted strain gauges. Further incremental cuts and associated strain measurements are made through the work piece to a predetermined depth as shown in figure 3.

## Incremental slot cutting and strain measurement, Figure 3

These strain measurements are then used to determine the residual stress in the component as a function of depth. For shallow cuts, a top gauge will provide good measurement sensitivity. However, for deeper Cuts/ slots, as the cut progresses, the leading face of the cut becomes further away from the gauge, and the strain readings will eventually plateau and become meaningless. However, this problem can be overcome by fitting an additional gauge on the bottom of the sample. With both top and bottom gauges as shown in figure 4.

## Slitting method schematic, Figure 4

The top gage gives good sensitivity for shallow cuts, and the bottom gage gives good sensitivity for deep cuts. As the sensitivity at the front gauge decreases the bottom, gauge sensitivity increases. When using top and bottom gauges, the top gauge will improve the results for the first 5-10% of the cut depth, whereas a bottom gauge will provide good results between 5% and 95%.

Slitting is a stable, adaptable, and reliable method for residual stress determination in a wide variety of materials (metallic, plastics, FGMs, and single crystals) and geometries (plates, disks, cylinders) [5].

## Limitations of Single Slitting Method

As we discussed above that the single slitting method is a good alternate to hole drilling method but the conventional single-slitting method is sensitive only to the stress component perpendicular to the slit direction, and thus has a strong directional bias [2].

## CROSS-SLITTING METHOD

As we know in a single slitting method, a slit is cut in the specimen and the resulting deformations are typically measured using strain gauges attached to the upper and/or lower surfaces [5]. However, only stresses perpendicular to the slit face, Ïƒx, Ï„xy, are released and can be calculated from the strain measurements as shown in figure 5a.

In order to avoid this directional bias from single slitting method a new cross-slitting method can be used [2]. In cross-slitting method, two perpendicular slits are cut into the surface, vertical slit 1 releases in-plane residual stress components Ïƒx, Ï„xy, and horizontal slit 2 releases Ïƒy and Ï„xy as seen in figure 5b. The slits length use to determine the capability of the method to determine subsurface stresses. Stresses down to about half the slit length can be evaluated.

In hole drilling method, the equivalent circular hole (Fig 5c) would have a diameter equal to the slit length and would allow subsurface stress evaluation down to about half its diameter.

2

1

1

## Figure 5a Figure 5b Figure 5c

In order to maximize the four adjacent areas of highly deformed material around the slit intersection the slit width would be very small. These data-rich areas contain high surface deformations that greatly enhance the accuracy of cross slitting measurements. They are lost during hole drilling using the equivalent circular hole shown in Fig 5c.

## Non destructive Methods of Residual stress Determination

There are many non-destructive methods of residual stress determination. It has been seen that over the past few years there has been a significant increase in the scope and of applications of optical interferometric methods for residual stress analysis [7] .Most common methods are holographic Interferometry, white-light techniques and speckle techniques [2,12,13].The main advantage of optical interferometric techniques is that they are Nondestructive, Noncontact , have high resolution, and can allow full-field inspection. One of the most common and useful optical methods is electronic speckle pattern Interferometry (ESPI).

## Electronic speckle pattern Interferometry (ESPI)

Now a day's Optical interferometric metrology methods are being increasingly used in industry. These methods provide a greater accuracy in measuring displacements caused by deformations. One of the important interferometric technique is electronic speckle pattern Interferometry (ESPI). Electronic speckle pattern Interferometry (ESPI) is considered as a full-field noncontact experimental measuring method, based on the optical physics of surface generated laser speckle. ESPI provides rapid and highly accurate measurement of the three components of deformation and generation of strain/stress distribution with high resolution. It is well suited for the determination of the true peak strain and the strain distribution in regions of strain concentration that are usually the most critical in an investigation [11, 12, 13].

## PHYSICAL PRINCIPLES OF ESPI

The basic principle of ESPI technique is to produce a speckle pattern by illuminating the surface of the object or sample with laser light [2,12,13]. This speckle pattern is imaged onto a CCD array and allowed to interfere with a reference wave (may or may not be speckle) to obtain a resultant speckle pattern. This resultant speckle pattern is transferred to a frame grabber on board a computer and after saving in memory, displayed on a monitor.

So if the object or sample to be tested has been displaced or deformed, the resultant speckle pattern changes owing to the change in path difference between the wave front from the surface and the reference wave. This second resultant speckle pattern is transferred to the computer and either subtracted from or added to the previous stored pattern and rectified. The resultant of these two is interferogram, which is then transferred on the display monitor as a pattern of dark and bright fringes. These dark and bright fringes are called correlation fringes.

It is possible to grab frames continuously while a deformation is occurring in real time standard video rates and then subtract them in succession from the first speckle pattern. The above process makes it possible to observe the formation and the progressive changes in real time of the fringe pattern related to the deformation of the surface/sample.

There are two most common configurations of EPSI System

In plane EPSI System

Out of plane EPSI System

## In-Plane Electronic Speckle Pattern Interferometry (Single Axis) [12, 13, 2]

In this method two beams that generate their own speckle patterns as shown in figure 1 illuminate the surface of the object or sample.

## Figure 1 Basic setup of an in-plane ESPI system

Figure 2 shows a Schematic arrangement of Electronic Speckle Pattern Interferometry (ESPI) arrangement for in-plane displacement measurements [2]. It is shown that the light from a laser source is divided by a beam splitter into two parts, one becoming a reference beam and the other an illumination beam. Both beams interfere after reflecting from the mirrors at the surface of the test Sample. To record and image the resulting interference (Speckle) pattern a CCD camera is used.

Conventional ESPI does not use mirrors. Therefore, the optical arrangement in figure 2 shown differs from conventional in-plane ESPI systems by the use of this adjacent mirror. It enables the illumination and reference beams to be close to each other over most of their span, thereby improving ESPI measurement stability.

## Fig. 2 Schematic arrangement of in-plane ESPI measurement

Slitting method produced surface deformation, which is evaluated by subtracting the phase maps measured before and after slitting procedure. These phase maps are evaluated by measuring sets of speckle patterns with 90Â° phase steps introduced into the reference beam by a piezo- actuator behind one mirror. For the arrangement shown in Fig. 2, the displacement sensitivity vector is in the plane of the specimen surface and perpendicular to the adjacent mirror.

## LIMITATIONS OF SINGLE AXIS ESPI SYSTEM

Conventional ESPI systems use a single axis illumination, which allows to measures only the displacement along a particular vector direction that lies normal to the viewing direction and is in the plane of two illumination beams. This method only gives a single directional displacement measurement. Therefore, from figure 1 it can measure the displacement only along the X-axis. In order to measure the displacement along the Y-axis, the illumination beams should be in the Y-Z plane. [2, 13]. Conventional ESPI causes a bias in residual stress measurements because the associated displacement components derive mostly from the parallel in-plane stress. The perpendicular in-plane stress produces much smaller displacements in the sensitivity direction, mostly due to the action of Poisson's ratio.

## Cross-slitting and Dual-axis ESPI Technique [2]

As we discussed the limitations of hole drilling and slitting method , Cross-slitting has been demonstrated to be an effective and accurate alternative to hole-drilling as a method for measuring in-plane residual stresses and their variation with depth. Cross Slitting provides all three in-plane stress components to be evaluated [2].

By considering the geometry of the cross-slit, it has the advantage over a circular hole that it leaves available for ESPI measurements four substantial areas of highly deformed material adjacent to the cross-slits. These areas provide a rich data source for the residual stress calculations, thereby enhancing evaluation accuracy. In addition, the cutting of cross-slits removes much less material than from an equivalent circular hole. This feature reduces the volume of chips produced and minimizes the occurrence of surface damage as the chips exit the cut.

In order to remove the directional bias inherent in a conventional single-axis system a dual-axis ESPI system has been developed. The additional data from the second axis enhance the available data and therefore enhances the measurement accuracy of the system. This benefit is not limited to the use of cross-slits, and could be gained when using the hole-drilling technique. With organized arrangement of the data handling, the residual stress evaluations from dual-axis data are only about 50% more demanding than an equivalent single axis calculation, and can be performed with an ordinary desktop computer [1, 2]

In order to make a system sensitive to displacement in both the X and the Y Directions, four illumination beams are required. This Arrangement can provide a complete in-plane displacement measurement. It is possible by sequentially recording the two separate interferograms and combining them vectorially. The two pairs of beams should not illuminate the surface at the same time [2, 13].

Dual-axis ESPI system is capable of providing the displacement measurements in two perpendicular directions. This arrangement eliminates the measurement bias inherent in single-axis ESPI measurements. Typical arrangement of dual -axis ESPI is shown in figure 4.

## Fig. 4 Dual-axis ESPI system

In this method, light from the laser is divided by beam splitters into three switchable parts. The first part of the light goes to the lower of a pair of diagonal mirrors and is reflected to the sample surface. The second part goes to the upper mirror and is also reflected to the sample. The third part acts as a reference beam and It illuminates the specimen surface after reflection from a mirror attached to a piezo actuator. This actuator steps the length of the reference beam by quarter wavelength intervals to enable use of the phase stepping method. The lower and upper mirrors can be illuminated separately by controlling some shutters.

From figure 5, the two sensitivity vectors for the dual-axis ESPI system can be identified. In the plan view, all beams are (approximately) parallel, with reflection angle Î¸. The reference beam has vector direction k0, while the illumination beams have vector directions K1 and K2 after reflection from the diagonal mirrors.

For diagonal mirrors that are perpendicular to the specimen surface in the plan view and Â±45Â° in the front view, the sensitivity vector in direction 1 (using the lower mirror) is:

And for the direction 2 (using the upper mirror) is:

## Fig. 5 Diagonal-mirror assembly and sensitivity vectors

where Î¸ is the reflection angle and i, j are the unit vectors in the x and y directions. The two sensitivity directions S1 and S2 are orthogonal, thereby balancing the calculation sensitivity for the in-plane normal stresses and making the residual stress evaluation more accurate overall.

The phase shift change measured using the ESPI technique is:

Where a 5-step phase stepping procedure [10] is used here to evaluate phase change. By subtracting the phase maps measured before and after slitting, "wrapped" phase maps, i.e., with modulo 2Ï€ discontinuities are obtained. The discontinuities can be removed mathematically to produce unwrapped phase maps [11], from which the displacements in the two sensitivity directions can be determined.

## Cross- Slitting and Dual Axis ESPI Experimental arrangement

For demonstrating Cross slitting dual axis ESPI method [2]

Material: T6061 Aluminum Plate

Dimensions: 203 x 102 mm and 12.7 mm, was used. By loading plate in four point bending fixture, known residual stresses were produced and monitored the applied load and the surface strains in the central section as the load was increased substantially into the plastic range and then removed. During loading the plastic deformation, followed by elastic unloading created an in-plane residual stress profile within the specimen/ sample. This profile could be determined from the uniaxial stress-strain curve computed from the bending load and surface strain data. In this case, where the beam specimen was a wide plate, the central portion underwent plane strain deformation. The transverse stresses were also created, which is Î½ (Poisson's ratio) times the longitudinal stresses [2, 13].

Before any slitting an initial reference, set of images was recorded in the two sensitivity directions. After then a milling cutter used to cut the cross-slits in five depth increments of 1.27 mm to a maximum depth of 6.35 mm and after each depth increment, a new set of images was recorded in each sensitivity direction and corresponding phase maps were produced. Each phase map, which is produced, was used as the reference for the next depth increment. This practice improved correlation between images and therefore improved the quality of resulting fringe image. By using this approach, the measured fringes represented the incremental changes in the surface displacements.

The above-mentioned five incremental directional ESPI fringe patterns measured in sensitivity direction 1 are shown in figure # 8

## Fig. 8 Incremental fringes measured in sensitivity direction 1: (a) 1st increment, (b) 2nd increment, (c) 3rd increment, (d) 4th increment, (e) 5th increment

The diagonal tilt of the fringe patterns reflects the 45-degree tilt of the sensitivity direction 1. The opposite diagonal tilt occurs in the fringes measured in sensitivity direction 2. These fringes have following qualities.

1) They are well-defined, indicating good image quality.

2) They are numerous, indicating a high sensitivity.

3) They have distinctly different shapes, enabling the inverse calculation to separate the various stress components well.

Stress profiles calculated from the dual-axis ESPI cross slitting shown in figure 9a.

## Fig. 9a Residual stress vs. depth profiles computed using dual-axis measurements

## (ESPI in-plane stress results)

The above graph shows the stresses within half the sample thickness. At the surface when depth is zero the bending-induced residual stresses are compressive , changing to a tensile peak at 4-5 mm depth, and then reducing to zero at the neutral plane at 6.35 mm depth.

The normal stresses Ïƒx is parallel to the original bending loading are the largest as expected and due to Poisson's ratio the normal stresses Ïƒy are about one third of the Ïƒx stresses in plane-strain bending. Because of the symmetry the shear stresses Ï„xy are close to zero. The Same experiment conducted six times and obtained ESPI/cross-slitting measurements. All the measurements gave similar results and provided the consistency of the measurements.

Now consider figure 9b that shows a comparison of the dual-axis ESPI measurements and the stresses, which is evaluated during the bending test.

## Fig. 9b Residual stress vs. depth profiles computed using dual-axis measurements (Comparison of Ïƒx stress from ESPI and bending tests)

The expected and measured stresses closely agree. The similarity of the stress values computed from single-axis and dual axis data shows that the fringe images obtained in these measurements are mutually consistent. The dual-axis calculations give stress results between the results obtained from the two single axes. This is not always happed, for example, the dual-axis calculated stress for the fourth increment in Fig. 9(b) is closer to the expected curve than either of the associated single-axis results.

The Advantages and benefits of the dual-axis ESPI method is clearly shown in figure 10.

## Fig. 10 Shear stress profiles from single-axis and dual-axis measurements

## RESULTS

As we discussed the conventional methods of residual stress determination and the cross-slitting method can be considered a variant of the hole drilling [2, 5, 6] .The great advantage of cross slitting is that it requires removal of much less material. The surface displacements have the same general response to sub-surface stresses, with greatest sensitivity to near surface stresses and diminishing sensitivity to deeper stresses.

In conventional hole-drilling [3, 4], the stress sensitivity extends to a depth equal to about half the hole diameter but for cross-slitting [2] , the analogous depth dimension is half the slit length. After cutting, there remain four large areas of highly deformed material around the intersection of the cross-slit. These areas provide high-sensitivity data for calculation and then improving computational stability. In addition, the reduced volume of chips produced during cutting is beneficial because these chips tend to scratch the specimen surface as they exit the cut, and impair the ESPI measurements.

The measured stress profile by cross slitting and Stress profiles of similar smoothness can be achieved from conventional hole drilling measurements. Stress solution stability decreases when a greater number of small depth increments are used. Thus, it is possible that in that case some modest regularization could be required with cross slitting, but still less than with similar conventional hole drilling.

A unique feature of the Dual axis ESPI design [2] is the use of a single camera with the multiple beams. Thus, the pixels in all measured images are similarly arranged, with no cross-registration of pixels between multiple cameras required. The computations to give the stress profile results in Fig. 9 took approximately 20 s using a low-end desktop computer. The additional time to collect the second axis images is negligible because most of the overall experiment time is consumed in the slit cutting. Correlation of the two single-axis measurements can provide important capabilities for data consistency checking.

## CONCLUSION

We have discussed the conventional Hole drilling method and it was concluded that the Cross slitting method is an accurate and accurate alternative to hole drilling as a method for measuring in-plane residual stresses and their variation with depth. All three in-plane stress components can be evaluated by using Cross-Slitting method. Further, if we consider the geometry of cross-slit, it has the advantage over a circular hole that it leaves available for ESPI measurements four substantial areas of highly deformed material adjacent to the cross-slits. These areas provide a rich data source for the residual stress calculations to improve the accuracy of their evaluation. In addition, the cutting of cross-slits requires less material to remove than an equivalent circular hole. This feature of cross slitting minimizes the occurrence of surface damage as the chips exit the cut and reduces the volume of chips produced.

We also discussed single axis ESPI system which has the directional bias .The dual-axis ESPI system can removes the directional bias inherent in a conventional single-axis system. In addition the additional data from the second axis enhance and enriches the available data, and can improve the overall measurement accuracy of the system.