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A Photomechanics Study of Wave Propagation John Barclay Ligon Iowa State University

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A Photomechanics Study of Wave Propagation John Barclay Ligon Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1971 A photomechanics study of wave propagation John Barclay Ligon Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Applied Mechanics Commons Recommended Citation Ligon, John Barclay, "A photomechanics study of wave propagation " (1971). Retrospective Theses and Dissertations. 4556. https://lib.dr.iastate.edu/rtd/4556 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 72-12,567 LIGON, John Barclay, 1940- A PHOTOMECHANICS STUDY OF WAVE PROPAGATION. Iowa State University, Ph.D., 1971 Engineering Mechanics University Microfilms. A XEROX Company, Ann Arbor. Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED A photomechanics study of wave propagation John Barclay Ligon A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject; Engineering Mechanics Approved Signature was redacted for privacy. Signature was redacted for privacy. Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1971 PLEASE NOTE; Some pages have indistinct print. Filmed as received. UNIVERSITY MICROFILMS. 11 TABLE OP CONTENTS Page INTRODUCTION 1 INTBODUCTOBY PHOTOMECHANICS 3 Historical Background 3 Basic Theory 4 Dynamic Photoelasticity 7 Photomechanical Analysis 7 LITEBATUEE SURVEY 10 Dynamic Photoelasticity 10 High Speed Photography 16 Wave Propagation 17 General wave mechanics 18 Cylindrical waves generated from a cylindrical cavity in an infinite medium 19 PHOTOGRAPHIC SYSTEM 22 Spark Gap System 27 Optical System 34 Synchronization and Calibration System 41 Detonation Systems 46 Exploding wire system 46 Heating wire system 50 Arcing wire system 56 MODEL MATERIALS 60 Model Properties 60 Allyl diglycol carbonate 62 Polyme thymethacrylate 66 Ill Model Preparation 6? Plates 6? Routing 70 Reaming 70 Lapping 71 Boring 71 Liners 72 Explosives 74 PETN 7^ PbN^ 75 Auxiliary Equipment 76 Material wave velocity determination 76 Resistance strain gages 77 Photoelasticity 81 Quartz load cell 82 Photographic techniques 90 Black and White 90 Color 92 WAVE PROPAGATION 97 Plane Waves in Bars 97 Cylindrical Waves in Two Dimensions 101 Generalized plane stress 101 Generalized plane strain IO6 Analytic approach IO7 Numerical computer approach 111 DATA ACQUISITION 115 DATA REDUCTION AND RESULTS 127 DISCUSSION 149 Multiple Spark Camera 149 Explosive Pulse Sequence 151 Reproducibility 153 Fracture Criteria 154 Validity of Material Fringe Coefficient 158 Iv Validity of Stress-Strain Helatlons at High Loading Hate 159 Validity of the Uniform Plane Stress Assumption l60 RECOMMENDATIONS FOR FUTURE WORK l63 Multiple Spark Camera 163 Polarized field 163 Intensity control 164 Frame rate control I65 Synchronization I65 Time sequence gapping I66 Explosive Pulse Sequence 16? Model materials 16? Dispersion effects I69 Intermediate field 170 Close field 171 Material Properties 171 SUMMARY AI^D CONCLUSIONS 172 BIBLIOGRAPHY 174 ACKNOWLEDGEMENTS I89 APPENDIX A: ELECTRICAL ANALYSIS OF THE HIGH VOLTAGE SYSTEM 191 APPENDIX B; OPTICAL SYSTEM DESIGN OF THE MULTIPLE SPARK CAMERA I98 Illumination System 199 Camera System 201 Calculations 205 Requirements for illuminating the model 205 Requirements for recording the image of the model 207 APPENDIX C: LIST OF PHOTOGRAPHIC SYSTEM COMPONENTS 209 APPENDIX D; PHOTODIODE DESCRIPTION AND ADJUSTMENT 215 APPENDIX E: TOODY II: RESULTS AND DISCUSSION 218 1 INTRODUCTION In recent years, Interest in wave propagation has grown considerably with increasing emphasis on earthquake phenomena, petroleum exploration and nuclear detection. The electronic computer has also aided this growth since in the past even the simplest problems in wave mechanics required a lengthy, and usually impractical, pursuit in order to extract numerical results. At the present, straight forward theoretical problems in wave mechanics can be handled with modest effort when mathematically convenient approximations to the loading functions are assumed. However, when analyzing stress waves propagating in complex regions, theoretical solutions become extremely complicated and experimental information is often used to provide insight into the problem. In order to compare a theoretical solution with experi­ mental results, complete knowledge of the manner in which a transient stress wave forms and attenuates in a medium is a necessity. With the characteristic of the pulse known, the effects of dispersion, dissipation, and geometric attenuation can be examined and compared to that predicted by theory. In the current study, dynamic photoelastioity was chosen as the experimental technique used to investigate the for­ mation of a stress pulse that is transmitted from an explosive charge ignited in a circular cavity in an infinite plate. In order to accomplish this task, an ultra high speed photographic 2 system was constructed by the author to record the dynamic photoelastic event. Motivation for studying the formation of the stress pulse resulting from detonation of an explosive charge in a circular cavity arose from apparent inconsistencies in the method frequently used for determining the pulse shape. The method relies on extrapolated data from far field studies to approximate the shape and magnitude of the loading function. This data indicates that the stress pulse that is formed in the far field of the medium is simply the geometrically attenuated wave originally applied to the boundary. Par field studies indicate that the radial component of the com- pressional stress wave exhibits a tensile tail as it propagates through the medium. The inconsistencies arise when the magnitude of the radial tensile tail established by the far field trend are extrapolated to the loading boundary where the stress would be expected to be a maximum. However, when the explosive has ceased to burn, the compressive stress acting on the hole boundary diminishes to zero and the cavity boundary remains free of stress in the radial direction. Therefore, the hole boundary cannot support a tensile radial stress. This Indicated that the stress wave must not be formed completely until it has traveled a short distance into the medium. This was indeed the case as will be shown in subsequent chapters. 3 INTBODUCTOHY PHOTOMECHANICS Photomechanic methods of ezperiaental stress analysis are based on the property of temporary double refraction exhibited by certain transparent materials when they are stressed or strained. Historical Background The photoelastic phenomenon was first presented in 1816 to the Hoyal Society of London by Sir David Brewster (1). Brewster reported that glass, which otherwise, had no influence on a beam of polarized light, when subjected to tension or compression, exhibited properties of double refraction similar to natural crystals such as quartz. He later suggested that the stresses in structures could be analyzed by use of these stressed transparent models. In 1823, Brewster described the apparatus that he used to load his models» This apparatus consisted of a source of polarized light, a frame for placing a measurable load on the specimen, a lens, and a screen thus establishing the forerunner of the present day polarlscope. Although significant contributions were made through the years by physicists such as Nicol, inventor of the polarizing prism, and Neumann (2), James Clerk Maxwell (1831-1879) (3) probably did more in the period to put the science on a firm basis as well as to develop equipment k which gave satisfactory results. However, it was not until 1931 when Coker, an engineer, and Filon, a mathematician, collaborated on their historic Treatise on Photoelasticity (4) that interest was revived in photomechanics and the move towards engineering applications was initiated. In Mas M. Frocht greatly extended the work of Coker and Filon in his book Photoelasticity, Volume I (5) and later in 1948 with Photoelasticity, Volume II (6), Since that time, photoelasticity has become a useful experimental tool, applicable to numerous engineering problems. The introduction of texts by Dally and Riley (7)» Durelli and Riley (8), Jessop and Harris (9) and Heywood (10), indicate the extent of interest in the method. Basic Theory As stated earlier, the basic concept upon which photomechanics methods in general and photoelasticity in particular is based is the optical property of double refraction. Certain materials such as quartz are permanently double refracting. To distinguish these from the materials that are used in photoelasticity, which exhibit the phe­ nomenon only when subjected to stress or strain, the term temporary double refraction or birefringence was adopted® When observed in a field of polarized monochromatic light, the photomechanics effect of temporary double refraction manifests itself in the form of alternate dark 5 and light bands which are referred to as interference or isochromatlc fringes. At a given point in a material, the fringes will be ordered according to the number of dark and light cycles that appear as the load is increased from zero to its final value. This isochromatlc
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