This application also claims priority to U. S. patent application serial no. (not known yet), entitled"Interferometric Residual-Stress Analysis,"by inventors Gregory J. Hayman and Scott C. Keating, filed October 12,2000, and U. S. patent application no. (not known yet), entitled"Real-Time Interferometric Deformation Analysis,"by inventors John A.

Hanlon and Gregory J. Hayman, filed October 12,2000, both of which are hereby incorporated by reference.

Field of the Invention The present invention relates generally to interferometric systems and methods for residual stress determination.

Description of Related Art To determine the stress of a test specimen of a stressed material, one technique is to drill a small hole into the surface of a component or test specimen. Examples of such materials are plastics and metals such as aluminum alloy 7075.

With the removal of the material from the hole portion, the boundaries of the hole experience relief from the stress that existed without the hole. Surface displacements of the area surrounding the hole are indicative of the stress within the removed region. These techniques are sometimes called stress-relaxation techniques because the change in surface shape of the areas surrounding the hole is due to the relief of stress by the removal of the hole material.

The measurement of residual stresses has long been an issue solved by tedious and error prone techniques that utilize precision mounted strain gauges to measure the change in residual stress resulting from a small hole being drilled in the specimen. Engineers use this information to improve the life of the part and to potentially avert disastrous failures.

Holographic techniques have been used to determine residual stresses from a holographic interference fringe pattern. However, these techniques have been time consuming, have used bulky hardware, and do not provide the accuracy or efficiency desired.

DISCLOSURE OF INVENTION The present invention provides a system and method for residual stress analysis using electronic speckle interferometry. A phase shifting interferometer is used with a coherent light source to produce phase-shifted interference patterns that are digitized in real time so as to produce computer usable values of intensity per pixel, wherein each pixel represents a point on the object under test in a particular test set-up. A computer implemented residual stress analysis sub-system receives the computer usable values. This sub-system comprises a quantitative interferometric analysis module and a residual stress module. The quantitative interferometric analysis module comprises computer instructions adapted to compute the phase change at each point between a reference state and a stress-relaxed state using a phase shifting based algorithm. The phase change data is used by the residual stress module comprising computer instructions adapted to determining the components of a stress tensor for at least one triad comprising three pairs of phase change points around a drilled hole. In one embodiment, the phase change points in each pair are diametrically opposite each other around the drilled hole. Using the determined stress components, the residual stress module further comprises computer instructions adapted to compute the principal stresses. The invention provides a digital method of utilizing hundreds of thousands of possible data points to obtain a measure of the residual stress experienced by the object, thereby increasing the accuracy and efficiency of the analysis. In one embodiment, the components of the stress tensor are obtained for numerous triads and averaged. The average stress tensor is then used to compute the principal stresses. In another embodiment, a user can select through a user input interface of the computer-implemented analysis system that the stress tensor and the principal stresses be represented by a least squares fit solution for an overdetermined system based on a sample of pairs of phase change points.

BRIEF DESCRIPTION OF THE DRAWINGS The figures depict one or more embodiments of the present invention for purposes of illustration only. One skilled in the art will readily recognize from the following discussion that alternative embodiments of the system and method illustrated herein may be employed without departing from the principles of the invention.

Figure 1 illustrates an embodiment of a system for interferometric residual stress analysis in accordance with the present invention.

Figure 2A illustrates an embodiment of a phase-shifting speckle interferometer in accordance with the present invention.

Figure 2B illustrates another embodiment of a phase-shifting speckle interferometer in accordance with the present invention.

Figure 3A illustrates an embodiment of a real-time data capture sub-system and an embodiment of a computer-implemented residual stress analysis system.

Figure 3B illustrates another embodiment of the real-time data capture sub-system.

Figure 4 illustrates components of a stress tensor in a plane-stress state characterized by u,,,, which is the average stress state of the material removed by a hole-drilling process.

Figure 5 illustrates a definition of propagation vectors and angles of illumination and viewing with respect to a test object after the hole has been drilled.

Figure 6 illustrates an embodiment of a computer-implemented method for residual stress analysis in accordance with the present invention.

Figure 7 illustrates an embodiment of a display showing residual stress results.

DETAILED DESCRIPTION Figure 1 illustrates an embodiment of a system for residual stress-analysis using electronic speckle interferometry in accordance with the present invention, the system comprising a coherent light source 102 coupled to a phase-shifting speckle interferometer 104. The interferometer 104 generates two beams, an object beam 106, which is directed to illuminate a diffusely reflecting object under test 108, and a reference beam 110 which is coupled to a real-time data capture sub-system 112. A speckled object beam of scattered light 118 from the object as a result of the illumination is also coupled to the real-time data capture system 112. The data capture system 112 communicates computer usable intensity values 114, each intensity value associated with a pixel for each point in the interference

pattern, representing points on the object under test, to a computer-implemented residual stress analysis system 116.

Figure 2A illustrates an embodiment of a phase-shifting speckle interferometer that may be used in accordance with the embodiment of the invention of Figure 1. In this embodiment, a coherent beam of light 103 is generated by a diode pumped solid-state laser (DPSS) 102. This beam is optically coupled to a phase shifting interferometer via an optical coupler 126 and two alignment mirrors 222,224. Examples of an optical coupler include a lens, free space, and a fiber optic. In this embodiment, the DPSS laser has a wavelength in the range of visible light, 532nm, a line width <2MHz for intervals less than 2microseconds, and a coherence length > 150m for intervals less than 2 microseconds. Using a laser that provides a very narrow line width or approximately a single frequency eliminates the need for path length matching of earlier configurations. Furthermore the system can be miniaturized, and flexibility is added to the test set-up since the light can now be brought in on an optical fiber.

The phase-shifting interferometer 104 comprises a polarizing beam splitter comprising a half-wave B/2 plate 220 and a beam splitter 212 which splits the single laser beam into two separate linear, mutually orthogonal polarized beams, henceforth referred to as the object beam 106 and the reference beam 110, respectively, having approximately the same single frequency as the coherent light beam 103. In this embodiment, about 90% of the polarized light emerging from the beam splitter 212 will be directed toward the test object 108 and about 10% emerging from the beam splitter will be coupled via fiber coupler 214 into a reference beam optical coupler 210, shown here embodied as an optical fiber, attached to a fiber optic mount 216, the fiber directing the reference beam to an imager 238 which focuses the light on the image plane of the real-time data capture sub-system 112 (see Figures 3A and 3B below). Other percentages of light, such as 95%/5%, may be coupled from the respective beams and still be within the scope of the invention.

The object beam 106 is directed to a phase shifter embodied here, as two computer- controlled piezo-electric transducer (PZT) controlled mirrors 202,204. In this embodiment, both mirrors 202, 204 are shown having a control link 240 to the computer-implemented system 116, through which the PZT receives commands to adjust the position of the mirrors to introduce a known phase shift into the object beam.

The object beam is then coupled via fiber coupler 207 into an object beam coupler 209, shown here as optical fiber 209 which is attached to fiber optic mount 208. From the other

end of the fiber optic cable 209, the object beam 106 is collimated via optical lens 232, to the test object or test specimen 108. Speckled object beam 118 of scattered light from the surface 236 of the test object 108 is captured by an imager 238. The imager 238 directs the speckled beam 118 to the real-time data capture sub-system 112. Figure 2A illustrates the test object with the hole 234 already drilled. Data will be taken both before and after the hole is drilled.

Figure 2B illustrates another embodiment of a phase-shifting speckle interferometer wherein a phase shift is introduced into the reference beam. Figure 2B illustrates the positioning of a computer-controlled PZT controlled mirror 215, attached to control link 240, in the path of the reference beam 110 for introducing the phase shift. An attenuator 213 is positioned between the beam splitter 212 and the mirror 215 for reducing the amount of light directed to the reference beam 110 that is coupled via fiber coupler 214 into the reference beam fiber 210 which directs the reference beam to the imager 238.

Figure 3A illustrates an embodiment of an imager 238, a real-time data capture sub- system 112 and an embodiment of a computer-implemented residual stress analysis system 116. Imager 238 comprises a capture lens 338 and a beam combiner 312 for imaging an interference pattern created by the speckled object beam 118 and the reference beam 110 onto the image plane 324 of the real-time data capture sub-system 112. The real-time data capture sub-system comprises a photosensor 112. Examples of photosensors include a charge- coupled device (CCD), a Complimentary Metal Oxide Semiconductor (CMOS) detector, and a charge injection device (CID).

In this embodiment, capture lens 338 is a zoom lens which allows flexibility in the test set-up since it has more versatility with respect to the distance and size of an object. A fixed focused length lens can also be used as a capture lens. The captured light is optically coupled via lenses 320 to beam combiner 312.

The other end of the reference beam's fiber 210 is shown here mounted on a fiber optic mount 316. Beam combiner 312 is a 90/10 beam combiner in this embodiment, which combines about 10% of the light from the reference beam 110 onto the photosensor's image plane 324 with 90% of the captured speckled object beam 118. Other ratios of light are possible, such as 95% speckled object beam/5% reference beam, and are within the scope of the invention. Optical coupler 306 focuses the interference pattern onto the image plane 324 of the photosensor.

In this embodiment, the photosensor is a charge-coupled device camera 112. A CCD is a light-sensitive integrated circuit that stores and displays the data for an image in such a way that each picture element, a pixel, in the image is converted into an electrical charge whose intensity value is converted to a computer usable value.

Frame grabber 126 of the computer-implemented residual stress analysis sub-system has a pixel synchronous coupling 302 to the CCD camera through which it receives the computer usable intensity values 114 output by the CCD camera 112.

The computer-implemented residual stress analysis sub-system comprises frame grabber 126, quantitative interferometric analysis module 120, residual stress module 122, mirror control unit 128, memory 124 and display 130. In one embodiment, the frame grabber stores the intensity values in memory 124. The frame grabber 126 also provides the computer usable values 114 to the quantitative interferometric analysis module 120, which embodies computer instructions to calculate a phase change for each point on the test area between an undrilled reference state and a stress-relaxed state using a phase-shifting based algorithm. An example of a phase-shifting based algorithm is a four bucket analysis method. Furthermore, the quantitative interferometric analysis module comprises computer instructions adapted for performing phase unwrapping of the phase changes to remove a modulo 27 effect caused by an arctangent equation, described below.

The quantitative interferometric analysis module 120 communicates these phase changes to the residual stress module 122 which embodies computer instructions adapted to utilize the phase changes for each point to determine the components, arr X rvlf v of a stress tensor for a triad of three pairs of points. In one embodiment, the points in each pair are located diametrically opposite each other around the hole. The components are then used to compute the principal stresses ap, (top2. In one embodiment, the residual stress module comprises computer instructions adapted to computing stress tensor components for numerous triads for averaging. A sample size of the number of triads may be selected. The computed average stress tensor is used to calculate the principal stresses. The module then displays the residual stress as modeled by the average stress tensor.

The residual stress module 122 further comprises computer instructions adapted for acquiring a sample of pairs of points and modeling the residual stress using a least squares representation of an overdetermined system, and further comprises computer instructions for displaying the stress tensor components and the principal stresses of the object as modeled by the least squares representation.

Figure 3B shows an alternate embodiment of the imager in Figure 3A wherein the additional alignment mirrors 340 and 342 are used to assist in optically coupling the reference beam 110 to the beam combiner 312. Mirrors 340 and 342 may be embodied as PZT controlled mirrors that are controlled via control link 242 by the mirror control unit 128.

In the embodiments of the system according to the invention of Figures 3A and 3B, the intensity values for each point in a phase-shifted interference pattern are recorded once a frame. Once a frame, a mirror control unit 128 communicates over control ink 240 to the two PZT controlled mirrors 202,204 in the embodiment of Figure 2A to change the phase shift of the object beam or the PZT controlled mirror 215 in the embodiment of Figure 2B to change the phase shift of the reference beam 110. A typical frame speed used is 1/30 of a second.

For example, it would take 4/30 of a second to obtain a complete state of intensity values for each point in each of the four phase shifted interference patterns.

The introduction of a hole in a previously stressed material produces a displacement field which can be found from the difference between two known stress solutions. The displacement field caused by localized relief of residual stresses in the form of phase changes can be readily measured using holographic techniques. The physical behavior of a hole to a given stress field is quantitatively related to the phase changes for each object point through a series of equations, based on those developed in A. Makino and D. Nelson,"Residual-stress Determination by Single-axis Holographic Interferometry and Hole Drilling-Part 1: Theory,"Experimental Mechanics, pp. 66-78, March, 1994, hereafter Makino and Nelson, which is hereby incorporated by reference.

Figure 4 (see Figure 1 in Makino and Nelson) illustrates components of a stress tensor in a plane-stress state characterized by cr 11', which in one embodiment is the average stress state of the material removed by a hole-drilling process.

In order to determine the residual stress, these unknown stress components are computed for triads of object points where the phase changes resulting from the hole-drilling process have occurred. By computer-implementing the real-time data capture and the residual stress analysis calculations, data for thousands of points can be obtained. The statistical mean residual stress solution can therefore be obtained by obtaining hundreds of stress calculations, each based on three different triads of phase change points. Alternatively, a least squares solution based on an overdetermined system can also be obtained to solve for these components of the stress tensor.

In cylindrical coordinates, the displacement field produced by drilling a through hole of radius ro can be expressed in cylindrical coordinates as <BR> <BR> <BR> <BR> (1) ur = r0/2E {(1+v)( #xx + #yy)# + [(#xx - #yy) cos 2# - 2#xy sin 2#] [5p - (1 + v) p3]} (2) u# = -40/2E{[( #xx - #yy ) sin 2# - 2 #xycos 2#] [ 2 (1 - v) p + (1 + v) p2 ]} (3) u2=vt/E p2[(#xx-#yy) cos 20 + 2rr, sin 2 #] where ure us, U-cylindrical components of the displacement field E Young's modulus v = Poisson's ratio p = ratio of hole radius to radial coordinate (ro/r) t plate thickness Assuming a plane-stress state, these equations can be conveniently written as: (4) ur =# (#xx + vyy) + B [(#xx-#yy) cos 2# + 2rXy sin 20] (5) u#=C [(#xx - #yy ) sin 20-2 rr », cos 20]

(6) uz = G [(#xx - #yy) cos 2# cos 20 sin 2T,,, sin where (7) A = r0/2E (1+v)# (8) B = 40/2E [4p = (1+v) p3] (1) C = -r0/2E [2(1-v)p +(1+v) p2] (10) G = vt/E p2 Figure 5 illustrates a definition of propagation vectors and angles of illumination and viewing with respect to a test object after the hole has been drilled. (See Figure 3, Makino and Nelson).

Based on Figure 5, the following relationship is defined: (11) # = K # # Where # phase shift sensitivity vector ú = displacement vector # = #2 # #1 In the embodiments of Figures 2A and 2B, the image plane of the capture lens 338 is aligned perpendicular to the z-axis of Figure 5 as represented by z, If the capture lens or observer is at zlp oo, then the sensitivity vector components become: (12) Kx0 = cosγ1 cos#, and

(13) K ! °= cos y, sin ; (14) Ko=l +sin 7, where grazing angle of the illumination source inclination of the illumination direction with respect to the axes of Fig. 5 Figure 6 illustrates an embodiment of a computer-implemented method 600 for residual stress analysis using electronic speckle interferometry. The embodiment of a system in Figure 1 can be used to implement the method. In the embodiment described, the method uses the equations above and others discussed below to compute the residual stress tensor from the phase change for various combinations of three different pairs also called triads, of in this embodiment, diametrically opposite points around the hole. In this embodiment, a four bucket phase-shifting based algorithm is used.

The phase change for each point between an undrilled reference state and a stress- relaxed state is determined using a phase shifting-based algorithm. Examples of such algorithms include four bucket methods, 2+1 bucket algorithms, and five bucket algorithms.

The number and time criticalness of the phase-shifted interference patterns used is determined by the phase-shifting based algorithm selected. The method obtains a reference state of intensity values for each pixel representing a point on the object in each one of a plurality of phase shifted interference patterns. A stress-relaxed state will also be obtained after the hole is drilled for each pixel representing a point on the object in each one of a plurality of phase shifted interference patterns.

Before the hole is drilled, an intensity value for each point in each phase-shifted interference pattern to be used with the phase-shifting based algorithm is collected 602 to obtain an undrilled reference state.

The four bucket algorithm is implemented in this embodiment using the following equations. The general two-beam interference equation gives the resultant interferogram intensity as a function of the pupil coordinates corresponding to the position of the capture lens as

(15) I (x, y) = A (x, y) + B (x, y) cos [ç6 (x, v) + a (t)] where si (x, y) is a speckle phase, and a (t) is the introduced phase shift or phase step in either the reference beam or the object beam. For each of the following phase shifts, a (t) = 0, z/2, # and 37/2 in the four bucket algorithm, the intensity is as follows: (16) l, (x, y) =A (x, y) + B(x,y)cos [#(x,y) + 0], (17) I2 (x, y) = A (x, y) + B (x, y) cos [ç6 (x, y) + #/2] = A (x, y) + B (x, y) sin # (x,y) (18) I3 (x, y) = A (x, y) + B (x, y) cos [0 (x, y) + 3#/2] = A (x, y)-B (x, y) cos (x, y), and (19) I4 (x, y) = A (x, y) + B (x, y) cos [Si (x, 7) + #] = A (x, y)-B (x, y) sin # (x, y). where Il (x, y), I2 (x, y), I3 (x, y) and I4 (x, y) are the intensities of the four phase-shifted interference patterns.

After the hole is drilled, a user request indicates when the residual stress is to be determined. The user request may be received through the user input interface 166. Upon user request, an intensity value for each point in each phase-shifted interference pattern is collected 604 to obtain a stress-relaxed state. Next a phase change at each point between the reference state and the stress-relaxed state is computed 606 using the phase-shifting based algorithm.

After the hole is drilled, a phase change at each point A 0 (x, y) indicative of the displacement of the stress relaxed surface at that point of the test object will result.

#' (x,y) = (#(x,y) + ## (x,y)) so that the general two beam interference equation becomes (20) I1'(x,y) = A(x,y) + B(x,y)cos [#(x,y) + ## (x,y) + 0], (21) I2' (x, y) = A (x, y) + B (x,y)cos [#(x,y) + A # (x,y) + #/2] <BR> <BR> <BR> <BR> <BR> = A(x,y) + B(x,y)(sin #(x,y) + ## (x,y))<BR> <BR> <BR> <BR> <BR> <BR> <BR> (22) I3' (x,y) = A(x,y) + B(x,y)cos [#(x,y) + ## (x,y) + #]<BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> = A(x,y) - B(x,y)cos(#(x,y) + ## (x,y), and (23) I4' (x, y) = A (x, y) + B (x, y(cos [#(x,y) + A # (x,y) + 3#/2] = A(x,y) - B(x,y)sin(#(x,y) + ## (x,y)).

(24) I1 - I3 = 2Bcos#(x,y) (25) I2' - I4' = 2Bsin#(x, y)

(26) I1' - I3' = 2Bcos(#(x,y) + ## (x,y)) (27) I2' - I4' = 2Bsin(#(x,y) + ## (x,y)) 2Bcos (#(x,y) + ## (x,y) - #(x,uy) = (I1' - I3')(I1 - I3) + (I2' - I4')(I2 - I4) = 2Bcos A 0 (x, y) (28) 2Bsin ## (x,y) = I2' - I4' (I1 - I3) - (I1' - I3') (I2 - I4) (29) Then A 0 (x, y) = tan-' [2Bsin A 0 (x, y)/2Bcos A 0 (x, y) Next, the phase changes are unwrapped 608 to remove any discontinuities caused by the modulo 2z effect of the arctangent equation. Examples of unwrapping algorithms are discussed in Henri A. Vrooman and A. M. Maas,"Image Processing algorithms for the analysis of phase-shifted speckle interference patterns,"Applied Optics, Vol. 30, No. 13, May 1,1991, pp. 1636-1640, which is hereby incorporated by reference.

If the user request has indicated 610 that a least squares fit solution be applied, then a sample of pairs of points is acquired 618. The sample size may be predetermined or user selectable. The points to be used in the sample may be selected by the user or randomly selected by the computer. For example, random number generation can be used to select points based on radii and angles data. Also, the entire field of points could be used as the sample. Examples of sample sizes include hundreds of pairs of points or thousands of pairs of points or over 100,000 pairs of points. A stress tensor is modeled using a least squares representation for the overdetermined system using the acquired sample to solve for the three components of a stress tensor.

If the least squares fit solution has not been requested, then the components of the stress tensor for a selected triad are determined 612 and stored. Another triad is selected 620 until a sample size of triads has been obtained 624. Again the sample size can be hundreds of points. An average stress tensor or statistical mean stress tensor will then be computed for each of the triads in the sample 622 from which principal stresses will be computed 622.

The stress tensor can be related to the displacement indicated by the phase shift through the following equations comprising the parameters discussed above in reference to Figures 4 and 5: (30) {} =/47i [C]'' {A}

where [C] = (31) Cil = (K0x cos Oi + K°ysin 0i) (A + B cos 2 6 ;) + (-K0, sin Oi + K0Y cos #i) C sin 2#i (32) Ci2 = (Kx0 cos #i + K°ysin #i) (A - B cos 2 #i) - (-K0x sin 6 ; + K°y cos 0 ;) C sin 2#i (33) C13 = 2 {(K0x cos #i + K°ysin #i) (B sin 2 #i) - (-K0x sin #i + K°y cos #i ) C cos 2#I] (35) # #(r1, #2) - # #(r1, #2 + #), (36) A si (rl, #3) - # # (r1, #3 + #)} where ri = radial location from the center of the hole at which r = 0 and 0 = the angle location around the hole.

{ # # } has units of radians.

If a least squares fit solution has not been requested, { # } = #/4# [C]-1 { ## } is recalculated hundreds or thousands of times using different (r, #) triads as may be selected by the user or randomly selected by the computer. For example, random number generation can be used to select points based on radii and angles data. Also, the entire field of points could be used as the sample. An average stress tensor or statistical mean stress tensor is obtained such that, { # } = Average ({#1},{#2},{#3},..., {#i}... {#n}) where #i is the stress tensor obtained using the i'l' (r, S) triad.

The following equations are used to find the principal stresses #p1,#p2, pi Pz-2 2 xy 2 27' =45deg (1-sign [6..,-, , )) vl-56. ,-6, ,)) +-tan 2 -o-,, J 5 = the angle between xx axis and the principal stress, up, 8 () = impulse function sign [] = sign function

+lif x0 Oif x0 i [] +lifx>0 () Oifxw0 The stress tensor and principal stresses will be displayed as modeled 622 by the average stress tensor or as modeled by the least squares representation 618.

Figure 7 illustrates an embodiment of a display showing residual stress results. The stress components of a stress tensor in the Cartesian plane are displayed as well as the principal stress vectors. In Figure 7, S z = ß.

The above description is included to illustrate the operation of one or more embodiments and is not meant to limit the scope of the invention. The scope of the invention is to be limited only by the following claims. From the above discussion, many variations will be apparent to those skilled in the art that would yet be encompassed by the spirit and scope of the invention.

What is claimed is: