WW 3 129 OVERDUE FINES: 25¢ per do per item RETUMING LIBRARY MATERIALS: \ P lace in book return to new charge from c1 mulation recon AN EXPERIMENTAL STUDY OF LARGE COMPRESSIVE LOADS UPON RESIDUAL STRAIN FIELDS AND THE INTERACTION BETWEEN SURFACE STRAIN FIELDS CREATED BY COLDWORKING FASTENER HOLES By Rajab Adaki Sulaimana A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 1980 ABSTRACT AN EXPERIMENTAL STUDY OF LARGE COMPRESSIVE LOADS UPON RESIDUAI.STRAIN FIELDS AND THE INTERACTION BETWEEN SURFACE STRAIN FIELDS CREATED BY COLDWORKING FASTENER HOLES By Rajab Adaki Sulaimana This thesis investigates three related areas, namely (1) the evaluation of the residual strain redistribution around an initially coldworked fastener hole in a semi- thfinite plate subjected to large in-plane compressive loads; (2) the determination of a straight edge effect on a IOW’Of coldworked holes parallel to such an edge, and the possible creation of a strain climate at the straight edge which could lead to stress corrosion problems; and (3) the interaction of surface strain fields between the rivet holes. The strain distributions were obtained by a moire technique, with the aid of coherent optical processing and digital data reduction. Residual strain theories and other eXperimental works are discussed and compared to the results obtained in this investigation for the case of the initially cold- worked hole in a semi-infinite plate. Rajab Adaki Sulaimana Many useful aspects about the residual strain field near coldworked holes were observed. Specific important deductions include: a. In-plane compressive loads tend to decrease residual hoop strain parallel to the axis of applied load and to increase residual hoop strain transverse to the load axis. The effects of cycling of the in-plane loads were complex, but in general increased residual hoop strain around the fastener hole boundary. In-plane loads have little effect on radial strains. Coldworking a fastener hole or a row of holes intro- duces undesirable tensile strain climate at a plate edge, whereas peak compressive residual radial strains are shifted away from important areas near fastener holes. A minimum effective coldwork fastener hole separa- tion is about 2 hole diameters for a radial interfer- ence level of 6 mils. Below this limit, the effect of coldworking the holes diminishes the residual compressive strain field. The interaction of coldwork-induced strain fields with one another and with free boundaries is quite complex. Unexpected reductions and increases of residual strains are common with practical situa- tions involving several holes and plate edges. ACKNOWLEDGEMENT I wish to express my sincerest appreciation and gratitude to Professor G. Cloud, my thesis advisor, for his helpful information, encouragement, and immeasurable support throughout my study. Similar feelings are ex- pressed to Dr. J.E. Bernard, Chairman of my committee, for his thoughtful guidance during the course of my stay at Michigan State University. I would like to extend my warmest thanks to Dr. G. Ludden and Dr. L. Segerlind for serving on the Doctoral guidance committee. V Also, I want to extend grateful acknowledgement to the Materials Laboratory of the American Air Force for financial support of the project, and to the University of Malawi and to the Malawi Government for sponsoring my graduate program. A special tribute is owed to my wife Annette for her encouragement and understanding. TABLE OF CONTENTS Li St 0f Tables. 0 O O O O O O O O O O O O O O LiSt Of Figures I O O O O O O O O O O 0 O O 0 CHAPTER I. II. III. IV. INTRODUCTION . . . . . . . . . . . 1.1 Purpose and Motivation . . . . . . . 1.2 Organization . . . . . . . . . . . . DEVELOPMENT OF COLDWORKING-RESIDUAL STRAINS IN AND AROUND COLDWORKED HOLES . . . . . 2.1 Deve10pment of Coldworking . . . . . 2.2 Experimental Coldworking Procedure . 2.3 Residual Strains in and Around Cold- worked Holes . . . . . . . . . . . . 2.3.1 Introduction . . . . . . . . . 2.3.2 Analytical Approaches to the Problem. . . . . . . . . . 2. 3. 3 Discussion of Theoretical Studies. . . . . . . . . 2. A Overview of Experimental Studies . . MATERIALS AND SPECIMEN PREPARATION . . . 3.1 Material Specification and Specimen Preparation. 0 O O O O O I O O O O O 3.2 Moire Submaster Grating Production . 3.3 Grating Frequency Measurement of Submasters . . . . . . . . . . . . . 3.A Specimen Gratings. . . . . . . . . . 3. A. l Photoresists . . . . . . . . 3. A. 2 Photoresist Application. . . . 3.5 Printing and Development of Specimen Gratings . . . . . . . . . . . 3. 6 Deposited Copper Film Gratings . . . GRATING PHOTOGRAPHY AND OPTICAL DATA PROCESSING . . . . . . . A. 1 Specimen Grating Photography . . . . A. 2 Grating Recording System . . . . . A. 3 Optical Data Processing - Fundamental Concepts . . . . . . . . . . . . . . A.A Spatial Filtering for Moire Analysis iii PAGE WWW amnvx A8 49 5A 6A CHAPTER V. VI. VII. EDGE EFFECT STUDY . . . . . . . . . . VIII. CONCLUSIONS. . . . . . . . A.5 Creation of Moire Fringe Photographs. . A.6 Moire Data Reduction. . . . . . . . . . A.6.1 The Geometrical Approach. . . . . A. 6. 2 The Displacement-Derivative Approach. . . . . . . . . . . . M 7 Digitization of Moire Fringes - Radial and Tangential Strains. . . . . . . . . EFFECTS OF LARGE COMPRESSIVE IN-PLANE LOADS ON RESIDUAL STRAIN FIELD. . . . . . . 5.1 Introduction. . . . . . . . 5. 2 Overview. . . . . . . . . . . 5. 3 Experimental Procedure. . . 5.A Results and Discussion. . . . . . . 5.A.l Axial Hoop Strain Distribution. 5. A. 2 Transverse Hoop Strain Distri- bution. . . . . . . . . 5. A. 3 Radial Strain Distribution. . . . HOLE INTERACTION STUDY. . . . . 6.1 Introduction. . . . . . . . . . . . 6. 2 Experimental Procedure. . . . . . . 6. 3 Results and Discussion. . . . 6.3.1 Radial Strain Distribution. . 6. 3. 2 Hoop Strain Distribution. . . 7.1 Overview. . . . . . . . . . . 7. 2 Material and Experimental Procedures. 7. 3 Experimental Results and Discussion . 7.3.1 Hoop Strain Distribution. . . . 7.3.2 Radial Compressive Strain Distribution. . . . . . . . . . . 8.1 Introduction. . . 8. 2 EXperimental Apparatus. 8. 3 Summary of Results. . . 8.A Future Research . . . . REFERENCES 0 O O O O O O O O O O O O O O O O 0 APPENDIX 0 O C O O O O O O O O O O O 0 iv PAGE 68 7A 7A 77 80 82 82 82 83 89 104 116 125 125 126 127 127 1A0 1A9 1A9 151 153 153 167 179 179 179 180 185 186 190 LIST OF TABLES TABLE PAGE 3.1 Typical Diametral Mgasurgmentg at Three Angular Locations 0 , A5 , 90 from the Horizontal Line (SP2). . . . . . . . . . . . . 28 3.2 Typical Determination of Radial Interference (in) from Repeated Diametral Measurements (SPP). o o o o o o o o o o o 32 LIST OF FIGURES FIGURE PAGE 2.2.1 Schematic of coldworking using mandrel and sleeve (King process). . . . . . . . . . . 9 2.2.2 Schematic of the coldworking procedure . . . .11 2.2.3 The Instron coldworking set-up . . . . . . . .13 2.3.1 Geometry and coordinate system used in Coldworked Hole Theories . . . . . . . . . . .16 3.1.1 Dimensions and fiducial mark system of the in-plane compressive overload specimen: di- mensions in inches . . . . . . . . . . . . . .26 3.1.2 Dimensions and fiducial mark system of the "plate edge effect specimens": dimensions in inCheSO I I I O O O O 0 O O O O O O O O O .29 3.1.3 Dimensions and fiducial mark system of the "hole interaction" and "plate edge effect" specimen; dimensions inches. . . . . . . . . .30 3.2.1 Optical system for contact copying sub- maSter O O O O O O I O O I O O O O C I O O Q o 35 3.2.2 System for grating submaster production. . . .36 3.3.1 Optical creation of Fourier transform of in- put signal in the form of a transparency . . .Ao 3.5.1 Optical system for printing grating on Spec imen O O O O O O O O O O O O O O O O 0 g .45 A.2.l Schematic of Apparatus for grating photography. I I O O O O O O I O. O O O O O O .50 A.2.2 Equipment for grating photography. . . . . . .51 A.3.1 Arrangement of components of Optical spatial filtering system . . . . . . . . . . . . . . .55 A.3.2 Diffraction of light by two superimposed sine gratings having slightly different spatial frequencies. . . . . . . . . . . . . . . . . .57 vi FIGURE PAGE A.3.3 Formation of two-beam interference fringe pattern by light diffracted through 2 sine gratings having slightly different spatial frequenCieSo o o o o o o o c o o o o o o o o 59 A.3.A Diffraction of wide collimated beam by two sine gratings to form whole-field inter— ference pattern. . . . . . . . . . . . . . . 60 A.3.5 Diffraction of narrow beam by two bar and space gratings to form ray groups containing higher diffraction orders. . . . . . . . . . 61 A.3.6 Schematic used for coherent optical pro- ceSSingI I I I I I I I I I I I I I I I I I I 63 A.3.7 Example of optical spatial filtering to create bar grating from a grid of dots or crossed lines. . . . . . . . . . . . . . . . 65 A.A.l Optical system for spatial filtering in Fourier transform plane and creation of inverse trans- form of filtered image . . . . . . . . . . . 67 A.5.l Data processing system . . . . . . . . . . . 69 A.5.2 Baseline Moire fring photograph of specimen SP0 0 O O I I I o o o o o o I I O I o o O O o 72 A.5.3 Moire fringe photograph of specimen SPC after coldworking holes, 1,2 and A . . . . . 73 A.6.l Moire fringe geometry. . . . . . . . . . . . 76 A.7.1 Digitizer components . . . . . . . . . . . . 81 5.1 Apparatus for overload compressive test applicationI I I I I I I I I I I I I I I I I 85 5.2 Moire fringe photograph of specimen SP2 after 15,000 lbf load application. . . . . . . . . 86 5.3 Moire fringe photograph of specimen SP2 after 20,000 lbf load application. . . . . . . . . 87 5-4 Moire fringe photograph of specimen SP2 after 25,000 lbf load application. . . . . . . . . 88 5.5 Effect of in-plane compression on residual axial maximum hoop strain at a point on hole boundary . . . . . . . . . . . . . . . . . . 90 vii FIGURE 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.1A 5-15 5.16 5-17 PAGE Residual axial hoop strain distribution along several axes at different radial interferences 5.6 mils radial inter- ference. . . . . . . . . . . . . . . . . . . 91 Residual maximum axial strain distri- butions at various points on a radial line for zero mils radial interference . . . 92 Residual maximum axial strain distri- butions at various points on a radial line for 5.6 mils radial interference . . . 93 Measured residual axial h00p strain dis- tributions along several axes at different radial distances for 6.5 mils radial in- terference . . . . . . . . . . . . . . . . . 94 Residual axial h00p strain distributions along several axes for 7.2 mils radial interference (load 15,000 lbf) . . . . . . . 95 Residual axial hoop strain distributions along several axes for 7.2 mils radial interference (load 32,560 lbf) . . . . . . . 96 Residual axial hoop strain distributions along several axes at different radial distances for 7.2 mils radial interference (load 37,120 lbf) o o o o o I I o o o o o O o 97 Measured residual axial hoop strain distri- butions along several axes near a non- coldworked hole (load 18,600 lbf). . . . . . 98 Measured residual axial h00p strain distri- butions along several axes near a non- coldworked hole (load 23,360 lbs). . . . . . 99 Measured residual axial hoop strain distri- butions along several axes at different radial distances for 6.5 mils radial in- terference (load 28,1(fl+1bf) . . . . . . . .100 Measured residual axial hoop strain distri- butions along several axes near a non- coldworked hole (load 32,560 lbf). . . . . .101 Measured residual axial hoop strain distri- butions along several axes near a non— coldworked hole (load 37,120 lbf). . . . . .102 viii FIGURE 5.18 Effect of in-plane compression on residual transverse maximum hoop strain distributions at a point on hole boundary (Specimen SP2). . 5.19 Effect of in-plane compression on residual transverse maximum hoop strain distributions at a point on hole boundary (Specimen ClO). . 5.20 Measured residual transverse hoop strain dis- tributions along several axes at different radial distances for 6.5 mils radial inter- ference (load 5,000 lbf). . . . . . . . . . . 5.21 Measured residual transverse h00p strain distributions along several axes at different radial distacnes for 6.5 mils radial inter- ference (load 10,000 lbf) . . . . . . . . . . 5.22 Measured residual transverse hoop strain distributions along several axes at different radial distances for 6.5 mils radial inter- ference (load 15,000 lbf) . . . . . . . . . . 5.23 Measured residual transverse hoop strain distributions along several axes at different radial distances for 6.5 mils radial inter- ference (load 20,000 lbf) . . . . . . . . . . 5.2A Measured residual transverse hoop strain distributions along several axes at different radial distances for 6.5 mils radial inter- ference (load 25,000 lbf) . . . . . . . . . . 5-25 Measured residual transverse hoop strain distributions along several axes at different radial distances for 6.5 mils radial inter- ference (load 30,000 lbf) . . . . . . . . . . 5.26 Residual transverse hoop strain distributions along several axes for 7.2 mils radial inter- ference (load 18,600 lbf) . . . . . . . . . . 5-27 Residual transverse hoop strain distributions along several axes for 7.2 mils radial inter- ference (load 32,560 lbf) . . . . . . . . . . 5-28 Residual transverse hoop strain distributions along several axes for 7.2 mils radial inter- ference (load 37,120 lbf) . . . . . . . . . . ix PAGE 105 106 107 108 109 110 111 112 113 11A 115 FIGURE PAGE 5.29 Effect of in-plane compression on residual axial maximum compressive strain distri- butions at a point on hole boundary . . . . .117 5.30 Compressive (radial) surface strain distrié bution near a coldworked hole for 6.5 mils radial interference . . . . . . . . . . . . .118 5.31 Compressive (radial) surface strain distri- bution near a coldworked hole for 6.5 mils radial interference (load 15,000 lbf) . . . .119 5.32 Compressive (radial) surface strain distri- bution near a coldworked hole for 6.5 mils radial interference (load 20,000 lbf) . . . .120 5.33 Compressive (radial) surface strain distri- bution near a coldworked hole for 6.5 mils radial interference (load 25,000 lbf) . . . .121 5.3A Comparison of experimental results with theoretical predictions of Nadai (Al), Hsu and Forman (2), and Adler and Dupree(29).123 6.1 Specimen SPB Moire fringe pattern . . . . . .128 6.2 Moire fringe pattern for specimen SPB after coldworking hole #1 . . . . . . . . . . . . .129 6.3 Specimen SPB after coldworking all holes in order 1,2,3,A. . . . . . . . . . . . . . .130 6.A Moire fringe pattern of holes 2-A in specimer: SPC after coldworking in order 1,2,A. . . . .131 6.5 Fringe photograph of holes 1-3 in specimen SPC after coldworking in order 1,2,A,3. . . . . .132 6.6 Measured residual compressive strain distri- bution along an axis .1 inches from the centerline between holes 3 and A. . . . . . .133 6.7 Measured residual compressive strain distri- butions along an axis .13 inches from the centerline between holes 1 and 2. . . . . . .13A 6.8 Measured residual compressive strain distri- bution along an axis .2 inches from the centerline between holes 3 and A. . . . . . .135 FIGURE 6.9 6.10 6.11 6.12 6.13 6.1A 6.15 6.16 6.17 6I18 7.2 7-3 Measured residual compressive strain distributions along an axis .06 inches from the centerline between holes 2 and Booooooouoooooooooooooo Measured residual compressive strain distrubutions along an axis .13 inches from the centerline between holes 2 and 3. . . . . . . . . . . . . . . . . . . . . . Measured residual compressive strain distributions along an axis .06 inches from the cneterline between holes 3 and “I I I I I I I I I I I I I I I I I I I I I . Residual hoop strain distribution along several axes after the coldworking of hole #1 for 9 mils radial interference. . . . . . Residual hoop strain along several axes on the "eastern" side of hole #A for 6 miles radial interference. . . . . . . . . . . . . Measured residual h00p strain distributions; along several axes between holes 3 and A for 6 mils radial interference . . . . . . . . . Measured residual hoop strain distributions along several axes between holes 2 and 3 for 6 mils radial interference . . . . . . . . . Measured residual h00p strain distributions along several axes between holes 1 and 2 for 6 mils radial interference . . . . . . . . . Moire fringe photograph of specimen SPC after coldworking all holes (1,2,A,3). . . . Measured residual hoop strain.distributions along several axes between holes 2 and 3 for 6 mils radial interference . . . . . . . . . SPP after hole coldworking; grating parallel t0 aXiS N-So o o ' SPT after hole coldworking . . . . . . . . . SPP Moire fringe photography for compressive strain evaluation near plate edge; grating Parallel to aXiS w-E o o o o o o o o o o o 0 xi PAGE .136 ~13? .138 .1A1 .1A2 0143 .lAA .1A5 I146 .1A7 .15A .155 .156 FIGURE 7.4 7.5 7.6 7-7 7.8 7.9 7.10 7.11 7.12 7-13 7.1A 7-15 PAGE Residual hoop strain distribution along an axis tangent to the hole boundary for 8.9 mils radial interference. . . . . . 157 Measured residual h00p strain distributions along several axes near a plate edge at dif- ferent radial distances for 8.9 mils inter- ference (Specimen SPP). . . . . . . . . . . 158 Measured residual hoop strain distributions along several axes near a plate edge at dif- ferent radial distances for 8.9 mils inter- ference (Specimen SPT). . . . . . . . . . . 159 Residual hoop strain distribution along an axis 0.2A in. from a plate edge for 8.9 mils radial interference. . . . . . . . . . 160 Residual h00p strain distribution along an axis tangent to the hole boundary for 8.9 mils radial interference. . . . . . . . 161 Measured residual hoop strain distributions along several axes near a plate edge at dif- ferent radial distances for 8.9 mils inter- ference (Specimen SPE). . . . . . . . . . . 162 Residual hoop strain along plate edge for 8.9 mils radial interference. . . . . . . . 16A Peak residual hoop strain along radial line from hole boundary to plate edge . . . 165 Measured residual h00p strain distributions along specimen edge for various coldwork Situations I I I I I I I I I I I I I I I I I 166 Moire fringe photograph used in the evalu- ation of radial compressive strains near a plate edge (Specimen SPC) . . . . . . . . . 168 Residual radial strain from hole boundary to plate edge . . . . . . . . . . . . . . . 169 Residual compressive (radial) strain between the plate edge and hole #1 after coldworking the hole #1 only for 6 mils radial inter- ference . . . . . . . . . . . . . . . . . . 170 xii FIGURE 7.16 7.17 70‘18 7.19 7.20 7.21 PAGE Residual compressive (radial) strain between the plate edge and hole #1 after coldworking at 6 mils radial interference. . . Residual compressive strain distributions after coldworking. . . . . . . . . . . . . . . Residual compressive strain from hole boundary to plate edge for multi-hole pattern SpeCimen o o o o o o o o o o o o o o 0 Residual compressive strain distributions after coldworking holes 1,2 and A. . . . . . . Residual compressive strain distributions for holes 2 and A after coldworking all holes. Residual compressive strain distributions after coldworking all holes. . . . . . . . . . xiii 171 172 173 174 175 176 CHAPTER I INTRODUCTION Studies of fatigue crack initiation and growth in- dicate that the distribution of residual strains (stresses) produced by the drawing of an oversized mandrel through a joint fastener hole in a machine assembly markedly improves the fatigue life of the structure (30). This procedure is particularly useful in the aerospace industry where one of the major problems common to today's aircraft is that of structural fatigue beginning at joints. To counter this problem, two of the techniques that have evolved are the fatigue improvement fastener systems--(1) the IFF (in- terference fit fastener system) and (2) the C/W (cold- working fastener system). Structures in which flaw-induced fracture may be responsible for failure are easy to find. Among these are tanks, pressure vessels and turbines. In a turbine, for instance, bolt holes in high speed rotating parts, such as the engine fan and compressor disks, act as stress raisers. The local stresses and strains around the hole are higher than the nominal values in the bulk of the ma- terial. Flaws, which are always induced by the hole 2 generation processes, form a focus in a high-stress region for the beginning of crack growth and eventual failure. Most engineering structures are primarily load- transmitting devices in which high ductility allows yield- ing in small regions of stress concentration under static or cyclically changing stresses. Thus, ductility and strength are the important considerations in material sel- ection in these situations as an alternative approach to the problem of structural fatigue (36). The material strength is utilized in carrying the imposed loads,where- as stress concentrations are blunted by plastic flow so that crack initiation and failure of the machine part is prevented. This design approach, however, is relatively uneconomical (A0). The manufacturing process of drawing an oversized mandrel through the fastener hole is considered to be one of the most economical and effective (45). The essential principle is the same for the two classes of the fatigue improvement fastener systems. That is, the material around the fastener hole is coldworked and the surfaces adjacent to the hole are left in a state of residual compression. In order to utilize prestressing effectively, one must understand the relationship between interference in- duced stress and the subsequent redistribution of stress by applied external loads. Analytical tools are helpful in understanding interference-induced stress in a few simple cases, but in 3 practical applications, experimental techniques are needed to gain the required insight. 1.1 Purpose and Motivation The objective of this investigation is to use empiri- cal tools to further our understanding of fatigue-rated cold- work fastener systems, particularly in situations which pose intractable analytical problems. Three useful application problems are studied, viz.: (i) (ii) The effects of large compressive in-plane loads on the residual strain field surrounding a coldworked fastener hole. The interaction between the surface strain fields which are created by coldworking a row of holes which are parallel to and near the straight edge of a semi-infinite plate (row of rivet holes). (iii) The effects of the straight edge of the semi- infinite plate on the surface strain field and establishing whether coldworking a hole creates a strain climate that could lead to stress corrosion on the straight edge. 1.2 Organization of Dissertation The next chapter deals with the development of cold- working and residual strains in and around coldworked holes. 4 Chapter 2 also contains some of the experimental procedures pertaining to coldworking procedure and an overview of the analytical and eXperimental approaches to the problem. Chapter 3 presents material Specifications and specimen preparations procedures. Chapter A discusses grating photography and Optical data processing. The fifth chapter tackles the first phase of the project, dealing with the effects of large in-plane com- pressive loads on the residual strain field. Chapters 6 and 7 deal with the results of the in- teraction of the surface strain fields for a row of rivets, and the edge effect on the residual strain climate for the multi-hole pattern in an infinite plate. Chapter 8 presents the conclusions. CHAPTER II DEVELOPMENT OF COLDWORKING-RESIDUAL STRAINS IN AND AROUND COLDWORKED HOLES 2.1 Development of Coldworking The fatigue-strengthening effects of coldworking were accidentally discovered by the Buick Motor Division of General Motors in 1929 (35) where it was noticed that valve springs which had been grit-blasted to remove scale possessed superior fatigue properties. Today this technique, commonly known as Shot-peening, is widely used with gears, connecting rods and Springs of all kinds. Forces imparted by the shot-peening Operation leave the surface material with a residual compressive pre- stress, whereas the material in the subsurface goes into a state of residual tension pre-stress. Shot-peening is by no means the only method Of im- parting residual stresses to a material. In general there are three ways of producing residual pre-stresses, (i) chemically, (ii) by heat treatment and (iii) by mechanical treatment 6 Chemical methods alter the material composition of the surface layers. Carburizing and nitriding are two of the common processes used in surface hardening of ma- terials. An example Of the second method is flame hardening. Unlike the chemical method, this process does not alter the chemical composition of the material. Rather, its metal- lurgical structure is changed. Coldworking, rolling, peening and coining are mech- anical treatments for creating residual stresses in a ma- terial. These residual stresses (strains) can be thought Of as unevenly distributed mean stresses (strains), and they can be viewed as static values upon which alternating loads are to be superimposed. It was briefly mentioned in Chapter I that the two fatigue enhancement methods for holes are: (1) the IFF, (or Interference Fit Fastener system) and, (2) the C/W, or coldworking system. The IFF is Older than the C/W. An example of the IFF is the Taper-Lock bolt. The C/W system seems to be slowly replacing the Taper-Lock bolt because the Taper-Lock is highly sensitive to fastener hole prepar- ation and fastener installation anomalies. Some of these anomalies are installation of a fastener with a fastener- to hole interference level below minimum specifications; and-hole surface conditions--rough finish, scratches, rifling, ovality and bell mouthing. In addition, the 7 preparation Of tapered holes requires great care and skill, and hole and installation factors must be confirmed by ex- tensive and frequent inspection (45). There are basically four different types of C/W fasteners, viz.: (i) the seamless sleeve (ii) the Split sleeve (iii) the EXL Lockbolt and (iv) the "Op-One" In the seamless-Sleeve method Of coldworking holes, a pilot hole is first drilled and then reamed to Size. A mandrel and sleeve are then inserted into the hole from either side in the case of the split sleeve method and from the head side in the seamless technique. With the help of a puller nose piece, the mandrel is installed into a puller and the mandrel is pulled through the Sleeve and hole. In the Split sleeve technique, the split Sleeve is removed from the pilot hole. Final reaming of the hole is made and, after countersinking it, the fastener and nut are installed. Neither removal of the Sleeve nor final reaming and countersinking Operations are necessary in the seamless sleeve method. (This will be discussed in detail in section 2.2). Patents for the seamless and Split Sleeve methods are held by J.O. King, Inc. and Boeing Aircraft, respectively. 8 Op-One, a process based on a patent held by Lockheed- Georgia Company, is intended as a means of automating the J.O. King seamless sleeve method. A distinctive feature of this process is that part of the mandrel serves as a fastener when the mandrel pull stem is broken away from the fastener portion. The EXL Lockbolt, patented by Huck Manufacturing Company, is similar to the "Op-One" in that the mandrel por- tion serves as a fastener when the stem breaks Off. Pilot drilling is followed by drilling the hole to size. The "EXL" is then inserted into the hole, a puller is attached and the mandrel pulled through. The pull stem portion of the man- drel is broken Off and discarded. 2.2 Experimental Coldworking_Procedure The coldworking procedure and apparatus studied in this research is the seamless sleeve method marketed by J.O. King, Inc., 711 Trabert Avenue, N.W., Atlanta, Georgia, 30318. This system was chosen because Of its apparent advantages over the other procedures in hole pre- paration and fastener installation. Figure 2.2.1 shows a Schematic of this coldworking process. The mandrels used are part numbers JK65AO-O6-188 to 192. These oversized mandrels cause plastic flow at the edge of the hole when they are pulled through, and leave behind residual compressive stresses that aid in the fatigue life improvement of the structure. Mandrel Drawing Head Fastener Sleeve \ N \ \ \_ /// Fastener ‘ W/II Anvil “ q Tapered Mandrel Figure 2.2.1 Schematic of coldworking using mandrel and sleeve (King process) 10 In the experiments, diametral measurements of the tapered mandrels were made before mandrelizing. Likewise, the thickness Of the sleeves that were to be inserted into the hole were measured. This was generally accomplished by first measuring their inside and outside diameters with a ball gage and a micrometer. The difference was Obtained and used in the computation Of radial interference Of the hole. The radial interference was computed as: Mandrel diam 2 + Sleeve Thickness - Hole Radius. Uncertainties encountered in the determination of radial interference come from three sources. First, the quantity sought is the small difference between the meas- ured values Of large quantities. Second, when the mandrel is pulled through the specimen, a degree of elastic spring- back occurs. Third, the sleeves come with their own anti- corrosion coating and lubricant on the outside and inside. Since the lubricant coating has uneven thickness, the sleeve thickness is not constant. Two set-ups were employed in this coldworking pro- cedure. The first is Shown in Figure 2.2.2. Only one specimen was coldworked on this set-up, where pulling force is provided by a hydraulic ram in a small table-top testing frame. The rest Of the speciments were mandrelized in an Instron. 11 {—Mandrel g—Sleeve with Washer Base (Specimen ) 1U Clamp—g 0) @@ F1 are 2. 8 2.2 Schematic of the coldworking procedure 12 In the first set-up, a sleeve that was carefully cut to match the thickness of the specimen was first in- serted into the hole with its collar on the unpolished side Of the Specimen. The Specimen was then laid on the base with the grating side upwards and a mandrel inserted into the hole, small end first. The ram Of a double acting 2-ton capacity hydraulic jack was then clamped to the threaded end of the mandrel underneath the bench. The hydraulic jack was then pressurized to pull the mandrel through, thus cold- working the Specimen. The sleeve for this particular specimen was not lub- ricant coated, SO molybdenum disulfide grease (Molycote) was applied to the stem of the mandrel to prevent seizing and galling of the hole Sides. The other set-up used was an Instron testing ma- chine, Figure 2.2.3. .A Sanborn TwianiSO-Cardette recorder was used to monitor the mandrel pulling force via strain gages attached to a tension rod linking the mandrel to the machine's crosshead. This force was recorded as a function of the mandrel diSplacement during the coldworking Operation. The mandred drawing rate was set at 0.5 cm/min. In this investigation several coldworking levels were used. The values chosen depended on the mandrel sizes available. Figure 2.2.3 The Instron coldworking ‘sat-up. 1A 2.3 Residual Strains_In and Around Coldwgfid lees 2.3.1 Introduction Although strength and stiffness are customarily computed based on the elastic properties of the member, it is a well-known fact that at some highly stressed areas, for example, around fasteners in aircraft structural com- ponents, the stresses do exceed the theoretical elastic limits of the materials without necessarily causing struc- tural damage (5). One of the major problems facing the structural designer is to Obtain the most efficient strength- tO-weight ratio around these highly critical areas. The problem is highly complex and does not lend itself to straight forward analytical solutions. This is not to say that analytical efforts to under- stand the problem are lacking. Rather, theoretical solutions have been advanced by various authors. These will be dis- cussed in the next section. 2.3.2 AnalyticalgApproaches to the Problem This section presents an overview of the anayltical work which has been published in the general area of cold- working holes. None of these theories apply directly to the problem under investigation here since the present problem is highly nonlinear and because of its complex geo- metrical boundary conditions. 15 Probably the simplest of all analytical theories is the case where the mathematical assumptions boil down to treating the problem as being linear. Deductions for the finite specimen are then based on linear elasticity. In some cases, the specimen is treated as an infinite Sheet. treating the problem Of the hole in the finite- width specimen as a small hole in an infinite plate with a state of plane stress existing everywhere in the sheet on loading the specimen (A0). Some theories assume that the material unloads elastically with no reverse yielding when the mandrel is drawn all through. Still other theories neglect work- hardening effects during the coldworking of the specimen (2). Figure 2.3.1 presents a simple Specimen model which is of some importance in practice. The fundamental equa- tions of elasticity in the given coordinate system take the following form: a'e-ar - rda'r/dr = 0 (201) vflfixfllis the differential equation of the equilibrium state for an element of volume in the wall of the tube. Here 09 is the circumferential stress, r is the distance from the axis of the cylinder, and a is the radial stress. 16 Figure 2.3.l Geometry and Coordinate System used in Coldworked Hole Theories 17 Equation (2.1) is applicable to all states Of the material be it elastic or plastic. The assumption Of an infinite specimen would then imply that "b" is infinitely large and thus a<< b. Because of the loading nature Of the hole, assuming uniform radial mandrelizing the problem Simplifies to being symmetric about the longitudinal axis.‘ Thus the strains are given by (38): r—au 3? (2.2) 6:11 6— r (2.3) where u is the radial displacement of an element origin- ally located by r,a . The radial displacement u satisfies the compatibility equation. r dr (2.A) For an elastic radial displacement, Little (21) shows that the stress, strain and the displacement fields are given by: “r = as a "3 N 0‘ (2-5) (2.6) (2.7) F10 b2 l—J (2.8) (2.9) where 1+v +_(l-u_) a a b2 hole radius £1) ll radius of the stress free external surface YOung'snmdulus Cirilo‘ II a the radial displacement at r=a V = Poisson's ratio Plasticity considerations must be made when the radial displacement exceeds U5, where Ué = 9y 1+v + l-ll a E9 a E 1 + b SE :3 (2.10) where 9y is the yield stress of the material as determined in a standard tensile test. l9 Swainger considered this problem with the assumption that the large plate with a circular hole was in a state of plane stress (A3). .Furthermore he assumed uniform radial pressure loading on the hole and yielding Of the plate ma- terial according to the energy Of distortion theory--the Mises-Hencky criterion: 202 = (09 - 0r)2 2 y ) + ( a - (7)2 (2.11) a ._ + ( 9 oz z r where 09 is the hoop stress or circumferential stress at = the longitudinal stress and or = the radial stress The details of his method Of approach and all the assump- tions that he made can be found in reference (A3). Extension of these ideas, which form the transition from elasticity to plasticity, is based on different theories of plastic flow. For our purpose here, it suffices to con- sider only two of these: viz., the maxium shear and the energy Of distortion theories. According to Tresca, or maximum shearing stress theory, yielding will begin when the maximum Shearing stress is Tmax = % ( ”max — 0min) = % 0y (2.12) where “max = maximum principal stress, 0min = minimum principal stress, and a = the yield stress Of the material as determined y in a standard tensile test= twice the flow stress. 20 According to (2.12) plastic flow occurs Whenever the difference between the largest and smallest principal stresses is equal to the flow stress, Say. In the specimens under consideration here, the long- itudinal stress is zero, the radial stress or is always negative and the hOOp stress or circumferential stress is always positive. This is true during mandrelizing only. Afterwards a 0 is the largest principal stress and “r is the smallest. is negative although 60 is positive. Thus “a The condition of yielding during coldworking can be eXpressed as (2.12) or simply 00 - Or _ 0y (2.13) According to the Mises-Hencky or energy of dis- tortion theory, the condition Of yielding is 2 ayz = (”9- ar)2 + (‘79 - 0Z)2 + ( 02- or)2 (2-14) But because the longitudinal stress at = 0, Eq. (2.1A) reduces to 2 _ 2 2 2 - 2 0y _ (GO-or) + 09 + ”r (2.15) Nadai (Al) utilized a linearized approximation form Of this energy of distortion theory (Mises-Hencky criteria) to solve the plate problem. His other assumptions were (1) uniform pressure at the edge of the hole and (2) a perfectly plastic material response. He cal- culated the stress and displacement fields to be: Qr " M (-l + 2 ln _JE_) (2-15) {5' rP 09 :1 (1+ 21n _§_) (2.17) \f3— rP U = U' ('3 a r. (2+ 1n 1‘ }1 (2.18) {2 rP where rp = the interface between the elastic and plastic regions. In l9A8, however, S. Taylor (A20 developed essent- ially the same equations as Nadai's for the case of a thin plastic sheet. Likewise Hsu and Forman (2) in 1975 making use of the Mises-Hencky yield criterion and assuming uniform pressure at the hole and a Ramberg-Osgood characterization of the stress-strain curve Obtained basically the Nadai formulae. They considered an infinite sheet with a circular hole sub- jected to internal pressure, P. Their solution was based On J2 deformation theory together with a modified Ramberg- Osgood 1aw, viz.: for (05 5 . and 6= “/E y n-l a e = JL. 6 for a' 2 y (2.1 (E ) I I 9) 0' y where E, “y and n are the Young's modulus, the yield stress and the parameter defining the shape of the uniaxial stress- strain curve and is equal to or less than 17- 22 Carter and Hanagud (1H3 in 197A attempted the solu- tion of this problem based on the Tresca yield condition and elastic-plastic material behavior. Based on these con- ditions they proceeded to seek a relationship between the displacement and the elastic-plastic boundary and arrived at the result: -2 (1- v) a 1n (:2) (2.20) a Besides the analytical work mentioned here, numerical and finite element methods have been attempted. Adler and Dupree (29) developed a finite-element model idealization to determine the stress states for a cold- worked fastener hole. They used a Ramberg-Osgood relation: 2p = (E/K)n '(2.21) in their develOpment of the constitutive behavior Of the material.‘ Here Ep is the equivalent plastic strain for an equivalent stress state 3 , a state of stress that comes from employing the Von Mises yield criterion Eq. (2.12) for the case of plane stress and is defined as (2.22) 23 Parameters K and n took the eXperimentally determined values Of 87.5 ksi and 5A respectively. Even though their finite element analysis attempted to model a 0.25 in. (6.35 mm) thick 7075-T6 aluminum Speci- men Similar to the ones employed in this study, the loading conditions differed. Their program was based on uniaxial tension loading after coldworking, whereas, for this study compressive loads were considered with coldworking levels slightly higher than those used by Adler and Dupree. Never- theless, their results are shown in Figure 5.3A to permit a comparison of the results later. The interaction between surface strain fields at the edge of a plate and the effect of that edge on the strain field have no analytical or numerical solution in the literature. 2.3.3 Discussign of Theoretical Studies None of the analytical work mentioned above pre- dicts the strains very well. Furthermore, the general under- lying assumptions for all these theories, that the plate is infinite in extent with a state Of plane stress, is not satisfactory, especially in the case where the fastener hole is located close to a plate edge. It is also noted that there is some degree Of var- iation in the results obtained by the earlier investigators 2A due to differing assumptions concerning the constitutive material representation and the assumed mode Of yielding. Nevertheless for modeling practical coldworking Operations the analytical work is useful,providing reason- able predictions in areas removed from the hole boundary. 2.A Overview of EXperimental Studies The experimental work that has been performed in this area is relatively recent. Adler and Dupree (29) in 197A evaluated the stress and strain distributions around an initially coldworked hole in a plate and the subsequent redistribution Of the stresses and strains when the plate was subjected to a uniform tensile loading. Sharpe (AA) and Chandawanich and Sharpe (A0) in- vestigated the change of residual strain during crack in- itiation, the stress intensity factor for the crack eman- ating from a circular hole and the strain ahead of a crack tip. Cloud (2A) 1978, measured surface strain distributions in the vicinity Of holes in % in (6.35 mm) thick alumian1 alloy plate which had been coldworked to various degrees by the J.O. King commercial process. He focussed his at- tention mainly on radial strains, and measuring hOOp strains at two coldworking levels. CHAPTER III MATERIALS AND SPECIMEN PREPARATION 3.1 Material §pecification and Specimen Preparation The material used in this investigation is struc— tural material from a sheet of 7075-T6 aluminum alloy % inch (6.35 mm) thick made by Aluminum Company of America (ALCOA). There were three types of Specimen. Part One of the exPeriments was a study of the effects of large in-plane compressive loads upon the residual strain field surrounding a coldworked fastener hole. Two specimens, measuring #.5 in. (11.43 cm) long and 2.5 in. (6.35 cm) wide, were fabricated according to the design shown in Figure 3.1.1. The length dimension was larger than the width so that the moire grid printed on its surface would not be damaged during load ap- plications. The hole design diameter was 0.261inches (6.63 mm). Various methods of hole preparation, including dril- ling with honing and drilling with reaming, were tried out in the beginning of the investigation. The best procedure involved drilling the specimen hole undersize and then boring to size with an adjustable boring tool. H019 size 25 26 mucosa ca mGOHmcmsaw mamaaomam vmoaum>o 0>Hmmmuasoo mamaalcw mnu mo amumhm xuma Hmaozwfim new maOHmaoEHa H.H.m ouswwm .V. 9&1 .wN. u o j---‘ lllllll . —.-----’-- mmv. “ 27 checking was done with an adjustable ball gage and micro- meter and a microsc0pe. Table 3.1 shows the hole diameter measurements. The figures in the table indicate that this measurement deviated from the nominal diameter by : 8'888: :3 E:g'8égggg A microsc0pe equipped withaulx-y stage was used to verify the diametral and fiducial measurements of the speci- mens. Difficulties in locating the edge of the hole in this fashion led to differences in the measured values. Second and third specimens 'were designed to deter- mine the effects of an edge upon the surface strain dis- tribution and/or the interactions between the surface strain fields which are created by coldworking two or more fastener holes which are near each other. The configuration and di- mensioning of such specimens (including a multi"hole pattern) are shown in Figure 3.1.2 and 3.1.3. In these specimens, attention was focused upon the edge distance/diameter or e/d ratio. Here "e" is defined as the distance between the edge of the plate and the hole center. An e/d ratio of 2.0 is used in the design of aircraft structures as a working min- imum,and it is ‘believed that lower ratios degrade fatigue life (24). The e/d ratios used were chosen to be on either Side of the threshold value of‘e/d = 2.0, viz., e/d = 1.8, 9/6 = 2.25, and at the threshold value of e/d = 2.0. 28 TABLE 3.]. TYPICAL DIWTEAB MEASUREMENTS AT THREE ANGU'LAR 0 5 LOCATIONS AND 90 FROM THE HORIZONTAL LINE (SP2) HOLE DIAMETER TRIAL 0° .55° 90° 1 0.2615 0.2615 0.2610 2 0.2616 0.2606 0.2611 3 0.2620 0.2611 0.2610 4 0.2608 0.2612 0.2605 5 0.2610 0.2619 0.2611 6 0.2618 0.2610 0.2610 7 0.2619 0.2622 0.2612 8 0.2617 0.2619 0.2610 9 0.2615 0.2620 0.2609 10 0.2620 0.2610 0.2610 Average Hole Diameter = 0.2613 (6.637 mm) (Measurements by microscope) 29 F 3.5 ). l 1 A + Y ‘ 2.5 E - ‘6’- l8 D= .26l r 3.5 -————> I Y fL .522 Y ‘ 2.5 E '5- 20 D= .26l “‘fi 3.5 -—>- I I A + Y . 25 E D - 2.25 D ' .26l pm. 549. Effect Specimens Figure 3.1.2 Dimensions and fiducial mark system of the "plate edge effect specimens"; dimensions inches A N .337 -—- -- -- —— +——-.Lfi I - __ _. I“; A J (_-:| 2 3 43 E 402 T"- I ”””””” "T" E 2.5 w T A Hole Separation =I.75 D D= Hole Diameter Fi Sure 3.1.3 Dimensions and fiducial mark system of the "hole inter- action" and "plate edge effect" specimen; dimensions inches 31 The preparation of the holes followed essentially that described for the in-plane load study. The main goal was to obtain holes which were not tapered and whose sides were square and straight so as to permit easy determination of the amount of coldworking that was to be subsequently imposed. Table 3.2 shows a representative sample of the diametral measurements for this part. Reference marks were scribed on all the specimens. These fiducial marks took various forms as the eXperiment progressed and as more eXperience was attained. The first method adopted was the machinists' technique of gaging and scribing with a vernier height gage placed on a smooth flat surface. To avoid disturbing the strain distributions the scribed marks were made extremely light. These marks tended to disappear in the final photographic prints of the speci- mens. For the majority of the specimens, a number of "natur- al" fiducial points, such as edges far removed from the in- fluence Of the mandrelizing process, were identified with "Prestype" lettering to aid as fiducial marks. In addition, line rulings on master gratings printed on the specimen were included and located as part of the fiducial marks SYStem. Since it was always possible to locate at least one of'these markings, these several forms of fiducial marks tended to facilitate data collection. In some cases, the iredundant markings provided a good way 0f double-cheeking 32 TABLE 3.2 TYPICAL DETERMINATION OF RADIAL INTERFERENCE (in.) FROM REPEATED DIAMETRAL MEASUREMENTS (SPP) _:§leeve Diameters Trials gigggiir (in) Eggigier ggggigzr ggigeter 1 0.2590 0.2385 0.2546 0.2615 2 0.2585 0.2375 0.2539 0.2616 3 0.2595 0.2385 0.2540 0.2617 4 0.2590 0.2375 0.2550 0.2615 5 0.2594 0.2376 0.2540 0.2615 6 0.2580 0.2372 0.2551 0.2612 7 0.2582 0.2380 0.2549 0.2616 8 0.2590 0.2379 0.2550 0.2605 9 0.2583 0.2381 0.2545 0.2616 10 0.2587 0.2375 0.2542 0.2619 Average sleeve thickness = 8.3 mils (0.211 mm) Average outside diameter of sleeve s 0.2552 in. (6.48 mm) Average inside diameter of sleeve = 0.2378 in. (6.04 mm) Mandrel average diameter = 0.2587 in. (6.57 mm) Radial Interference = 6.2 mils (.158 mm) (Measurements by microscope) 33 specimen measurements from the enlarged photographic prints of moire fringe patterns. When the diametral and fiducial measurements were completed, the specimens were lapped on.a Laplfiaster model 12C machine manufactured by the Crane Packing Company of Illinois. Before machine lapping was introduced the speci- mens were successively lapped with a 350 or 240 emery cloth followed by a 400 and 600 grit metallurgical preparation paper dipped in mineral spirits to serve as a lapping fluid. These operations were done on a flat surface. The flat lap- ped surface of each specimen was then polished. The final polishing was performed on spinning metallurgical polishing wheels with 1 andiflmn1.3 microns alumina particles suspended in oil as the abrasive. Acetone was then sprayed over the surface to degrease it. The specimen was then ready for printing of a moire grating on the polished surface. 3.2 Moire Submaster Grating Production The production of submaster 00pies of high frequency gratings has been eXplored and discussed by several authors including Luxmoore and Herman (18), Holister (37) and Cloud (24). The 1000 lpi (39.4 lines/mm) master gratings used for the production of the various submasters were purchased from Photolastic Inc., Malvern, PA, and from Graticules 34 Limited, Sovereign Way, Towbridge, Kent, U.K. The setaup for reproduction is shown in Figure 3.2.1. The figure indicates that the light source was a Mercury arc lamp placed approximately 11 in. (27.94 mm) from a green Kodak Watten filter #74. A plane mirror folded the light beam through an angle of 900. Between the mirror and the master plus photosensitive plate assembly was placed a collimating lens having 39.37 in. (1 meter) focal length. Both Kodak HRP and Kodak 649F plates were tried for submaster produc- tion. Exposure time of .5 sec. to 1 sec. gave the best results with develOpment times of approximately 3.30 min. in D-8. Fixing was done in Kodak Rapid Fixer solution for about 5 minutes. To establish correct grating mis-matches, it was found necessary to produce a set of submasters other than the 1:1 contact c0pies described above. Four different grating groups were made. The first category comprised those submasters clustered around 1000 lpi (39.4 lines/mm). The remaining three groups were clustered around 960, 980, and 1500 lpi (37.8, 38.6, 59.1 lines/mm). In each cate- gory, spatial frequency deviations ranged from i 2 to i 8 lpi (.1 to .3 lines/mm). Figure 3.2.2 shows the submaster grating production set-up. A Schneider Xener 1:4.5 350 mm focal length lens at f/ll was used,and a Besler enlarger light head served as a source with a circular diffuser placed between the light source and master. Although the resolving power of 35 1r ‘ .ou_oz\ >35o3< 32a one .3362 umummansm wcH%aoo uomucoo you Eaumhm Hmofiuao H.N.m muawfim «com 2:66:30 e e r a 4! Acflfibww 1 .25 I... III II outaom 9:04 0.4 o: :03 OON 36 coauosvoum Houmaensm waaumuw you smum%m ~.N.m shaman socom toaasm tomato ecu 22a .8332 Sac... 3:33. 3:95; O O W 22a oaoEoo ouSom 29... .33: amalgam 223:8 33:5 37 the whole system was barely adequate, working submasters were obtained. Most of the photo c0pying was done on Kodak HRP (High Resolution Plates) eXposed for 57 sec. and developed for 2 minutes in D-8 and fixed for 3 minutes in Kodak Rapid Fixer. Kodak type 649F spectroscopic plate was also used but it did not seem to work as well for this purpose as the Kodak HRP plates. For high-density c0pying, precise focusing of the image is crucial. A 50X microscope made by Bausch and Lamb was used as an aid in focusing. The grating pitch values mentioned above are a multi- ple of the fundamental spatial frequency of the Specimen grating images as determined by the 1000 (lpi) (39.4 lines/ mm) grating divided by the base magnification used. In ad- dition to this base pitch,negative and positive frequency mismatches are introduced by changing the base magnifica- tion slightly. The procedure for focusing at the correct magnification is as follows. After the rough determination of camera-to-master separation, an image of the master was brought to a focus in the back of the camera on ground glass. At this point a rough check on the desired submaster fre- quency was made. The image was focused "permanently" in a Plane Which remained fixed with respect to the lens. The ground glass was then removed and, by use of the microsc0pe, the precise location of the ariel image was established. 38 With the micrOSCOpe in place, a blank undevelOped photo-plate having scratches in its emulsion was put in the back of the camera. By moving the camera plate holder back and forth, the scratches on the plate were brought into the same focal plane as the master image. Best results were obtained at an aperture of f/ll. Vignetting and cosine“ light fall-Off were troublesome. The quality of the submaster was always checked during processing by observing its diffraction characteristics under a pen pocket light or by holding ,it Lqpto bright room flurescent light. In a number of cases the quality of the finished submasters was checked by observing the grating lines under a micros00pe. It was important that the table supporting the camera had to be as vibration-free as possible. Air bags were used to isolate the cast iron bench from mechanical disturbances. 3-3 grating Frequengy'Measurement of Submasters Strain determination by use of the manufactured submasters requires knowledge of the Spatial frequency of master and submaster. Initially the spatial frequency of a submaster was determined by means of dial gage indicators and a.microsc0pe. Repeated measurements by this method tended.to vary widely. Since an error of even 1 2 grating 39 lines/1000 lpi could result in strain measurement error, the method was discontirnied. Next, the diffraction characteristics of the sub- master were used in the (ietermination of their spatial fre- quencies. Figure 3.341 shows the basic Optical system. The first lens collimates the beam.and the second lens acts as a transform lens. .An array of images of the source ap- pear in the focal plane of'the field lens. Each of the image sources is comprised of all the rays that emerge from the pair of grating in a specific direction. This will be explained in detail in Section 4.3 These images on the screen are in the form of a dot pattern called "ray groups" or diffraction 0rders-—thus are obtained the 0, 1,1, 1,2, . . . diffraction orders. Separation between successive images is approximately AF where d A is the wavelength of the monochromatic light used, F is the focal length of the decollimating lens, and, d is the basic pitch of the gratings. The laser employed was a He-ne HN7 Laser by Jodon Engineering of Ann Arbor, MI. With some modifications the distance between the diffraction orders ‘WaS calculated from the formula: ———§—- (3-1) 40 honoumqmamuu a we show on» 5 .3835 355 mo Eommamuu “mans—om mo coaumauo Hmowuao H.m.m shaman €22.50 . « mzua accumz. 050500 \a. \ \r— “K A \ : K t \ \\. X \ T 56 diffraction of light by an amplitude grating, and finally the lens as a Fourier transformer. When a coherent monochromatic laser beam is made to transilluminate a grating, part of the light suffers a de- viation from its original path--the optical axis. The de- viation in this case will depend on a number of factors, viz.: the wavelength of the monochromatic light, the grat- ing frequency and the angle of incidence. The simplest example is that of a sine grating. The light transmittance, T of the grating is given by T = To (1 - K Sin 21Tx) (4.1) p = TO (1 - K sin 2N f) and (4.2) the deviation of the diffracted beam is given by: e = sin—13L (4.3) p where p = grating period, x = distance in the grating plane, f = grating Spatial frequency, and A is the wavelength of light. This idea can be extended to a two—grating assembly instead of one. The component beam deviations of each of the two grating transparencies will be as shown in Figure 4.3.2. Altogether, there will be five different ray groups that emerge. The outer ray groups, orders 1 2, are not of much interest in moire work, having come from a Single ray diffracted at each one of the two gratings. 0f considerable 57 SN .wamv moaosoavoum :3st opossum: Dorm“? wags: mwawusum mafia monogamous 25 .3 ”Em: mo cowuomumgn a.miu 0.»:me 622.519 02:4m0 mwzi mmmm353: mafia: mwaauwuw scam N swoops“. wouomuwwww H n auauuwn awcwuw mucouowuouaa awonuoau mo coaumfiuom m.m.q ouswwm Eo muczEu wed}. 44.3 130cc 23. kc mauou b< own; 3» co «zuztu 239.3 0.5020 >48 .0 >420 to... w><¢ wbwdaiou a It] / x 5... 3550933 2.2382. 3.2% 132.55 flux... to form whole-field interference pattern (Ref. 24) Figure 4.3-4 Diffraction of wide collimated beam by two sine gratings 61 remoumwww muamuo coauomummav Harman wowsfimusoo museum map Show Hume woman was nan can an Swan zones: mo aowuomummwn m.m.s shaman nu mate I 6‘ _-d:o¢o sates 1 o ozcamo - m n «:36 u, .3. «To ”IF,- 0 Some 9.8 -W‘ . >3. 5.362. . . . ........o "R ~uu.~.0 \ :::::: u attritox an 1r :\\:amMem0: K xxxeu. .. 8.25845 _+ Some \Auméo 62.04% 62 diffraction pattern. It is convenient to confine discussion to Fraunhofer diffraction for simplicity. The mathematical details of the Fraunhofer diffrac- tion pattern of the input signal distribution are amply ex- plained by Thompson (26) and Chiang (28). This explanation is based on their work. This Fraunhofer pattern in this complex field is a Fourier transform of the input signal. For a two dimen- sional grid input, i.e. grating lines in two orthogonal directions, a two-dimensional array of dots corresponding to a two-dimensional Fourier transform is produced. If a constant input signal is imaged at the input, then the re- sulting transform will consist only of a dot--a d.c. signal output. For a signal with multiple frequency components ranging from low to high the distribution spectrum will be such that all the low frequency components will show near the optical axis, whereas the higher frequency components will be distributed away from it. Consider Figure 4.3.6 shown below. The amplitude transmittance of the grating is designated as f (f,y). The Fourier transform of f (x,y) occurs in plane P2 with co- ordinate axes p, q and is represented asF (p,q). The final image amplitude lies in the plane P3 ( §,n) and is rep~ resented as Z (g ,n ). Note that the (,g.11) plane is in reflected geometry to account for the sign change that oc- curs during the retransformation by the camera lens L2. 63 \\ \\ .\ wfiwwoooum Hmowuao uaouozoo mo Emuwmav owumaasom 06..» 0.3me We «4 ma 7. _d YIIII mmlllle {Null III! _h_:l.llv etlll-_....|..l..v. A 64 Where spatial filtering is desired, it is done at the plane P2. The diffraction spectrum of the complex amp- litude of the light flux at the plane Pl (f(x,y)) is ex— pressed by the Fourier transform “ .1 (px + qy) Iff(x,y) e dxdy (4.4) --00 F(p.q) The Fourier transforms, and therefore the spatial distri- butions of their diffraction spectra will be produced cor- responding to various spatial frequency contents in the signals (26). This principle allows us to eliminate any unwanted signal in the final picture by preventing its diffraction spectrum from entering the inverse transform lens (the camera lens). The process is called Spatial fil- tering. Figure 4.3.7 illustrates these ideas for a grid input signal (24). 4.4 Spatial Filtering for Moire Analysis As suggested above, spatial filtering is an optical procedure that takes advantage of the diffraction prOperties of light, and consists of blocking portions of the Fraun- hofer (far-field) diffraction pattern of superimposed sub- master and specimen grating photo-plates or images. There are various forms of filters which can be used in the transform plane. Among them are phase filters which are used to control the phase, and complex filters 65 SN .wmmv .mwcHH vommouo Ho muom we flew m Eouw wSHuwuw ems. mucosa ou wceuoufim Hawumaw Hmofiao mo oHamem ~66 Tasman Shanna? zzemzée 95 35>; x9: 55.... amino... .2286 5.12. \\\\\ ... e O . 0 e . e O C .e . e e . 0 e .\\\ 66 which change both the amplitude and phase. Amplitude fil- ters are used to control the amplitude transmittance in the transform plane without changing the phase of the signal components. Figure 4.4.1 Shows an optical system for spatial fil- tering in the plane P2 (24). For moire analysis, the fil- tering is accomplished by eliminating all but one of the dots from the transform. For a filter, one can use a hole slightly larger than the diameter of the dot (diffraction order chosen) in a dark mask. When placed in the transform plane, it al- lows only the particular diffraction order through. When the filtered light strikes the camera lens, this order forms the desired inverse Fourier transform--a modified image of the input tranSparency. Some of the orders which produced good moire fringe patterns had high background noise. Since the noise and moire fringe order Signal had the same Spatial frequencies, the noise could not be removed. Had that not been the case, the diffraction spectrum of the noise and that of the moire fringe would occupy different positions at the transform plane P2. As mentioned previously, some of the specimens had a crossed grating printed on them so as to facilitate the complete determination of the state of strain at a point. From such specimens the U-field and V-field displacements were obtained separately by filtering. 67 hem .memv Owns“ wououafim mo Showmamuu mauo>cH mo coaumouo vac oamfia snowman: noun—5m. 5 wsfiuouzm 13an you 539? H.333 214:» ouswwm ecu—a 89... .5839: 3.28.... S 3 2.2.: 5.; .32.. 98232 .Junuw eoszico 9520 \ 2... £338... .82 8.2.5 _ . , sewage: . All 283%... 0253:: .o .3 all .08.. 82.. l .28 a . , x J as... a». 3 9.230 econ 683:2. 68 In general, where symmetry of the strain field is lacking, the u and v isothetics (lines connecting points of equal components of displacement) may interfere to create other fringe families, and a complex moire pattern may re- sult. To eliminate this problem, the specimen gratings were made of a rectangular dot array, and the master or submaster grating used was unidirectional. The moire fringes of each family are obtained separately by rotation of the master grating through an angle of 90°. The center dot in the Fourier transform plane designated as the (0,0) order is the D.C. output signal, and any one order along the central horizontal array of orders contains only the u-field fringes; and any one order along the central vertical array of orders contains only v-field fringes. Therefore, if a black paper mask with a hole is placed at the transform plane to let through the optical system one order along the central hor- izontal (or vertical) array the u- (or v-) field fringes will be obtained, again making sure that the order allowed to pass has the least entanglement with the spectrum of noise. 4.5 Creation of Moire Fringe Photographs The apparatus used to obtain the fringe photographs in this investigation is shown in Figure 4.5.1. An effective monochromatic and coherent point source of light was provided by a Helium-Neon 10 milliwatt laser made by Jodon Corporation of Ann Arbor, Michigan. The laser 69 539mm w... 3895 «Jun ..m.q ougw.e 7O beam passed through a Jodon model LPSlOO pinhole spatial filter which converted it to a clean diverging beam. The lens L1 was located at roughly its focal length from the spatial filter to collimate the beam. The near-parallel beam of light transluminated the sub- master and Specimen assembly at the plane P1. The spatial filter-waround black paper with a 3/16 in. (n.76 mm) hole was contained in a filter mount of the camera lens. The Nikon F camera was fitted with a Coligon zoom lens with a focal length range of 95 mm - 205 mm. Even though zoom lenses have the disadvantage of decreased image quality and speed, and though this disadvantage gets worse with greater zooming ranges, this type of arrangement seemed to work better here than "normal lens" or wide-field lens. The camera mount consisted of a cylindrical cast iron base roughly 5 in. (12.7 cm) long with a standing u in. (10.16) cm) post serving as the support attachment. The whole camera-stand assembly could be moved across the bench sideways to locate the optimum fringe diffrac- tion order. Pinhole spatial filter and laser separation distance was 2.75 in. (6.98 cm) and the distance between the colli- mating and decollimating lenses approximately 18 in. (Q5. 72 Cm). The two lenses were 15 in. (38.10 cm) in diameter and had focal lengths of 39 in. (1 meter). 71 The procedure of obtaining the fringe photographs 'began with locating the position of the ray groups with a 'white cardboard. With the aid of a mounted diaphragm fil- ter, the orders were examined one by one and the one with the least noise identified. During the examination, it was important to be sure that the far field (no strain) fringes were vertical. If slanted, relative inclinations of the plates were altered by rotating one with respect to the other slightly until maximum fringe spacing was obtained, which automatically implied fringe uprightness. The camera and filter assembly was set in position already loaded with Kodak Plus-X Pan (PX 135-136) black and White film. Most of the pictures were taken with a zoom setting of 205 mm and eXposure times in the range of % - 5 sec. The development of the 35 mm negatives of the fringe patterns was done in D-76 develOper, an all-purpose develOper that produces negatives of normal contrast and moderate to low grain. Average develOpment times were 5% min. Then the films were processed in Kodak Indicator StOp bath for 30 sec. and Kodak Rapid Fixer for 4% min. After the films were washed for 20-30 min. they were dried and printed on 8 x 10 in. (20.34 x 25.4 cm) Kodalith paper for fringe analysis. Samples of the moire fringe patterns are shown in Figure 4.5.2 and Figure 4.5.3. 72 Figure 4.52 Baseline Moire fringe photograph of specimen SPC. 73 Ii: VI.."".I.’DZ$‘ I... ‘. ‘v‘.-ll‘ivi"l ‘0 Figure4.5.3 Moire fringe photograph of specimen SPC after coldworking holes l,2,and 4. 74 4.6 Moire Data Reduction The moire method of strain measurement utilizes the fringes observed when two grids are superimposed and slightly displaced. The method is relatively old, dating back to 1874 when Lord Rayleigh first put it to practical use (11). In the measurements of surface strain fields, two approaches for the interpretation of moire fringe patterns are useful, viz.: (a) geometrical approach, (b) displacement-derivative approach. The former approach was recognized by Tollenard, in 1945 (53). But it was not until 1952 that Kaczer (lO) put Tollenard's ideas into practice. Weller and Shepard (13) in 1948 suggested the second approach. Extensive development of this method is attributed to Dantu, who employed it in the measurement of elastic and plastic strains (10). In this investigation the displacement-derivative method was employed. However, a brief description of the geometrical approach will also be illustrated as it gives a good insight into the general theory of the moire method of determination of strain. 4.6.1 The Geometrical Approach Moire fringes are produced whenever two superposed gratings, the master and specimen grating (assumed equal in 75 pitch, say p,) are either rotated one with respect to the other or when the specimen grating pitch p is changed to p' due to deformation. In general, both these sources of fringe formation occur simultaneously at a point. Figure 4.6.1 depicts the geometry of the moire fringes in terms of fringe separation. The following is a relationship between the rotation angle 6 of the specimen grating with respect to the master orientation, fringe sep- aration distance 6 and the master grating pitch p. Thus we have: AB = AC AC = .AC sine sin 90° ’ sin (ab-9) sin 90° = 5 . . . Eigfi— sin.(¢—9) ,now uSing the addition formula. sin (Ab-9 ) = sin!) cos 0- coszp sine and solving for 6 we get: _—. -Siaw tane 5/13 + cosw In terms of the angle of orientation (9, the law of Sines yields: 4b = __ PI sin (W-¢)' sin (W-—9 ) Solving for p' as a function of the other parameters,the following relationship is obtained: 76 zo_.—.dhzw_m0 92:35 «5.542 / tome—om» awfium 9502 H6... ops»: \.. , ,/ / N a o . , \ x / 7 20.2595 / ozzhmw Zerume 77 IV = 5 fL + (__¢_5_)2+ 2(____6_ 0034: (4.5) \ p p) where ¢ is the fringe inclination angle and p and 6 are the pitch of the master and the fringe separation respec- tively as before. For negligible rotations, the specimen grating pitch takes the form p' = pg . This eXpression is then sub- 22:6 stituted into the definition of normal strain, in this case for the direction perpendicular to the lines of the master grating. 4.6.2. The Displacement - Derivative Approach The displacement derivative approach to moire-fringe analysis of strain is basically a graphical differentiation process. Moire fringes represent the loci of points of con- stant displacement in a direction normal to the grid lines. The mechanics of this process involve first plot- ting the curve of fringe spacing versus fringe order, the zero order being chosen arbitrarily. The order of a fringe is given by the parameter m. Denoting the horizontal displacement as u, we ob- tain the relation: u =mp where m is the fringe order and p is the master pitch. 78 For the determination of vertical displacements, v, the grating is oriented perpendicular to the vertical axis and the strain determination procedure is repeated. From the above displacement field the strains are obtained from the definition of strain; that is: ex = pp = aanp) = 12 am (4.6) 8x 8x 8x 6y: agmB) = 28m (“-7) 8y By and 7xy = a_u + Q = p am+am (4.8) By 8x 8y 8X where p the master grating pitch is constant. The accuracy with which the strain can be calcul- ated depends on the effective gauge length which is given by the spatial distances between fringes. The smaller the pitch of the submaster employed, the more precise the re- sults obtained, a factor which is eSPeCially' crucial in areas of the highest strain gradients. Submasters come in densities of 10—50,000 lpi (.4- 2000 lines/mm reSpectively). For most structural ma- terials one might eXpect the measurement of maximum strain in the elastic range of the member to require at least 5000 lpi (200 lines/mm) submaster with normal moire procedures (1). Unfortunately even this submaster would not give re— liable results in areas of very high strain gradients. In 79 order to surmount this obstacle a "mismatch technique" was utilized. In this method, different specimen and analyzer grids are chosen. The pitch difference between the Speci- men and analyzer was obtained by a photographic technique. If we suppose for a moment that the pitch or fre- quency of the Specimen grid exceeds that of the master analyzer by a multiple (1+r), 0mx CHAPTER V EFFECTS OF LARGE COMPRESSIVE IN-PLANE LOADS ON RESIDUAL STRAIN FIELD 5.1 Introduction Work was begun on this tapic at Wright-Patterson Air Force Base by Cloud (24). Three Specimens designated C9, C10, and 011 were tested for the effect of in-plane load and cy- cling of that load on the residual strain near a coldworked fastener hole. At a design stress level of 24 ksi; (165 MPa) for aircraft Skins,specimens C9 and 010 (011 was used as a control Specimen) were cycled for 50 cycles to study the cycling's effect on the imposed residual strain field. The 50 cycles represents to a limited degree aircraft wing loading during landing. In this study, Cloud's results are verified and ex- tended with the testing of two Specimens designated SP1 and SP2. These Specimens were tested to investigate further the effects of large in-plane compressive loads upon the residual strain field surrounding a coldworked fastener hole. Axial hoop, transverse hoop, and radial residual strain fields were evaluated. The results are presented in section 5.4.1, 5.4.2, and 5.4.3 respectively. The radial 82 83 residual strain results are compared to the results of Adler and Dupree (29) and Hsu-Forman (2) for the coldworked state only. 5.2 Overview The reasons for overstraining and thus prestressing machine or structural elements depend to a large extent on the nature of the applied loads--that is, whether the load iS steady (static) or cyclic (fatigue). This overstraining of the structural material may result in the reduction of high peak stresses and stress gradients when the applied loads are static in nature. In some cases this Operation will accomplish the reduction of the maximum stress in the assembly at the eXpense of raising the average stress level-- a price which can be tolerated (7). Ultra-high pressure de- vices and heat exchanger tubes are two application examples among many to be found in industry. In structural design, the overstraining or cold- working of a fastener hole results in improvement of the fatigue life of the structure. In this case, cyclic tensile stresses are lowered by the deliberate introduction of res- idual compressive stresses. Without them, the tensile stress at the edge of the hole would rise to approximately 3 times the applied nominal stress (35). Although some details about the effect of residual compressive stresses are understood, there is still a major unanswered question about the 84 modification of this residual stress distribution by an ap— plication of compressive loads on the structure. For an example, consider an aircraft landing when the undersides of the wings go into a state of compression. 5.3 EXperimental Procedure The Specimen design used to eXplore this problem was illustrated in Figure 2.2.1 and that for specimens C9, 010, and 011 by Cloud can be obtained from his earlier technical report (24). Later on in the investigation it was deemed necessary to print the grid on the specimen in two directions so as to facilitate the measurement of strain distributions along both axes, x and y. Loading of the Specimens SP1 and SP2 was performed on a TiniuS Olsen machine (Figure 5.1) in load increments of 5000 lbf (22.24 x 103 N). The Specimens were loaded to failure, which turned out to be roughly 32.5 x 103 lbf (144.57 x 103 N). This was equivalent to a nominal remote compres- sive overload stress of around 52 x 103 lbf/in2 (358 MPa). Cloud's specimens C9 and C10 endured the same type of load- ing as SP2 except for a 50 cycle cycling at a nominal stress of 24'ksi (165 MPa). Specimen Cll experienced the same type of loading history but with no initial hole prestress. Figure 5.2, 5.3 and 5.4 Show typical fringe photo- graphs for Situations where the strain distribution Showed Significant departure from the coldworked state. 85 ‘\ Figure 5.l Apparatus for overload compressive test appHcaflon. 86 ’0)??? at l guri fringe o specimen SP 2 after I5,000 lbf load application. . A Agnes..- ‘ v _ __ '— —.———.— - . r V I ‘T A A ‘ ‘4 A... . . .4 v - w V— ‘ M ""' A ’ A... .s.__' - Av “v... v s e-- ' ' ' V _ __. 4A -.... A; I .- -- W“. I .A --—-.—- ~— vw *1 V - _..- A. w h— -M r" A *— 4 __._... .- "a.” - I — A __‘ fl ‘W—‘u—fl .. ‘- A _4 ...—-.—--——- ‘0‘.” v A I-.." ¢mf v I A 4A ..'_..o.o<. .—— v A A _._ - --—' 'w. #_ ‘_ A "-— "‘"‘-" ' A ..__ Figure 5.3 a re r nge otogro of specimen SP2 after 20,000 lbf load application. Figure 5.4 Moire fringe photographof specimen SP 2 after 25,000 lb, load application. 89 5.4 Results and Discussion 5.4.1 Axial Hoop Strain Distribution The results from Cloud's experiments, namely Speci— mens C9 and 010, do not quite agree (Figure 5.5 and 5.6). For 010 the results do not depart appreciably from plasticity theory (36) except for the initial material response for the second part of the continuing remote in-plane compressive overload stress application. As might be eXpected from theo- retical predictions of the dependence of mean residual strains on cyclic plastic strains, the residual strain climate tended to become smaller as cycling progressed (36). The results of Specimen C9 reveal the same material characteristic re- sponse as that of 010 for radial distances of roughly 0.100 in. (2.54 mm) from the fastener hole. For distances less than 0.040 in. (1.02 mm) from the hole edge the results for C9 and C10 agree very well. Also, the overall material re- Sponse before and after the cyclically imposed load for both Specimens is in good agreement; that is, that increasing re- mote loading haS a residual strain relaxation effect. Results from Cloud's specimen 011, which served as a control Specimen (Figure 5.7, a summary plot), indicate that residual hoop strains start Showing up only in the region of the stress raiser, the fastener hole, at near buckling and buckling specimen failure loads. Figures 5.8 through 5.17 are the detailed results of the axial hoop strain evaluation versus distance from 9O 431) 115- Figure 5.5 Effect of in—plane compression on residual axial maximum hoop strain distributions at a point on hole boundary 91 P? 1‘0 x 2 E (D u 1D 3 In u m U 2 fi 2 I ",5” 0: .____® a: m U c. ‘- Ew ._ E 34 o 8 .' O 22 >‘ .- 69 9Q + m LIJ o x 95" 3 05-1 0; "C“ en "’ o o {- :- U) 0) - . LU V (D ’ " -l .- 4)’ Nox ‘ >-Q’ as UN . e. 8" e v S E 4 TN 0 C) O o- 0 (>2 E 0 (E 4r "0 f ‘ ‘ 2 f :- o :——— 2 - , N IN 0 to Q '0 sueoied‘oa: lo“9'ugous dooH |ong umuuxow ions along several axes Fi ure 5.6 Residual axial hoop strain distribut 8 at different radial distances for 5.6 mils radial interference 92 ,1: '0 3‘ ‘D . '0 .E -: o_'t O '98 QQQ .g 3.. COO ). 3‘0: ..- '.. >= + ;x53 >>,>- >>-»9 _ 04332 on 12 2E 52 ;,¢: 8: F: 't .-<) a 4" £0- 0 =3 a: :D__ o (3 a U (D .502 'Q» .. 'U‘v a) a. 8 E; e (0 .JK 3 in N 8 ’Ml E) m 0 3 U L) to _e>- 8 NO E C) +0 .5 ‘2. .g, E K »9 r0 EST, 13 u) '3' §) 8; £5 53 C2 C? C? C2 C2 (3 . c) 08X W'Ia‘ugous dooH wmgxow logw Figure 5:7 Residual maximum axial strain distributions at various points on a radial line for zero mils radial interference 93 u: C) . 0. g . 91, u ._E "d .. z I m 1; 3.7.??? _0 M t i‘ Y‘ . , ‘\‘\ ‘1‘ x; x \a‘: t g Q\‘h~“\\ d K .‘EKH Fl .j‘. ,-/);I\}. ‘2 - i t, t? 3‘ I” i ' v 4 N. ,0 Lu I .4 :7— m I 3 C) V: r I L I I + J— 1 ? I? 1700 £00 ZO'O IO'O OO'O IO'O- ZO'O- 20'0- ugous dooH Figure 5.8 Residual maximum axial strain distributions at various Distance From Hole (in) points on a radial line for 5.6 mils radial interference 94 o. 24 0'32 036 L E, G E N D on 04 0.00 1, - lb. 0.0% Distance From Hole (in) SPECIMEN Lona=sooo -b.le 10.24 -b.32 leOLE N0. cob zoo io"o 00:0 06- zoo- soo- 8 ugous dooH Figure 5.9 MEasured residual axial hOOp strain distribution along several axes at different radial distances for 6.5 mils radial interference 95 2.5 0.0... ES“. 8:035 , «no eflo 0:0 80 004.0 000.. 90. 5.0.. Non. 0...,00. . . . 0 C... .2 000.0733 0.0 zustuwam 3 20'0- v IO'O- 00:0 IO' 0 20'0 i t l 20' 0 .32 MIDI _ _ _ f . m i . .mmgmw “invite" .. {0; MO fl u _ _ 22.191 L 900 uyous dooH axes for 7.2 mils radial interference (Load 15.000 lbf) Figure 5.10 Residual axial hoop Strain distributions along several o “9 96 " N *0. 2 l0) s“! I 5.». 09. I 0‘ ‘ I I 3 I a. - 7 rt 2 "' FN. E co 0 0 Q U " N 3’ o T «2 o ’0' < o r .J ' ,_ '0' 3 - Loos—(u . C3, O 5 ' o : LLJ: g __Ii ' a: C? _O I ‘2 .0 0 ------------------------------------------------ v If.) : cu .. (Y) 1 9 C) Q : Z C3 5 -—J : . N __J an . C) <3 ' I F” ; L_J . ' 900 20 0 20'0 IO'O OO'O IO'O- ZO'O- 20'0- ugoJIs dooH Figure 5.11 Residual axial hOOp strain distributions along several axes for 7.2 mils radial interference (32.560 lbf) Distance From Hole (in) 97 0732 dz; SPECIMEN ClC) die oioe 0 Distance From Hole (in) -C----—--—---—---—----b L FGFND 0.08 1 -b.I6 HOLE N0. -.C108 LDD4U 10.24 -b.32 D Q 3 C) N) C) C) 200 do 0070 05- 200 so'o- ugous dooH Figure 5.12 Residual axial hoop strain distributions along several axes at different radial distances for 7.2 mils radial interference (Load 37,120 lbf) Hoop Strain 0.0l 0.02 0 .03 0.04 0.00 98 LE...G. EN. D 0 .01 .02 .04 .i .Zin. <-<-<-<-<-< HOLE NO. C11 LODZO ..-..--...--- Figure 5.13 6. i 3 S). ; i E : SPECIMEN N ; : C II a s : W O E . : :LOAD-t8,600 lbf-w j). 0. . i . | , .02 ~04 5 : -' :2 s : l N, : l 0. = ' .0 I :I I J' l I -o.24 -o.I6 -o.oe 0.00 0.08 0J6 oT24 6'32 Distance From Hole (in) Measured residual axial hoop strain distributions along several axes near a non-coldworked hole (Load 18,600 lbf) 99 C) .9? ‘““ "‘ C) U - Fcuv .E .vm “I; ELISE "‘i g; .1; “fr 2 0 ll O a I I J, UJ: + : (v.3 . .. 0 _1i , l' - I o. 11 ll >3. .8 -_ - __.. _ 9" O 2? <3 at I _ 0 cs - '1 _‘§ L) to 3.: N E: 3 .i Eaja’ O v 2 J? 0 Cd 2: CD CD :2 E __i O u a» 2—4 'J C LJ _-:.2 C3 C) C 2: to .£? LLJ O __i C) 3: , C) ................................... .0. CD 1 a) . Q i .9 ‘r— 1 v V T I . 600 900 £00 000 EO'O- 900- 600- El 0- quus aAIssedeoo Figure 5.14 Measured residual axial hoop strain distributions along several axes near a non-coldworked hole (Load 23,360 lbf) lOO Q. C) O i l LEGEND , :3——a—-EJYO- : "5 o———e———e v.31 1 0‘ a—a—etfli E 0———e———0 v.2 g; at o_ C)‘ HOLE N0. C11 LODBO 5. .S 0‘ E (7) CD :1 C2 . 8 o I: 5, O. ' SPECIMEN N c II a: y=0 (::> E 0, LOA0- 28,I04 Ib-w 9| t O < .02 .—___.O4 ' ___.__;===dfia§__. M O- l 910.24 -‘0.Ie -‘o.os 0.00 0.08 O.l6 024 Distance From Hole (in) F1 ure 5.15 “Measured residual axial hoop strain dis ributions 8 along several axes at different radial istances for 6.5 mils radial interference (Load 23,104 lbf) lOl o" : ‘- 3 LE..QLND N, ‘ m———e———m r a CD ; o———0———e r 01 o. : b—fi—A Y .02 : +—————+——+ r .04 : x——x———x Y .t. : L" 6 . ° "2'1"--- N : 0. E 0' : HOLE NO. C11 LUD35 5. E ,g (3‘ : 9 : c7) 5 . o 5 g 0.. o O ---- I . g 0 i l 9* 1 l ; SPECIMEN N : ' c II N . i o : "o 0' : i L0A0- 32,560 lbfw O E ' q . . Wt : i 02 fl“ ; . -' 7:: s m : i O. : ' 9 ’ . L . , , -D.l6 -o.oe 0.00 0.08 0.l6 024 632 Distance From Hole (in) Figure 5.16 Measured residual axial hoop strain distributions along several axes near a non-coldworked hole (Load 32,560 lbf) 0 .0l 0 .02 0 .03 0.04 Hoop Strain 0 00 102 E LEGEND Y Y H—A Y Y Y Y HOLE NO: C11 |_ 0 . Figure 5.17 Measured residual axial hoop strain distribution along Distance From Hole (in) several axes near a nan-coldworked hole (Load 37,120 lbf) E5 9* SPECIMEN N c II o e 8 LOAD-37.I20 Ibrw __,o. - .02----ro4 9’“ J 1::::2 s t I t M I Q I o — v ' e I I I ' -O.32 -o.24 -b.l6 -o.08 0.00 0.08 0.!6 0.24 103 the hole centerline at various locations, y, for specimens C9, C10 and 011. The axial hoop strain evaluation for specimens C9, C10 and C11 were performed along the axes labeled y=0.00, y = 0.01 in. (0.254 mm), y = 0.02 in. (0.508 mm), y = 0.0# in. (1.016 mm), and y = 0.1 in. (2.5# mm), where y = 0.00 was an axis drawn tangent to the fastener hole parallel to the direction of loading, and the rest of the axes were arbitrarily marked off relative to it to facilitate the de- termination of the strain distribution at different dis- stances from the hole boundary. The figures indicate that at approximately a radial distance from the point at which the residual hoop strains attain their maximum values, the residual strain passes through zero and then attains a local minimum before van- ishing entirely in progressing to the edge of the plate along any one of the y axes. The region gets wider and wider with higher compressive loads. The residual hoop strain at the hole edge decreases with the applied load until a point of instability is reached, a possible indication being the increasing fluctuation (oscillation) of the strains as the buckling (failure) load is approached. (See Figures 5.12 and 5.17)- The plot of Figure 5.8 for specimen C9 portrays the variation of this residual strain distribution with y. The slight variation in the magnitude of the strains is due to slight differences in radial interference employed. 10# The results for specimen C10 are included here to emphasize the unsymmetric nature of the mandrelizing process. Analytical solutions to the basic problem of expanding a hole in a plate assume a rotationally symmetric state of plane plastic strain or stress. Figure 5.8 and Figure 5.9 show a strain component for two sides of the centerline. For the former set of plots the assumption of symmetry is probably satisfactory. But Figure 5.9 indicates that such an assump- tion is not always valid, and could lead to serious errors in the practical application of this process by the designer. For a rotationally symmetric process some kind of duplication would be eXpected in the results; however, these plots show quite a variation in the strain magnitudes and indicate that, for this specimen, there may have been asymmetries in the loading under which the left side of the hole would yield first under high in-plaNe compressive loads. 5.4.2 Transverse Hoop §trainfiDistribution Figures 5.18 through 5.2&.which were processed from data measured from grating lines along the loading axis, re- veal that transverse hoop strain increases with increasing remote applied loads within an annulus bounded by an ap- proximate radial distance x = 0.07 in. (1.78 mm) and the fastener hole boundary. Further'away from the hole the ef- fect of the applied stress is negligible. 1105 .93 X 2 T a u '9 (o I 8m 4’9 ‘i O 2; (n5; ..: Z + 05:: In :2 P- o 1' 3‘ pz~¢ in: '- 2: <1 —- on g mg_: 01: EN 0 .236 "”0 use ' 33 '- .- W‘“ 3 (:4 U) o > 8 O- m m s m nfirfie 30' a. o'u E “K O I L) o c .400 O. I c o .— o E <~¢oo (I '5 Q Q 0. Q g 0 o' o o o o o ' ‘3'“!0183 dooH asunsuou uInuIIxon Figure 5.18 Effect of in-plane compression on residual transverse maximum hOOp strain distributions at a point on hole boundary (specimen SP 2) N.» ¢® mm 106 p .mx.umo._.m 2.33568 225m. 9.. cc h o..o~.o.x ..O—.Onx m.3 «:3 “Sci. 2.! NE a 00:98:25 .053. 20_.r<.rzu_m0 z 02:55 3 3 0. 0 ZmZCmaw 0 NM VN 0. m 00.0 .50 rNo.0 .m0. 0 la‘upus dooH IVOO r00.0 OSJORSWJ J. hoop strain distributions at a point on hole boundary Figure 5.19 Effect of in—plane compression on residual transverse maximum (Specimen C 10) 107 o.‘ 32 its SP2 TLDS "L *0 s 0‘24 ’1 '1 HOLE N0: 0:l6 1: gm. II 6Q 310: In / / "in“---i--- _ oioe LOAD-5000 b, 600 Distance From Hole (in) ---------------------‘ 0.08 -.J 05'. 2 30in. —1 n.’ L -b.l6 H—H ,(3.0.135 +——-—-t-——-+ [4:0 LEGEND m——-m~——m XIXJD°0 0.24 1 . -b.32 I I : i I I V vo'o coo zoo Io“o oo’o Ioo- zoo- zoo ' 40.40 ugous dooH Figure 5.2() Measured residual transverse hOOp strain distributions along several axes at different radial distances for 6.5 mils radial interference (Load 5,000 lb?) 108 U] R Q N,— r:) 2 __J K 9’) *— "0' N 3 Q_ .- 07 0 3i .. E o ”0 E” 0 Z gm 0 7 22 LL] 0 _. _I 3 ° C ..l I 0108 0 00 Distance From Hole (in) END L EU / / ~‘ooe .l6 —0.24 t70'0 zoo zoo Io"o 00:0 03- zoo- 20'0- ugous dooH Figure 5.21 Measured residual transverse hoop strain distributions along several axes at different radial distances for 6.5 mils radial interference (Load 10,000 lbf) 109 U? S: D m 0 _. 5—3 F— :3“ q "’ 0 m, I ‘ N' O I i 3': Z \ : 'o‘ LLJ I 3‘ (I 3 _J \i - Q \: :I (.2 I ' >0. SPECIMEN SP 2 0.08 ...._...___.__.._..-...... --v--pr- I X X: X I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I t I I I I I I V -0 O 0 .‘J -0 i 000 Distance From Hole (in) LEGEND I9~—-——H———F‘J I 0—-—-9-——-vl) I,____.&i-._,s, ' +———-—+———-+ I - 0 08 ' -‘o.I6 0.24 'T . .32 I too 200 zoo Io"o oo’o I0'6- zoo- 20'0- uyaus dooH Figure 5.24 Measured residual transverse hOOp strain distributions along several axes at different radial distances for 6.5 mils radial interference (Load 25.000 lbf) 112 Q m I CD .._J I.— C\J £1. at w z; . i; " .- C3 :9 ZZ E5 c> g; z N 0 Lo. __J g ‘0 g C) II I 2 o (9, -' O 8‘5"? i o . 0055‘ (I): .‘l " .. i: o . ------------------------- ’O + ' 1 m - 0. __O I £9 . ’ Q - i , : / . ’ v . N. ll 1 (P 1700 £00 200 l0'0 00'0 IO'O- 20'0- 20'0- ugoJIs dooH Figure 5.25 Measured residual transverse heap strain distributions along several axes at different radial distances for 6.5 mils radial interference (Load 30,000 lbf) Distance From Hate (in) .113 Figure 5.26 ugous dooH Residual transverse hoop strain distributions axes for 7.2 mils radial interference (19,600 lbf) CD cg u) CD CD _J I . z = :CLg 94 C) i _______ 15 ._. ; “gt—.8 LJ : (Q.——'b; P: \ ' ‘ 2. _— ¢ .1 \§\_'~ 3- FN c3 <, <3 22 E; :3 z . us E352 52 C3 0’ < 0 I s 15 2: D‘ V 2 uJ' t3. --.i€g 5 U4} T" "”"""""""" 0 c . , LL _i 0 : 'm ‘c’ ;._ ' o 2 i (5 2! i "'I O ' 2. £3 \ I ................. " , V at 5? . N . 'I "? -- ‘ I I 1 t 'r f T 9 900 20' 0 20'0 l0' 0 00'0 l0'0- 20' 0- 20'0- along several 111i r U? u: (Y) 3 N O O o to . ____,~Il Gas—Q" N—_' e 3 N. s- '0 5 z (D g '0. a 9 :3, 9 Lu 1’ ' V’ < 3 PCJQ 0 03:3an a 0308 E B F. L‘}-—-t'}——t’1 x ——0 I I i I i E I I I l l I I i . o‘.oo DIstance From Hole (In) ~10 08 b. l6 -O.24 1 .32 {700 zoo zoo Io'o oo’o Ioa- zoo- zoo- ugoJIs dooH Figure 5.27 Residual transverse hoop strain distributions along several axes for 7.2 mils radial interference (Load 32,560 lbf) 115 .. 4-------- )7 .l N =08 024 ' . E 5a—S" t= ~—-- : 3 § «2 c: c5 5 e 8 f, '0 a 2 g ,. c: 3 e Z % LL}; 0 8 I LL": --------------------------- .d S __J; LL 8 co c (3.2 ' In ~53 a £2 15 I """"" C) .7 v .. v , or O I: .1 .9 Z O " __J Lu ; 5' Z s a: CD ? 3: ._, I? T Li I v I I V 11 1700 £00 ZO'O I00 000 IO'O- 20'0- 20'0- ugaJIs dooH Figure 5.28 Residual transverse hOOp strain distributions along several axes for 7.2 mils radial interference (Load 37,120 lbf) 116 Cycling at 24 ksi (165 MPa) does not seem to alter these observations since the transverse hoop strain evalu- ation for C10 (Figure 5.l9) is similar to that of SP2 (Fig- ure 5.18) both in magnitude and rate of increase with the applied remote compressive loads. For specimen SP2 the detailed hoop strain evalua- tion was performed along the axes X = 0.00 in, XC= 0.065 in. (1.65 mm), X = 0.135 in. (3.43 mm) and X = 0.239 in. (6.07 mm), where the axes are oriented as shown in Figure 5.18. These results are shown in Figures 5.20 through 5.25. Speci- men ClO results (Figure 5.19 and Figures 5.26 through 5.28) are in agreement with the trends illustrated via specimen SP2 that the strains increase with load. The results for specimen SP1 are not reported be- cause they turned out to be unreliable. Data for this specimen was obtained in the initial stages of the investi- gation before enough eXperience was gained. 5.4.3 Radial Strain Distribution Examination of the residual compressive strains re- veal that for the case of a fastener hole in an infinite plate (semi-infinite to be exact) the strain distribution assumes an eXponential nature see Figures 5.30 through 5.33. The strains attain their maximum value at the edge of the hole and rapidly diminish to zero with distance from the hole edge. .117 ” ¢> Q’ #X 3 2 z .- t) 15 l‘? ”CD 10 V I II 0 U C 0 b >. .2 _: «s 3 (O 2 E, E ..:" x 233 ._ In N :5 .9 g (L 3 E2: 8 h ..g 5 3 In ‘2’ o b a ‘E O (9 ..w 2 - 2 E G g- 0 0 1% {pm a: 0. °. 0. <5, <3 <3 5 o h- to I) q. "5 oi .4 oaK‘ogx w %"3‘u!0133 aAIssaJdqug '0ng wnngow Figure 5.29 Effect of in-plane compression on residual axial maximum compressive strain distributions at a point on hole boundary 118 a £2 0 _ ‘t T’“"“‘“‘ 0 a [j 55 z. . > 38 us. (3 -€}--—t'_} Y:I {9- 0'30 Q : 5 m 53; z ..N L n: a. a: 9, w 1. CA "I L045 7: O- 1 .9 . o i 225 f/ : ”Ga. 3 o ' U ‘ C c: .712 O N U .. E) i \ 0'05 010 0.00 ‘0.05 I I I soo soo zoo ooo sob- eo'o- soo- zro- ugous OMSSOJdWOD Figure 5-3() Compressive (radial) surface strain distribution near a coldworked hole for 6.5 mils radial interference JQL9 (D P". .......... __ 0 )~ C3_ 72 a) 2:. *. -"? 'I_‘._' Ti 3 O 0‘ § “‘ I 5' is} L: . 0 O s 8 g s : s o b- «q (3 o .I Ova- T _°Q.E 0" £9 0 I V .3 .ng A 8 Ad 5 :7: 9 z; 0' 0 CJ : 2: - l0 / ; L8 _. f : C) /j{ ; I: i C) ____________________________________ _o 1 C) i u) ' Q —rs . ‘P eoo son 260 060 206- sob- so-o- aro- ugous eAIssaJdqug Figure 5.31 Compressive (radial) surface strain distribution near a coldworked hole for 6.5 mils radial interference (Load 15,000 lbf) 120 O 5’. _.____, O ; i >~ , i ' ‘ '- ’ '5‘ I m Z *' I _h") LL13 "I; 59: o Q; 3 Lu; EV ‘ i a 5 Q 5 GE: <3 ”(5 __..._...i....; : z 0 ' 0 EJ' U . : g N o i U Q a: If) 1; a) ,0! a : g 3 0 i 0 E3; .3 E C>r$ : _N_ .E : C>" ' .9 ' o I x: , E C) ' g L.‘ (\J : .J. 3 c» N z 8 O. : o no : .9. .72 : C3 C) O E 7 a /_ . l0 . .0 Lu 3 0 _1 : C3 5 I: i <3 .................................... .0 5 C) m = 0. Tf’ T f i ‘ ’T ' . E) 600 90 0 £00 00 0 20'0- 900- 600- El 0- ugous amssaldwoa Figure 5.32! Compressive (radial) surface strain distribution near a coldworked hole for 6.5 mils radial interference (Load 20,000 lbf) 121 C) ______ ..: D? C) I >~ (:9 :i ' >—T m 21 g t"? Ll—Jé é o C)? Lu: o P ‘ ...---__.~. 2 O 0 g 0. _. N ID a a ‘2' to m o _N 1‘ C3 0 .3 CD 5‘! C) K LO ‘ :2 (\J 3 O N 5 0. E m : 9 s '0' O 5 2: i . LO : L-O. LLJ ; O _l I ‘_ 5 CD .................................... c------_-------__-_------_-_____-_--_-----------.C? I C) 5 u: ; O. . , ' 9 666 900 200 oo'o 5:06- 9023- 606- aro- ugous anyssaadwog Figure 5-33 Compressive (radial) surface strain distribution near a coldworked hole for 6.5 mils radial interference (Load 25,000 lbf) Distance From Hole (in) 122 The effect of the applied loads is to slightly in- crease this value at the fastener hole edge from around 5.25 percent to a value roughly equal to 6 percent at a maximum attainable load (42.# lbf x 103) (188.6 x 103 N) before speci- men failure. Figure 5.29 depicts the subsequent redistri- bution of the residual radial strains near the coldworked hole for specimen SP2. Low remote load compressive stresses cause no change in the residual strain field. For higher loads the effects begin to be noticeable only after a remote compressive stress of 24 ksi is reached and then only close to the hole boundary where the strains gradually vary by slightly over one percent. The residual strains, which vary with y, take on a steady value on reach- ing an applied nominal stress of around 2# x 103 lbf/in2 until specimen failure by buckling and subsequent fracturing of the material. Figure 5.3# shows a comparison of the results for zero load. The Hsu-Forman and Nadai results are based on a 4 mil (.101 mm) radial eXpansion whereas the Adler and Dupree finite element result is based on a 6 ml radial expansion. The eXperimental data is from specimen SP2 with a radial in- terference of approximately 6 mils (.152 mm). Total agreement of the different results is not ex- pected due to the assumptions made in the formulations of the 123 «2.0:. .025 0.0: Ea: 3:330 ..x «3.0 n36 emmd 3.6 62.0 :3 30.0 mood 2.! Nd .- 0055......5 350m. ahzmiwuw whit: wmmaao uco awn—o4 III 2.! 06¢ cocoa-tot: .200: N am zugowam 45.40 44P2w8r¢mmxw 0 000 2.: v - 00:03:25 .203. .4042 2.2 v a 3:33.25 3:3: Z4210mnam1 IIIII. wowed 'ulous logpoa of Nadai (41), Hsu and Forman (2), and Adler and Dupree (29) Figure 5.34 Comparison of experimental results with theoretical predictions 124 problems. Nevertheless the essential features of the re- sults are apparent and in qualitative agreement at least. CHAPTER VI HOLE INTERACTION STUDY 6.1 Introduction In this chapter the interaction between surface strain fields which are created by coldworking two or more fastener holes lying in close proximity to each other is in- vestigated. Needless to say, this situation occurs in al- most all fastening situations. Conventional machine design fastener techniques are based on simple analytical formulae develOped from the assumption that there are basically three modes of failure, viz.: (l) shearing of rivets, (2) bearing failure of the plate or rivet, and (3) tensile failure of the plate. Under such considerations the Stiffness Of a solid plate not subjected to buckling is expressed by the product (gt). Here g is the shear modulus of the ma- terial, and t is its thickness. For the case under consideration (a shear web) the effective shear modulus, g.te, is given by the empirical formula (4) 125 126 gte = gt (1 -p)(1 - Q3) (6.1) b h where D is the diameter of the hole, b is hole separation distance and h is the width of the plate. This and other analytical solutions have only limited applicability, if any, to the new and more sephisticated fas- tener systems designed to improve joint fatigue life of struc- tural members. 6.2 Experimental Procedure The material and experimental procedures have been described in sections 2.2 and 3.1. The specimen configur- ation which was illustrated in Figures 3.1.3 is a four hole pattern in a plate dimensioned 2% x 4% inches, & of an inch thick, (6.35 x ll.#3 x .635 cm). Two such specimens desi- gnated SPB and SP0 were tested. Both specimens are of the same material and geometry. In these specimens, the (e/d) ratio was 1.8, which is below the threshold value of (e/d) 2.0 commonly em- ployed in the industry. These same specimens, in addition to others, were utilized in the study of plate edge effects on the residual strain fields. An attempt was made to hold constant most of the crucial independent factors. Among these are the hole sep- aration distance, b, which was 1.75 d; the radial inter- ference which was approximately 6 mils; plate thickness which was % in; and the mandrel drawing rate, which was .5 cm/min. 127 6.3 Results and Discussion 6.3.1 Radial_§train Distribution Both hoop strain and compressive residual components of strain were evaluated at various locations around the fas- tener hole. A comparison can be made with results measured using specimen SPP (a single hole in a plate with roughly its centre located a distance .469 in. (11.93 mm) away from the plate edge), whose e/d ratio is equal to 1.8. (See Figures 7.4 and 7.5) Figures 6.1 through 6.5 have been included to show the locations and the moire fringe pattern obtained on pre- stressing hole #1 and the overall moire fringe pattern re- sulting from coldworking of all the four holes. The moire fringe pattern of Figure 6.3 goes with plots illustrated in Figure 6.6 through 6.11 This is a case of specimen SPB after all the fastener holes were cold- worked. The departure from symmetry in the pattern was largely a result of the mandrelizing order followed. The coldworking of hole #1 was followed by hole #2. Hole #3 was the last hole in the coldworking process, after hole #4. Data was collected between each of the coldworking stages. Here, only the final strain state of the specimen will be discussed. As seen from the moire photograph of Figure 6.3, relatively high residual compressive strains dominate a ,. D“( ‘5‘ .I.-('- I’* w..— Figure 6.! I. Specimen SPB—Kilo?" fringe pattern. J 129 ”C'."“. . g. Q-.' ”Figure 6.2 Moire fringe pattern for specimen SPB after coldworking hole #I. 130 .as..‘ enn- .A‘~.—..—~‘- l243. n der o o r: 8 h o 3 '0 o o In or 131 131:..v. Figure . Moire fringe pattern of holes 2-4 in specimen SPC after coldworking in order l24. 132 NH: ig'ure 6.5 Fringe photogrop l-3 in specimen SPC after coldworking in order I243. 133 IL! - X; c) fi' ,; ,._-...._....._.;__; O 3: '° 5 f :2 a) :1, 3'3 0 N : L13 Z T- I ' O 0 LL!) T 3 __,* o O l 2 LU ' rm if 5 E 0°. = 0 2m 3 I." i an 3 = 3;”) 0 mo : m ‘-’ ; .01. c": : o 1 E O : .N . : O V E (\i : IE 2 ,0 c.) ’5 m s 03 : CL 2 (f) i r2 z :0 C) E ZZ . U) 2 +0 L11 : O ..: . C3 5 3: : C) ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ;_,___,,_,,_,_____-----,--_,,___,__,__------_,_-.C? : o E m i O. ._ r . .' . .v r . 9 600 90 0 £00 000 9200- 90 O- 60 0- 8| 0- ugous angssaldwoa Figure 6.6 Measured residual compressive strain distribution along an axis .1 inches from the centerline between holes 3 and 4 Hem Hme(m) Distance 134' “1 C) or g 5 con 9 l .- | z m t. V ' Q m .. N C] 1. ; c: > T"? Z; ‘ 3 0 LL! cf 1 U — (”W . - u; 1' i 33 __. p . m - . 4: . x O " : E, g m. . ' Q ' LIJ W o P . n O O 0.20 S P B 2 C N 9 L L 015 Distance From Hale (it?) obs O.IO 0.00 '0.05 666 90-0 260 060 zoo- 906- 605- aro- uious emssadeoo Figure 6.7 Measured residual compressive strain distributions along an axis .13 inches from the centerline between holes 1 and 2 135 C) w ~23 ’ 2 U ¢>m 6? o n if ,. a) ‘4' I z: 0’ t"? . 2: H a: CV C) 1 L... i ”(9' ..: . 3 .8 a - ‘3 C) -._...- _ Li) 5a, 8 1°- 2— 3 .. m on Q N . '“ o n .0 v n N _ u o a e m .. z odm coczooam m U vmfiu mumw .QZ use: 3.1.. u: ..rlllidiilia. :1” I» ovillmtiiie $57.25: TTé azmomi ugaus daaH Residual hOOp strain along several axes on the "eastern" side of hole #4 for 6 mils radial interference Figure 6.13 :5 so: as... 8:23 Nnh0 ¢NHO 0.0 mo..0 00.0 000.- 0_.D- v~.0.. NMD- mu “ a . c. m _ s f _ .0 > . - o u no ”u my . a, o _ - Im- " 7» v n N _ . O @ ® ..:..23 . o m a . D 2 cam coczuoam . _ n .. 143 vmflu Noam .02 N. \. who: i\m\ . " ....é%;;:a...;- . _1 " X217: tilt-Tlé ” . amtts» oIlImTllmcm " r mzzzhnm» mwliiwrlllnw_ “ _ QZMQma 20'0 l0'0 000 20' 0 b0'0 uyaus dooH Figure 6.14 Measured residual hOOp strain distributions along several axes between holes 3 and 4 for 6 mils radial interference um 25 so... set. 8:2...5 Nn 0 ¢Nw0 0:0 000 00.0. 00.9- 9.9- QNd... de- mu . .0 _ a: w u . . m N» u .0 r . - o . Nu m c» m _ - Iwi " 2 ¢ n N . _ © @ @ 63.33200 u 0 m ..n.u z cam :95".on " nlu m n - .............. T0 llll""lu-"|I""'--I'I-II "I. .l. O O ugaus daaH axes between holes 2 and 3 for 6 mils radial interference . . . u . ..nu " D . m : . ..o n O u z . u . sale Noam .oz U -;;::-:.. g .o r 3.25”: ..TI-iT-lc O umwzn: ell-Te C. a _ {£5.17 N» Elli _ u _ m M QZMQMJ 1700 Figure 6.15 Measured residual hoop strain distributions along several 145 NM .0 ¢N .0 In! - 3.; «.0: Soc“. 8535 9.0 mowo cod 8.0.- 9.9- v~.o.. ¢> n> 3% 3 or?” w 00x503—u-OU u U 73$: mumm ' ""‘""'-'--l"--l-l'-l"'l'-" 0 am .563qu b o . _ . . . . . _ . . o . . _ _ . . . . . // . . rewrzmcdac +i|l-+.iiilw. Jill .. ”—1 Q» {iii-i m . _ .~27¢_unc sell-isiiilu .QZ Mao: QZMQLD 33..-: Iii-s9 _ . _ _ m _ _ _ Nm. I 20'0- 00°0 £700 200 l0'0 l0'0- 20' 0- 20' 0 ugaus doaH Figure 6.16 Measured residual hacp strain distributions along several axes between holes 1 and 2 far 6 mils radial interference 146 .nvus 60.2. :o 05.263309 3:6 cam .3632.» we £92022... .2...» 0:62 .26 052m .104- -‘ t.) I. ‘ P > ol..l W‘- .5. «.0: ES... 3:220 2.4qu mumw \. . . . . . . - 0.. - VN.0.- Nmfii 0?. - Nm 0 ¢N .0 0. .0 8.0 00 ..0 00 0. 0. .mu “ m m m h . . > Y m» 0 " mu U 0 3 0.. u III _ .n/Uv > U . w n N _ w e e e . .n .. z cam cmczuoaw“ U u - u T0 1 nu . o u H. . .. . \\\ u ‘ ..o _ n . . . / . , / /{L _ . to 4 H O / . : z /fl////x/// ark/la. " ”a.mz;.um. eiiiiiw-i-ie .mu . .. Umuzum» .wii-iieiii-m. nu . . z.wz7¢.”n» .miii-im-iiis. oz .mu7. m..hu+. [/mrw V... 02.0mm {70'0 ugaus doaH Figure 6.18 Measured residual hoop strain distributions along several axes between holes 2 and 3 for 6 mils radial interference 148 respectively. Axijs y3 passes through the center of the holes between y2 axui y“. The same procedure was followed for the set of axes y6. y7 and y8 with y7 passing through the center of holes 4 and 3. Figure 6.14 and 6.15 are the results of the above two sets respectively. Examination of these results reveal that the resi— dual hoop strains are highly localized along the hole center- line and approach zero on either side of the holes. It is also apparent that, due to the presence of an adjacent hole, the magnitude of the residual hoop strain increases all around the fastener hole. The implications of the fanned-out shape of the moire fringe pattern in the photographs presented in Figures 6.2-6 requires special attention. Chapter 7 is devoted to this topic. Figures 6.17 presents the final moire coldworked state photograph and Figure 6.18 presents the results ob- tained from the photograph. Hoop strain values of these magnitudes have not been observed before. This behavior can only be attributed to the presence of the other holes. CHAPTER 7 EDGE EFFEC T STUDY 7.1 Overview The investigation of the effects of a plate edge upon the resulting surface strain field created by the cold- working of the fastener hole is presented in this chapter. Locating the rivet hole near a straight edge in a plate complicates the matter of evaluating the strain dis- tribution theoretically far beyond the case of a hole in an infinite sheet. For the plane stress problem a trans— formation of coordinates from rectangular (x,y) to a bipolar system of coordinatescx and p is almost a necessity so as to render the plane stress biharmonic function say -p a linear equation in the latter system. The bipolar coordinate system is a family of circles through two poles, A, B and the family of circles orthogonal to those of the first family in the x,y plane. The trans- formation equations are given by 149 x = a sing cosha -cos3 y = asinha cosha - 0033 For plane stress “2 = 0'X = 2.2.9'_ ! C'y ayz where w equation: Vail; :0 in which V4 = VZVZ and 150 a: 2 t3= l = z 0 and 32w 3x2 _ loge (x+a)2 + y 6x ’ O'y i loge x2 + Ly-ialz x2 + (y+ia)2 2 (X-a)2 + y2 (7.1) take the form: (7.2) is the Airy's stress function satisfying the (7.3) V2 is the laplace's aper— ator which takes the following form in a bipolar system: v2 = ;_ (coshe -COSQ?§« + 321,: + a2 a2 332 323: 32 Jefferey (33) gives the solution to (7.3) for the relatively simple case of nonplastically stressed hole in a plate sub- jected to tensile force T as: 151 m _n ‘II = aT _1_ sinha, (l + 2 E e a coshaB 2 n=1 + BO [ oz (cosha - cosfi) + sinha (coshacosg-l)] + A1 (cash 2a - l) 0083 on . +2 An[ cosh (n +l)oz - cash (n-1)a] n=2 +En [ (n - l) sinh (n+l)a - (n + l) sinh (n - l)a cos n3] The constants B0’ A1, An, E are determined by the n use of boundary conditions. Because of the nature of the boundary conditions (a row of holes in close proximity to each other near a plate edge) encountered in practice, the use of this analytical solution has not been attempted. It is not known whether the solution could be extended to in- clude nonlinear material behavior. 7.2 Material andeExperimental Procedures There are two groups of specimens used in this phase of the investigation. All the specimens were cut from a single plate of 7075-T6 aluminum. Group A had all but one factor constant, and consisted of three specimens SPP, SPT and SPE. Hole diameters were held constant at a nominal value of 0.261 in. (6.63 mm); radial interference for each 152 one of the specimens during the prestressing operation was maintained constant by a proper selection of sleeve thick- ness and mandrel combination. The machining of the critical edgesnearest the fastener hole was, in-so-far-as possible, made identical, and care was taken to ensure that there were no machining-introduced stress raisers on that edge. Again the mandrel drawing rate was set equal for all specimens at .5 cm/min. The variable of interest is the edge distance/dia- meter ratio. The edge distance, e, is defined as the dis- stance from the hole centerline to the nearest edge of the sheet material. Denoting the hole diameter by 9d", then the ratio (e/d) is of practical significance in the design of structural joints (38). In the design of fatigue-improvement fastener sys- tems an attempt is made to keep the (e/d) ratio above a threshold value of 2.0 Values of (e/d) greater than 2.0 are known to result in increased fatigue life of the assem- bly (32). The degree of life increase and the physical rea- soning why e/d = 2.0 is a threshold value are not known. The effects on life of using e/d less than 2.0 have not been ex- plored. Specimens SPP, SPT and SPE were designed with (e/d) ratios of 1.8, 2.0 and 2.25 respectively and specimen SPC of Group B, an in-line multi-hole pattern comprising four holes, was designed with an (e/d) ratio of 1.8. 153 Moire fringe photographs of specimens SSP and SPT are presented in Figure 7.1, 7.2 and 7.3. 7.3 Experimenta;_Results and Discussion 7.3.1 Hoop§train Distribution Both residual radial compressive and hoop strains were obtained. The evaluation of hOOp strains at the hole boundary along an axis parallel to the plate edge resulted in the plot of Figure 7.4 for specimen SPP with an (e/d) ratio of 1.8. From the graph it is observed that the high- est strain occurs at the hole edge (point x = 0, y = 0). Like a damped harmonic wave, the residual strains vanish with increasing distance away from the fastener hole. Fig- ure 7.5 displays the detailed analysis of residual hOOp strain distribution at various locations, y = 0.00, 0.072, 0.181, 0.260 and y = 0.330 inches (0.00, 1.83, 4.59, 6.60 and 8.38 cm) which is close to the straight edge. Similar detailed results for specimens SPT and SPE whose (e/d) ratios are 2.0 and 2.25 respectively are presented in Figure 7.6 through 7.9. For specimen SPE the hacp strain distribution at the fastener hole is illustrated in Figure 7.8, whereas Figure 7.7 shows the location and magnitude of the minimum residual hoop strain obtained for the same specimen. Examination of Figure 7.5 and the rest of the re- sults of this section reveal that midway between the hole edge and the straight edge of the plate the strains almost vanish: 154 -. -._-. .- '- — u .4 - -V-’ v” ’C ’- ' -- .—......_.~- 0.“- .~—~.--- .- ‘4‘ . r o- .0 nca—u.‘ ..-.-- ~. . - - --- ~ . ... -'* ----.--...._ .- ~---. ~ .- -.- - .0.. .—.-—-— --—.—--. “,“.._._-.-~- ~ 0.» . ~ . H - - - —..---—---H‘---.- --,.--- - e. - -- — -- - . .-- ..._.-.__,_, o - a”--. m-—~*‘~ --o--- - -~ < - - - - --- - ~ -- — - ~- u- ‘- M W-.- ~.*- w>-> -\ ~ -—-~ - . ~— 0- -- . . .----. _ .-.-—- -. -. -. .- - «non-o -.o-ru-- - .0"- - -v- on M ..fl. ._ .r -o- '. . . .. ~< 0*... .-.—-.'-s -~ .0 o~-——-o.--—- ~---— -..o- ---. 5 - ....~ - ‘." «ww~~‘ c- o-o- >c..~ p~...—Q--._- aw...- Fioure 7.I SPP after halo coldworking, grating parallel to axis "-3 .uEfotEoo 0.2. .330 haw NS 952... : “ - 155 “ --v4-~ ”-v ‘Afih- _.._ L w - wwv—w '1 . A1. 1". 1.: . -v—v ‘ v a; F ..v. .— h ' \ ' I‘. - ll -..‘_.A 4.7"“- V ‘ I A U ‘ ‘ -. V , v . l. .. . - . e ’ , - \ ‘ I . , 4 ,-> , _ r. ‘. j 0 ., p, A . ' . A . . \ ~ I u ' . .- ". '.. I A , ‘ ‘. . - - ' .» " o0 " ‘6' _ ‘ ‘ r ‘ - 1' 'Q a. “‘ o .’ ' , e ‘l-F. l‘ ' . ‘ . ~ ‘ b -_ - ‘. - ’ ..- W' ' o a“ "I‘ O"‘. yr“ ‘ 'I . - _ . o l v ,‘ ‘- . .- - ‘ , o .r~ . _ .r N M- l. . J .- ' ‘r ... - . c g ‘ , r- - ’ ‘I ~ g ‘ e ‘ ., . " d ’ '7 ‘ ' u . ‘ ‘ ‘ " . ‘ ..~ ‘ . ’ ' l; l, if H . :5 llilgl-z V .l s- ‘l W . ll 1 I ~ ! Figure 7.3 SP P Maire frin e t f compressive 8'qu!" “giggtrgghheg: plate edge, grating parallel to axle w-E 157 Q: _J N .__. l"? 0 0. 0. <0 3’- '0' CD 22 £2 LLJ ‘0 _J CD I: 0108 0730 Dislance From Hole (in) i l I I | lr9——r+——+thmrmw I ~0MJB -'o.l6 0.24 / -b.32 .40 fi r T I . boo coo zoo io'o oo'o loo- zoo U!DJls dooH Figure 7.4 Residual hacp strain distribution along an axis tangent to the hole boundary for 8.9 mils radial interference ‘ ul o: \ __J 1 )9 N 1 1 =* K) .. 7 * m 'o' a. "‘ I 2 CL g: Q’ " . 3 N. U? I .0 ‘ ., El (D O 1 . gm -' Z '/ U ll / £91on .9. Lu +4 0 __J a CD I: 008 l i .. 1 .E .— 1 | g : .-.. 4| E O I 33-33-2933. ' O g 90'?” 1 ___1__-___------- -— -— -- "- "'"o ‘- 5 ' 9.9.0.??? 1 u, 3 Cl «hngl 4; fl 3 DJ . O .3, i (_3‘; : " l i ,o -- i LLJl i . ' 0 .41 i : l ‘ . . . l A a .2 i _o' l 0 . v " : N. : “ ,0 : N 1‘ '9 . ': 1? l . ,1 1 3 o \' fit ,. Ti 1 Y Y 1 .v . v . U £700 90' 0 20'0 l0°0 00'0 l0 0- 20 0- 9.0 0- ugolls dooH Figure 7.5 Measured residual hoop strain distributions along several axes near a plate edge at different radial distances for 8.9 mils interference a: _J L0 1 ‘ l— 1 In R’- 4 .' g '0. 0— ‘ l (0 g I” n ' 1 9 O - ’0' Z , 3 l LLJ ' z 0. S a g. a? .8 I ' gg wlo o 5 1 .92 i f ‘ ----------------------------- ~§ s 3 l.-.. E 3 g 8 § ' 0‘) g r? a 8§§2§ 1 Q (I) 333333 '9 Z >>>>> Lu ‘3 11'- __JI ’0 i l a“. boot 20"0 'zob lo'o oo‘o Ioo- zoo- coo- U!DJl$ dooH Figure 7.6 Measured residual hoop strain distributions along several axes near a plate edge at different radial distances for 8.9 mils interference (SpeCimen SPT) . 0.23m D. Y4: ‘ L 160 0. 24 s (he ------_--—"- 02% SP E8 LR i is. 2° ' i L 000 Distance From Hole (in) HOLE NO. 4603 0. l6 1 - C-------.--------------b-----. ----— 3024 ibsz bO'O 20' 0 Figure 7.7 d -040 U zoo l0'10 oo‘o 06- 206- so ulolls dooH Residual hOOp strain distribution along an 8X18 0-24 inches along a plate edge for 8.9 mils radial interference 161 .5. so: Ea... 8:220 3.0 0.0 000 000 00.0.- . .7! / w: mm. mm .0: 95: .--_--.----------h-------------- ------.-- -0--- O t------.. 0.0- 30.. NB” . £00.: "Tll1¢lll2 W 3.08-. oe. .. zoo loo oo'o loo- zoo- soo- 90' 0 b0'0 ago-us do 0H Residual hoop strain distribution along an axis tangent to the hole boundary for 8.9 mils radial interference Figure 7.8 162 NmAv ¢NAV .0.. 0.0: » mm mm o w mNgw-lll u an ,mtsowmm .9 .l / .QZ mmo: 0_ .0 00.0 00.0 ' ""I"|--"'lfl ES... 0000.05 mod.- -——- - -———------------d 9| ‘- %///i O 1-- o- n ', E q / _ --1—----—--- - - 0. .0.- VN.0.- N09- 00. S. 2. mm .6... .13 on J coocoooi um» .0» av» ..m» up“. u: 0 110 1111* 11.1.1 1.- J11 +1 L... 01 .é 11m. ...P1+11 la 22-5 ML. .. ago-us dooH Measured residual hoop strain distributions along several Figure 7.9 axes near a plate edge at different radial distances for 8.9 mils interference 163 but that they increase again as one approaches the straight edge. Therefore in structural fastener applications there seems to be the possibility that this radial expansion of the hole generates a significant tensile strain climate at the plate edge. This could result in serious problems in stress corrosive environments. Figure 7.11 is a summary of the results presented in Figures 7.4 through 7.10. Peak residual hoop strain values were plotted as a function of the distance from the fastener hole edge for (e/d) values of 1.8, 2.0, and 2.25 as shown. Specimen SPP (e/d = 1.8) had the highest tensile residual strain at the straight edge, approximately 0.5 percent. Spe- cimen SPT (e/d = 2.0), and SPE (e/d = 2.25) had lower res- idual strains of 0.25 percent. Figure 7.12 is a summary plot of the residual hOOp strain distribution along the plate edge for the case of a row of rivet-fastener holes. Mandrelization order of this specimen (e/d = 1.8) was holes 1, 2, 4 and #3. It is ob- served that the strain distribution around hole #3 attains its local minimum which is almost equal in magnitude to a single fastener hole in a semi-infinite plate as shown on the same graph. It can also be seen from the same plot that the strain magnitude increases by a factor of almost 2 when single hole and multi-hole pattern results are com- pared. The strain distribution, both in magnitude and ex- tent, increases for only one fastener hole coldworked in a 164 .0.. 20: 60.“. 8007.5 0:0 wow 00.0 009- m_.o.- vmdn mmfi- 00.0- atom . .0 . Cs . u u . in..- ..o u N O 3 MNN 1 w m . o m mm H > z ZUvéUWQm . . ..0 u m u . -1--------111--."----l--------------:---z:-----:-- - --:.0 m... 0101 a .1... «m. a n. U. m. m. 1m. A... 3 m1 0? w ..o D ..0 0 .2 M: mm. mm .02 m5: ..o .. an...» www-- - ._ m _ Q25: _ .i .9 ..1- 1...: ..-..._-...l--- .3. . .ro ugous dooH Figure 7.10 Residual hoop strain along plate edge for 8.9 mils radial interference 165 .9 E- 0 .5. -‘.-’ a- .3 8 O .3. u g -d>8 :' 0 2 § 9.‘ ‘ 2 fl. :0 8 § 8 9- 0 ea 4N 1 o l 8 ,5 °' 5' ul .2 0 .1a 1 . s 5 a. .Q g 0 ’ ‘6 i5 .8 O o 0 ° 3 8 3 8. .9- 3 8 -' — o' o (meal-e) opus Owl-l m Figure 7.11 Peak residual hoop strain along radial line from hole boundary to plate edge 166 and mud OQN «one... .oouw 22d 0:03 .2335 u x ._ no So 8M. on. 8.. oo . L p . F ii 000 . m 05.2: 0.0.. co 3:0 . .b. VODAU *kC. bVOO m . u 69 \\v . n . _ u u u . . u n u n u _ .09 . . . n u u n _ . . .OQ~ o 2... a 3:055 catatonom 23.. c n N _ «2.2: .mmduo 10nd £33620 Bo: ..:. o . + 00:93:02: .0501 60m mtm. .230 05.203300 cam :53on # 0m.» waoud'obpa now w ulous doc“ 12 Measured residual hoop strain distributions along specimen Figure 7. edge for various coldwork situations 167 row of holes compared with the case of the strain distribu- tion obtained with only one fastener hole existing in a semi- infinite plate. 7.3.2 Radial Compressive Strain Distribution Compressive residual strains are presented in Figure 7.13 through Figure 7.21. Specimen SPE (e/d = 2.25) had the highest radial compressive strain (3.5 percent) occurring at the hole boundary, followed by specimens SPT (e/d = 2.0) and SPP (e/d = 1.8) with 2.5 percent and 2.25 percent respec- tively. Figure 7.14 presents plots of compressive residual radial strains between a single fastener hole and the straight edge in a semi-infinite plate. For the multi-hole pattern the results are given in Figures 7.15 through 7.21. Figures 7.17 through 7.21 summarize the findings of the multi- hole pattern configuration with regard to residual radial come pressive strain distributions as a function of order of fas- tener hole coldworking. The graphs show a peak residual strain and zero strain values between the fastener hole edge and the straight edge boundary of the plate reSpectively. (The radial stress should of course go to zero at the edge). In a multi-hole pattern, the prestressing of a hole markedly affects the strain distribution of adjacent holes. Coldworking of hole #1 resulted in a residual strain value of approximately 2.5 percent. Subsequent coldworking of holes 2, 4, and 3 lowered the strain value to approximately 168 3am 008.0003 .0000 20.0 0 .00: 50...... 03308800 .0200. “.0 00:00.0: 2: E 00...: 70:4, . . aei‘."'i;§‘§ ...Is?v.-\ul‘?JL .I.\.t:‘ \t,‘.l.\ ,.r . L ‘...\.V..4\l‘§“‘v«i.. 14 . ‘ ‘Dhi‘ .11.. ‘~-‘.“1o§ , nu; \ \ . HUI»)! Hsffki . \ ‘0‘! . ‘7'... t. n ..i‘...’.}’- .10 . l ..v‘ . . , .9 0.030.050 00:5 0:02. ..m: 22.1% n;lI..‘1v‘. Fri} Ill... {WM 169 O .45 0.40 SPT E/D'I 2.00 035 3 030 filo-Lao 0.25 030 Difloncc From tho Hole Edoofln.) ms 010 0.55 5 . 8 3 <5 I5. _ 0 mad“ 3‘ugnus 9ng Figure 7.1A Residual radial strain from hole boundary to plate edge 170 l 640’ O 4 035 L. EC E ND. 1 O 2 030 i l mv—ak—ae: Y4 :t ‘ 1 SP C 025 C = Coldworked l I 0.20 “JO Specimen V SPCZR CNHI 0J5 Distance From Hole (in) \m‘N\fi duo 0‘05 HOLE N0. 000 ‘0.05 600 900 200 060 9200- 900- 606- zro- ugous aAyssadeoo Figure 7.15 Residual compressive (radial) strain between the plate edge and hole #1 after coldworking of hole #1 only for 6 mils radial interference 171 '52 -___.__.__ .. “r0 ‘ : @¢ 2 f C] : @n L". Z " z “8 . LLJ '1 0') e @~ 3 us" ; _lr o—@— '._..-V-.--_ -0. 3 U *0 0. o (n ‘f :8 r . s 3 “f O u _ .E 3 II 3 U 06 3 " “’ 0 W5 23 g) (3.! _J O _J I E ‘ 9 5 ('0' [,5 rm «0 U § E}: .2 .15 ’ C) c: D I Z - IO - -§? LL.I ; O —J E Q : I I 8 ................................... é--—--—---------—------------------—----—---——-- .0. U3 . 0 e . . 9 600 900 9.00 060 206- 900- 606- am- ugous anyssadeoo Figure 7.16 Residual compressive (radial) hoop strain between the plate edge and hole #1 after coldworking at 6 mils radial interference 172 «0:00. .003 0.0: 60...“. 0000.05 ; 0nd 0N0 0N0 9.0 0.0 00.0 00.0 o IONO 0 r8.- mzs. w u 00:03:02. .2001 ( .nNN 02.33200 2. .3: 2:0 . 0000 v 03.503300 00.0... :4 u anon .# 0.0: .00...” .0. 5030 020003600 0 6s.» v m N _ .A 0 O O O 3 Z tom.v :1 0 00 00m 0 6.0 m BNO wound ‘uyous wssamo Figure 7.17 Residual compressive strain distributions after coldworking 173 x O ' '9 O O S ' CD 2 "‘4 r0 0 O >. U ; a to ‘t >. C c O _ 5 - 0 ‘——-@— 0 2 «IN a O u 6 Q U U) m 055 Distance from Hole Edge, Inches o'.Io (105 HOLE 34 Y '0 0 «3 S vb - ' O V M n N "' ' O 0 we 0190 ' ugous angssaidmog Figure 7.18 Residual compressive strain from hole boundary to plate edge for multi-hole pattern specimen 1 7L:- C) at W"). 0 .2 U ¢§ N0 «1 g)fl’ " l s. 0 K) 0 o N 1: C TC) 5 0 Q) .- 82 «n rg§ <~"’ UN :25 ‘ v ‘5- E 3 3.2 0 .,, >’ g 0 ll 0 a )0 .c Q 00¢ O a) 3 c: o 0- '0 .2 Lu 0 o 0 3E E 0 3- O 04- 0-1 0 o 0 c 5‘ 0 ‘— 6' n o +~°- " 0 a 0 ' 0 .2. '1 .0 a, .‘3 0. 3 ‘0 N. 8 N to I: o in' c m ,6 N ‘ 0 iuoaud 'ugous angssudwog Figure 7.19 Residual compressive strain distributions after coldworking holes 1, 2, and 4 2175; >< _Eg T m 1’ u: :?:E <30 >. a A Q U) “ 0 (:8 ,0! 85 0 G)” 35% w w 8 Z ‘0 E0§ I (D >. u N 0.2-E g Sixhz - E 05" 8 - .2. @— ggd ' -0 E g 0.19 3 u: 3: difia: E; - .. g 0 ' '6 I u: .9 ‘5’ ' C5 .- 2- a) e“ a “0" o $* II 0" " _8 - O r v ‘ Lb 0 t0 K3 ‘3 F: C5 “58) g :3 g N' ‘2 0 11133836 'NIVULS 'IVIOVB Figure 7.20 Residual compressive strain distributions for holes 2 and 4 after coldworking all holes 176 00:05.3000000 0.0: E0: 0000.05; 0nd 000 00.0 0.0 00.0 00.0 .0: . n: m .20 .00.. -000 0:2 0 _- 00:20:02: _0_00¢ 1.00.n 03.33200 . 0 m 000 008.025 .. :) .1numn c n m _ .A. 0 © © 0 z a — .000 1 0 1 f 80.0 iuaoaed‘ugous |ogpog Figure 7.21 Residual compressive strain distributions after coldworking all holes 177 1.5 percent and reduced the residual compressive area from around 0.25 in. (6.35 mm) to roughly 0.15 in. (3.81 mm) radially away from the fastener hole, thus partially wiping out the beneficial effects of the coldworking operation. The overall message presented in these figures is that the peak compressive residual strains are shifted away from the most critical and important area, near the fastener hole, to the interior in between the prestressed holes. Also, the subsequent final coldworking of hole #3 seems to be in- effective after the coldworking of the rest of the holes in the row (Figure 7.21). One possible deduction from the results of a single fastener-hole in a semi-infinite plate might be that with in- creasing (e/d) ratios the residual compressive strains at the fastener hole boundary increase. The case of mandrelizing a fastener hole in an infinite plate for a given material, specimen configuration, and loading, the strain distribution represents a limiting state. Specimen SP2 with a hole in an infinite plate gave a radial strain value of around 5 percent for a corresponding prestressing radial interference of around 7.5 mils. Nevertheless, for a radial distance greater than 0.05 in. (1.27 mm) the residual strains are approximately of the same magnitude and the values differ by less than 0.5% at any point in this region, Figure 7.14. In general, it is observed that, for the case of a single fastener hole near a plate edge, regardless of the 178 (e/d) ratio used, the radial strain starts high at the hole boundary and decreases to zero as the plate edge is approached. Contrary to this behavior the summary plot of resi- dual hoop strains as a function of the radial distance from the edge of the fastener hole for the same Specimens indi— cate a high value at the hole boundary diminishing to a local minimum, at a distance of approximately 0.168 in. from the hole. A localized higher strain value at the plate edge di- rectly Opposite the fastener hole is then attained. CHAPTER 8 CONCLUSIONS 8.1 Introduction This investigation has been concerned with the study of: 1. the effects of large in-plane compressive loads on a mandrelized fastener hole, 2. the interaction between the surface strain fields which are created by prestressing two or more fas- tener holes drilled in close proximity to one another. 3. the effects of a near plate edge on the residual surface strain field, and, #. ramifications of the existence of a residual strain climate, produced by coldworking a near hole, on the edge of the plate in a corrosive service environment. The moire method of strain analysis has proven very useful for the investigation. With this methodology, the measurement of small and large elastic and plastic strains over an extended field was accomplished. 8.2 Experimental Apparatus Optical spatial filtering proved to be indispensi- ble in separating the u-field and v—field isothetics. 179 180 The fringe analysis system minimized data reduction problems. The micr0processor-controlled digitizer was in- strumental in obtaining reliable displacement field data. This was an extremely important factor since the data must be differentiated to find the strains. Additionally, mis- match techniques were introduced in the fringe formation process to improve the accuracy of the measured displace- ment gradients in the x and y directions. In the optical analyzer, ordinary focusing errors are not significant since for a lens whose aberration char- acteristics are smaller than the diffraction limit of the lens aperture, about 80 percent of the energy from any point of the specimen and master grating assembly falls in a small region called the Airy disk on the image plane. The rest falls immediately outside it. As long as the area of this Airy disk is smaller than the separation distance between the moire fringes, focusing problems are negligible. This was almost always the case in this investigation. 8.3 Summary of Results The results can be summarized as follows: 1. The axial residual hoop strains decrease with increasing remote in-plane compressive applied stress, es- pecially in areas close to the fastener hole. 181 2. The effect of cycling is a decrease in the res- idual hoop strain around the hole except in areas where flaws exist at the fastener hole boundary. 3. The transverse residual hoop strain increases with increasing overload applied sfiress in areas within 0.135 in. of a (0.261 in. diameter) hole boundary. 4. Remote in-plane compressive loads smaller than buckling loads and cycling of loads have no effect on a non-coldworked fastener hole. 5. The residual strain climate around a coldworked hole is not symmetric. The assumption of uniform radial loading in the analytical theories is not entirely an ac— curate model. 6. The residual radial compressive strain remains essentially constant with remote compressive load applica- tion. 7. The residual radial compressive strain distri- bution assumes an exPonential nature. The strains attain their maximum value at the edge of the hole and rapidly diminish to zero with distance from the hole edge. 8. For the specimens subject to large in-plane compressive overload, the results fer the initial stages (after coldworking only) agree quite well with those ob- tained by previous investigators, notably W. Adler and D. Dupree (29), and by Cloud (20). The discrepancies probably result from experimental factors such as levels of cold- working. 182 9. The observed results for specimen 010, Figure 5.8, seem to be quite in agreement with the theory that under loading that produces cyclic plastic strains, the residual stresses, which are nothing more than unevenly distributed mean stresses, tend to become smaller with cycling. This behavior is commonly called cycle-dependent stress relaxation. 10. However, the results presented in Figure 5.6 for specimen ClO indicate that, in the presence of residual stresses, the material is eXperiencing cyclic creep on being cycled. This phenomena does indeed occur under tensile mean (residual) stresses. The moire fringe photographs suggest that there existed a flaw, a micros00pic crack, at the fas- tener hole boundary of this specimen. In those small but critical neighborhoods near a crack, the presence of even moderate residual tensile stresses could be detrimental, and a runaway crack condition is possible especially under a load control test as in this particular case. Neverthe- less, there is one strong message that is clear in the re- sults of the compressive overload study: a machine part may be properly mandrelized to introduce beneficial compres- sive residual stresses and the service loads in the member kept small enough so that the residual stresses are stable for a good part of the machine's life. But should large over- loads be encouraged. the benefit of the original compressive residuals would be lost. 183 11. Two hole diameters is approximately a minimum hole separation distance,for a radial interference of 6 mils, below which the effect of coldworking a row of fastener holes diminishes the residual compressive strain field around the fastener holes, thus mullifying the advantages of the coldworking process. 12. The coldworking of a single fastener hole or a row of holes near an edge of a plate results in an unde- sirable tensile strain climate on the plate edge. (See also conclusion no. 16.) 13. The results also indicate that the level of rad- ial interference for a multi-hole pattern prestressing oper- ation needs to be given some consideration. Maximum fatigue life presumably would be obtained if the resultant stresses were evenly distributed across the member at max- imum load. But, eXperiments indicated that (test specimens SPB and SPC - a multi-hole pattern), if the level of cold- working was kept constant from hole to hole, the beneficial overstressing effects originally sought tended to be nul- lified. In general, the compressive residual strains were higher away from the hole boundary. This is in contrast to what is observed with a coldworked single hole in a plate. A partial eXplanation is that the hole edge (side) adjacent to the one being prestressed goes into a state of tension, and this state of strain must first be overcome before establishing the permanent strain that is to be imposed. 180 14. Nullification of the pre-stress would not be a serious flaw if there were not the possibility of premature structural failure in service due to high levels of cold- working. Plastic flow occurs when the difference between the circumferential and radial stresses equals the yield strength. Since these stresses have opposite signs, the difference can become very large without the appearance of detrimental tangential stresses large enough to cause failure. 15. Examination of the specimen photographs and the data photographic plates in an optical analyser revealed that the hole eXperiences some sort of "rigid body motion" perhaps more so than the actual deformation imposed by the mandrel in the direction perpendicular and towards the straight edge boundary of the plate. This effect is more pronounced in specimens with (e/d) ratios smaller than the threshold value of e/d = 2.0. 16. For a single fastener hole in a plate, residual hoop strains attain a high value at the hole boundary dimin- ishing to a local minimum at a distance of approximately 0.168 in. from the hole. A localized higher strain value exists at the plate edge directly opposite the fastener hole. (6 = .0025 for e/d = 2, for example.) 17. In a row of rivet holes, the peak compressive radial residual strains are shifted away from the most critical and important area near the fastener hole to the interior between thepre—stressed holes. 185 18. Experimental projects of this nature have their own shortcomings. Nevertheless, in spite of the limitations on the results presented in this study, drastic assumptions commonly made in analytical work about the materials con- stitutive behavior and magnitudes of the strains were not made here. Possible asymmetries found in real fastener joints which present formidable difficulties in formulation were pointed out. 8.4 Future Research Future fastener research should be directed towards the determination of the effects of the factors that were not considered in this investigation, namely different levels of coldworking on the multi-hole pattern in order to arrive at an Optimum coldworking levelas a function of (e/d) ratio. An extremely important step is to measure residual stresses and to correlate them with the residual strains de- termined in this study. Other pertinent variables should include plate thick- ness, hole straightness and ovality, sheet material, and hole separation distance. These variables and others un- doubtedly play a significant role in the redistribution of the resulting residual strains and therefore on the fatigue life of the structure after the coldworking Operation. REFERENCES 10. REFERENCES Mangasarian, O.L., "Stresses in the Plastic Range Around a Normally Loaded Circular Hole in an Infinite Sheet" (J. Appl. Mech., Vol. 27, 1960), pp. 65-73. Forman, R.G. and Y.C. Hsu, "Elastic-Plastic Analysis of an Infinite Sheet Having a Circular Hole Under Pressure" (J. Appl. Mech., Vol. 42, 1975), pp. 347-352- Sachs, 0., and J.D. Lubahn, "The Strength of Cylincrical Dies" (J. Appl. Mech., Vol. 10, 1943), pp. Al47-A155. Kuhn, P., Stresses in Aircraft and Shell Structureg (McGraw-Hill, New York, 1956). Calcote, L.R., and C.E. Bowman, "Experimental Determin- ation of the Elastic-Plastic Boundary" (Exp. Mech., V01. 5, Aug. 1965), pp. 262-2660 Oppel, G.U., and P.W. Hill, "Strain Measurements at the Root of Cracks and Notches" (EXp. Mech., Vol. 4, Regalbuto, J.A., and O.E. Wheeler, "Stress Distributions from Interference Fits and Uniaxial Tension" (EXp. Mech., Vol. 10, NO. 7, July 1970), pp. 274-280. Kasgard, P.V., E.E. Day, and A.S. Kobayashi, "Exploratory Study on Optimum Coining for Improvement of Fatigue Life" (Exp. Mech., Vol. 4, 1964), pp. 297-305. Dechaene, R., and A. Vinkier, "Use of the Moire Effect to Measure Plastic Strains" (J. of Basic Eng., Vol. 82, Series D, June 1960), pp, 426-434. Morse, S., A.J. Durelli, and C.A. Sciammarella, "Geo- metry of Moire Fringes in Strain Analysis" (J. of Eng. Mech. Div., Proceedings of the American Society of Civil Engineers, Vol. 86, No. EM4, Aug. 1960), pp. 105-117. 186 ll. 12. 13. 14. 15. l6. l7. l8. 19. 20. 21. 22. 23. 24. 187 Schiammarella, C.A., and A.J. Dureli, "Moire Fringes as a Means of Analyzing Strains" (J. of Eng. Mech. DiVe’ V01. 87, N0. EMl, FGb. 1961), pp. 55-714‘0 Theocaris, P.S., "ISOpachic Patterns by the Moire Method" (Exp. Mech., Vol. 4, June 1964), pp. 153-159. Weller, R., and B.M. Shepard, "Displacement Measurement by Mechanical Interferonetry" (Exp. Stress Analysis, VOlo 6, N00 l, 19%), pp. 35-380 Chiang, F., "Production of High-density Moire Grids-- Digcussion" (Exp. Mech., Vol. 9, June 1969), pp. 28 -288. Post, D., "The Moire Grid-analyzer Method for Strain Analysis" (Exp. Mech., Vol. 5, Nov. 1965), pp. 368- 377. . Post, D., "New Optical Methods of Moire Fringe Multipli- cation" (Exp. Mech., Vol.8, Feb. 1968), pp. 63-68. Post, D., "Sharpening and Multiplication of Moire Fringes" (Exp. Mech., Vol. 7, April 1967), pp. 154- Luxmoore, A., and R. Herman, "An Investigation of Photoresists for Use in Optical Strain Analysis" (g. ogBStrain Analysis, Vol. 5, NO. 3, 1970) pp. 1 2-1 a Zandman, F., "The Transfer-grid Method, a Practical Moire Stress-analysis Tool" (EXp. Mech., Vol. 7, July 1967). pp. 19A-22A. Sciammarella, C., "Moire-fringe Multiplication by Means of Filtering and a Wavefront Reconstruction Process" (Exp. Mech., Vol. 9, April 1969), pp. 179-185. Little, R.W., Elasticity (Englewood Cliffs, N.J., Prentice-Hall, Inc., 1973). Sokolnikoff, I.S., Mathematical Theory of Elasticity, Second Edition (McGraw-Hill, New York, 1956). Nadai, A., Theory of Flow and Fracture of Solids, Second Edition, Volume 1 (McGraw-Hill, New York, 1950). Cloud, 0., "Residual Surface Strain Distribution Near Holes Coldworked to Various Degrees" (AFML-TR-78- 153, Air Force Materials Laboratory, Wright-Patterson AFB, Ohio, Nov. 1978). 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 36. 188 Cloud, 0., "Simple Optical Processing of Moire Grating Photographs" (Exp. Mech., to be published Aug. 1980). Thompson, B.J., "Coherent Optical Processing--A Tutorial Review, 1972" re roduced from "Optical Tranforms" (Ed. H.S. Lipson , Chapter 8, “Optical Data Processingfi 1970, p.267. Chichener, N.A., A.J. Durelli and J.A. Clark, "Develop- ments in the Optical Spatial Filtering of Super- imposed Crossed Gratings" (Exp. Mech., Vol. 12, July 1972), pp. 496-501. Chiang, F., "Techniques of Optical Spatial Filtering Applied to the Processing of Moire-Fringe Patterns" (Exp. Mech., Vol. 9, Nov. 1969), pp. 523-526. Adler, W.F., and D.M. Dupree, "Stress Analysis of Cold- worked Fastener Holes" (AFML-TR-74-44, Air Force Materials Laboratory, Wright-Patterson.AFB, Ohio, July, 1974). Ford, S.C., B.N. Leis, D.A. Utah, W. Griffith, S.G. Sampath and P.N. Mincer, "Interference-Fit-Fastener Investigation" (AFFDL-TR-93, Air Force Flight Dynam- ics Laboratory, Wright-Patterson AFB, Ohio, Sept. 1975)- Cathy, W.H. and A.F. Grandt, Jr., "Fracture Mechanics Consideration of Residual Stresses Introduced by Coldworking Fastener Holes" (preliminary Draft Re- port . , Moore, T.K., "The Influence of Hole Processing and Joint Variables on the Fatigue Life of Shear Joints" (Tech- nical Report AFML-TR-77-l67, Vol. 1, Air Force Ma- terials Laboratory, Wright-Patterson AFB, Ohio, Feb. 1978). Jeffery, G.B., "Plane Stress and Plane Strain in Bi- polar Co-ordinates" (Transactions of the Royal Society, 221, London, 1921). p. 265. Parks, V.J., "The Moire Grid-analyzer Method for Strain Analysis--A Discussion" (Exp. Mech., Vol. 6, May 1966). pp. 287-288. Juvinall, R.G., EngineeringgConsiderations of Stress, Strain and Strength (McGraw-Hill, New York, 1967)? Sandor, B.I., Fundamentals of Cyglic Stress and Strain (The University of Wisconsin Press, Madison, 1972)“ 189 37. Holister, G. S., and A. R. Luxmoore, "The Productions of High Density Moire Grids" (Exp. Mech., Vol. 8, May 1968), p. 210. 38. Timoshenko, S.P. and J.N. Goodier, Theopy of Elasticit , Third Edition (McGraw-Hill, New York, 1970). 39. Dalley, J. W., and W. F. Riley, Experimental Stress Analy- sis, Second Edition (McGraw-Hill, New York, 1978). 40. Chandawanich, N., and W.N. Sharpe, Jr., "An Experimental Study of Crack Initiation and Stress Intensity Factor Around Coldworked Holes" (Proc. 1978 SESA Spring Meeting, Wichita, Kansas, May 1978). 41. Nadai, A., "Theory of the EXpanding of Boiler and Con- denser Tube Joints Through Rolling" (Transactions, American Society of Mechanical Engineers, Vol. 65, Nov. 1943), pp. 865- 880. 42. Taylor, G. 1., "The Formation and Enlargement of a Circular Hole in a Thin Plastic Sheet" (J. of Appl. Mech. and Appl. Math, Series 7. l, 1948), pp. 103- 124. 43. Swainger, K.H., "Compatibility of Stress and Strain in Yielded Metals" (Phil. Mag., Series 7: 36, p.443. 44. Sharpe, W.N., Jr., "Measurement of Residual Strains Around Coldworked Fastener Holes" (AFOSR-TR- -77- -0020, Air Force Office of Scientific Research, Bolling AFB, Washington, 1976). 45. Gibson, H.S., Jr., C.G. Trevillion, L. Faulkner, "Thick Section Aluminum Hole Coldworking," (AFML-TR-78-74,) Air Force Materials Laboratory, Wright-Patterson AFB, Ohio, May, 1978. 46. Carter, A.E. and S. Hanagud, "Stress in the Plastic Range Around a Normally Loaded Circular Hole in an Infinite Sheet, " (J. Appl. Mech. 42: 2, 347- 352.1975)- APPENDIX A Computer Program and Subroutines 190 APPENDIX A Computer Program and Subroutines PROGRAM HOOP (INPUT, OUTPUT = 65) C C COMMON/INTP/TINT (101,2) COMMON/DIFY/YDIF (101), DY (100) COMMON/FLOTER/XRAY (900), YRAY (900), INUM COMMON x (80,2), Y (80,2), NPTS (2), XPL (101), XL, XH,YL, YH, XMIN, XMAX REAL M LOGICAL FIN C FIN=. FALSE. IC = 0 INUM = 0 C C ------ ENTER RUN DATA C READ 1, ISET 1 FORMAT (A10) 100 CALL READIN (P,M,C,XO,IPR,FIN) IF (FIN) GO TO 500 x0=.2 C C e ----- DETERMINE X-RANGE FOR INTERPOLATION & DELTA VALUE 0 CALL RANGE (DEL) C C ----- -COMPLUTE INTEROLATED SMOOTH CURVES THRU DATA AND BASE SETS C CALL INTERP (DEL) C C ------ CORRECT ABSCISSA ARRAY C CALL CORRECT (x0) C C ------ COMPUTE CURVE DIFFERENCES & DERIVATIVES C PMC=P*M*C CALL DIFF (PMC,DEL) C IC=IC+1 GO TO 100 500 CALL PLOTH (IC,ISET) STOP END (2),XPL(101),XL,XH,YL,YH,XMIN,XMAX ,IPP,FIN) IN (P n c x0 ISTNHf9S fST v A P m \ Z q— H z I ..I QH m NU w ">U t H II 3 to AZ (DI-H I- I- V- 3 Hz Q DVD 2 G>U 7 I I I U FUUU GO TO 999 Y(I,2).LT.XLAST) GP TO 999 ) :0 999 N .OR. J,2),J=1,N) I—AI- OJVVAXOPO Fv-AH ZV>~NVO ll ow ' ll NVLU MVV 0H0 2 ' H \x: 'l FUND-I 2 ll H II 2 a.mi- l—MI-Hr—mvp—H GZ- \ V) I .J x O. \ .I I x I Q A E F a: O D ‘- IL v 2 _l D m U X \ I- A G N 2 v m V) t- w 0. C. AA 2 O = 3 \ mm A < UJU A(\l '- 22 .J \ C < _1_] Luc- ' 0 << 900 + o- u.»- A DA-u.l D CPI-nerv- Hx H": m Oxvvvvh I- AZ 2 I-Z O-lr—O-I-N =2 CNH a: 'mi—<<<< to N 0- : IIDZ££.2ELL 12 H2 .- rt-chcraazcocct CV0 U HLUKC.DDDO—ZZO O>u m ummuuumwmmo OPnzm 00000 U C! ()(JLUI) “U0 L'U‘ U‘OO‘O-O‘ .X(1,2)) GO TO 20 LE ) kn 0 O p. 0 L9 A A N \ N 2 V X 0 Lu GA A '1- N A 9‘ m PPN FF \2 \K‘ V \ c—vmoo X!- 2X2 IIV VIIVO 2X XXX.- HII V- V II >- I II >- .J >- A A A N A § N N ‘ 2 ‘— v V >- )- o ' l- 0- £9 _1 o IAA AANQ- NC- \ s \ WP uvuv JBIK >H>H 193 U> ID I— A” z\Nv HQ «.3 0-01 U2” ZHVZ :\xo OPOOOOOKT'I x4! I! I: 41 4t 1! \O OOOOC'OCC zoooomsoocc-oor-N G\\\\\\LUP HAHGDZZZZ:\ PPZZ z :zzmomzmxuwohz vvvv m Doozcz >>>> 2 mzzw~w<<<<<<<< Pcmtttwthhhhhhhh wZDCDHVH<<<(<<<< mwwuuogooooooooo 1 101 HfN+DEL*(I-1) ll qu H ll : CHH «Vb C1D OXU OAA NGDHH \ \ \ \ PF‘a-J II II UV H‘5X> I! II (“AAA Q’P‘I-a vv COCO COX)- 1N1(NPTS(I),KNOTS,XD,YD,HD,RD,XN,FN,GN,DN,THETA,H, 194 LU ‘I 22 A A 4! 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N NO." 0 >NZN2 DI-ZMZOC GN(KK) ROUTINE SPLIN3(M,N,XD,YD,HD,RD,XN,FN,GN,DN,THETA,H,IPRINT) V.JI—JI-Dm ELI-LCD“- MDC Oil-51C DISC-NV‘ATU- 0.“; EAWXOXOH-kU-‘QUJZS H \ 120 3C1 ),YD(8I),UD(80),RD(80),XN(80),FN(80),GN(80) q. AND INSERT EXTRA KNOTS AT ENDS CF RANGE ,XD(M)) TRANSFER KNOTS TO N, MAX1(XN(N) 196 A II AA A AA A AA [\A In 1 V F" V~t + A I 4 3V '5 A I I! I .3 V N AA A I 2' -I- AA MA I .3 HN was A V VI.- 3V N 3 CH5 V3 + I XV IIV A A I 3 A; v q A I AA 3 + «A VOA V '5 + H VM 1: V ‘IV 3 3V A 3 Va I 3 A V 3x 2 A I ~t I! VV H F‘A + A A A '3 ¢ Vin ‘5 A A A 00 05 3V V P e- d‘ + + 2 V3 1 + + + MMMM O I! V I A '5 '5 t «I i I! H A! A V V V i I! I! 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H ‘— ~ A‘- v s 3 00 = O \ ' m z ‘ C ‘ .4 H AA: A ONT 0 < NN 0 hr- : m st¢ 0"- = U I— UUCJ \ D ' z u) 'I I2 I z' s c \ s 0 m1 2 III NNIIJ I (DUN IL > ~7~74I— IIJ ' I-I OODIU 40 III In "‘wa 3 ‘ u U) \ 5‘ H ~4- z u; I I \ \ N 0 t m QNNN coo .— CL \ \ I I20 I wAzA 0 'UL‘Qv W : o: C‘ I 000(0‘0 QI- fi-N‘I‘O I ‘N N \ Iv Iv \ WOO-INN org» I I I I_] I I K KOFPM‘NP Ig Imy'vvavv m OXO>2244I-42 Cs‘I’O‘OOOO V‘VUJODHDJ IIIIIII mnmnzzmmzm: NINBC‘I-(‘I— HFHFM'WiiI-IZWIAII II II II II II II XOXO<<>> >¢¢AAAAAAA (v-(I-ODIDIOGIDO 'I-NMN'I‘IAN‘I'IA v v z vivvvvs.» 4>4>4444IU44IIIDIDIDUIIDLDID 4(4C4444I944OIUIIJIUUJIULLJILI > --PRINT PLOT LINES C A M \ In \ P \ O O P \ )- < a: >- \ AA >- 022 < u C-++ mo H P'I-I x2 ‘ WV VII-Ll I- I-X>- MID II II II IIIIJZI-L' F. xfifihz‘H—I i fifi24 OPOOVVH '- VI'°N>>P42 HI- <(24H C II IIDCKKD- I C- I O I- I 0 I x C‘- I I I O 4 O I XA O A V'I AQ‘ H Ac mo V AAAA P!- O I Z ITIfstI'r Ov ‘0 It Pc-q-I- I-> o I 2 0000 VD Io .— I I I I _34 o I If) I I I I to 0N H QITITQ' XI U!- I I-I—I-I- A I I I I I? 0000 0AA : w I I I I on I“ AC) I I I I PVC Om ¥ ' 0000 VII)!- IO 0 PI- . 0 A >I—V ID on: v- I IZNN I—hon X m “G W I I I I uJN I20 “1 co I-IT QOUK‘ A II) IA I4 0- NM IO I-I I I o Hg—I-Ao Lu A P@ M ' 0000 0 ICON: Z O I 2 II I I I I u 0.1-I- I I a I o II-I LDC 0000 I HVVIDA (I h- “: O = a DJI— Ig—I— O O VI—l-I-wN ( m 0. 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