9... 1n 3% ftll 19- 1.- Iv. .r-quOPIOssVV‘ fit-C(‘q .dw§.r..i. . n 0‘. lo. 571. $252 - I l: ’41... E). .62!!! :- :strvvtz 03!... .al. 3. .3 3.2 .1 lilifi .ol 3‘ ..n.. Q. : 953.1. E. 6|! {pro it,“ f4”!....p0i.ufltut5¥ vii! r. .I. L . hflflnp‘la : T . 3.1 '5 . 1.1.9.! \u! v)..€cl,a-I4\I:rx It]! v Lfi. .1 n. 3.... p fa.fvl.f:»0r.l.l...\4.r v v.1 11111.... .3111}. I»: (- P!..vé ‘ 315...! o. . 4 ,4 9... .5. 53):. f :): ...;.. e. if... . a . Z. {1323.}... “IR. . x .i: 55%;... L ’ Tim-ts MICHIG GAN STATEU ii I llell Him 00910 5994 This is to certify that the thesis entitled A Interferometric Strain Rosette presented by Henry J. Wede has been accepted towards fulfillment of the requirements for Master's degree in Mechanics WM Major professor Date II/JO/qg' O-7639 MS U is an Affirmative Action/Equal Opportunity Institution F LIBRARY Michigan State i University L I —— PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE ” figfi 3: a! N ‘ i i =1 H i. MSU Is An Affirmative ActioNEquel Oppoctunity Institution ammo-9.1 AN INTERFEROMETRIC STRAIN ROSETTE BY Henry John Wede A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Material Science and Mechanics 1992 ABSTRACT AN INTERFEROMETRIC STRAIN ROSETTE BY Henry John Wede While basic interferometry is the origin of most optical methods of strain measurement, it has rarely been used for its own sake. Some researchers have found methods to produce interference patterns from reflective specimens and have used these interference patterns for strain measurement. However, most of these methods have only provided systems to measure uniaxial strain or, at best, strain in two orthogonal directions. This paper describes a method which makes the interferometric strain rosette a potentially viable tool for the experimentalist. By using a icircular indentation, interference patterns are produced which allow strain measurement in any direction or directions. Different methods of computer interfacing which further extend the capability of this technique are also discussed. To my parents iii ACKNOWLEDGEMENTS I would like to thank Dr. John Martin for giving me the opportunity to do this work and the freedom to monopolize his laboratoryu I*would also like to thank my committee, Dr. Gary Cloud and Dr. Dashin Liu, for their patience towards my seemingly endless revisions. Also, Kurt Niemeyer and Leonard Eisele provided me with a great deal of help in working out the electronic and mechanical problems. Their help was greatly appreciated. iv TABLE OF CONTENTS LISTOFFIGURES......OOOOOOOOOOOOOOOOOO ...... O ........ Vi Introduction to interferometric techniques ............ 1 Young’s experiment and displacement equations ....... 2 Brief history of interferometric techniques ......... 4 A discussion of different indentations................ 7 Pyramidal indentations .............................. 7 Experiment using pyramidal indentations ............. 8 Circularindentation......OOOOOOOOOOOOOO0.0.0.000... 12 Experiments using circular indentations ............. 15 Comments on both types of indentations ... ..... ...... 22 Methods of measuring fringe translation ............... 24 Photomultiplier tube, scanner and laser arrangement . 25 Partsaescription0.0.0.0..........OOOOOOOOOOOOOOOOO. 28 Software techniques ................................... 30 Information from the initial fringe pattern ......... 30 OSCillatingteChniques ............OOOOOOOOOOOOOOOOO. 33 Stress - strain experiment using anmoscillating technique ......................... 36 Stationary“techniques ......................... ...... 40 Computer code for uniaxial testing .................... 43 Conclusion .......... ...... ....................... ..... 54 References ......OOOOOOOOOOO.........OOOCOOOCOOOOOOOOOO 55 ListOfreferences......OOOOOOOOOO......OOOOOOCOOOOO55 GeneralreferenceSOOOOOOO ..... 0.0.00000000000000000057 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 10 11 12 13 14 15 16 17 LIST OF FIGURES Page Young's two slit experiment ................... 2 Derivation of displacement equations .......... 3 Patterns for pyramidal indentations ........... 5 Setup for uniaxial measurement by tracing fringes ...O................OOOOOOOOOOOOOOOI... 9 Fringe tracings for uniaxial strain using pyramidal indentations ........................ 10 Deformation of a circular indentation ......... 13 Circular fringe pattern ....................... 13 Device used to scribe circular indentations ... 14 Tracings for determining axial strain using a.circular indentation ........................ 17 Setup for transverse strain measurement using a circular indentation .................. 18 Fringe tracings for measuring transverse strain using a circular indentation ........... 19 Setup for measuring 645- using a circular indentation0......OO.......OOOOOOOOOOOOOOOOOO. 20 Tracings for measuring 645. using a circular indentation...OOOOOOOOOOOOOOOOOOOO00.0.0000... 21 Setup of a PMT and scanner mirror measurementsystem ...... 26 Detailed setup of a PMT and scanner mirror measurementsystem 27 Computer representation of a fringe pattern ... 31 Use of an oscillating technique on a fringepattern 34 vi Figure 18 Load vs. fringe shift ......................... 38 Figure 19 Stress vs. strain for Aluminum specimen ....... 39 Figure 20 Using a stationary technique on a fringe pattern0......0.0.0..........OOOOOOOCOOOOOOOO.41 vii INTRODUCTION Interferometric strain measurement has been used sparingly by experimentalists for the past twenty years. The apprehension towards this technique is primarily due to the difficulties in the setup and certain limitations in measurements. This paper addresses both of these problems. First, this paper will serve as a guide to constructing an interferometric strain gage. Many problems were encountered while setting up this system, and many different schemes were tried with varying degrees of success. This paper will prove to be a useful guide which is free from the space limitations of published papers. Second, the limitation of uniaxial or orthogonal measurement has been eliminated. A circular indentation is introduced which allows strain measurement in any convenient direction or directions. This raises the idea of an interferometric strain rosette from the drawing board into the laboratory. Many modern interferometric techniques are siblings of Young’s two slit experimenth Figure 1 shows schematically this experiment. Monochromatic and coherent light shines through two small slits in a thin sheet. Because of the small size of the slit, the light emitting from each one can be considered a point source of light. The close spacing of the light sources produces interference patterns, parallel bands of light. Two sets of interference patterns are produced; and the position of these interference patterns may be correlated to the spacing and the displacements of the slitsz. Int-throne. Pattern § lnbrbrenee Pattern U 0 0 Figure 1. Young's two slit experiment 3 If the slits are separated by a distance d (see figure 2) the following relation can be made; . . .21 mm: d (1) where n is an integer and A is the wavelength of the light. If d changes the interference patterns will translate. Rearranging the above equation yields 6d - xbm (2) sina where 6d is the change in d and 6m is the fractional percent that the bands translate. Thln Plate 1‘. .l V9 Figure 2. Derivation of displacement equations 4 However, the change indicated by 6m reflects both the change in d and any rigid body displacement between the light sources and the observation point. To eliminate rigid body motion, two values of 6m are recorded, one from each (top and bottom in figure 1) interference pattern. The average of the two values represents the change of d. If the original value of d, denoted as do, is known, then the above equation can be written in terms of strain. .ié.__1__ 11111212. e do dasinczx 2 (3) where 6m, and 61112 are the two percentages of fringe translation measured from opposing interference patterns. The above equations will serve as the base for the techniques described in this paper. W The key to applying this idea to practical strain measurement is to generate interference patterns from two closely spaced points on a specimen - then record the translation of these patterns during specimen loading to determine the displacement of the points. This was first done by scribbing two V shaped groves on a round specimen and illuminating them with a laserz. The parallel faces of 5 the groves produced two sets of interference patterns. Measuring the translation of these patterns during loading proved the above strain equations to be true. Obtaining interference patterns from flat specimens required a bit more creativity. Interference patterns were obtained by pressing pyramidal indentations into the surface’- The pyramidal indentations were made with a Vicker's hardness indentor, see figure 3a. As with the circular specimen, the parallel faces of the indentations produce two interference patterns. These patterns only allowed for uniaxial strain measurements. Biaxial measurements were achieved by arranging three pyramidal indentations as shown in figure 3b. This pattern produces two pairs of interference patterns. T T “.... LU“ \3?’ \{97 (a) (b) Figure 3. .Patterns for pyramidal indentations 6 The next logical step was to produce interference patterns that would allow for measurement in three directions allowing complete plain strain information. An arrangement of several pyramidal indentation‘ and hexagonal indentations’ were tried with varying success. Expanding this method even further, this paper introduces a new type of indentation which allows strain measurement in any arbitrary direction - a circular indentation. This indentation produces concentric fringe patterns that contain average displacement information in any.direction. Using this new idea the interferometric strain gage can continue to evolve into a valuable laboratory tool. A DISCUSSION OF DIFFERENT INDENTATIONS As with all methods of interferometry, this method starts with the interference of two coherent beams. When using this technique, the indentations are responsible for providing this interference. Proper indentations must be made on the specimen to produce adequate interference patterns. Applying the indentations, a seemingly easy task, proves to be one of the hardest parts. Not only do the indentations have to be located and oriented correctly but they have to produce fringe patterns that can be easily recorded. A brief discussion of the different types of indentations will help show which is appropriate for specific testing. When choosing an indentation type a good balance between simplicity and utility must be maintained. Each type has certain advantages and restrictions. E .3 1 I i ! !° Pyramidal indentations have been used almost exclusivly with this technique. They have proven to be very versatile. The key to using pyramidal indentations is the arrangement of the indentations. They may be arranged to give interference patterns related for simple uniaxial measurement or measurement in several directions. Uniaxial and biaxial arrangements are shown in figures 3a and 3b. These arrangements are not too difficult to set up, although arrangements for multi-directional measurement are very time consuming. When using a Vicker’s hardness tester to apply the pyramidal indentations, it is helpful to rotate the indentor 45° from the conventional position. This orients the axis of the x-y table with the direction of the interference patterns. The micrometer adjustments will then read the gage length directly, without the need for trigonometric formulas. Due to the time required to rotate and center the indentor, a dedicated hardness tester is very desirable. Since the experiments using the circular indentation will not be using the computer apparatus it is necessary to get an idea of the accuracy obtained from using an alterative method. The method chosen was simply to trace the fringe patterns on a piece of paper. The idea of this particular experiment was to show just how crude the fringe processing can be and still get accurate results. 9 Two pyramidal indentations were set up to measure axial strain. The specimen was placed in a large MTS load frame and the laser and mirrors were positioned as shown in figure 4. A positioning mirror was used to aim the laser at the indentations. Besides being easy to adjust, the positioning mirror kept the laser and stand out of the way of the fringe patterns. Fringe! Figure 4. Setup for uniaxial measurement by tracing fringe patterns The upper fringe pattern was reflected down to a table using a second mirror. The lower fringe pattern was found on the platen of the load frame. Paper was taped down and the fringes were traced. A load was placed on the specimen and the new position of the fringes was traced. The fringe tracings are shown in figure 5. Vernier calipers were used to measure the distances on the tracings. The strain indicated by the fringe translation was compared to strain 10 indicated by the MTS displacement readout. The displacement readout was used due to problems with the load control section of the MTS controller. ——--b—— I I l I I I l I 1 I I I Hlilii | || | l Figure 5. Fringe tracings for uniaxial strain using pyramidal indentations The load chosen produced a fringe translation (6m) of approximately 1%. This translation over a 150p gage length indicated a strain of 0.83%. The displacement readings of the MTS unit indicated a strain of 0.90% over the 2.5" gage length. The error between these two methods is 7.7%. This is pleasantly acceptable given the accuracy of the MTS displacement indicators and the tracing of the fringe patterns. 11 The motion of the fringe patterns indicated almost no rigid body motion of the specimen. This was a surprise. Even with such a massive load frame, some degree of rigid body motion was anticipated at such a large strain. Another observation about this experiment is the ability to accurately trace the fringe patterns with normal vision. Once adapted to night vision, the eye can distinguish the edges of the fringes well and fringe translation can be easily noticed. The data from theexperiment follows: From the tracings: 6122, = 1 + (0.115"+0.375") 1.307 6222, = 1 + (0.050"+0.164") = 1.305 6111 = (6m, + 61112) -:- 2 = 1.306 1 1 1 0.6328p e - ' . °0n2= ' . °1.306 = 0.0083 d5 31nd 150p 31n42° From the MTS displacement readout: Al = 0.2256" - 0.2031" = 0.0225" Al-z-lo = 0.0225" + 2.5" = 0.0090 12 Ci at“ s The circular indentation shown in figure 6 is made by spinning a pyramidal indentor around an axis perpendicular to the specimen. When monochromatic light is aimed at this indentation it produces concentric fringe patterns, shown in figure 7. As the specimen deforms, the circular indentation becomes elliptic and the concentric patterns change into elliptical patterns, as shown in figure 6. The translation of the pattern in any direction can be used to find the strain in that direction. Obviously, measuring displacement in three known directions results in complete plane strain information. With the concentric fringe pattern the user is free to pick any convenient directions while still using the same indentation. To eliminate unnecessary measurements the directions choosen may be aligned with principle strain directionsor with the geometry of the specimen. 13 Maximum Strain Dlrectlon (O Clrcle Before Loadlng Circle Alter Leading Figure 6. Deformation of a circular indentation Figure 7. Circular fringe pattern i A i t l i Figure 8. Device used to scribe circular indentations The circular indentations were made with a relatively crude device shown above in figure 8. The indentor from the Vicker’s hardness tester was attached to the bottom of a small x—y table. The top of the x-y table was attached to a shoulder bolt that ran through a slip-fit hole in the support. By moving the x-y table the indentor was adjusted to trace out small circles and the diameter measured using a metalurgical microscope. The play in the system generally did not produce very good circles. A more precise fixture would produce even clearer indentations and fringe patterns. An improved fixture would also allow better control of the indentor pressure. Regulating the downward force by hand is somewhat difficult but can still produce adequate results. 15 Also, a different shaped indentor may be better suited to carve out the circular grove. Using the Vicker’s indentor was very convienent and seemed appropriate. Although it produced satisfactory results, an indentor shaped more like a tool bit should produce smoother cuts. A design for a different apparatus to scribe circular indentations was drawn up but never used because of the lack of equipment and funding. The new design employed a rotating platform placed on the x-y table of a standard Vicker's hardness tester. This aproach is opposite of what was finally used; it keeps the indentor stationary while moving the specimen. E . e !s . i J . i ! !' Once it was determined that tracing the fringe patterns on paper could produce adequate results, the circular indentation was tested. The setup for this experiment was very similar to the previous experiment. The strain was determined at 0°, 45°, and 90° with respect to the axis of .the specimen. To simplify the setup, measurements were made after three different loadings with the mirrors being repositioned between each. 16 Determining e AXIAL First, the axial strain was measured. The setup for this measurement was almost identical to that of figure 11. The fringe tracings shown in figure 13 indicated a strain of 0.78%. The MTS displacement readout indicated a strain of 0.84% for an error of 7.1%. The data from this experiment follows: From the tracings: 6m1== 1 + (.0768"+.186") = 1.413 612:, = 1 + (.177"+.434") = 1.408 6m = (6m1+ 61112) -:- 2 = 1.411 1 A 1 0.6328}; 6 = _. . '6!” = . . .10411 = 000078 (10 Sina 170p 81n42° From the MTS displacement readout: A1 = 0.3726" - 0.3517" = 0.0209" A1+lo== 0.0209" + 2.5" = 0.0084 17 l l l ——-i—-— ll! Figure 9. Tracings for determining axial strain using a circular indentation Determining emsvma To measure the fringe translation in the transverse direction a second mirror was added to the system. This measurement was the easiest of the three. The mirrors could be adjusted to widen both of the interference patterns and project them onto the platen of the load frame. Figure 14 details the mirror setup and figure 15 shows the tracings of the fringe patterns. The fringe translation indicated a strain of -0.27%. The MTS display and Poisson's ratio 18 indicated a strain of -0.28%. The error between the two readings is only 2.54%. This results of this experiment were very encouraging. The data from this experiment follows: From the tracings: m, = -(.201"+.408") -0.493 61212 = -(.236"+.497") -0.475 6111 = ((5111l + 6m,) + 2 = -0.484 1 1 1 ,0.6328}g €=_-_06 = . . "-0.484 = -0.00269 d5 31nd 170p 81n42° From the MTS displacement readout: A1 = 0.3194" - 0.2963" = 0.0230" Ali-10 = 0.0230" + 2.5" = 0.0092 X -0.30 = -0.00276 Load / ............. (3'74 ...... \ . : Leeer Positioning Mirror Speclmen 3 K ' f Fringe Peeitlonlng Mirror Frlnoc A Prince 3 Figure 10. Setup for transverse strain measurement 19 Figure 11. Fringe tracings for measuring transverse strain using a circular indentation Determining a“. A To measure the normal strain on a 45° angle, a piece of graph paper was attached to the specimen. The graph paper was used to position the mirrors which projected the interference patterns down to the platen of the load frame. Once again the fringe patterns were traced before and after loading. The mirror setup is shown in figure 12 and the fringe tracings are shown in figure 13. The fringe translation indicated a strain of 0.34% and the MTS display, along with Mohr's circle for strain, indicated a strain of 20 0.30%. The error between the two readings is 13%. This is the largest error of the different readings and can be attributed to angular misalignment and eye fatigue. The data from this experiment follows: From the tracings: m, = .391"+.616" .635 61112 = .240"+.400" .601 6111 = (innl + 5121,) + 2 = .618 1 1 1 0.6328p 6 = _. . '6!" = . . .0618 = .0034 d5 s1na 170p 31n42° From the MTS displacement readout: A1 = 0.2886" - 0.2671" = 0.0215" A1+10== 0.0215" + 2.5" = 0.0086 X 0.35 = 0.0030 1’ Leeer Load a 4 I, . . I / I / O"‘/"\ ' . LOCO! Poultionlng Mirror Specimen ‘ ".\ d Fringe Poeltlonlng Mirror Fringe A Fringe B Figure 12. Setup for measuring 5“. 21 Figure 13. Tracings for measuring 64,. using a circular indentation Some things were learned while conducting these experiments. First, the fringe patterns should be projected onto a very sturdy object such as the load frame. A table may get bumped into while moving around in the dark. Second, the eye needs a few minutes to adjust to darkness. Any bit of stray light, such as around doors, was very detrimental when tracing the fringes. A red light nearby can illuminate the floor while still preserving night vision. Lastly, a fine pencil should be used. A line was first drawn perpendicular to the fringe patterns and the intersections were just checked off on this line. This eliminated tracing all of the fringes. 22 The circular indentation was completely sucessful. The indentations contained all of the information necessary to determine the complete state of plain strain over the gage area. The error was also very much within experimental limits. Comments on Bot es o e ns Surprisingly, specimen preparation for either indentation scheme is not overly critical. The finish obtained from wet 600 grit sandpaper was used throughout the tests. After polishing the specimen with the sandpaper it was cleaned with alcohol and the location where the indentations were to be made was marked with a pen. The indentations can be difficult to see with the naked eye; an ink mark on the specimen makes the laser alignment much easier. Additionally, lubrication on the indentor did not have a noticeable effect on the interference patterns. Obviously, the indentations must remain reflective throughout the test. There are two methods that have been used to measure non-reflective materials with this method. One method is to apply a reflective coating in the area of the indentations. This can be done with a vacuum-sputtering operation“. The second method is to make seperate tabs from 23 a reflective material. Indentations are placed on these tabs and the tabs are applied to the specimen in a manner similar to a strain gageK METHODS OF MEASURING FRINGE TRANSLATION Once the appropriate interference patterns are produced, a method to monitor the pattern translation (determining 6m) must be found. A suitable method must be able to determine the translation in a direction normal to the fringe patterns. Recording the fringe and measuring the translation can be done a few different ways. Different methods may be more appropriate for faster recording times, larger fringe translations, or obtaining permanent records of the fringe patterns. The most basic way to monitor fringe translation is to project the fringe patterns on a piece of paper and trace the fringe patterns before and after loading. This method, however simplistic, can produce decent results for large fringe translations. The human eye is very good at determining fringe locations and tracing them. This method has been used (see section 2) with an error less than 7%. Another basic way to determine fringe translation is to take a series of photographs of the fringes. The fringes can project directly onto the film or onto a screen. -A suitable reference point can then be used to measure the translation of the fringes. This method is slow, due to the development time, and quite tedious. Still, conceptually 24 25 speaking, it is a clear method and provides great presentation material. See reference 2 for the particulars of this method. The most recent method to measure the fringe translation is to use linear diode arrays“. These devices contain a row of small diodes which provide a voltage cooresponding to light intensity. When a fringe pattern falls on the array a digitized version of the pattern can easily be recorded. Modern arrays have acceptable resolution (upwards of 4096 pixels) and interface well with computer controlled systems. They are also somewhat easy to position, similar to a camera. A photomultiplier tube (PMT) and scanning mirror arrangement was used for some experiments in this paperMK The primary reason for using this system was availability. It is also easy to visualize the operation of the system and is very flexible to setup initially. This device is shown schematically in figure 14. For the sake of clarity, the figure illustrates only the arrangement for uniaxial measurement. Multiaxial measurement is simply done by arranging more uniaxial 26 systems in different planes. For example, a system for measuring orthogonal normal strains (see figure 3-b) would include a pair of scanner mirrors and PMTs arranged as shown in figure 14 plus another set perpendicular to the paper. PMT [ Laser } Figure 14. Setup of a PMT and scanner mirror measurement system A laser illuminates the indentations and the interference of the scattered light produces fringe patterns. The mirrors are positioned in the resulting fringe patterns and reflect them into the photomultiplier tubes that provide a voltage proportional to the fringe brightness. The computer then directs the scanner controllers to rotate the mirrors in a step-wise fashion so as to sweep the patterns past the photomultiplier tubes. 27 The voltage output from the photomultiplier tubes is received into the computer and stored with the step number of the mirror. A more detailed setup is shown if figure 15. From the computer programs point of view, a voltage is sent out and then a voltage is read in. The output voltage is sent to the scanner controller to rotate the mirror to the next step. The input voltage is the voltage from the PMT. This voltage is proportional to the brightness of the fringe shining on the PMT. The number of the mirror step and the PMT voltage are then stored as a data pair. Scanner Controller III “I". O O < jg AID I”. Ieeaeaea LOO. Saaaaer I'M PMT Power Supply Figure 15. Detailed setup of a PMT and scanner mirror measurement system 28 Par s scr' The following is a brief parts description of the arrangement used above. The photomultipler tubes, model R1213, are made by the Hamamatsu Corporation. They are magnetically shielded by a close fitting tube as well as being protected by an outside container/mount. A band-pass filter is used over the tube to filter out room light and allow only the HeNe laser light to reach the tube. The tubes have proven to be very reliable devices. The laser that was used is a 15mW unit from Jodon Incorporated - Ann Arbor, MI. This unit is strong enough to produce bright fringe patterns for most tests. When using stationary software techniques, discussed on page 39, a laser unit with less drift is required. The laser drifted enough to make this technique ineffective. The mirror scanners, model GlZODT, and the scanner controllers, model CX6120, are made by General Scanning Inc. A 15V input to each scanner controllers sweeps the mirror scanners through a maximum rotation angle of 15°. An amplitude setting on the controller is used to limit the mirror rotation angle. This allows only a few fringes to be swept past the photomultiplier tubes. Internal heaters in the scanners help to eliminate the influence of room temperature variations. 29 The computer interface is a model DT2811 I/O board manufactured by Data Translation. This is a 12 bit card with eight analog bipolar inputs used for photomultiplier input and two bipolar analog outputs used to control the scanner controllers. Typically, one of the outputs is daisy-chained to control all the scanner controllers. The other is used to output a signal corresponding to strain, displacement, etc. for plotter use. The computer that was used to control the system was a Zeinth personal computer. It uses an 8088 processor and a CGA video interface. All the programming was done in MicroSoft QuickBasic version 4.5. The disadvantage of using this antiquated computer system is that the recording/processing time was very limited. However, as a tribute to the interferometric technique, the tests still produced favorable results. A more modern computer would simply increase the flexability of the system. SOFTWARE TECHNIQUES Before discussing the processing of the fringe patterns, it is worth noting that this interferometric technique can measure displacement as well as strain. In fact, the displacement is found first and the strain is calculated using the initial gage length. Although the experiments in this paper center on finding strain, this method of interferometry has been used to measure crack opening displacementsfi WW. Once the fringe pattern is recorded by the computer there are different ways to monitor the fringe translation. However, certain variables must first be determined from the initial pattern. The essential variables are the spacing of the fringes.(nn) and a starting location to keep track of. Using the setup discussed previously the computer can record the fringe pattern as shown in figure 16. The .intensity (brightness) of the fringe, seen as voltage from the photomultiplier tubes, is plotted as the ordinate. This intensity is stored as a voltage but can be converted to light intensity if desired. The position of the mirror is plotted as the abscissa. The mirror position is in arbitrary units. 30 31 The mirror positions are uniform and must be consistent throughout the test. The mirror position can also be thought of as the voltage level output to the scanner controllers or the angle of the scanner mirrors. PMT Voltage - Fringe Brightneae Mirror Increment Number Figure 16. Computer representation of a fringe pattern Typically, the amplitude on the scanner controllers are set so that a full scale output signal (15V) from the computer will pass two or three fringes past the PMTs. This gives the best resolution. A 12 bit I/O card provides 4096 discrete voltage levels. Each voltage can produce a different mirror location. At each of these mirror locations a voltage corresponding to fringe brightness can be recorded. To speed up the process only 256 or 512 discrete mirror steps are generally used. If more (and therefore closer) mirror steps are used the resolution will be increased but the scanning process will take considerably longer. 32 An alternative method of obtaining the voltage vs. position information is to use a function generator to provide the input voltage to the scanner. The function generator can be set to produce a ramp voltage from -5V to +5V when triggered by the computer. The voltages sweeps the fringe pattern past the PMTs. This technique relieves the computer from the burden of calculating the mirror steps and sending out the appropriate values to the scanner controllers. However, the problem of not having a definite location for a given intensity value is presented. Experience has shown that the difficulty of this idea outweighs the speed advantages. The most obvious method of monitoring the fringe translation is to pick a spot on the curve and follow it during loading. The maximum intensity value is the best choice, since it is more defined (due to its brightness). Also, a simple "if" statement included in the software is all that is needed to locate the maximum spot during the initial scan. Alternately, a minimum point on the curve may be chosen. This requires a bit more computer code since all the minimum points are (ideally) equal to zero. In finding minimum values the slopes of the adjacent points must be considered. The code included in section 5 locates the minimum points only on the initial scan and uses these positions to calculate the fringe spacing, m0. 33 After each change in load a new scan is made to find the new position of the key point. Fortunately, subsequent scans of the fringe pattern do not have to be as complete as the initial scan. Recall that only 6m is now needed to determine the relative displacement of the indentations. Since the fringe spacing 1a,, was found from the first scan, all that is needed to find 6m is the amount of translation. There are two general techniques to determine the amount of translation: oscillating techniques and stationary techniques. ; .1] !' T l . These techniques oscillate the mirror around the previous position of the key point to decide the new position of that point. For example, if the loading is known not to produce strain equal to twenty mirror spacings, then the mirrors only need to scan twenty positions on either side of the previous position. If more is known about the load, then the scanned range may be shifted even more; for example, five spacings one way and ten the other. Once the new location of the key point is found, the range is updated for the next scan. This is illustrated more clearly in figure 17. 34 An advantage of this technique is that the large fringe translations can be measured easily. If the applied load were to move the key point beyond the limits that the mirror is set for ("off the screen") a new key point can be easily chosen. The search range is moved back into the range of the mirror by a distance equal the fringe spacing. This is rarely necessary because a large strain is needed to cause a an of 2. Range ler eabeeaeent aaaae Prlaae Irlaatneaa Figure 17. Use of an oscillating technique on a fringe pattern The disadvantage to this technique is that the resolution is limited by the number of mirror increments in the fringe spacing; an. For example, if the fringe spacing is 200 mirror increments then the smallest detectable fringe 35 movement is 2004. Using the standard values of a = 43° using Vicker’s indentor A - 0.6328u He-Ne laser light 0 +6 - .1 x ml m, =0.95x200'1=0.00475p. Sing 2 If the gage length, do, is 17511 then the resolution for strain measurement is 27pe. The fringe spacing can be increased by setting the scanner amplitude controls so that only one or two fringes pass by the PMTs. As expected, this decreases the range of the system. A happy medium must be found that will give adequate resolution and sufficient range. Another item that needs to be mentioned regarding this technique is the rigid body motion problem. Since the subsequent scans must contain the maximum point, the scanning range must be wide enough to include translation due to strain and rigid body motion. The rigid body motion may or may not be very important. The experiments in this paper were conducted on a very large load frame that ”appeared to have little rigid body motion. Presumably, if a less massive loading system was used then rigid body motion may be a significant problem. A simple uniaxial tension test was used to illustrate the operation of the software shown in section 5 and the PMT scanner mirror system described in section 3. The software recorded the specimen load and the fringe shift for each fringe pattern. Figure 18 shows the load and the average fringe shift. By using the displacement equations derived in section 1, the fringe shift, 6m, is converted into a displacement. The displacement is also shown in figure 18 as the right hand ordinate axis. Since the cross-sectional area and the gage length are known, the load and displacement data can be readily converted to stress and strain information. The stress - strain diagram is shown in figure 19. The non-linearity of the curve could be attributed to a few factors. The most likely factor is vibration in the system. Although unlikely, it is possible that electrical interference caused mirror oscillation or fluctuations in the PMT output. Even with this non-linearity, a value of Young’s modulus was found to be 9.88e6 psi. This is very acceptable. Repeatability tests indicated that the system used above would drift 11 mirror increment for a fringe spacing around 75 to 100 mirror increments with no specimen load. At first this does not seem to be very alarming. However, a false fringe shift of one mirror increment with a fringe 37 spacing of 75 increments gives a 6m of 75'1 and a displacement of 0.0124u. Over a 150p gage length, the indicated strain is 82ue. Even though for most situations this is acceptable it must be considered whenever using this type of system. 38 Indentation displacement (microns) c2502.» E::_E:_< Lo. :23 cactu— .o> one; .9 952m Ann: 98.. oom. ooo. ooo ooo oov oom o O _ _ _ i _ . 3 O oqoi , ;io H m. .D 6 to- . w A . : to, S N oto- , to. w: w... No- , . _-om m. m 6 moo- ‘ .. on w U m... o.o on raw most .9 98.. 39 Doom .3502; 8352:? ...o. 525 .2. :25 .3 «onto: 555 2:2“. ooor ooow ooo o. q q d :8: 303m. 595 .m> 825 o or 0w ON 40 W This technique solves the resolution problem by using curve fitting techniques. However, the range is somewhat limited. A section of the curve from a minimum point to a maximum point is fitted with an nFidegree polynomial. The mirror is then held stationary at a point contained in the curve. The voltage input from the PMTs at that location is used to determine the position that the mirror should be. If this position is different from the actual mirror position the fringe movement can be calculated by subtracting the two. Figure 20 helps to illustrate this idea. It is necessary to limit the length of the curve as shown so that any voltage input (ordinate value) will only give one value for a mirror position (abscissa value). If the entire curve were to be fitted with an equation, a given voltage could suggest several possible mirror positions. 41 " a” ’I I MMmrnwuheat thle poeltlon Prhge Irlalitaeae um MM Figure 20. Using a stationary technique on a fringe pattern Point A is where the mirror remains. After a fringe shift, the voltage from the PMT and the curve equation indicate that the voltage used to be at position B. The difference between A and B is the amount of the fringe shift. For each strain reading it is only necessary to input one voltage and calculate two simple equations. With a fast computer this can almost be done in real time. A disadvantage of this technique is that it is very susceptible to drift in the setup. If the laser intensity, voltage to the scanner controllers, or the scanner controllers themselves drift, then false fringe translations will be reported. The setup used in this paper tended to have too much drift to use this method reliably. 42 Since both of these methods involve the use of a computer, a warning must be expressed. Computers are very good at generating numbers and somewhat poor at interpreting whether they are ridiculous or not. The use of a computer to monitor interferometric measurement is especially dangerous since the interference patterns are not always easily seen. Care has been taken in the programs to warn the user of unusual inputs. Obviously, not all situations can be foreseen; and certain inputs can be both good and bad depending on the circumstances. With this warning in mind two recommendations are made. First, there is no substitute for knowing what the results should be (within reason) and what is happening to the specimen. A few simple calculations should show whether the results are correct or not. Secondly, the use of an oscilloscope to monitor inputs and outputs is encouraged. A multichannel digital storage oscilloscope can give a good indication of what is happening. In fact, a good oscilloscope could be substituted for the computer setup for certain measurements. This is the oscilloscope analogy to taking pictures of the before and after fringe patterns. Early experiments using interferometric measurement used oscilloscopes in this way”. COMPUTER PROGRAM CODE During the course of this research many different computer routines were written to try different ideas. These programs ranged from simple voltmeter type programs to many different versions of fringe intrepreting programs. A representative of the latter is shown here. It will soon become obvious that this program was written by an engineer and not a computer programmer. The program is not stream-lined very much. As an example, the conversion of the A/D input from the card to a decimal number is very long. It was left in this rather ineloquent form so the the process could be followed more closly. Also, rearanging the code to fit in the prescribed page format left the arangement of some sections slightly cluttered. Note that these programs were written in MicroSoft QuickBasic Version 4.5. This programming language is more than adequate for what was required, and it is very easy to use. As an unpaid testimonial, it is a shame that so many people shy away from this langauge since they still have the idea of Basic "not being a real language". 43 ‘\\\‘ \‘\\ 44 TEST1.BAS This program only finds two fringe distances between minimum voltage values on either side of the maximum voltage value. This allows the fringes to be more spread out. The maximum value should be centered and it should contain two minimum values. This program must stop when the followed peak goes off the screen. Also, this program was written for the 0 to +5V UNIPOLAR input setting and the -5V to +5V BIPOLAR output setting. NOTE: After the initial constants/locations have been figured out the maximum value is the location on the curve that will be tracked to determine strain/displacement. 10 CLOSE DIM PKSl(260, 2), PKSZ(260, 2), CH$(260, 2), PKS(260, 2) FLOG = 0: L1Max = 0: L2Max - 0: FlagForLimit - 0 LMaxN(1) = 0: LMaxN(2) = 0: RP = 6 FMTS = " ### ##ff #### " FMT2$ = " ##f #f## ff}! if}! #f##" FMT3$ = " # ### ### ###" FMT4$ = " ff} ##.### If.##f " FMT5$ = "8 +##f###.f +#.#f##ff# +#######.f +##.f# +f.##fffum" ’ . 75 FMT6$ = "Minimum value found at ##f for PMT_f #" ------ Get initial information----------------------------- CLS : COLOR 5: PRINT PRINTTAB(25);"CALCULATE STRAIN" PRINT TAB(25); " (Small Displacement Version)" COLOR 13: PRINT STRING$(80, 205): COLOR 3 LOCATE 8, 5 INPUT ”Enter the value for Young's modulus.... ", ES E - INT(ABS(VAL(E$))) LOCATE 8, 67: COLOR 9 PRINT USING "###.##“‘“ "; E: COLOR 3 LOCATE 10, 5: PRINT STRING$(74, " ") LOCATE 10, 5 INPUT "Enter the gage length in um............ ", Gl$ G1 = INT(ABS(VAL(Gl$))) IF (Gl <- 0 OR Gl > 1000) THEN G1 I 150 COLOR 9: LOCATE 10, 68 PRINT USING "ff#.f "; Gl 45 COLOR 3: LOCATE 12, 5 PRINT "Save data as a Harvard Graphics file (Y or N) ? II 77 OP$ = INKEYS: IF OP$ = ”” THEN GOTO 77 IF UCASES(OPS) = "Y" THEN COLOR 9: LOCATE 12, 43: PRINT UCASE$(OPS) COLOR 3: LOCATE 13, 5 INPUT "Enter the filename to save as (8 characters) ", HGNAMES IF HGNAMES = "" THEN HGNAMES = ”IMPORT" HGNAMES = LEFTS(HGNAME$, 8) + ".HG" OPEN HGNAMES FOR OUTPUT AS 2 PRINT #2, "Strain, Stress, Displacement, Load" + CHR$(34) HGLOG = 1 COLOR 9: LOCATE 13, 68 PRINT USING "\ \"; HGNAME$: COLOR 3 ELSE COLOR 9: LOCATE 12, 48 PRINT "N": COLOR 3 END IF LOCATE 15, 5: PRINT "Record session in an ASCII file (Y or N) ? " 80 OP$ = INKEYS: IF OP$ = "" THEN GOTO 80 IF UCASE$(OPS) = "Y" THEN COLOR 9: LOCATE 15, 38: PRINT UCASE$(OP$) COLOR 3: LOCATE l6, 5 INPUT "Enter the filename to save as (8 characters) ", FILENAMES IF FILENAMES = "" THEN FILENAMES = "NOTE" FILENAMES = LEFTS(FILENAMES, 8) + ".DOC" COLOR 9: LOCATE 16, 68 PRINT USING "\ \"; UCASE$(FILENAME$) COLOR 3 OPEN FILENAMES FOR OUTPUT AS 1 PRINT #1, "Log file started on "; DATES; " at "; TIME$ LOCATE 18, 5 PRINT "Please enter a description for the ASCII file " LOCATE 20, 5: INPUT "-> ", TITLES PRINT #1, TITLES: PRINT #1, " " PRINT #1, STRING$(79, "-") FLOG = 1 ELSE COLOR 9: LOCATE 15, 43 PRINT ”N": COLOR 3 END IF ' --------------------------- Load Array With Data -------- 500 LOCATE 23, 1 510 2) 46 PRINT STRINGS(38, " "); : LOCATE 23, 5 PRINT "Press any key to start data collection"; DO WHILE (INKEYS = ""): LOOP CLS : SCREEN 1: VIEW: ' 320x200 with 4 colors (CGA) WINDOW (o, -1)-(256, 5) LINE (0, 0)-(256, 0), 1, , &HAAAA LOCATE 21, 36: PRINT "0v" LINE (0, l)-(256, 1), 1, , &H3333 LOCATE 17, 36: PRINT "1v" LINE (0, 2)-(256, 2), 1, , &H3333 LOCATE 13, 36: PRINT "2v" LINE (0, 3)-(256, 3), 1, , a33333 LOCATE 9, 36: PRINT "3v" LINE (0, 4)-(256, 4), 1, , &H3333 LOCATE s, 36: PRINT "4v" LOCATE 23, 5: PRINT "Dark = PMT#1, Bright = PMT#2"; FOR XX = 20 TO 220 STEP 32 LINE (xx, -.2)-(xx, .2), , , an3333 NEXT XX OUT &H218, EHIO FOR I = 1 TO 400: NEXT I Ii 0 LB = INP(&H21A): HB = INP(&H21B): Counter LMax(2) = 0: LMax(1) - 0 FOR V = 4096 TO 32 STEP -16 VS = HEXS(INT(V)) VS a STRING$((4 - LEN(VS)), "0") + VS LVol = VAL("&H” + RIGHTS(VS, 2)) HVol = VAL("&H” + LEFTS(VS, 2)) OUT &H21A, LVol OUT 8H21B, HVol Counter = Counter + 1 OUT 8H218, &H0 OUT 8H219, 128 + 1 CSR = INP(&H218) IF CSR < 128 THEN GOTO 510 LB 8 INP(&H21A): HB - INP(&H21B) LBS = HEX$(LB): HBS = HEXS(HB) LBS = STRING$((2 - LEN(LB$)): "0") + LBS HBS - STRINGS((Z - LEN(HBS)), "0") + HBS XXS = "&h" + RIGHTS(HBS, 2) + RIGHTS(LBS, CHS(Counter, 1) = XXS V1 = VAL(XX$) * (5 / 4096) PSET (Counter, V1), 2 IF V1 > LMax(1) THEN LMaxN(1) = Counter 47 LMax(1) = V1 END IF OUT &H218, 6H0 OUT &H219, 128 + 2 511 CSR = INP(&H218) IF CSR < 128 THEN 511 LB = INP(&H21A): HB = INP(&H21B) LBS HEX$(LB): HBS = HEX$(HB) LBS STRINGS((z - LEN(LB$)), "0") + LBS HBS STRINGS((Z - LEN(HBS)), "0") + HBS xxs ”8h" + RIGHTS(HBS, 2) + RIGHTS(LBS, 2) CHS(Counter, 2) = XXS V2 = VAL(XXS) * (5 / 4096) PSET (Counter, V2), 3 IF V2 > LMax(2) THEN LMaxN(2) = Counter LMax(2) = V2 END IF NEXT V LINE (LMaxN(1), 0)-(LMaxN(1), 5), 2 LINE (LNaxN(2), O)-(LMaxN(2), 5), 3 ' Use lines 23 and 24 for messages LOCATE 23, 1: PRINT STRINGS(39, " fl); : LOCATE 23, 4 PRINT USING "PMT_I1 maximum of #.## at fffi"; LMax(1); LMaxN(1); LOCATE 24, 1: PRINT STRING$(39, " "); : LOCATE 24, 4 PRINT USING "PMT_#2 maximum of #.## at ###"; LMax(2); LMaxN(2); DO WHILE (INKEY$ = ""): LOOP ' ------ Redo the fringe pattern or continue --------- LOCATE 24, 1: PRINT STRING$(39, " n); LOCATE 23, 1: PRINT STRING$(39, " "); : LOCATE 23, 1 PRINT " Press C to cont. another key to redo"; 150 OPS = INKEYS: IF OP$ = "" THEN GOTO 150 IF UCASES(OPS) <> "C" THEN GOTO 500 ' ------------------------- Find the valleys -------------- 700 LOCATE 23, 1: PRINT STRING$(38, " ”); LOCATE 23, 5: PRINT "Resetting array values..." FOR N = 5 TO 256 PKS(N, 1) = o: PKS(N, 2) = 0 NEXT N LOCATE 23, 1: PRINT STRING$(38, " ”); LOCATE 23, 5: PRINT "Calculating minimum values..." FOR I = 1 TO 2 48 FOR N B 6 TO 250 IF (VAL(CH$(N - 1, I)) > VAL(CH$(N, I))) AND (VAL(CH$(N + 1, I)) >= VAL(CH$(N, I))) THEN IF (VAL(CH$(N - 2, I)) > VAL(CH$(N, I))) AND (VAL(CH$(N + 2, I)) >= VAL(CH$(N, I))) THEN IF (VAL(CH$(N - 3r I)) > VAL(CH$(N, I))) AND (VAL(CH$(N + 3, I)) >= VAL(CH$(N, I))) THEN IF (VAL(CHS(N - 4, I)) > VAL(CH$(N, I))) AND (VAL(CH$(N + 4, I)) >= VAL(CH$(N, I))) THEN IF (VAL(CH$(N - 5, I)) > VAL(CH$(N, I))) AND (VAL(CH$(N + 5, I)) >= VAL(CH$(N, I))) THEN PKS(N, I) = N . PSET (N, (VAL(CH$(N, I)) t (5 / 4096))), (I + 1) DRAW "8H2 r4 d4-14 u4" IF FLOG = 1 THEN PRINT #1, USING FMT6$; N; I END IF END IF END IF END IF END IF END IF NEXT N NEXT I LOCATE 23, 1: PRINT STRING$(38, " "); LOCATE 23, 5: PRINT "Press any key to continue" DO WHILE (INKEYS = "”): LOOP ' ------ Find the distance between fringe valleys ---------- FOR I = 1 TO 2 900 FOR N = (LHaxN(I) + 1) To 255 IF PKS(N, I) <> 0 THEN DH(I) = PKS(N, I) GOTO 902 END IF NEXT N 902 FOR N = LMaxN(I) TO 0 STEP -1 IF PKS(N, I) <> 0 THEN DL(I) = PKS(N, I) GOTO 903 END IF NEXT N 903 NEXT I 905 ABS((DH(1) - DL(I) U ..o m rt H II II )) AES((DH(2) - DL(2))) 49 IF Dist1 = 0 OR Dist2 = 0 THEN SCREEN 0: WIDTH 80 VIEW PRINT 7 TO 22: CLS : VIEW PRINT COLOR 12: PRINT : PRINT : PRINT : PRINT PRINT TAB(15); "One of the peak distances was found to be zero." PRINT TAB(lS); "This will cause division by zero in the main" PRINT TAB(1S); "displacement equation. Please re-run this " PRINT TAB(IS); "program making sure that the initial fringe" PRINT TAB(15); "pattern is scanned in correctly." COLOR 3: PRINT : PRINT PRINT USING " DL(l) - ##f DH(1) = ff! Dist1 = fff”; DL(I); DH(1); Dist1 PRINT USING " DL(2) - ### DH(2) = ##f Dist2 = ##f”; DL(2); DH(2); Dist2 >" 906 LOCATE 23, 5 PRINT "< Press to Exit, any other key to continue COLOR 4: LOCATE 23, 13: PRINT "X” OP$ 8 INKEY$: IF OP$ I "" THEN GOTO 906 IF UCASE$(OP$) = "X" THEN GOTO 1300 GOTO 10 END IF RESOLUTION = (.95) * ((1 / Dist1) + (1 / Dist2)) \ N SCREEN 0: WIDTH 80: CLS : COLOR 5: PRINT PRINT TAB(25); "C A L C U L A T E S T R A I N " PRINT TAB(25); " (Small Displacement Version)” COLOR 13: PRINT STRING$(80, 205): COLOR 3 PRINT : PRINT PRINT "LMaxN(1) = "; LMaxN(1); " LMaxN(2) "; LMaxN(2) PRINT PRINT USING "DL(I) = if! DH(1) = ff! Dist1 ##f"; DL(1); DH(1); Dist1 PRINT USING "DL(Z) = ### DH(2) = ### Dist2 fff"; DL(Z); DH(2); Dist2 PRINT PRINT "Resolution of displacement data is ..."; RESOLUTION - PRINT "Resolution of strain data is ......... "; (RESOLUTION / 61) PRINT PRINT : PRINT : PRINT "Press any key to continue": DO WHILE (INKEYS = ""): LOOP IF FLOG = 1 THEN PRINT #1, " " 50 PRINT #1, "Brightest point for PMT#1 is at position "; LMaxN(1) PRINT #1, "Brightest point for PMT#2 is at position "; LMaxN(2) PRINT #1, " " PRINT #1, "Peak distance for PMT#1 is........ ..... "; Dist1 PRINT #1, "Peak distance for PMT#2 is............. "; Dist2 PRINT #1, ” " PRINT #1, "Resolution of the displacement data is "; RESOLUTION PRINT #1, "Resolution of the strain data is ...... "; (RESOLUTION / G1) PRINT #1, n " PRINT #1, ”The gage length is "; Gl; " um” PRINT #1, "The value for Young's Modulus is "; E PRINT #1, " " PRINT #1, STRING$(79, "8") PRINT #1, SPC(31); "Start of test data" PRINT #1, STRINGS(79, us") PRINT #1, ” " PRINT #1, "TIME LOAD STRAIN STRESS 6m1-6m2 DISPLACEMENT" END IF ' ------ Start the main testing loop ------------------- CLS : LOCATE 6, 1 PRINT "TIME LOAD STRAIN STRESS 6m1-6m2 DISPLACEMENT" 950 PRINT : LOCATE 23, 5: PRINT STRINGS(74, " ") COLOR 3: LOCATE 23, 5 INPUT ”Enter the load for the next scan.... ", LOADS LOAD = VAL(LOADS) ’ ------ Scan in a smaller range of values --------------- LNaxNOLDu) =- LMaxN(1): LHaxNOLD(2) = LMaxN(2) IF LMaxN(1) < LMaxN(2) THEN LLimit = LNaxN(1) - 3o HLimit = LMaxN(2) + 30 ELSE LLimit = LMaxN(2) - 3o HLimit = LMaxN(1) + 30 END IF IF LLimit < 0 THEN LLimit = 0 FlagForLimit = 1 END IF 1000 -_>” 1010 2) 1011 51 IF HLimit > 255 THEN HLimit = 255 FlagForLimit = 2 END IF HL LL INT((4128 - (LLimit * 32))) INT((4128 - (HLimit * 32))) COLOR 11: LOCATE 23, 5 PRINT STRINGS(70, " fl): LOCATE 23, 5 PRINT "< Press any key to start data collection>"; DO WHILE (INKEYS = ""): LOOP LOCATE 23, 5: PRINT STRING$(70, " ") LOCATE 23, 5 PRINT "Incrementing from "; LLimit; " to "; HLimit; " L1Max = 0: L2Nax - 0: Counter = 0 OUT &H218, &H10 FOR I = 1 TO 100: NEXT I LB = INP(&H21A): HB - INP(&H218): Counter = LLimit FOR V = HL TO LL STEP -16 VS =- HEXS(INT(V)) VS = STRING$((4 - LEN(VS)), "0") + VS LVol = VAL("&H" + RIGHTS(VS, 2)) HVol - VAL("&H" + LEFTS(VS, 2)) OUT 8H21A, LVol OUT 8H218, HVol Counter = Counter + 1 OUT 8H218, 8H0 OUT &H219, 128 + 1 CSR = INP(&H218) IF CSR < 128 THEN 1010 LB = INP(&H21A): HB = INP(&H21B) LBS = HEX$(LB): HBS = HEXS(HB) LBS = STRING$((2 - LEN(LB$)), "0") + LBS HBS = STRING$((2 - LEN(HBS)), "0") + HBS xxs = "8h" + RIGHTS(HBS, 2) + RIGHTS(LBS, IF VAL(XX$) > LMax(1) THEN LHax(1) = VAL(XX$) LMaxN(1) = Counter END IF OUT &H218, 8H0 OUT 8H219, 128 + 2 CSR = INP(&H218) IF CSR < 128 THEN 1011 LB - INP(&H21A): HB - INP(&H218) LBS = HEXS(LB): HBS = HEX$(HB) 2) ' --- ’ --- 1200 / 2) 52 LBS = STRINGS((2 - LEN(LB$)). "0") + LBS HBS = STRINGS((z - LEN(HB$)), "0") + HBS xxs = "&h" + RIGHTS(HBS, 2) + RIGHTS(LBS, IF VAL(XXS) > LMax(2) THEN LMax(2) = VAL(XXS) LMaxN(2) = Counter END IF LOCATE 23, 45: PRINT Counter NEXT V ----Calculate peak shift within the range --------- Shiftl = LHaxN(1) - LHaxNOLD(1) Shift2 = LMaxN(2) - LHaxNOLD(2) ---Ca1culate the strain and stress -------------------- Stress - 0 DeltaD = (.95) * (((Shiftl / Dist1) + (Shift2 / Dist2)) Strain = DeltaD / Gl RBM = (Shiftl / Dist1) - (ShiftZ / Dist2) IF E <> 0 THEN Stress = Strain * E END IF IF HGLOG = 1 THEN PRINT #2. STR$(Strain) + "," + STR$(Stress) + n," + STR$(De1taD) + n," + STR$(LOAD) + CHR$(34) END IF IF FLOG = 1 THEN PRINT #1, USING FMTSS; TIMES; LOAD; Strain; Stress; DeltaD END IF RP = RP + 1: VIEW PRINT 7 TO 22: COLOR 11 IF RP < 22 THEN LOCATE RP, 1 PRINT USING FHTSS; TIMES; LOAD; Strain; Stress; DeltaD; END IF IF RP >= 22 THEN LOCATE 22, 1 PRINT USING FHTSS; TIMES; LOAD; Strain; Stress; DeltaD END IF VIEW PRINT: COLOR 3 IF FlagForLimit THEN COLOR 20 LOCATE 23, 5: PRINT STRING$(70, " "); 53 LOCATE 23, 5: PRINT "One of the limits has reached the end of the screen!” 1210 DO WHILE (INKEYS = ""): LOOP LOCATE 23, 5: PRINT STRING$(70, " "); END IF LOCATE 23, 5 PRINT "< Press to Exit, any other key to continue >" COLOR 4: LOCATE 23, 13: PRINT "X" OP$ = INKEYS: IF OP$ = ”" THEN GOTO 1210 IF UCASE$(OP$) = "X" THEN GOTO 1300 GOTO 950 1300 CLOSE : VIEW PRINT: CLEAR : CLS : END CONCLUSION The ideas presented in this paper advance the techniques of basic interferometry. A circular indentation was used to construct an interferometric strain rosette. Testing of this strain rosette proved it to be both reliable and accurate. A renewed interest in basic interferometry will certainly promote this technique even further; By combining' the computer techniques, described in sections 3 and 4, with the circular indentation a convenient optical strain gage can be constructed. This gage will aid in many areas of experimental strain analysis. 54 REFERENCES LIST OF REFERENCES 1. Sears, F.W. and Zemansky, M.W., university Physics, Addison Wesley Book Company, NewYork, ch.46 (1955) 2. Sharpe, W.N., Jr., "The Interferometric Strain Gage," Experimental Mechanics, 164-170 (April 1968) 3. Sharpe, W.N., "A.New Biaxial Strain Gage," The Review of Scientific Instruments, 1440-1443 (October 1970) 4. Bofferding, C.H. , "A Study of Cyclic Stress and Strain Concentration Factors at Notch Roots Throughout Fatigue Life, " unpublished.master’s thesis, Michigan State University (1980) 5. Hex. indentations reference 6. Martin, D.R. and Sharpe, W.N., Jr., "An Optical Gage for Strain /Displacement Measurements at High Temperature near Fatigue Crack Tips," AFML-TR-77-153, Air Force Materials Laboratory (September 1977) 55 56 7. Sharpe, W.N., Jr. and Wang, K.C., "Small Attachable Interferometric Strain Gages, " Experimental Mechanics, 136-141 (June 1988) 8. Sharpe, W.N., Jr. and Su, X., "COD Measurements at Various Positions Along a Crack," Experimental Mechanics, 74- 79 (March 1990) 9. Guillot, M.W. and Sharpe, W.N., "A Technique for Cyclic-plastic Notch-strain Measurement," Experimental Mechanics, 354-360 (September 1983) 10. Sharpe, W.N., "Dynamic Strain Mbasurement with the Interferometric Strain Gage," Experimental Mechanics, 89-92 (February 1970) GENERAL REFERENCES 1. Bell, J.F., "Diffraction Grating Strain Gage," Proc. Of the SESA, 17, 51-64 (1959) 2. Guillot, M.W. and Sharpe, W.N., Jr., "A Technique for Cyclic-plastic ~NotCh-strain Measurement," Experimental Mechanics, 354-360 (September 1983) 3. Hoge, K.G. and Sharpe, W.N., Jr., "Specimen Strain Measurement in the Split-Hopkinson-pressure-bar EXperiment," Experimental Mechanics, 570-574 (December 1972) 4. Sharpe, W.N., "Interferometric Surface Strain Measurement," Intl. J. of Nondestructive Testing, 3, 59-76 (1971) 5. Sharpe, W.N., Jr. and Sukere, A.A., "Transient Response of a Central Crack to a Tensile Pulse," Experimental Mechanics, 89-98 (March 1983) 57 58 6. Sharpe, W.N., "A Short-gage-length Optical Gage for Small Strain," Experimental Mechanics, 373-377 (September 1974) HICHIGRN STRT rm 1| my) )mmflmunmfimumr 312 3009105994