METHOD FOR DETERMINING INTERNAL STRESSES IN POLYCRYSTALLINE SOLIDS

Abstract: Method of using a position-sensitive diffractometer having two or more sets of channels in its detector, arranged relative to one another and the x-ray beam (96) and that when properly positioned relative to a sample (12), the x-ray sensitive surfaces of the detector sets (32) will be effective to intercept the diffracted beam and convert it to usable information to determine stress in seconds. The novel calibration method is critical. The method of determination of stress includes the steps of: (1) receiving diffracted beam on surface (32), (2) transmitting the relative beam location to a remote location, (3) scanning the image, (4) converting same to a corresponding electrical image, and (5) transferring the electrical image to a suitable data processor where the angle between the incident beam and the diffracted reflection is revealed and stress is calculated while being corrected for the specimen to detector distance using the novel calibration parameters. Superior measurement accuracy with a broad tolerance for the dimension between the x-ray sensitive surfaces of the detector (32) and the sample or specimen (12) is provided.

Description: -1- METHOD FOR DETERMINING INTERNAL STRESSES IN POLYCRYSTALLINE SOLIDS This invention involves a new process or method which utilizes for example a device described in Industrial Research and Development, January 1983, "Position-sensitive detector improves X-ray powder diffraction", by Clayton 0. Ruud, and Advances in X-ray Analysis. Vol. 27 (1984), "A miniature instrument for residual stress measurement" by CO. Ruud, et al. Other prior art shown to the applicant are United States Patents Nos. : 4,095,103 3,402,291 3,517,194 2,386,785 - 3,483,377 4,042,825 3,011,060 3,717,7θ-5 3,126,479 3,934,138 BACKGROUND OF THE INVENTION: The determination and analysis of internal (residual) stresses in crystalline solids is an old and well- known art. In essence, the diffraction of X-rays directed at the surface of the material being analyzed comprises the analytical tool by means of which the spacing between adjacent internal atomic planes is determined. This information is collected in the form of diffracted intensity and position data which, in turn, provides the analyst with what is needed to determine internal stresses. Mope specifically, the so-called "Bragg Relation" expressed as where n * 1 ,2 . . . , i .e. , any integer ■ wavelength of the diffracted radiation d * interplanar spacing β * Bragg angle is employed to determine the position and intensity of the diffracted x-ray beam impinging upon the surface of the solid crystalline substance. In those applications where the Interplanar spacing (d) is unknown, either Λ or θ 1s known. From the practical standpoint, when using either polycrystalϋne or powdered materials, becomes a constant and 28 1s a measured angle. In measur ng the latter, however, the diffracted x-ray beam undergoes some diffusion and, therefore, 1s spread out over a range of from a few tenths to several degrees. This necessitates , of course, ascertaining a mean dif¬ fraction angle 2Θ, and such 1s accomplished by taking Intensity measurements at several angular positions. The prior art Includes several different ways of measuring the Intensity and position of the diffracted x-ray beam, four such methods being quite widely used. The comprise the following: 1. Scanning Goniometer (Diffractometer) 2. Film Camera 3. Electro-Optical Corti nations 4. Position Sensitive Proportional Counters The first of these, namely, the scanning goniometer, consists basically of a mechanical turntable upon which the sample can be mounted and oriented at a selected angular position (θ) with respect to an Incident x-ray beam and at double the chosen angle (2Θ) with respect to a suitable detector such that the latter is in a position to intercept the diffracted beam. Details con¬ cerning the construction and operation of the aforesaid apparatus can be found 1n any one of the following references: 1. Barrett, C.S. , Structure of Metals , 2nd Ed. , McGraw-Hill , N.Y. , 1952. 2. CulHty, B.O. , X-Ray Diffraction, Addi son-Wesley, Reading, Mass. , 195β While the scanning goniometer still constitutes one of the most widely used instruments for determining the position and intensity of a diffracted x-ray beam, it suffers from many shortcomings , not the least of which is Its bulk and excessive time per measurement. Moreover, 1t requires an extremely stable power supply along wi th complex and highly sophisticated auxllHary instru¬ mentation. Last but by no means least 1s the fact that it 1s quite complicated to use and requires service at periodic Intervals to keep It operating satisfactorily. Cameras of one e or another are also used to record both the position and intensity of the diffracted x-ray beam. Certain of these cameras are described in the literature references already listed. While less expensive, simpler and easier to use than the scanning goniometer, most of the cameras developed for this purpose suffer from the inherent disadvantages of being both slow and Inaccurate in a field where speed and accuracy are highly desirable. The remaining two methods used to position and measure the intensity of a diffracted x-ray beam, namely, the electro-optical devices and the conventionally used position-sensi ti ve proportional counters , share the pro¬ blems of the goniometer in that, while they provide accurate measurements in a reasonably short time, they are both bulky and require mechanical movement to provide internal stress measurement, as well as call ing for precise control of the specimen to detector distance. Even so, aside from the device described herein, such methods represent the highest state of the art. A detailed description of the various electro-optical methods presently employed in the location and measurement of the intensity of the diffracted x-ray beam can be found 1n Green, R.E. , "Electro-Optical Systems for Dynamic Display of X-Ray Diffraction Images ," Advance in X-Ray Analysis , Vol . 14, Plenum Press , N.Y. , 1971. Similarly, an Informative description of the position-sensitive pro¬ portional counters can be found in James , M.R. and J. B. Cohen, The Applica¬ tion of a Position-Sensitive X-Ray Detector to the Measurement of Residual Stresses ," Advances in X-Ray Analysis , Vol . 19, Kendall /Hunt Publishing Co. , Dubuque, Iowa, 1976, and in U.S. Patent 4,095,103. From the foregoing, it should be apparent that the Ideal comb nation of method and instrument for determining the internal (residual ) stress in polycrystalUne sol ids via diffracted x-ray beams must, first of all , be fast and accurate. Consistent with the above, it should be easy to use and, preferably, portable. While cost 1s always a factor of some considerable importance, it may be outweighed by others such as , for example, the elimi¬ nation of the need for complex and expensive auxiliary equipment and fixtures for applying the Instrument (apparatus) . It has now been found in accordance wi th the teaching of this invention that the shortcomings of the prior art methods and apparatus can, in fact, be jpvercome whi le, at the same time, providing the sought-after speed and accuracy contained in a highly portable piece of equipment. Not only is the method combined with a suitable instrument accurate, 1t 1s easy for relatively untrained technicians to learn to use. Further, its unique feature of tolerance for variation of the sample to the x-ray sensiti ve detector surface distance, which is not present in any other similar type of combinatio of method and Instrument, provides for unprecedented speed and convenience of application, without the need of special fixtures or measurement devices . Accordingly, it 1s the principal object of the present Invention to provide a novel method to calibrate and apply a novel and improved device of the electro-optical , proportional or sol id state type, of position-sensitive dlffractometβrs for ascertaining the precise angle of a diffracted x-ray beam while allowing broad tolerances in the sample-to-detector distance. Another object of this Invention 1s to provide a novel method for use with an electro-optical or proportional types of diffractometers which allows broad tolerances in the distance between the detector and the sample to be measured. Another object of the Invention herein disclosed and claimed is to provide a method for determining the Interplanar spacing in a solid crys¬ talline sample that reduces the need for auxiliary apparatus , fixturing, and Instrumentation to a near-minimum level . Yet another objective 1s to provide an Improved method by which the user can quickly ascertain both accurate and rel iable data concerning the mean diffraction angle 2Θ in the Bragg Relation , while allowing broad tolerances in the sample-to-detector distance. Further objects are to provide methods that an instrument of the class described can be simple to operate, easy to learn to use, compact, free of frequent alignment problems , and one that is readily adaptable for use 1n most of the common x-ray diffraction applications. Other objects will be in part apparent and in part pointed out specifically hereinafter in connection wi th the description of the drawings that follow, and In which : Figure 1 1s a schematic view of the probe of an apparatus suitable for applying the method; showing it in relation to the sample. Figure 2 is an exploded perspective view of an electronic package of the Figure 1 probe but to a somewhat larger scale, certain portions having again been broken away to better reveal the interior construction. Figure 3 is a diagram illustrating certain critical angular and spacial relationships which must be either known or measured in order to determine the residual stresses present in a sample by means of the most simple procedure wherein the positions occupied by the two beams of reflected radiation are located at the same time. Figure 4 1s a block diagram showing the components of the position sensitive scintillation detector Including its connections with a computer and other related elements. Referring next to the drawings for a detailed description of the present Invention and a suitable position-sensitive diffractometer for its application, reference numeral 10 has oeen selected to identify in a general way the head or probe portion of the apparatus while numeral 12 refers to the surface of the sample to be tested. A tubular x-ray tube shield 14 of conven ional design houses an x-ray tube 16 which is , in turn, connected to a suitable power supply (not shown) by x-ray power cables 18 that enter the case at the end opposite that upon which the x-ray sensitive surfaces of the detector channel sets 20 are attached. Other insulated power cables 22 supply power to the detector electronic subasse blies 21 , in the probe 10 along with other electronic components thereof that will be identified and described in detail presently. An apparatus to position the x-ray sensitive surfaces, in this example a fiber optic holder 1s shown as 24. Also, an Incident x-ray beam col 11 m tor is shown as 28. Components 28 and 24 are Interfaced into the x-ray tube shield 14. The head, or probe, 10 is the most important feature of a suitable position-sensitive di f f ractometer unit and, as will be seen in Figures 2 and 3 to which detailed reference wil l now be made, 1t includes , among other things 1n one example of a suitable unit, two fiber optic channel bundle sets 30A and 30B each of which 1s made up of many individual fibers arranged in coherent relation such that a given fiber occupies precisely the same position at the Input face I as it does at the output face K on the opposite end there¬ of. The size of the individual fibers 1s , of course, a function of what degree of Image resolution 1s desi red and this, 1n turn, depends upon the resolving power of the scintil lation phosphor coating 32 on the input faces of the bundles, the electronic scanners and other elements of the head sub- assembly. For Instance, if the phosphor coating 32 the input faces of the fiber bundles 30A and 30B has a special resolution of only about 30 microns , then any fiber having a diameter equal to or less than 30 tf will have no adverse effect upon the quality of the transmitted beam. Fiber optic bundles 30A and 30B made up of 10 fibers are readily obtainable and they exceed the resol ving capabil ities of other elements of the head subassembly. From the standpoint of the phosphor coating 32 it must, of course, respond to the ionizing radiation in the form of the reflected x-ray beam falling thereon by emitting light photons . Those phosphors capable of the most efficient conversion of the ionizing radiation to visible light, un¬ fortunately, also scatter the light the most and, therefore, have poor spacial resolution. Thus, the selection of a suitable phosphor and its physical characteristics on the face of the fiber optic bundles , i .e. , thick layer or thin, etc. , largely becomes a trade off between the desired resolution and energy conversion efficiency. From a practical standpoint, it has been found that a phosphor having approximately a 30 -/ spacial resolution and 10% energy conversion efficiency works quite wel l . While these are the prime con¬ siderations, the phosphor chosen should, in addition, remain stable over long periods of time and under varying climatic conditions . Also of prime Importance is the transmlssibiHty of the visible light because it 1s not enough to emit the light if the phosphor will not transmit 1t the fiber optic channel bundles 30A and 30B. Next, detailed reference will be made to the diagram of Figure 3 in which certain Important relationships have been revealed. The size of the input surface I of each fiber optic channel bundle 30A or 30B controls the range of allowed distances separating this surface from the surface of the sample (or specimen)12, i .e. , the so-called "R " distance in the diagram. It is the tolerance for this distance that provides a unique feature of this invention. Obviously, the longer this surface is , the greater the distance -9- and broader -the range can be of R o . The spacing between the two channel or bundles 30A and 30B is , like¬ wise, an Important consideration and one that is determined from the angular relationships revealed in Figure 3. In x-ray stress measurement applications , it is the angle 277 on each side of the incident x-ray beam together with the desired spedmen-to-detector surface distance R that determine the proper spacing between bundles 30A and 30B. It can be shown, for example, that if the system Is ultimately capable of producing a SOU final spacial resolution, R 0 1s selected to be 1.6 inches, and 2Θ 156° (ZTj * 2^ - l7) z • 180 - 156* ■ 24°) , for Cr K-alpha radiation and a powdered aluminum specimen, then a spacing of about 1.0 inches center to center of the optic bundle surfaces I will be optimum. A spacing such as this will accommodate a 29 angular resolution of 0.08°. Moreover, this same spacing would accommodate ferritic or martensitic steel or iron spaced (R ) 1.6 inches from the detector surface also having a 2Θ of 156° using CrK radiation. Other metals and ceramics may, of course, require a different spacing between bundles 30A and 30B in order to achieve optimum conditions ; however, as above noted, once the values for R , Z j , and the x-radiat1on wavelength are known, this distance can be easily calculated. For a powdered, i .e. zero residual stress specimen, 2T ■ ZTj ^ ■ 27? 2 . A length of the input surfaces I of the fiber optic detectors 30A an 30B of one-half inch for each such surface has proven to be entirely adequate for application of the method. In width , one-tenth of an inch has , likewise, been proven satisfactory. The tilt of these input surfaces I is also important and, ideally, they should conform to the circle whose radi us is R , as shown in Figure 3. When this relationship is present, optimum resolution of the reflected beam is Insured. However, flat rather than curved input surfaces I , see Figure 2 , have been shown to provide adequate results when using the cal ibration and appl ication method which 1s an integral part of this invention. Finally, with regard to the leng* of the fibers relative to those in the same bundle or those in the other bundle, it does not appear to make any difference that they are not the same other than, perhaps, a negl igible loss in Intensity In the longer fibers due to the fact that the light has to travel a slightly greater distance. Returning again to Figure 2, it can be seen in this example of a suitable position sensitive detector that the output ends K of the fiber optic channel sets are joined to the face of an image intensifier 34 in essentially s1de-by-s1de parallel relation. This Intensifier has no other function than that of Increasing the intensity of the image appearing at the output end of the detector bundles to a level where it can be read by a scanner subasseπύly and photo diode array within a reasonable length of time, the latter sub- assembly having been designated broadly by reference numeral 36. In Figure 3, numeral 96 Indicates the path of the x-ray beam pro¬ jected from the x-ray beam collimator 28 and striking the surface of sample 12. The x-ray beam 96 1s positioned at an angle^ to the normal N surface of the sample 12. Fiber optic bundle sets 30A and 30B are positioned at a distance R from intersection of the surface of sample 12 and the x-ray beam 96 and are adapted to receive x-ray beams from the surface of the sample 12. Other designations set forth in Figure 3 are more ful ly described in the foregoing specification. Referring to Figure 4, an instrument rack 70 contains a computer 72 connected to a dual floppy disc drive 74 and to a computer teleprinter 76. The computer 721s also connected to a position sensitive scintillation detector control panel 78 and to a CRT 80 located In rack 70. The electronic package 21 of Figure 2, also referred to as electronics cube 21 1s connected to a diode array scanner and power supply 84 which in turn 1s coupled to the computer 72 through an AID converter 86. The diode array scanner and power supply 841s also directly connected to the computer 72. Thermal monitor 91 1s connected between the electronic package 21 and computer 72. The elec¬ tronic package 21 1s coupled to the computer 72 through an image intensifier power supply 88. Likewise the electronic package 211s connected to the control panel 78 through a solid state cooler power supply 90. The control panel 78 Is then coupled to a water monitor 92 which controls a cooling water supplied to the electronic package 21. Likewise the control panel 78 is connected to a nitrogen monitor 94 which controls the nitrogen supplied to the electronic package 21. The nitrogen circuit is not needed when the electronic package 21 1s hermetically sealed. The fiber optics channel bundle sets 30A and 30B and related components extend from the electronic package 21 in a manner set forth in Figures 1 and 2 and previously described. Even after the analogue of the x-ray pattern has been intensified, it still 1s not visible to the naked eye. In fact, it must accumulate photons for several fractions of seconds to seconds in order to produce usable data. More than one type of intensifier is available for this purpose, however, only the proximity focused type containing a multi-channel solid state electron multipl ier is smal l enough and sufficiently l ighweight to answer the needs of a portable unit. Of equal importance is the fact that such units util ize hol low fibers which are much more compatible with the fiber optic channel bundles 30A and 30B than other types which employ either electrostatic or magnetic focusing of the image in that the transition from fiber optics in the detector to a non-fiber intensifier results 1n considerabl Inefficiency at the interface therebetween. On the other hand, by going from a fiber detector to a fiber-type intensifier, these losses are minimized thus producing a usable image on the output screen at the rear of the Intensifier in the shortest time interval with the least gain. While no novelty is predicated upon the image intensifier 34 per se, 1t consists of an Input photocathode positioned to mate with the output surfaces K of the detector or channel bundles 30A and 308 and take the dim signal therefrom. This photocathode then delivers the Image thus received to a multichannel plate consisting of hollow fibers filled with a solid state material capable of producing electron multiplication. Approximately 2-300 volts are applied between the photocathode and the Input to the multl -channel plate for the purpose of Inducing the electrons to leave the photocathode and enter the latter. The voltage Impressed across plate is general ly made variable and usual ly runs somewhere between 4-800 volts . This 1s sufficient 4 to produce an electron gain of about 1 to 10 . The voltage between the plate and screen, on the other hand, 1s generally around 5KV which is effective to accelerate the electrons efficiently to produce a visible Image. Behind the image intensifier 34 Hes a mask 44 containing apertures filled with fiber optic windows that register with the analogue signal appearing onjthe output screen of the image intensifier 34 and also with photodlode arrays 36 therebehind. These windows cooperate to transfer the Image on the screen to the photodiode arrays 36 with minimal transmission losses 1n much the same way that the fibers in multi-channel plate do with respect to the image picked up by the latter at photocathode. It has been found that windows made of quartz or optical glass (lenses) severly reduce the intensity of the transmitted Image. For this reason, 1t 1s Important that the fiber optic bundle be used as a light transmission medium throughout the system In order that a detectable signal be produced in a short time Interval, 60 seconds or less, and with minimal amplification. The window-forming fiber optic bundles are, in essence, just short segments of the detector bundles as they perform similar functions and are subject to the same design parameters, i.e., be of a diameter no greater than that of the maximum spacial resolution of the phosphor, etc. Photodlode arrays 36 constitute a part of a scanner subassebly 50 which, like Intensifier 34, 1s a coπrnerdally available Item except that it has been modified as previously mentioned to replace the usual quartz windows with the fiber optic ones. A typical array has some 512 photodiodes arranged in side by side linear relation. Often the analogue signal is very weak thus necessitating a long data accumulation period (several seconds), the scanner must be cooled to reduce the leakage current. Accordingly, the scanner is cooled by a small thermoelectric cooler 54 of standard design and a water cooled heat exchanger 56. Even without the use of refrigerants, the foregoing cooling system has proven adequate to maintain the scanner at a temperature some 40 β C. below ambient which is more than enough to allow photon collection -14- for 60 secoøds or more. In Figure 2, reference numeral 58 designates a conduction member which cooperates with the thermoelectric cooler 54 against which 1t lies to maintain the necessary scanner temperature. Other types of cool ing systems may, of course, be substituted for the one Illustrated provided only that they do not Interfere or otherwise detract from the portability of the probe and the various electrical and coolant lines associated therewith. The scanner 36 also includes a shift register which samples each of the 512 photodiodes sequentially in accordance with an 1mput clock rate. A typical one used 1s a "RETICON" Model RL 512C/17 solid state scanner which processes the information picked up by the. detector with which it 1s opera¬ tive, y associated and delivers same as an output signal for video display. No attempt has been made to incl ude either the scanner circuitry or any de¬ tails concerning the equipment used to evaluate the output signal . Finally, a typical version of a suitable apparatus will be seen to Include a computer 72 and certain peripherals as set forth in Figure 4. In operation the x-ray beam leaves the c-ray tube 16, in Figure 1 , and impinges upon the sample or specimen 12 after having been passed through a suitable aperture in the x-ray beam collimator 28, the design and construction of which are wel l within the skill of the art. The specimen 12 Is placed a fixed approximate distance from the input surfaces I of the fiber bundles 30A and 30B in Figure 2. The knowledge of this distance is Important to the measurement of stresses ; however, it can be determined by the novel method described herein when the apparatus is properly calibrated. The method for this calibration 1s a vital part of the 1nvent1on and' 1s described subsequently. By properly tilting the specimen with respect to the incident x-ray beam and the input surfaces of the bundles 30, the latter surfaces will be in a position to receive the reflection off the crystal planes of the specimen such that the Internal (residual ) stress 1n the specimen can be determined. In the example of a suitable position sensitive di f f ractometer described the output ends K of the bundles deliver their respective dim images to the Image Intensifier 34 as before where it 1s amplified, scanned, read, and delivered to the computer 72 which computes the stress using the Bragg relationship and the calibration parameters , as well as certain material constants . Once again, in this example of a suitable instrument, fiber optics are used throughout the image transmission chain to minimize the Inter¬ face losses and, most Important, to get the Information in a readable form as quickly as possible. The Improved method for ascertaining the unknown angle 29 in the Bragg relation 1s also unique n that the x-ray sensitive surface of the detector channel sets are placed an approximate Instead of a precise distance away from the specimen and 1n a position to intercept said diffracted beam. The x-ray sensitive surfaces fn the example apparatus are preferably oriented 1n right angular relation to the diffracted beam, and the fibers of the bundle should be essentially parallel thereto for best results . The fiber optic bundle 1s employed as a signal transfer mechanism by means of which the analogue signal (Image) of the x-rays Impinging upon the phosphor is reproduced at a remote location. The visible li ght image thus reproduced must be intensified in accordance with presently avai lable technology in order to make it possible -16- for the image to be scanned and analyzed wi thin a reasonably short time frame. In so doing, 1t is important to use an image intensifier 34 employing the same type of image transfer mechanism as the detector, namely, a fiber optic bundle, as opposed to tradi tional optical systems and the l i ke. The same 1s true of the windows transmitting the image thus intensified to the electronic scanning array. Ordinarily, quartz windows are used to this pur¬ pose ; however, In accordance with the teaching of the Instant method, fiber optic windows are substituted therefore. In the scanning step used by the example apparatus for appl ication of the method, the Intensified visible l ight image (analogue signal ) Is repeatedly scanned electronically and converted to an electrical image wherein the magnitude of the electrical output from an array of sol id state sensors is proportional to the Intensity of the visible light received by said sensor. This electrical image 1s then analyzed and used as the basis for an output which, when combined with the calibration Information described subsequently, provides the analyst with precise Information on the location of the dif¬ fracted x-ray beam relative to the Incident one Impinging upon the sample. STRESS MEASUREF€NT TECHNIQUES The primary application of the previously described apparatus and this method Invention 1s to measure residual stresses in polycrystal line materials . Therefore, an explanation of techniques for stress measurement by x-ray diffraction must be provided. There are three basic techniques for measuring stresses based on the x-ray di ffraction method. These are the double-exposure or two-angle technique (DET) ; the single-exposure or one- angle technique (SET) ; and the sin-square-psi or mul ti-angle technique (sin ψ ) . The angle of exposure which 1s referred to 1s that between the incident x-ray beam and the specimen surface normal , i .e. , beta (£) in Figure 3. The fol lowing paragraphs briefly discuss each of the three techniques ; more detai l may be found in the reference, SAE, "Residual Stress Measurement by X-Ray Diffraction - SAE J784a ," Soc. of Auto. Eng. Inc. , Warrendale, PA. DOUBLE-EXPOSURE TECHNIQUE (PET) The double-exposure technique (DET) measures the Interatomic spacing (d) of planes at two different attitudes ( ^ and ^ ) ^^ the specimen sur¬ face. One set of planes are usual ly those which are parallel to the surface, and thus the psi angle is zero, I .e. , T. | » 0°. The second set of pl anes are those that make a reasonably steep angle with the surface, e.g. , * ^ ■ 45 ° or 60" . These angles are often chosen because their sin Rvalues are 0.50 and 0.75, and this simplifies calculation. The DET has been the most commonly used technique and has been appl ied to film and diffractometer measurement. However, Its application presents the opportunity for the Introduction of large errors due to specimen to detector distance variations when the stress measuring head 1s moved from one » angle to another on any instrument except a conventional goniometer based diffractometer. It has mainly been appl ied because most conventional Instrumentation 1s Incapable of measuring two f angles simultaneously. The combination of method and suitable Instrument described herein 1s uniquely capable of applying the DET In a portable instrument without the Introduction of the error mentioned. SINGLE-EXPOSURE TECHNIQUE (SET) In order to measure residual stress , the diffracting angle (θ) from the same type of crystallographlc planes at two different angles with respect to the surface need to be measured (see Figure 3) . This 1s possible to accomplish with a single incident x-ray beam angle because x-rays are dif¬ fracted by a fine-grained polycrystalline surface as a cone of beams . By measuring the Bragg angle (θ) on two opposite sides of the cone, stress can be measured using a single beta (β) angle (see Figure 3) . Note that the diffracted beams are measured in a plane which 1s normal to the cone axis , i .e. the incident x-ray beam. Also, that the two positions of measurement on the approximate circle produced by the intersection of the cone of x-rays and the aforementioned plane are the closest and farthest away, I.e., opposite sides of the circumference, from the specimen surface normal. Actually, when beta (β) 1s not equal to zero, the plane-cone Intersection forms a circle only when the metal 1s unstressed. In a stressed metal the circle 1s deformed Into a skewed ellipse andTj, ≠ "h - Then as described In the previous paragraph, a single Incident angle ψ) can be used to provide readings at two psi (j) angles using the equation where E. 1s the Elastic Constant (Young's Modulus) , V is the Poisson's Ratio, and the rest of the parameters are defined in Figure 3, where L ■ S 2 and R * S- j . The major parametric difference between the single- and double- exposure techniques 1s that one psi (Y) angle is usual ly equal to zero degrees for the double-exposure technique. The combination of method and suitable instrument described herein is unique in its abil ity to efficiently perform the SET, as well as the DET and sin f . Further it is unique in providing for appl ication of the SET without the need of incorporating added steps in the stress measurement procedure to precisely measure or control the sampl e- to-detector distance for each indi vidual stress measurement. SIN-SQUARE-PSI TECHNIQUE (SIH Z Ψ) This technique uses the fact that in stressed, untextured ( I .e. , no crystal lographic preferred orientation) metals and cerami cs the Interpl anar atomic s pacings (d) of crystal lographic equivalent planes (i .e. , Identical mi l ler indices , hkJL) wi l l vary consistently with thei r psi (Ϋ) angle. Furthermore, a plot of this d space versus s1n-square-psi will produce a straight l ine. In order to calculate stress from such a plot, the data must be plotted as (d*--d 0 )/d 0 » i .e. , Interplanar spacing at some angle psi (f) minus the spacing of the unstressed metal di vided by the spacing of the unstressed metal . From this plot the stress in the surface 1s obtained by mul tiplying the slope of the l ine by E/(1- (V ) « Also, the sum of the two principal stresses 1n the surface may be obtained from the Intercept, £ orΔd/d Q , at psi equals zero (V * 0) . Details for accomplishing these cal culations may be found 1n the SAE reference previously cited. The method and suitabl e ap¬ paratus described herein 1s unique in Its application of the s1n-square-psi technique In that careful control and/or measurement of the sample-to-detector distance is ci rcumvented. APPLICATION OF STRESS MEASUREMENT A unique method and suitable apparatus capable of applying al l of the techniques of x-ray stress measurement more proficiently than heretofore ever possible has been discussed previously in this document. For the most rapid application the information about the diffracted x-ray beams on each side of the incident x-ray beam can then be used by the computer used with the position-sensitive diffractometer described as a suitable device herein to determine the internal mechanical stress in the irradiated portion of the specimen by using a single incident angle {β to provide readings at two angles, using equation (1) . It must be recognized that for precise adherence to the x-ray stress measurement single-exposure technique geometry shown in Figure 3, the left and right x-ray sensitive surfaces of the fiber optics channel bund es 30A and 30B must be tangent to the circle upon which the detectors lie. Note that the planar fiber optic surfaces in Figure 2 take the place of the curved film in Figure 3. Furthermore, these two fiber optic surfaces must be tangent at their exact center and exactly the same distance from the incident x-ray beam. In order to accommodate these conditions as nearly as possible, a precision circular track of the fiber optics holder 24 Figure 1 1s provided that 1s attached to the incident beam collimator 28. This fiber optic track provides an extremely stable base for mounting the fiber optics. The latter are mechanically held rigidly 1n retainers which are slid along the inside track of the holder, and when properly located are secured in position by a number of set screws. However, in spite of this precise hardware, the extreme alignment tolerances of less than -0.0001 Inches (-0.002 mm) cannot reasonably be met by conventional fabrication techniques. Therefore, to account for the error in location of the center of the x-ray sensitive fiber optics a correction is incorporated into the stress calculation algorithm based on equation 1. The parameters for this correction are derived from a calibration procedure which is an integral part of this invention and determines experi ¬ mental ly the relati ve misal ignment of the left and right fiber optic with respect to each other. In other words, a parabolic regression is used to fit experimental data to the equation R - A-L 2 + B-L + C , (2) where R and L are the location of the right and left peaks (S-j and $ 2 in Figure 3) , and A, B, and C are the constants for the empirically determined parabola. These constants are used in the equation as a substitution for the term S Λ -S Λ in equation 1, here °2 °1 S Q - S Q « AL 2 + BL + C - L . (3) The operational procedure for determining A, B, and C 1s described subsequently and is an Integral part of this patent. A linear equation in place of the parabolic equation (2) has also been found to be applicable in some cases. Thus other polynomials may be useful . If the constants are not correct, changes 1n R Q , the distance be¬ tween the specimen and stress head, will cause apparent changes in the measured stress. This can be tested by using a powder coupon standard or some other known stress standard at a angle and moving the head up or down to give a few percent difference 1n R and 1s a method of calibration confirmation. • There are two major errors caused by non-focusing conditions inherent 1n all techniques of x-ray stress measurement, incl uding the single- exposure technique (SET) . One is due to the uncertainty of the detector circle to specimen distance, R , in Figure 3, and it is corrected in the method of thts invention through its iterative calculation with respect to stress. The other 1s due to the need to use a beta ψ angle other than zero; 1t 1s ameliorated through application of a Lorentz-Polarization and absorption correction (LPA) which 1s a well-known procedure. The iterative calculation of R which is an integral part of this Invention uses the following equation for the first estimation of R , L + R + S n + S ft R o 0 ( ( l 1 ) } ' 2 tan 2 0 * • ( ) where L and R are the first estimate of the x-ray peak positions, S 2 + S j - *» 2x ( Ideal R Q ) sin Zfc - (L+R) R sIdeal »?J 0 ■ 90 - Θ Q , Θ Q ■ Bragg angle for the unstressed metal . For all iterations beyond the first, i .e. , n+1 , the calculation L + R + S„ + S o_, L RERR * R RERR R o(n+l) " (5) 2 tan 2 2 2 ttaannT ! • is used to determine R, , where R , SϋΔil sin 2 , {7) K£KR (E/HV) cotθ 0 κ with all terms previously defined, except * , * 0 ~~ * Q \ andjf R *β - R , where In other word curate estimation of<pat each n+1 iteration. This is continued until the R Q is , consistent from one iteration to the next by predetermined error allowance. It is more accurate, rapid, and convenient to determine R Q by this novel means rather than to careful ly measure or control it to the ideal R by some optical or mechanical method. The successive R terms are also used to calculate the Θ L and Θ R angles used in the LPA correction where θ, = 90 -^, and Θ R - 90 -} R The calculation of the terms used for the LPA correction is based upon the equation LPA » cot **V • (8) θ i • θ L or θ R The rationale and need for this equation is described in the SAE reference previously cited. The equations presented herein serve only to provide a description of the processes used by a computer in the use of the method of simultaneous R„ Co, . and stress determination which Is a part of this Invention. CALIBRATION METHOD The purpose of this method is to generate five (5) parameters which are necessary for the application of this method invention. These parameters are the calibration coefficients designated A, B, and C, average left and right peak positions at the ideal R . Their relevance has been explained previously. The first three parameters provide (S n -S. ), where 2 i S n - S„ * AL 2 + BL + C - L °2 °1 and the las + S Q = (Ideal R Q ) x 2 tan 2J> 0 - (L + R) R 0 » Ideal (9) In the (S Q + S Q ) relation,^ * 90 - Θ Q , where Θ Q is the Bragg angle of an unstressed metal or ceramic and (L + R) is the sum of the apexes of the diffracted peaks at R n * Ideal . S ή and S Λ , shown in Figure 3, can be calculated from these relations, and this 1s an Irrportant condition in pro¬ viding the unique feature of sample-to-detector distance tolerance of this method. The procedure for obtaining A, B, C, and (S Λ + S ) Involves the °1 °2 use of a specimen that is known to have a constant stress over the area irradiated by the x-ray beam. It is prudent to select a loose powder of a polycrystalHne material of as nearly the same composition as the material in which residual stresses are to eventually be measured. The powder 1s packed 1n a shallow well such that it has a planar surface. Standard x-ray diffractometer powder specimen holders are quite suitable and the technique of packing is well known. " This powder 1s then placed so that the incident x-ray beam strikes its surface at 90°; at the Ideal R„ o distance around which the operator desires to work. Several pairs of x-ray data (L and R) are obtained at this ideal R and the S, and S 2 (L and R) values recorded. The R Q 1s then lengthened; for example, 3% and more data 1s taken. This is repeated at three more distances approximately equivalent to e.g. R Q + 63. , R - 3%, and R - 6*. This data 1s then used to calculate A, B, and C through a mathematical regression solution procedure which is well known. The averag 3 e L and R reading * at the ideal R Λ o is used as S Λ O-Ϊ + S Λ o« . APPLICATION OF PARAMETERS In order to provide accurate residual stress measurement wi th the method and suitable position-sensitive diffractometer previously described, the following steps are followed. 1. The calibration parameters A, B, C, and (S Q + S Q ) R βϊdeaj . and elastic ] 2 ° the known val ue of the crystallographic /constants for the specimen metal or ceramic; and the angle^ are read Into the dedicated computer provided with a suitable stress measuring apparatus . 2. The x-rays are placed Incident upon a polycrysta Une specimen of unknown stress with the incident beam at an angle d to the specimen surface normal . 3. The detector is then Interrogated and the computer determines the x-ray peak position from each channel set using state-of-the-art x-ray peak fitting and location algorithms. 4. With the position of the peaks S- j and S 2 (L and R) established, the procedure then used by the computer for determination of accurate and C (stress) is Iterative and as follows, assuming that Lorentz-polarization and absorption (LPA) errors are accounted for when necessary. In the first iteration R Q is estimated from S, and S 2 (where S,*L and S 2 «R) by R o(n « l ) * F1 rst iterative estimation of R Q where 2» Q * 180 - 2Θ Q . The first estimates of if , 1 ' e - » n« τ ) ^ s obtained by -26- E (R - L) - (L - AL - BL - C) (n-1) — (11 ) ( 1 + ^ 4R o(n=l) s1π θ o sin2 ^ Then for all iterations greater than n»l , R is established by R o(n>l) * R ÷ (SQ τ * LR ERR * R RE , (12) 2 sin 2^ 2 sin 2^ where 207 • RERR (n-l) R o(n-l) sin 2j (13) co ottθθ Λ (E/l+V) 2tf7. , ,R R RERR " ^ °^ sin 2 R (14) RERR cotθ 0 (E/l+V) R • where 7* L (15) and ≠r _. E (R - L) - (L - AL 2 - BL - C) {n) 0 +V) R 0 (n) s1n * in Φ Iterations are continued until pn -<T"n-•,1) * • tf"n " 1s reduced to an error tolerance established by the operator, e.g., 0.01. This computational procedure provides unprecedently accurate^ "" . R , cessity of +β . The interpl anar spacing, d, of the planes contributing to θ^ and Θ R are d, »^ / sinθ L and d R * /2sinθ R from the Bragg equation (n^ » 2d si nθ , where n * 1 , A * wavelength of the x-radiat1on used) . Note n in the Bragg rel ation 1s not the same as the subscript n in the previous equations . TYPICAL EXAMPLES OF ADJUSTMENT, CALIBRATION , CONFIRMATION , AND STRESS MEASUREteNT PROCEDURES An unprecedently rapid, precise , and convenient method for deter¬ mining the Internal strain (residual stress) in polycrystalHne metallic and ceramic components 1s described in two examples which follow. However, preceding these example descriptions is the fol lowing introduction. INTRODUCTION A typical procedure Incl udes the adjusting of the position and attitude of the scinti l lation phosphor-coated ends of the fiber optics of the example position-sensitive diffractometer to the line of the incident x-ray beam and the detector ci rcle, described by the radius R 1n Figure 3. After this adjustment has been performed to accommodate the crystallographic para¬ meters of the polycrystalHne samples in which stresses are to be subsequently measured to the satisfaction of the operator, the calibration coefficients (A, B, and C in equation 9) are obtained, which al lows the algorithm, which 1s a part of the method of application described herein , to correct for errors of adjustment too precise for the operator to be expected to eliminate through mechanical adjustment. These errors Incl ude: 1 . Imprecision 1n location of the detector surfaces ( I in Figure 3) , such that the line of the incident beam bisects the distance between them. 2. Imprecision 1n location of the detector surfaces , such than an x-ray beam diffracted at precisely Zt or ZT (see Figure 3) at the pre- 86/ -28- selected R Q distance 1s centered on the detector surfaces (I in Figure 3) . 3. Imprecision in location of the detector surfaces so that thei r linear center 1s exactly tangent to the detector circle described by the pre-selected R ; or Imprecision In location of circular curved detector sur¬ faces so that their ci rcle coincides with the circumference of the detector circle described by the pre-selected R Q ; or some other Imprecise alignment of another shape of detector surfaces of a configuration for applied x-ray optics. After the calibration, which provides the coefficients A, B, and C and the precise location of the x-ray peaks on either detector at the pre¬ selected distance, R , is established (i .e. , L and R at the ideal R ) , the accuracy of the calibration 1s confirmed. Finally, the calibrated apparatus is applied to internal stress measurement of a crystalline solid. The unique feature of the calibration combined with a position-sensitive diffractometer with at least two detector channel sets, that 1s not present 1n any other simi ar processes, 1s that the distance between the specimen and detector surfaces need not be precisely controlled or measured in order to provide precise residual stress readings. EXAMPLE 1 The first specific example will be for Internal (including residual ) stress measurement In ferritic or martensitic steel . The crystalline para¬ meters of a -ter large range of useful Iron base alloys are sufficiently similar that a single calibration procedure of the apparatus, which is an important part sub^eet/of this patent, will provide the coefficients necessary for accurate stress measurement for nearly al l ferritic and martensitic steels. These alloys may be generically grouped into the category of ferritic and martensitic steels , but not austenitic stainless steels . For the following description the fol lowing is assumed. The x-ray sensitive surfaces are planar and rectangular, as depicted as 30A and 30B in Figure 2. The cross-sectional length of the fiber optic channel bundle, I .e. , 30A and 30B in Figure 2, and also the x-ray sensitive scintillation phosphor coating 1s 0.5 inches (12.7 mm) . This dimension represents the length of the linear position sensitive detector. Chromium K-alpha characteristic x-rad1a- fon 1s to be used to diffract from the (311 ) crystallographic planes of the Iron base crystal lattice. This diffraction occurs nominally at a Bragg angle of about 78 degrees. It has been found in practice that a convenient specimen-to-detector circle radius , see R 1n Figure 3, 1s about 1.57 Inches (40 mm) , I .e. , the pre-selected R Q * 1.57 Inches (40 mm) . However, distances as great as 2.4 inches (60 * nm) and as small as 1.2 Inches (30 mm) have been used, and larger and shorter distances than these are also feasible. 1 ,1 ADJUSTMENT The x-ray sensitive ends of the detector surfaces , e.g. , the fiber optic bundles (30A and 30B in Figure 2) of the example instrument are typical ly contained in collars which have circular tabs , approximately parallel , or tangent, to the long dimension of the fiber optic cross-section. These tabs are of a circular radius so that they slide into two weys in the fiber optic _ . __ -30- holder (24 in Figure 1 ) . Thus , the fiber optic col lars , and therefore the x-ray sensitive portion of the detector channel sets 30A and 30B, can be moved along the fiber optic holder arc while approximately maintaining the detector surfaces at the pre-selected R . Thereby, the distance between the line of the incident x-ray beam and the detector channel sets. 30A and 30B can be varied to provide different angles between a normal at the center of the fiber optic end and the incident beam, i .e. , 2& and 2 in Figure 3 can be varied. For this example, I .e. , ferritic and martensitic steels , this adjust¬ ment would be performed to provide ZYj-. ■ 23j « 180-156 β , where 156 β is twice the nominal Bragg angle for the steels, I .e. , 2 x 78°. Thus , with the R • 1.57 inches (40 irm) the arc distance between the center line of the Incident x-ray beam and the center of each fiber optic sensing surface (30 A and 30B In Figure 2) would be ZnR Q (24/360) * 0.65 inches (17 inn) . STEP 1 : Therefore, S, + S and S 2 + S Q in Figure 3 would be adjusted to about 0.65 Inches (17 mm) . This would constitute the only adjustment needed to prepare the stress-measuring apparatus for Internal stress measurements 1n ferritic and martensitic steels. 1.2 DETERMINATION OF CALIBRATION COEFFICIENTS STEP 2: The stress-measuring apparatus shown in Figure 1 1s next positioned with respect to a calibration specimen such that the incident x-ray beam emitting from the col l imator (28 1n . Figure 1 ) strikes the specimen at a normal angle. The cal ibration specimen is selected such that 1t has nearly the same crystallographic spacing as the steel and has a uniform stress field in the volume 1 eradiated by the x-ray beam. It has been found that the most convenient choice for such a specimen for steel is a fine (-400 mesh) i ron powder. This powder has been previously poured into a hol der such that a planar surface several times larger than the i rradiated area could be con¬ veniently molded. It is this planar surface to which the incident x-ray beam is placed normal . STEP 3: The distance between the x-ray detector surfaces and center of the Irradiated area 1s next adjusted to R ■ 1.57 ± 0.01 Inches (40 i 0.2 πm) using a template gage. STEP 4: The x-ray detector and x-ray source are then activated and five readings of $• and S 2 (Figure 3) are made, and provided by the dedicated computer, at the selected distance of R - 1.57 Inches (40 mm) . STEP 5: The R is next increased about 0.05 Inches (1 ,3 mm) and five more readings obtained. STEP 6: The R Q is Increased another 0.05 inches (1.3 mm) and five ■ore readings obtained. STEP 7: The R is decreased about 0.15 inches (3.8 mm) and five more readings obtained. STEP 8: • The o Λ 1s decreased about 0.05 inches (1.3 ππi) and five more readings obtained. Note: At any R other than that of 1.57 inches (40 urn) , the Irradiated area on the specimen is not at the center of the fiber optic holder circle. arc / In these non Ideal (I .e. , R t 1 .57 inches) R distances , R Q is usually measured as the distance from the intersection of the arc and the incident x-ray beam to the irradiated specimen surface (see Fi gure 3) . Also, 1t must be recognized that there are a number of constraints on the span of R which can be used with a given detector size, i .e. , length of fiber optic cross-section (30A and 30B 1n Figure 2) . Rule of thumb figures are that the R should be 3.0 ± 0.5 times the length of the fiber optic cross-section and the sp r an of R Λ o should not exceed 12% of R o. The computer Interfaced to the x-ray detector apparatus described herein therefore provides groups of five S, and S 2 (see Figure 3) values for each R distance used through Steps 4 through 8. 2 STEP 9: These then are fit to a polynominal equation, S« ■ AS- j + BS- ] + C, and the parameters A, B, and C calculated by a regression process. Also, the average S, and S- at the ideal R , i .e. , R * 1.57 Inches (40 mm) is calculated to provide the Information to calculate S Λ + S„ . °2 °1 For this example of calibration for steel , the coefficients de¬ termined were A - 0.67074 x 10 "9 Inches 2 , B ■ 0.96771 x 10 '3 inches , C ■ 3.3739, and at R - 1.57 inches (40 mm) the average S, ■ L ■ 0.25677 Inches and average S- ■ R ■ 0.25567 Inches. 1.3 CONFIRMATION In order to ascertain 1f the cal ibration coefficients determined are adequate for the Internal stress measurement to be undertaken, a con¬ firmation test 1s conducted. This Is done by placing a fine, loose powder of iron, with a planar surface, such that the Incident beam can be made incident upon it. A loose powder 1s selected because such a specimen is Incapable of supporting a macro stress between its grains and thus is a known, zero, stress specimen. STEP 10: The x-ray stress measuring apparatus is arranged such that the incident x-ray beam strikes the powder specimen at some angle beta (see^ in Figure 3) to the normal of the surface of the specimen. For steel a beta angle of 30° has been found to be convenient and to provide good precision and accuracy. STEP 11 : The R distance between the center of the Irradiated spot on the specimen and the detector is then adjusted to be roughly 1.57 inches (40 inn) and the detector and x-ray source is activated. elastic, STEP 12: The necessary crystal lograph1<Vand geometric parameters for steel , as well as the five calibration coefficients, are read Into the computer; the x-rays are activated; and the computer prompted to. determine the stress ft") and R distance (see equations 5 and 14) . Three readings are usually made at the first R distance, i .e. , about 1.57 Inches. STEP 13: The R 1s next increased about 0.04 Inches (1 mm) and three more readings are made. STEP 14: The R Is again Increased about 0.04 Inches (1 mi) and three more readings are made. STEP 15: The R 1s next-decreased about 0.12 inches (3 mm) and three more readings are made. STEP 16-: The R„ o Is next decreased about 0.04 Inches (1 inn) and three more readings are made. Thus , fifteen readings have been taken which span R distances from about 1.49 inches (38 mm) to about 1 .65 inches (42 mm) , I .e. , the range in which the operator expects to be measuring stresses in steel , and the mean and standard deviation of al l fifteen readings were -0.6 KSI (4 Mpa) ± 0.9 KS (6 Mpa) . The x-ray information for each reading of the set of three, at each distance of R Q , was obtained in six seconds , with a standard x-ray source, an unprecedented short time for collection of such information. The tolerance for variation 1n spedmen-to-detector distance, i .e. , the parameter designated R Q herein, 1s unprecedented. The abil ity to tolerate such variations and provide good accuracy (I .e. , -0.6 KSI compared with the true stress of zero) and precision (i .e. , 0.9 KSI) in a very short time 1s a unique feature not present in any other similar combination of apparatus and procedure. 1.4 STRESS MEASUREMENT With the stress measurement apparatus adjusted and calibrated, and with the quality of the calibration confirmed, Internal (including residual) stress measurements on martensitic and ferritic steel components can now be performed. STEP 17: In this example the x-ray stress head shown in Figure 1 was positioned over a large a loy steel weldment and the attitude of the head was adjusted so that the angle^ in Figure 3 was 30°. STEP 18: The distance between the stress head and weldment, i.e., R , was then approximately set between 1.49 and 1.65 inches (38 and 42 mm). STEP 19: The x-ray source was activated and the computer was prompted to determine the residual stress (<T) and R . Note: it was not necessary to read the crystallographic, elastic, and geometric parameters for steel, as well as the calibration coefficients Into the computer since that had previously been done during the confirmation. The resultant stress was 33.4 KSI (235 MPa) compressive and the R was 1.59 inches (40.3 mm). Stress measurements were continued for the rest of the day resulting in several hundred readings from the wel dment with residual stresses ranging from 34.7 KSI (244 MPa) compression to 27.5 KSI (194 MPa) tensile and R Q ranging from 1.50 to 1 .63 inches (38.2 to 41.5 mm) . EXAMPLE 2 The second specific example will be for internal (including residual ) stress measurement 1n copper and alpha copper al loys . The crystalline para¬ meters of a very large range of useful copper base alloys are sufficiently similar that a single calibration procedure of the apparatus, which is an Important part su eβt/of this patent, will provide the coefficients necessary for accurate stress measurement for them. For the following description the following 1s assumed. The x-ray sensitive surfaces are planar and rectangular, as depicted as 30A and 30B in Figure 2. The cross-sectional length of the fiber optic bundle, i .e. , 30A and 30B in Figure 2, and also the x-ray sensitive scintillation phosphor coating is ' 0.5 Inches (12.7 mm) . This dimension represents the length of the linear position sensitive detector. Copper K-alpha characteristic x-radiat1on 1s to be used to diffract from the (420) crystal lographic plane of the copper base crystal lattice. This diffraction occurs nominal ly at a Bragg angle of about 73 degrees. As noted in the first example it has been found in practice that a convenient specimen-to-detector circle radi us , see R 1n Figure 3, is about 1.57 inches (40 mm) , I .e. , the pre-selected R * 1.57 Inches (40 mm) . 2.1 ADJUSTMENT For this example, I .e. , copper and alpha copper al loys , the re¬ adjustment of the detector channel sets would be performed to provide 2 ϊl * ~~fo. * 180-146° , where 146" is twice the nominal Bragg angle for pure copper, I .e. , 2 x 73°. Thus, with the R * 1 .57 inches (40 inn) the arc distance between the center l ine of the Incident x-ray beam and the center of each fiber optic sensing surface (30A and 30B 1n Figure 2) would be 2ττ (34-7361 °) « 0.93 inches (24 mm) . STEP 1 : Therefore, S, I + S Λ O-j and S, z + S 0 Λ « 1n Figure 3 would be adjusted to about 0.93 inches (24 mm) . This would constitute the only adjustment needed to prepare the stress-measuring apparatus for internal stress measurements in copper and al pha copper al loys . 2.2 DETERMINATION OF CALIBRATION COEFFICIENTS STEP 2: The stress-measuring apparatus shown 1n Figure 1 is next positioned with respect to a cal ibration specimen such that the Incident x-ray beam emitting from the col l imator (28 in Figure 1 ) strikes the specimen at a normal angle. The calibration specimen is selected such that it has nearly the same crystallographic spacing as the copper and alpha copper alloys and has a uniform stress field In the vol ume irradiated by the x-ray beam. It has been found that the most convenient choice for such a specimen for copper is a fine (-400 mesh) pure copper powder. This powder has been previously poured into a holder such that a planar surface several times larger than the i r¬ radiated area could be conveniently molded. It 1s this planar surface to which the Incident x-ray beam 1s placed normal . STEP 3: The distance between the x-ray detector surfaces and center of the irradύted area Is next adjusted to R s 1.57 t 0.01 inches (40 t 0.2 mm) using a template gage. STEP 4: The x-ray detector and x-ray source are then activated and five readings of S, and S 2 (Figure 3) are made, and provided by the dedicated computer, at the selected distance of R Q * 1.57 inches (40 mm) . STEP 5: The R 1s next increased about 0.06 inches (1.5 mm) and five more readings obtained. STEP 6: The R is Increased another 0.06 Inches (1.5 rrai) and five more readings obtained. STEP 7: The R is decreased about 0.18 inches (4.5 mm) and five more readings obtained. STEP 8: The R 1s decreased about 0.06 inches (1.5 mm) and five more readings obtained. Note: At any R other than that of 1.57 inches (40 mm) , the Irradiated area on the specimen is not at the center of the fiber optic circle, holder arc / In these non-Ideal (I .e. , R Q t 1.57 inches) R Q distances, R Q 1s usually measured as the distance from the intersection of the arc and the Incident x-ray beam to the irradiated specimen surface (see Figure 3) . The computer. interfaced to the x-ray detector apparatus described herein therefore provides groups of five S- j and S 2 (see Figure 3) values for each R distance used through Steps 4 through 8. _ STEP 9: These then are fit to a polynomiπal equation, S 2 » AS^" + B j + C, and the parameters A, B, and C calculated by a regression process. Also, the average S, and S 2 at the ideal R , i .e. , R * 1.57 inches (40 ran) is calculated to provide the Information to calculate S n + S ft . °2 °1 FOT this example of calibration for copper and alpha copper alloys , -9 2 the coefficients determined were A - 1 .12508 x 10 inches , B = 0.40751 x -3 10 Inches, C * 79.4304, and at R Q ■ 1.57 Inches f4Q mm) the average S- j ■ L * 0.25495 Inches and average S 2 * R * 0.25643 inches. 2.3 CONFIRMATION In order to ascertain if the cal ibration coefficients determined are adequate for the internal stress measurement to be undertaken, a con¬ firmation test Is conducted. This is done by placing a fine, loose power of copper, with a planar surface, such that the incident beam can be made Incident upon it. A loose powder is selected because such a specimen Is Incapable of supporting a macro stress between Its grains and thus 1s a known, zero, stress specimen. STEP 10: The x-ray stress measuring apparatus is arranged such that the Incident x-ray beam strikes the powder specimen at some angle beta In Figure 3) to the normal of the surface of the specimen. For copper and alpha copper alloys a beta angle of 25° has been found to be convenient and to provide good precision and accuracy. STEP 11 : The R Λ o distance between the center of the Irradiated spot on the specimen and the detector is then adjusted to be roughly 1.57 Inches (40 mm) and the detector and x-ray source 1s activated. elastic; STEP 12: The necessary crystal! ographic and geometric parameters for copper, as well as the fi ve cal ibration coefficients , are read Into the computer; the x-rays are activated; and the computer prompted to determine the stress tø and R distance (see equations 5 and 14) . Three readings are usually made at the first R distance, i .e. , about 1 .57 inches . STEP 13 : The R„ o is next increased about 0.05 inches (1 .3 mπ) and three more readings are made. STEP 14: The R Is again Increased about 0.05 inches (1.3 mm) and three more readings are made. STEP 15 : The R is next decreased about 0.15 inches (3.8 ran) and three more readings are made. STEP 16: The R Q 1s next decreased about 0.05 Inches (1.3 mm) and three more readings are made. of Thus, fifteen readings have been taken which span/R Q distances from about 1.47 Inches (37 ran) to about 1.67 inches (42 ran) , I .e. , the range 1n which the operator expects to be measuring stresses in copper, and the mean and standard deviation of al l fifteen readings were 0.9 KSI (6 φa) ± 0.7 KSI (5 Mpa) . The x-ray information for each reading of the set of three, at each distance of R , was obtained in ten seconds , with a standard x-ray source, an unprecedented short time for collection of such Information. The tolerance for variation in specimen-to-detector distance. I .e. , the parameter designated R herein, is unprecedented. The ability to tolerate such variations and provide good accuracy (i .e. , 0.9 KSI compared with the true stress of zero) and precision (I .e. , 0.7 KSI) In a very short time is a unique feature not present in any other similar combination of apparatus and procedure. 2.4 STRESS MEASUREMENT With the stress measurement apparatus adjusted and calibrated, and with the quality of the calibration confirmed, internal (including residual) stress measurements on alpha copper alloy components can now be performed. STE 17: In this example the x-ray stress head shown in Figure 1 was positioned over a small alpha brass electrical switch and the attitude of the head was adjusted so that the angle/5 in Figure 3 was 25°. STEP 18: The distance between the stress head and switch, i .e. , R , was then approximately set between 1.47 and 1.67 inches (37 and 42 mm) . STEP 19: The x-ray source was activated and the computer was prompted to determine the residual stress (<T) and R Q . Note: It was not necessary to read the crystallographic, elastic and geometric parameters for the alpha brass as well as the calibration coefficients Into the computer since that had previously been done during the confirmation. The resultant stress was 3.9 KSI (27 MPa) tensile and the R was 1.50 inches (38.1 mm). Stress measurements were continued for the rest of the day resulting in several tens of readings from electrical switch components with residual stresses ranging from 22.8 KSI (160 MPa) compression to 25.9 KSI (182 MPa) tensile and R ranging from 1.49 to 1.65 Inches (37.8 to 41.9 mm). Although a position sensitive scintillation detector has been utilized in this invention, it 1s also possible that a position sensitive proportional detector or a position sensitive solid state detector be substituted to produce similar results. The invention has been described with a certain degree of particularity; however, it is understood that changes in device construction and method steps may be made without departing from the spirit of this Invention.

Claims: C L A I M S 1. -A method of obtaining residual internal stress measurements in polycrystalHne specimen without accurate control or auxiliary measurements of the specimen to detector distance, R Q ,* the method comprising the steps of: 1. utilizing an X-ray beam source and a position- sensitive detector attached computer means, said detector contacting a detector circle described by the radius R 0 ; 2. adjusting the position and attitude of the X-ray sensitive area of the detector to the line of the incident X- ray beam and the detector circle described by the radius R 0 ; 3. measuring and calculating the calibration coefficients A, B, C, s o 1 and s θ2 by computer means; 4. collecting X-ray data and confirming the accuracy of the calibration of coefficients A, B and C by computer means; and 5. applying the apparatus to calculate the internal residual stress measurement of crystalline solid samples in which: A, B and C = the constants for the empirically determined parabola R *= AL 2 + BL + C; s o 1 = distance between the reference end of one of the detector channel " sets and the nearest point of the 0> incident X-ray beam line; s o 2 = distance between the reference end of the other of the detector channel set and the nearest point of the incident X-ray beam line. 2. A method according to claim 1, which comprises by computer means collecting the X-ray data and iteratively calculating the stresses in a specimen of known quantity so as to confirm the accuracy of the calibration coefficients A, B and C. 3. A method according to claim 2, which comprises confirming the accuracy of the calibration coefficients by: 1. placing a zero stress loose powder upon the specimen; 2. adjusting the.X-ray stress measuring apparatus such that the incident X-ray beam strikes the powder specimen at an angle beta; 3. adjusting the R 0 distance between the center of the irradiated spot on the specimen and the detector; 4. reading into the computer the necessary crystallographic, elastic, and geometric parameters and calibration coefficients, activating the X-ray and prompting the computer to iteratively determine σ and R 0 distance; 5. increasing R 0 in one or more steps and make additional computer readings; 6. decreasing R Q in one or more steps and make additional computer readings; and 7. prompting the computer to determine the mean and standard deviation of all stress readings taken to confirm the values of the calibration coefficients. 4. A method according to any one of the preceding claims, which comprises utilizing the β angle technique (double-exposure technique) in which step no. 4 is comprised of the following steps: 4A. Collect the X-ray data at a β angle such that ψ L or ψ R = 0° and calculate by computer means Θ L or Θ R and ΨL or ΨR' 4B. " Collect the X-ray data at a β angle such that Ψ L and/or ΨR is greater than~0° and calculate by computer means Θ L or Θ R and ! ■ >_ or Ψj- * ; 4C. Calculate by computer, or other means, the stress using the equation in which: Ψ 2 - ^L or R# from Step 4B and θ 2 = Θ L or Θ R , whichever (L or R) was selected for Ψ 2 ; and e-ι = Θ L or Θ R , whichever had a ψ = 0 from Step 4A; Θ L = the Bragg angle of that diffracted X-ray beam between the incident X-ray beam and the specimen normal;. ΘR = the Bragg angle of that diffracted X-ray beam on the opposite side of the incident beam from the Θ X-ray beam; ΨR = 90 - θ j *-. + β ΨL ~ θ L ~ 90 + β - 5. A method according to any one of claims 1-3, using multi-β angle technique (sin 2 ψ technique) in which step no. 4 is comprised of the following steps: 4A. collecting the X-ray data at a β angle such that Ψ^ or ^R i* 3 near zero and iteratively calculate by computer sin 2 _, sin 2 R, d^ and d^; 4B. collecting the X-ray data at a β angle such that Ψ L is greater than zero and iteratively calculate by computer sin 2 ΨL or Ψj-», sin 2 Ψ R , d L , and d R ; 4C. repeating step 4B at increasing β angles as desired to provide two or more sets of sin 2 ψ and d; 4D. plotting the sets in sin 2 Ψ L and sin Ψ £, d L d R against and to provide a sin 2 Ψ plot and d α o d o determine the slope of a straight line fit to the data of that plot. 6. A method according to claim 5, in which the stress is calculated- as: σ (Slope of the plot) in which: d 0 = interplanar spacing of unstressed material; d L = V 2 sinθ , • = V 2 sinθ-^; λ = wavelength of the x-radiation. 7. A method according to claim 1, in which the position sensitive detector is a position sensitive scintillation detector. 8. A method according to claim 1, in which the position sensitive detector is a position sensitive proportional detector. 9. A method according to claim 1, in which the position sensitive detector is a position sensitive solid state detector. 10. -A method of obtaining the residual internal stress measurements in polycrystalHne materials without accurate control or auxiliary measurement of the specimen to detector distance, the method comprising the steps of: 1. utilizing a position-sensitive scintillation detector having: a. a source of X-ray radiation directed in the form of a discreet beam against the polycrystalline sample for the purpose of ascertaining the interplanar distances therein; b. light transmission means in the form of a pair of elongate fiber optic bundles terminating at one end of an image-receiving surface located in a predetermined angular range relation to the incident X-ray beam, said image receiving surfaces being the size and shape when placed in close proximity to a sample against which the X-ray beam impinges to intercept at least two beams diffracted as a Debye ring; c. a scintillating phosphor coating on said image- receiving surfaces, said phosphor being responsive to X-ray radiation and operative when so activated to reproduce an image thereof in the visible spectrum; d. - image intensification means located adj cent to the other end of said fiber optic bundle operative to receive the visible light image transmitted thereto and increase the intensity thereof; e. an array of photosensitive diodes and associated precharged capacitors arranged in face-to-face relationship to the intensified image, said photodiodes being responsive to visible light and operative when thus activated to store an electronic signal determined by -having a functional relationship to the visible light impinging thereon; and f. signal processing computer means adapted to scan the photosensitive array and display the signal derived therefrom so as to reveal the position and intensity of the diffracted beam; 2. adjusting the position and attitude of the scintillation phosphor coated ends of the fiber optic channel bundles to the line of the incident X-ray beam and the detector circle; 3. measuring and calculating the calibration coefficients by computer means; A, B and C, s θι and s θ2 in which: A, B and C = the constants for the empirically determined parabola R = AL 2 + BL + C; s o_ = distance between the reference end of one of the detector channel sets and the nearest point of the incident X-ray beam line; s o 2 = distance between the reference end of the other of the detector channel set and the nearest point of the incident X-ray beam line; and 4. collecting the X-ray data and calculating by computer means the internal residual stress σ and R 0 of a specimen of unknown stress quantity using the equation: E -R - L. - .L - AL 2 - BL - C_ σ (n) = (1+v). 4R o(n) sin 2 θ 0 sin 2 B in which: E = Young's Modulus; R * = distance between the reference end of the detector surface and' the diffracted X-ray beam nearest the specimen surface; L = distance between the reference end of the detector surface and the diffracted X-ray beam nearest the specimen normal; v = Poisson's Ratio; R o(n) *"" ■ * specimen to detector distance calculated after the nth iteration; β 0 - Bragg angle for the unstressed material; β = angle between the incident X-ray beam and the normal of the specimen surface at the point of incidence of that surface and that beam.

Inventors: RUUD CLAYTON O, RUUD, CLAYTON, O.
Applicants: RUUD CLAYTON O, RUUD, CLAYTON, O.
Application year: 1986
Main classification: G01N23
IPC codes: G01L1, G01N23