COLD REGIONS SCIENCE AND ENGINEERING Monograph ll-C2b THE MECHANICS OF ICE John W. Glen December 1975 GB 2401 CORPS OF ENGINEERS, U.S. ARMY .U58m COLD REGIONS RESEARCH AND ENGINEERING LABORATORY no.ll-C2b HANOVER, NEW HAMPSHIRE 1975 Approved for public release; distribution unlimited. 5 fl rolomis The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized docume* s. 0 Unclassified BUREAU OF RECLAMATION pENVER UBRARY C/ 92099625 ^ Y REPORT DOCUMENTATION PAGE ...............Q ? n Q 9 f i ? 5 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPt_______________ - ..------------ Monograph II-C2b -> 5. TYPE OF REPORT ft PERIOD COVERED 4. TITLE (end Subtitle) j m MECHANICS OF ICE 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER*» 7. AUTHORf» European Research Office r J.W. Glen ,r Contract DAJA37-68-C*0208 £ ■ '« • ' 1 "• - TO. PROGRAM ELEMENT, PROJECT, TASK 9. PERFORMING ORGANIZATION NAME AND ADDRESS AREA ft WORK UNIT NJUMBERS Dr. John W. Glen Department of Physics ^ DA Project 1T062112A130 University of Birmingham ( ^ Task 01 ____ Birmingham. England ____; '____ ; _______ — 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Office, Chief of Engineers ^ December 1975 u 13. n u m b er o f p a g e s ' Washington, D.C. 47 14. MONITORING AGENCY NAME ft ADDRESS*?/ different from Controlling Office) 15. SECURITY CLASS, (of thie report) UvS ^Army Cold Regions Research and Engineering Laboratory-^ Unclassified Hanover, New Hampshire 03755 15«. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of thla Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of tha abatraci enterad in Block 20, it different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverae aide if neceaaary and identity by btock number) Crystals Loads (forces) Engineering Mechanics Failure Growth (general) Ice ____________ ___________ -_________ ■■ ■ ■ " ----------------- — ---------------- 20. ABSTRACT (Continue on reverae atdd If neceawery and identify by block number) This monograph summarizes knowledge of the mechanics of ice. It is concerned principally with the, effect of stress on the mechanical properties of ice, including elasticity, anelasticity, sound propagation, plastic deformation and creep in single crystals and in poly crystalline ice, fracture, and recrystallization and grain growth that accompanies plastic deformation. The monograph also includes a comprehensive bibliography. DD 1 jSS*78 U73 ew Tio w O F I NOV e* is o b s o l e t e ____________Unclassified____________ SECURITY CLASSIFICATION OF THIS PAGE Data Entered) n PREFACE This monograph was prepared for the U.S. Army Cold Regions Research and Engineer­ ing Laboratory (USA CRREL) by Dr. John W. Glen, under a contract issued and adminis­ tered by the European Research Office, U.S. Army. The author is Reader in Ice Physics in the Department of Physics, University of Birmingham, England. Valuable suggestions and comments on the manuscript were made by Dr. Kazuhiko Itagaki and Dr. Malcolm Mellor, of USA CRREL, who served as technical reviewers. The monograph was written under DA Project 1T062112A130, Cold Regions Research, Task 01, Applied Research and Engineering. The manuscript was completed in June 1970 and reflects knowledge prevalent at that time. References to a few later papers were included during subsequent revision. HI CONTENTS Page Abstract.... ................. .......................... ............................................................. ...... i Preface................................................................. ........ ............... ......... ........ -.... ....... ii Editor’s foreword............. ............................. .......................................................... v Introduction ..... ................................................. .................... • .................... ............ 1 Chapter I . Elasticity and propagation of sound in ice.........................«........ ....... « 1 Elasticity..................................... ........ ........... ........ .....................*.....---- -------- 1 Propagation of sound in ice.............................. ..............•.............................. ....... 4 Chapter II. Anelasticity and damping of mechanical vibrations in ice................. 6 Chapter HI. Plastic deformation and creep of ice — single crystals ..................... 10 Creep of ice single crystals................................................................................... 11 • Constant strain-rate tests.............................. ....................................................... 13 Plastic deformation of ice crystals in non-basal glide.......................... .............. 14 Effect of surface conditions on plastic flow of ice crystals ............................. 14 Effect of an electric field on plastic flow of ice crystals.................................... 15 Effect of impurities on the flow of ice single crystals........................................ 15 Slip lines and slip bands in ice.............................................. ................... ............ 17 Effect of stress perpendicular to the slip plane on basal slip of ice crystals .... 18 Stress relaxation in ice crystals............................................................................ 18 Hardness of ice crystals............... ......................................................................... 19 Chapter IV. Plastic deformation and creep of polycrystalline ice---------------.... 19 Results of creep tests on poly crystalline ice ................................... ..............•• 20 Shape of the creep curve............ ......................................................... ........ ........ 20 The flow law variation of strain rate with stress.............. ................................ • 22 Variation of creep rate with temperature............................................................ 24 Constant strain-rate tests............................. ................................. ...................... 26 Stress relaxation..........................................................................................— ..... 26 Strain relaxation...,............................................................................................... 27 Effect of different stressing systems................................................................. 27 Physical processes occurring during the creep of polycrystalline ice................ 28 Chapter V. Fracture.................................................................................................... 29 Tensile tests......................... ........ ......................... ........................................... 30 Ring tensile and bending tests...................... ................................................... 31 Compression tests....................................................... ........ ................................ 31 Shear and torsion tests....................... ................................................................. 31 Other tests on ice fracture.................................................................................•• 32 General summary of fracture behavior............................................................... 33 Chapter VI. Recrystallization and grain growth of ice.......................................... 33 Recrystallization................................................ ..........................*— ............ 33 Grain growth in ice.............. .................................................................. ............. 35 Literature cited....................... ......... ........................................................................ 36 Appendix: Crystallographic indices used to specify planes and directions in ice 43 ILLUSTRATIONS Figure ^aBe 1. Matrix of coefficients of the elastic compliance for a hexagonal material such as ice Ih in axes in which the c-axis of the crystal is chozen as z-axis....................... 2 2 The effective Young’s modulus as a function of stress orientation............................ 5 3. Relation between relaxation time of pure H20 and D20 ice and the reciprocal of absolute temperature..................................................................................... 7 4. Temperature dependence of internal friction in pure polycrystalline ice 9 5. Temperature dependence of internal friction in NaCl-doped ice crystals................. 10 6. Creep curves of ice single crystals deformed under various stresses at -70°C ........ 12 7. Stress-strain curves of ice single crystals obtained at a strain rate of 2.7x 10‘7 s"*, and at various temperatures ........................................................................................ 13 8. Stress-strain curves for non-basal glide of ice single crystàls with various orienta­ tions of the 0-axis............................. 14 9. Creep curves and stress-strain curves of ice single crystals at — 70°C with various concentrations of HF, compared with pure specimens....................................... 16 10. A bent ice crystal viewed by shadow photography showing the slip bands.......... 17 11. Low-stress creep curves for fine-grained ice whose crystal orientation was initially random.................................................................................................................................. 21 12. Creep curves of randomly